Difficulties Quotes Information Sources Quotes Strategies Quotes
Assessing: Learners as People
Novice/ Advanced Beginner  Learning gaps "There are so many different reasons for why students aren't understanding. Where do you draw the line of the learning gap being too big to make a comeback?"  Student performance  "After I saw the results of his first assessment, I realized it was an issue… There was no indication until then that he was struggling."  Individual attention "Try to check in on students who are struggling one on one." 
Variability within group: Learning requirements  "He is different because he needs a lot of positive reinforcement that he's on the right page. He takes things very literally."  Observed behavior  "He wouldn't write down his homework on his agenda."  Relationship building "Don't push kids to their limit. Build a relationship with them, and don't make every conversation about school."
Participation / performance delta  "She is not a very good test taker, but her class work is fine, and she can do it on her own."  Perceived effort   "One of my students wants to do well, really badly. She's very grade driven. She tries so hard. She told me she goes home, sets up timers on her phone, and does her work."  Environment building  "The first few days, making sure there is a community feeling in the classroom. Making it a safe space for kids to take risks and share their ideas." 
Student defiance  "In the middle of the year, one student had a shift where he would say 'No' to anything. He didn't want to come out into the hall with me."  Perceived confidence    "During tests, she second guesses herself and gets very anxious."     
Behavior misconceptions  "I had a misconception that (bad) behavior kids would score lower. That's not true."         
Competent Class size "It’s hard because you have a class of 25 some kids." Self-comparison "Math didnt come easy for me. It was easy for me to zone out in class. I can understand when they aren't paying attention. I see myself in those students." Discovery "You have to get to know each kid. You have to build trust. Your job is to teach them and know them as human beings. You want to give students time to cope."
Variability within group: Performance "When she came to my math class she had a run of noone pushing her. Her friends were excelling in math. She wasn't bad at math, just didn't feel super successful." Observed behavior "When he felt confident about the content, his hand would shoot up and express that confidence. His confidence in his answer made me feel like there is something i could tap into. The checking out piece came when he didn't understand the content, didn't have the answer, or did not know where to begin. Would get frustrated and do little work. Correlation was the confidence level and his ability to do the work." "Defiance was “I'm not going this”. Put head down or pull out a book. Just put name on the paper. Needing to go to the bathroom right when independent time started. Had to send a student to go get him. Time wasting and work avoidance." Divide and conquer "I've been very specific on who I'm questioning, students on the cusp."
Social challenges "Unpacking identity was important with majority black and hispanic students. It was a lot of reflection but not action. How you relate to students. When it came to building relationships across different backgrounds, I didn’t have a lot to latch on to." Capability categorization "Class is split between high performing and low performing students. I focus more on the low performance. “Cusps” students are in the middle and we want to push them to green instead of yellow. They get extra attention." Enlist others "I pushed her friends to help push her."
Pre-existing math gaps "Post pandemic kids have larger gaps than we've seen before."  Prior interaction or proxy "I knew of him before from his 5th grade teachers." Observe performance process "The green students are firsts to participate, work is neat and organized, can tell reasoning behind work. Color scheme is what school uses. Based on how they score on first exam. Scores were low (IA)."
Perceived motivation "Some students just try different numbers instead of going through the process. They want to figure out the easiest way." Observed performance "They will mess up independent and dependent variables, multiplying and dividing on the ratio tables, etc. They might use addition and subtraction instead of multiplication and division. Those are common misconceptions they have. A common mistake with graphing: they will confuse the x and y axis." "He did well when we divide fractions. It was algorithmically taught. He could identify the key information and apply the algorithm. Conceptual part of ratios is what he was struggling with." Individual attention "I told students they can use their voice right or wrong. Teaching them it’s ok to get the wrong answer."
Participation / performance delta Reading gaps "When it comes to word problems, they don’t want to read or their reading level is low. I will see A students struggle with it but towards the end of the unit, they understand the context." "Kids participating in class wouldn't necessarily do well on exit tickets." Perceived preferences "I think my teaching style blends with him better than his full teacher. Only students I have the specific one on one relationship with. Works better when he gets attention." Model desired behavior "I had to pull him outside the class and ask him what’s up. Sometimes they aren’t paying attention, giving random answers, etc. Have to check in with them 1 on 1. I don’t want to take away from the actual teaching process."
Proficient Variability within group: Capabilities "Academically there was potential. A ⅓ of the students were potential. The rest needed more help. 5 or 6 students who really struggled, especially to their peers that were academically getting it." Observed performance: Innovation "I saw a kid solve the problem in a way I’ve never seen before. He broke it apart and he did the distributed property in his head and he found that answer quicker than everybody else." Relationship building "If you don't have classroom management, how are you going to teach? Building that relationship with the kids. I tell my colleagues, “Go downstairs for lunch. Have lunch with them. Go outside. You don't have to play with them, but just go outside and have a conversation with them.” Spend those 5 min with them. It's not gonna hurt." "At the beginning of the school year, I handed out a survey: What is your name? What is your favorite character? What is your favorite TV show? What kind of music do you like? What's your favorite snack? Just like, why?"
Absenteeism "Absenteeism is a huge issue for one of them. I’m just playing catch up all the time. I feel like we're giving kids chances to go into these higher level math classes but there are other things that have to be in place." Attendance record "60-65% of kids have missed 15+ days of school." Environment setting "I have seen situations where students come in and they're just very quiet and they are not confident in their math and teachers will create a learning environment that allows them to speak, allows them to share their thinking and that can really improve their confidence."
Math disdain or phobia "Some kids are math-phobic and don’t want to put themselves out there and take risks. It’s a long process in the first 2 months to build a classroom culture for students to be comfortable sharing their thinking."     Divide and Conquer: Need focused "Identifying students with highest needs in the class."
        Individual attention: Confidence and Autonomy "I think it's also really important for students to know that there's not a right or wrong way of thinking about math. What is your thinking? How can you express this? Is there more than one way to express this? Different students are thinking about math so differently and I continue to learn from students when they talk to me about math. I want to learn what it is you're thinking."
        Gap baselining "At the beginning of the school year, I handed out a survey: What is your name? What is your favorite character? What is your favorite TV show? What kind of music do you like? What's your favorite snack? Just like, why?"
Expert  Language barriers "Some students struggle reading English, and they have to translate instructions. One student had a difficult time understanding a word problem, and it took time out of the test." Observed performance: Unlearning "Once students know they can solve a problem, they’re willing to listen to some strategies that might make their solving more efficient. They’ll buy in and try more things, like 'I should stop skip counting and actually learn this multiplication problem.'" Bi-lingual resources "We have books that are bilingual, so we can teach in both Spanish and English. Bilingual students need practice to feel confident. I give them problems in English 4-5 times a year so they feel comfortable. I intentionally have them do the math both ways."
Perceived approval-seeking "Fourth graders just want you to love them. They want you to praise them. Sometimes they'll do things because they think that's what you want."        
Variability within group: Learning requirements "I had a group of nine seventh graders who really needed the room to be quiet. They needed to come in and know exactly what they were going to be doing. They needed to have the “menu of the day” on the board."        
Variability within group: Learning strategies "One student had a different way of perceiving things. She wasn't rationalizing how she answered questions, and she was just memorizing the steps. She would see the work, memorize, and replicate it every time." "If it was a word problem, she would just look for the numbers and go straight to the process. She wouldn’t do the steps beforehand. She couldn’t explain what she was doing."        
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Assessing: Prior Knowledge
Novice/ Advanced Beginner  Cross-grade alignment  "There is a lack of alignment from what students have already learned in previous grades."         
Data application "There is a lack of ability to respond to data."         
Competent  Perceived apathy "Some kids don't take the 'I-Ready' diagnostic assessment seriously."  Trends "We see the major gaps as a whole - Where most kids are struggling and where they are going wrong."  Diagnostic programs "Students did 'I-Ready' in 7th grade as an initial diagnostic to show which grade level they are on."
 Profound gaps "Some kids are on a 1st or 2nd grade level. Subtraction is an issue. We didn't have enough time to get them to a 4th grade level. Sometimes not every issue is able to be adjusted."  Performance observation "They don't understand why they would borrow. It doesn't come to their minds or what that number represents."  Data organization "Organize the missed problems by the common mistake."
 Missing data "There wasn't much background info on the students. Before we see the student we have their state test scores. You have numbers but don't know where they got to the number."      Data analysis Explorer problems "Going over data with the math school leader. Diagnostics give more data on what they are capable of. 35-40 questions. Some multiple choice. Info is scanned through the program and you can see which problems were most commonly missed."
         Prior assessment data "An explorer problem is a problem that students have prior knowledge of to complete it. That's where the most rigorous questions start. We expect students to struggle because some things they haven't seen before."
Proficient  Math evolution "Application is the big difference from elementary to middle."  Historic trends "So stats and prob for a long time has not been highly prioritized. Statistics and probability are not on the test, so they've never gotten any exposure at all."  Progressive problems "Giving them examples they've learned in the past. Applying the same strategy. Less about what is a “polynomial” and now that we see a visual, what can we do with it? Assuming they know what it is from previous years and I focus on applying."
 Data protections "Data was well protected and guarded. I was pulled to a meeting once and they let me look at the data on a screen but i can't take it."      Collaborative data sharing "Beginning of the school year, our first meeting, we took a look at the instructional report on how the students did on the state exam. Skills they struggle with. So then we talked about it. How are we gonna target those students who did not master that skill?"
 Data loss "Wasn't able to access work from previous years. Post covid."      Prerequisite testing "We will do a pre test and then focus on those skills. We actually saw students improve on those skills."
 Marginal gaps "Sometimes concepts from a previous year that just aren't solid."      Paper use "Given on paper."
 General difficulty "Generally it’s difficult to gauge where students are."      Note padding "I kept my own data for areas students were struggling with. I kept a note pad next to me to write down what I'm seeing."
Expert         Disregard  
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Assessing: Mastery of Mathematics
Novice/ Advanced Beginner  Variability: Student problem solving   "New teachers haven't seen the 3 other ways that students have tried to do this in the past. They don't have that sort of depth or experience in seeings students struggle like that."  Student work  "I can see the progress in the students' work. They answer questions with high mathematical thinking."     
Gauging understanding  "Not having a clear cut of when kids master a concept."         
Competent     Student work "I want to get the data from what I’m seeing. I want them circling and underlining the text." Circulating "Working story problems on my own and walking around watching them. If the kids can explain their way through the problems, I'm ok if there is a function wrong. They understand what they are being asked to do. If just grasping at anything, they have a page full of work but can’t explain it. I take understanding any day over fluency. Can follow a process. They are trying to repeat what they heard - cannot put an explanation together. Get this from one on one conversations with them. I don't want to put them on a stage knowing they will fail."
    Standards comparison "If they mastered a standard, they would score above network average." Quizzes and tests "We ask teachers to pick out high priority questions from a worksheet or practice book to assess the day's lessons. The hope is that teachers can collect data until there's 100% understanding." 
        Exit tickets "I look through exit tickets every day to see if it's a topic we need to review. We have data trackers for the school to see how many students mastered a topic."
Proficient  Gauging understanding and/or conceptual "If you take a problem and just give them the numbers on it without any words, they know the procedure, they can solve it. But then once you throw words in it and you realize multiplying fractions is actually taking part of a part and you're not able to conceptually see what that looks like when you get a word problem, you will have no clue how to solve it at all. That's where I see big gaps for the kids. They can’t prove it with a model. They're understanding step 1, step 2, step 3, but they're not going to be able to apply it to other things."  Entrance tickets "Formative and summative assessment data, in addition to exit tickets and entrance tickets, are the really important data pieces."  Questioning / Verbalization "Listen to their responses. Comparing what they say against what i know to be true - gauging distance from furthest to exemplar."
 False negatives "There are students that will always look confused no matter what they are doing. I'm not looking at student reactions."  Performance on power standards "Power standards are the things you want students to master. There are usually around 5 power standards per grade level."  Alternative representations "They have to understand question first: draw a picture, play a movie in their mind, etc. Problem solve, strategy use, then show your answer. Try to show picture for problem: relatable, easy to visualize, etc. important to talk to kids with mathematical terms."
 Time pressure "Teachers don’t have enough time for a thought pull."  Work products "They may struggle with 5/9 vs 3/7ths. They can’t visualize. If you see students are getting the wrong answers and don’t know why the answer is off. If adding fractions and adding numerator and denominator. Both the answers and the process to get to the answer."  Showing work "They are usually formatted in a way that students have space to show their work. Teachers strongly require students to show their work. They would get a zero if they didn’t show their work."
     Interpersonal cues "Top 20% is from scores and classroom discourse. You can tell how deep they are thinking about the math when they would verbalize in class. Questions that they ask, connections between topics, sophistication of language/correct vocabulary, strategy to solve that the teacher didn’t think of/efficiency. Exceeding the grade level expectation."  Timed assessments "On the assessment toward the end of the year, we started timing our assessments more. Why did this student understand it in class but not understand it now? Because they can't finish it within the amount of time or they don't know which questions they need to ask. So then I can target that a little bit more."
         Standards-based assessments "SOL snapshots (5 questions by SOL bullets) were helpful to gauge where students are. We would give at least 1 times a week. Students had to get 4 or 5/5 questions. This was just pen and paper. It was really effective. The kids would earn a sticker if they did well. I knew what to review for the SOL. It was a good visual for us."
         Self-signaling for confidence "They put colored cards on their desks. The red card is level one. That means I did not get it. I need help. The yellow is level 2, which means I did not get100%, but I can work on it. The green one is I got it. I can help the rest. They are showing this when I check for understanding. Getting them to actively think about how confident or comfortable they are with the answer. You're not in trouble if you put up a red card. That means you need extra help and I'm here to give you that."
         Cool downs "Students do a cool down at the end of the lesson for me to see their understanding. I will re-write the cool downs based on what they are learning within day 1 of the lesson."
         Check for reasonableness "Checking for reasonableness."
        Challenge questions for advanced learners "I would add a challenge question as well to assess my 'high flyers'."
         Polls and Tallies "After I feel confident 80% of kids are successful on the 2 by 2, we will able our understanding to the 3 by 3. I can monitor and check in with the students that didn’t get the 2 by 2 correct. Do I have now enough kids to move on?"
Expert          Open-ended and Novel problems "There might be an open-ended problem at the end of an assessment, and I’m very fluid grading those. That last problem is not really part of their academic grade, it’s more about their thinking and my own internal assessment to see if they can solve a problem they’ve never seen before. How would they go about doing it? Do they have perseverance? Where are they in their development of problem solving?"
         Projects "At the end of the projects, no matter what the students did in collaboration, there had to be proof that they could do it independently. So, there was some form of an independent exit tick attached. This was different, and it was more time sensitive, but it showed that they could do it on their own."
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Implementing: Lessons
Novice/ Advanced Beginner  Content knowledge    "The teachers' content clarity isn't as strong as it used to be."  Curriculum   "For a new teacher, the curriculum is very overwhelming but helpful. It gives you interactive assignments, PowerPoints to use, and quizzes. It's almost too much to look at."  Agenda  "I subbed for a teacher last year and she had a "do-now," agenda on the board, and a timer. She didn't have to talk, the kids knew what to do." 
Content delivery    "He knows he needs to switch up his delivery. He wasn't teaching urgent enough for the group. It wasn't engagin. He felt like he was just following the plan."      Supplemental worksheets  "If students are working on a worksheet, we will supplement with an extra worksheet. IM practice problems are too short, so we add worksheets." 
    Practice problems   "We always have a set of practice problems I can pull from." 
New curriculum   "Math was especially difficult with the new curriculum: IM Math."     
Classroom management    "It's just the classroom management piece. He felt like every time he taught he had to tell kids to stop talking-- like whack a mole."      Question sequencing  "My question sequence is big on sutdents having a conceptual understanding. I ask kids, 'Why?' A lot of kids can't tell me why."
Variability: Teacher confidence      "(The teacher's) classroom presence and body language. He didn't have a confident stance."      "I do, we do, you do" model   "I will model it for the kids first on a piece of paper. Then, we do it together, and I will question them what the next step is. Then, they do it themselves and work independently." 
Variability: Student capabilities     There is a gap of high performing and low performing kids. That was a challenge for meeting in the middle."      Procedural understanding    "My goal is to help them understand the procedural piece." 
Scripted vs. flexible      "A lot of our teachers don't take the liberty to go off script."      Word problem strategies     "We will learn strategies for word problems. For example, 'Read, underline, draw' strategy." 
Asking effective questions      "Teachers put their students' work on the board and say, 'Explain what you did,' but don't have questionst o ask other students."      Cheat sheets    "Sometimes, I'll make them a cheat sheet with rules they can refer back to if needed." 
Misconceptions     "It took me a while to learn misconceptions and how to respond."         
Inauthenticity     "As a new teacher, I would take the script literally if it was just handed to me. You learn in front of kids that you aren't coming across as authentic."         
Controlling      "One teacher had the best classroom management ever, but it was too controlled. Those kids could hardly speak. They were too scared to think. The teacher didn't want to let go of the reigns."         
Competent  Variability, especially trailing students "The training was helpful in certain ways. A lot was cognitive. Helpful to understand the meaning behind problems. There isn't a one size fits all for kids. It was fit for a certain group and some kids were left out. Training was techniques and strategies that would be for a certain group of kids. No techniques to support the kids that need extra help so they don't get left behind."  Professional programs "I got a lot of my resources from my Master's course. My professor gave me a lot of good material to implement."  Focus on known difficulties "I know where the most difficult part is of the problem and focus on that."
 Perceived standards of professionalism "I needed to look like I knew what to ask and how to answer questions."      Warm up/Do now "In their warm up, there should be something they are struggling with."
         Show multiple approaches "I show both ways to solve a problem and let the kid decide which works for them. I’m looking for one of two standards in their steps."
         Graphic organizers "I gave his class graphic organizers and different things to help them understand the concept."
         Convey new content "I usually really like to start my class off with a universal prompt to build engagement instead of students just doing the work to get it done. They have to know the reason why it makes sense. It's going to be related to the lesson for the day."
         Convey procedure step-by-step "Standard procedure to go step by step. Try to get them to understand the procedure. If we have time we go deeper dive into the reasonings."
         Individual practice "I would teach a lesson, do it together, and give students individual time to apply it."
         Centers "Having a “centers” approach. Ex: ¼ stations would use an educational program “I-ready”, lessons more remedial, mixed practice. Next would have students work with manipulates. Using play dough to figure out cross shapes. I would be with a small group. Last center would be a drill worksheet. Allowed me to meet with smaller groups of kids and rotate. Some stations were with partners and some independent. Also learned different ways to break down problems with kids. Courses build up to things you can bring into the classroom."
         Peer work "I tell the class to compare their work with peers. Ask how they got to the answer. Go through each line of work."
         Display individual work "Ask the class how she's setting herself up for success. She feels successful because she had her work displayed. Finding small places to find success. Putting up on the board. Getting the entire class involved. Allowing her to stay in the middle but still get the recognition."
         Relating content "With variables, try to use real world examples because the kids are dealing with them everyday. Putting variables in the concept of money, shoes, etc."
Proficient  Uncertainty about prior knowledge "Definitional approaches. Pre req does not diagnose everything."  Standard operations "In terms of operations, there is really only one way to do it. As for setting up the problem, there are several ways."  Visuals "We use a lot of visuals because my kids need to see in order to understand. I even start with them on the floor and we use a lot of the money. A lot of hands on."
 Curriculum ownership, errors, turnover "My district has a new curriculum every 3-4 years. A lot of my colleagues are resistant to a new curriculum, and change is hard. They are doing their own thing."  Curricula-embedded tools "IM is focused on having the cognitive load on the students. Building on their ideas."  Guided notes "I give students my notes with a side for them to add their own notes so they aren’t focused on writing my notes word for word."
 Deficient technology training "Didn't get training for Illuminate acess. I had to learn it myself."      Slide decks "Taught in class with more powerpoints. If they are absent, I can share the powerpoints."
 Inconsisent textbook guidance "Kids today don’t want to learn with a textbook. They are very digitized."      Role playing "This was the teacher who set up for her SOL review. All the students came in and they were doctors and they had a medical problem that they had to solve. She wore a lab coat and they had paper stethoscopes and it was just an all in. She would do that about once a quarter."
 Conceptual focus "Back in the day it was heres the topic, steps, now practice. Now its hard for me to adjust because that way is easy. If kids are writing things on their paper, you’ve done your job. Now its based on teaching kids the “why” and let them figure out how things are connected."      Purposeful classroom structuring "She structured her classroom in such a way that every part of her classroom had a purpose. She had a box, it was a crate. When she stood on that, she was giving direct instruction. She never stood there more than 10 min in any given class. But when she stood there, students knew. Pay attention because you are going to have a task that is going to involve this mathematics."
 Transitions "Starting new topics/Transition. Sometimes it’s just an abrupt transition."      Tools "White board, document cam, spinners for probability, graphing paper, etc."
 Variability: Participation "One class can be pretty shy. One class is very participatory. So it's in between the 2 where you're like, “I don't want to be the only one talking. I need you to participate as well. Your work on your paper looks great, but you need to be able to share it.”"      Metaphors "Think about an elevator. If you go down, that's negative. The basement. Think about the base, that's underground. On an airplane, altitude you go up, elevation you above sea level so you’re in the positive."
 Content knowledge "I think teachers do procedural because it's a quick way to solve it and they could master it quickly. However, if they don't understand the conceptual part of it, they're not gonna be able to tie in previous skills in math and future skills in math."      Videos "We have watched videos to kind of introduce them to real-life applications."
 Perceived micromanagement "There is more micro management because these common exams are given throughout the year. Pacing guide, assessments, and what I would teach is in constant friction."      Explanatory mindset "Never assuming a child knew what I meant."
 Uncertainty about when lead or facilitate "You’re making constant decisions on when to lead or let kids talk through."      Games "We play a lot of games."
         Do-know: Conceptual emphasis "The opening task is the main part where they are kind of wrestling with the conceptual part of it. The goal is for the children to be able to come to the big picture by themselves and for them to be able to stamp it."
         Taught example "There was a textbook curriculum we used and each unit came with a pre-test. I usually would not just hand them the pre-test and see how they do. We would look at each question together and discuss it as a class. We used Reveal math. It has a lot of real math involved. They do a great job at presenting concepts in different ways which makes the kids think of what they are doing."
         Individual work "I never wanted to tell students exactly how to do word problems. I give them a couple of minutes to think about it themselves. Draw a diagram, highlight keywords, draw a picture, etc. If students were stuck, I would give them a prompting question to get the ball rolling. I prefer to have them make sense in their brain. After a couple of quiet minutes to themselves, they needed to share with their tablemates on their strategies. I'm walking around the room listening to the conversations. Depending on what I heard, I might ask for volunteers during a group discussion to share what they did."
         Teacher guide "I sometimes check the teacher guide if I’m unsure or confused during the class. Mostly last year with 7th grade curriculum I last did that. Ex: I’m not used to tape diagrams. Last year was my first time. I had to refer back to the guide because I wasn’t comfortable with it yet."
         Small and large group work "The goal is for the students to lead the discussion on the opening task for the teacher to kind of be able to sit back and be a facilitator of it."
         Preteach and Challenge Questions for Advanced Learners "For the top 20% students, I would do a pre SAT question for a challenge on exit tickets or do now’s. If they got it right, give them incentives. Invite only for SAT math questions. In the classroom, they arent your top priority because they get it. I would sprinkle in challenge questions. Last page in the lessons are something called “Spicy” which is challenging. I don’t think many students are getting there."
         Relevance connecting "When students are learning new concepts, use their language. Listen to their language and use it. It usually makes sense. Then you can introduce more formal terms. Ex: corners of rectangles to right angles. Leverage their language and connect to the right turn."
         Sharing work "After the big question, groups coming up to board to put their work up. Giving story problems."
Expert  Demand "Sometimes I had like 42 students because kids said they wanted to be in my class, and I would take them."  State assessment problems "CAASPP released practice problems, and I love creating math tests."  Being entertaining "You don’t want to just sit down and listen. I tried to be as entertaining as possible because I had to entertain myself, too."
 Excess content "The curriculum included a lot of practice problems. We couldn’t do everything."  Self reflection "I knew what it felt like to be a middle school kid and a person in general. You don’t want to just sit down and listen. I tried to be as entertaining as possible because I had to entertain myself, too."  Many materials and manipulatives "I think you need to use all different possibilities of materials. Use manipulatives to demonstrate math concepts. Videos can be supplemental."
 Peer resistance "Two teachers thought doing big projects would be exhausting because there were a lot of materials involved. It could also get messy, especially with water and all the little tiles involved."      Facilitator "The teacher is the conductor/facilitator of the class 'orchestra.' The teacher is still in control, but the students are the ones playing. They aren't looking at the teacher for the answer. The students are doing the talking and thinking."
 Space constraints "If you’re in a smaller area, it’s hard to spread them out and make them productive. If I had a lot of behavioral issues, I’d have to get some more adult help."      Adaptive planning "I knew how much time we had, and I knew our goal, so I selected which problems we were going to do and how we were going to implement it."
 Content-focused curriculum "Some people think you have to follow the curriculum by the book. Education is uber complex and there isn't a simple solution. It’s not fidelity but more integrity. How are you following the philosophy of the curriculum? Some teachers are using it but not in the way it’s supposed to be used."      Day Before Problem "We might have had a problem from the day before in which kids struggled with it or didn’t struggle with it, and we’ll start from there."
 Student time management skills "For middle school kids especially, if you tell them to work on something but don’t give them the amount of time, they have no compass."      Multiple solutions "I give students the freedom to choose different ways to solve problems."
         Student discourse "The kids do their work on the whiteboard, and they’ll work together in pairs or threes. We’ll come back, and one group will explain what they did. I’ll interject as needed."
         Student thinking and explaining "Kids were thinking for themselves, talking about it, and revising it. I never just told them what to do and what to think."
         In-class practice "There should be some sort of practice/homework in class."
         Additive notes "Even when students took notes, I had them fill in notes, so they weren’t wasting time copying stuff down."
         Hallway huddles "We would do “huddles” in class. I would give the students a high rigor task and give them five minutes to work on it independently. After five minutes, I had students meet me in the hallway if they were done. If they hadn’t finished, I told them not to rush and to keep working."
         Late year independent learning "During the last two weeks of school, my goal was to give the students a little time where we did independent learning. I would introduce a topic we’ve never learned and have them teach themselves using YouTube or other videos and take notes."
         Timed activities "Say, “You have two minutes to unpack the problem. Go!” Then, “You have six minutes to come to a consensus. I need to hear a lot of talking. You got it!” Tell the students, “We’re doing this whole project in 60 minutes. Can we do it? Yes!”"
         Cross-cutting projects "The sixth graders do a survey of the trees, or they each have a section of the campus, and they map the campus with what they see around it. Then, they’ll collect the data. With that one project, we can do data analysis, pie charts, ratios, and percentages." 
         Master questioners "Then, I had the small group kids go to another student sitting down and ask them questions. At the end of the class, every kid had one-on-one support and got to talk about the problem with someone else."
         Student problems "By having students write problems in their own words, it will eventually click with them if their answers make sense or not. It also helps students stop to finish the question instead of giving a number and moving on. Slowing them down and reflect on their work."
         Independent think time "The big takeaway is that implementation matters. I had to focus on that: ask questions and protect thinking time. Once you find what works, stick with it."
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Implementing: Interventions
Novice/ Advanced Beginner  No standard remediation process  "There isn't a set standard for how remediation goes."      Action plans  "We create an action plan on the two areas he needs to work on. I would practice the lesson with him before other kids came in, so when he goes into the classroom, he's confident." 
Knowing when to step back vs. intervene   "I realized I needed to take a step back and let a student struggle a bit. Once you don't help them, they start to learn on their own."      Small group reteach  "I will see kids struggling and pull them out into the hallway to work together. I will do groups or one on one." 
        Individual focus   "I will pull out whatever kid needs help, whether they are Individaulized Education Program (IEP) students or not." 
        Individualized  environment   "She gets distracted easily, so I'll pull her intot he hall and give her noise cancellation headphones." 
        Grouping by achievement level    "I will group students in low, medium, and high by how much help they need. We do assessments to see where they are." 
Competent  Time constraints "Reteach days take away from new content."  Content errors "If we see a content error, that requires immediate intervention." Data review with students "I showed and explained to the student the data. We both reflected on the data. Asked how we can move forward with applying themself."
 Role underspecification "He thanked me afterwards. I wasn't supposed to be working one on one but I gave him the help."  Exit tickets "If they score low on an exit ticket, we might reteach the lesson. We look for about 80-90% of class mastering." Continuous check in and prompting "Had to prompt and check in with constantly to push forward. Once it was happening for a long time, i had to put something in place to try and change the behavior."
     Error trending "Have exemplar from the day and tally how many kids got it right or wrong. Helpful to gauge understanding of the class. If 75% or more, that’s great and keep them going. Pull 25% for small group intervention. If 50%, worth stopping the class."  Reviewing prior standards and requirements "Fractional and rational thinking are aligned. Prereq skills of fractions i had to go over with him." 
         Avoid singling-out errors "I don’t want to call out kids for an error and make them uncomfortable."
         Single out inattention "Class clown might not even be on the same page of work. I ask if he has questions."
         Incentives "He really wanted the incentive part. I would give him a one time homework pass one day a week, mechanical pencils, things like that. He wanted to do math in pen."
         Pre-teaching "I pre-taught the lesson/skills for the main lesson for the student. I would pull them at lunchtime and use 30-45 mins to pre teach. Give them some access into how they can apply for the lesson coming up. Did it for 4-6 weeks. Tracked exit ticket performance and behavior performance in class during pre teach."
         Procedural repetition "Give him one problem at a time. Doing problem over and over to fill in the gap. Step by step until he could do the whole thing by himself. Rewarding to see it click and get it."
         Behavioral tracking "Behavioral tracker. Asked a behavior specialist for a template and made copies. I had him come to me and get things signed off before the next class. I would look at the trends of his behavioral performance. My observations of his behavior in my class. Included: Did I put my head down? Did i give my best effort/attempt # of problems? We both signed off on them. He sees what I'm putting in the form. He would object to some things. I wanted to make it competitive for him so he won't slack off."
         Additional work "We will have intervention = a packet, khan academy, exercises, videos to have extra work."
         Reinforcing connections "I would make the connection and mention it in class. I wouldn't single him out but he saw the connection too."
         After school help "Some students will stay for after school or tutoring."
         Individual focus and planning "We look at the work they do. Remediation opportunity. 2-3 weeks to do this. On a general basis it did help them to go over/have a refresher. Time and opportunity to close the gap."
         Tutoring "We have tutors that would pull students for 30 mins during lunch and some that come after school."
         Student matching "I sat students that knew the work next to someone who needed more improvement."
         Circulating "I do a lot of circulating. We are leaning off providing too much scaffolding. Kids will give up and raise their hand for help. Ill circle their work and tell them to check it."
         On-the-spot remediation "If there is a major gap and i need to sit down with them to break it down, i will."
         Step-by-step problem breakdown "Students can read the problem but they're not comprehending. Having him read the problem to me and see if he can figure out the operation. How do we set up the problem. Having him walk me through it step by step. They feel more confident when you ask those questions instead of going through entire problem blindly. We do them until he can do it by himself."
         Prompt sharing from achievers "While teaching, if the majority of students are struggling, I’ll ask questions to the students that got it for the entire class. I’ll have them walk through their work."
         Software programs "I have access to I excel math which is a learning platform. I did use that for my strategy with him. He was engaged with anything online. Tapping into the technology piece was important. Platform has practice problems, explanations and videos. He got introduced to that during intervention block which is about 30 mins. I can tell when he's logging on based on the time of his practice."
         Small group reteach "Have exemplar from the day and tally how many kids got it right or wrong. Helpful to gauge understanding of the class. If 75% or more, that’s great and keep them going. Pull 25% for small group intervention. If 50%, worth stopping the class."
Proficient  Stigma "Didn’t want them to think they were in trouble. Phrasing it that they will get a chance for me to help them and other kids would be there."  Small group work "Clear with working in small group who needed extra work because of grade gaps, “lost learning period”, and working with slightly more with students that historically struggle. They required more scaffolding. Required a different approach."  Grouping by acheivement level "Group kids based on the strands they are struggling with. Listen for what they know and understand about a topic."
 Timeliness "We're seeing mistakes that are happening and we're not able to address it as quickly."  Assessment data review "After there's a big assessment, we have a day where we can respond to the data, look at questions that the students missed to respond to it or build in reteach days."  Grade exit tickets during class "I used exit tickets. If the exit ticket wasn’t at least a B, I would ask them to stay after school. I immediately would grade them before they left the class period. Has to be shorter so I can grade within 5 mins."
 Success uncertainty "If intervention isn’t enough at the end of the unit, those kids might perform poorly."  Student work review "If on paper, I would check it when they return it back to me. In the textbook, they can look at odd number question answers in the back of the book. It doesn’t walk them through the problems but they can check their answers on their own."  Reteach days "I’ll write down the names for my focus group, re-teach days to check for mastery, etc."
 Time/Value tradeoff "Have to decide if it’s going to be worth it to spend 3-5 days reteaching. Knowing what the test is going to look at. Knowing what they will need in future math. Judgment for how much time to spend on topics. There is a lot to cover in the year. Utilizing time you have for what the kids will get out of it. If they don't have a basic understanding, it can be a 4 week process. Considering how much it'll matter on the final exam."      Parent notification "If they didn’t have any fractional understanding, I would talk to the parents and have them stay after school."
 Achievement variance "We can't always think about our lower kids when we're doing our pacing calendars. We gotta think about all levels of our kids and what we should and shouldn't continue doing."      Learning specialists "I have a learning specialist that will pull out students during my class. Either they are IEP students or lower tier. Group of 6-10 students she pulls out to work with."
 Policy restrictions "If I’m working on a specific subject, I can assign teacher lessons to students, but I’m not supposed to do that very much."      Check-in during other classes "I would check in with the remediation students during PE and check their process."
         Admit teacher errors "One time, I stopped the class lesson because I couldn't make the connection between the student content and my teacher guide. I admitted to them I needed to do more research. I wasn’t afraid to admit to my students that I make mistakes. I want them to ask me and clarify with me. So many kids think you have to be perfect in math. I want them to see me doing that."
         Support/Alternative classes "We're very fortunate that we have support classes where kids who are outliers. I have 3 that are my outliers, eighth graders, that really struggle. There's opportunities that you could put kids like that into another math class to support them. Give them practice, get them more feedback, give them digital ways to teach it differently, etc. It's not just that they need another period of math. Some of it is a matter of development."
         Problems with answers "In the textbook, they can look at odd number question answers in the back of the book. It doesn’t walk them through the problems but they can check their answers on their own."
         Designate work to strugglers "I create “star work” = for students that need more help, remediation, hints."
         Error reviews "First thing in class tomorrow would be looking back at yesterdays exit ticket. We would do a side by side with one correct and one with the common error and not show they which is which. The kids could catch their own mistake. Or just put up the incorrect and have them identify the error and how to fix it. Revisiting yesterdays trending error to get the students tipped to the other side. You won’t get everyone but try to get as much as possible."
         Highlight partial correctness "It's about building students' confidence. So just because it's wrong, I tell them it's partially correct. And we're gonna find what the misconception is. Your way of thinking is not the same as the other students' way of thinking."
Expert  Student sharing skills "Sometimes when students help other students, they just give them the answer or tell them to multiply but not the reasoning why."      Avoid scaffolding early "I prefer not to give the scaffolding on problems up front because I like to see where students need it before giving it to them."
         Purposeful interruption "Experienced teachers know how to choose when it’s important to interrupt the class to help others understand or to wait until the end. They feel comfortable making those decisions at the moment."
         Efficiency seeking problem solving "We may have a day where we’re just practicing problems. Students can do it anyway they want, then I’ll pull them up one at a time and we’ll talk through it, asking, “Is there a more efficient way to do this problem?”"
         Class scheduling "Students who struggle a lot in math don’t take a language. Instead, they go to academic support and get help with whatever subject they need help with during language class."
         Saturday school "Saturday school focused on one standard. We did a mini test, huddles, and an exit ticket. We had about 2 and a half hours. We would start off with a little snack, then, we jumped into the work. It wasn’t so different than a usual class, except it was very hyper focused on one topic."
         Alternative problem solving "A lot of fourth graders haven’t seen particular strategies, so I’ll show them how someone else did it and explain how they did it. Then, I give them another problem to try it that way and see how their brain thinks and if they can figure out how it is working."
         Software augmentation "I had one student who struggled do everything on a computer. When he was trying to graph a line, he typed the equation into Desmos and answered the questions looking at the graph. He didn’t graph it himself. The computer did the stuff he couldn’t do, but then he could answer the questions based on what the computer created."
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Monitoring: Engagement
Novice/ Advanced Beginner  Knowing when to be stern vs. fun   "You have to know when to be stern. Kids will walk all over you."  Misbehavior  "The student's behavior was really concerning, and superintendents had to come in." Behavioral and academic taxonomy  "(The school) is strict with compliance and following through with learning. We have behavioral and academic taxonomy… We had discussions on what to do when kids are misbehaving." 
Distractions "If multiple kids are a distraction, how do you get your kids in order?" Asking for help  "She asks me for help in class if she's confused."  Call out misbehavior   "He's had to send kids out of the room."
Earning respect  "When trying to get 40 kids to lower their voices, I was raising my voice above theirs. I didn't know how strict I needed to be to earn their respect."  Facial expressions  "I could see in her face she was excited to do math." Stop teaching / talking to gain attention  "If a class is chaotic, I told the (teacher) to stop talking. When you stop talking, the students stop talking because they don't know why the teacher is quiet."
    Protesting / deflecting   "He started to deflect everything and was over it. He was protesting."  Circulate during practice problems   "I will bop around and make sure they are doing it correctly." 
    Sleeping   "Some kids were sleeping."      
Competent  Perceived disinterest in school and/or achievement "Students didn’t have a “why” to finish school. Their parents didn't finish high school. Kids always ask “why” they need to learn a concept in math."  Level of shown work "If a student is trying but not getting it, you’ll see some sort of work on their paper. It’s somewhat close but a little off."  Direct call in "During discourse I would call on kids that don’t usually speak."
   Perceived disinterest in showing work "Some students will just solve and not show the steps. They ask why they need to show the steps."  Hand raising for advanced learners "Raising her hand more to answer questions."  Challenge/Timed questions for advanced learners "Challenge questions help (with high fliers). Using their personalities. Challenge questions = race against the clock, questions they aren't used to seeing."
   Effort/Achievement misalignment "The high flyers put in less effort than the ones really focusing."  Private notes "Some will write a post-it and hand it to me with why they weren’t participating."  Review level of engagement in specific problems "I will look at which questions are more engaging and what changes I can make. I won’t do it with units that don’t have a lot of word problems."
   Lack of training in engagement approaches "I didn’t get trained on how to respond to the push back everyday or how to make problems applicable to their lives. No training on how to make content relatable to kids."  Attentive orientation "Facing forward, eyes on board, on the correct page. Level of focus comes from home or within them. They are writing down the work, correcting their work, writing what's on the board."  Proximity to low-level engagers "During the turn and talks, I would go to students that wouldn’t speak as much. I am listening to their conversations."
   Perceived disinterest in receiving attention "As I was pushing her, she was pushing back. She believed if she wasn’t causing a distraction then she should be left be. Didn't want to be noticed much- just a part of the crowd. Didnt raise hand and would avoid contact. Lack of engagement. Purposefully trying to blend in. Other two friends were outspoken, leaders of the class, hands always up. Watching interactions they were a tight knit group."      Turn and talk "Discourse would come before students work independently. A whole class “turn and talk”. They talk about the question being asked. After that, they come into a whole group discussion."
   Distracted focus, social "Students weren’t talking about the work. Then class gets less engaging."        
   Perceived boredom "The “I, we, you, do” approach was boring for kids."        
Proficient  Perceived disinterest in verbalizing "Middle school students don't want to talk."  Question asking "If you're not engaged, not asking questions, you’re not understanding something."  Circulating, with notetaking "That's why I'm asking you guys to work together. I'm actually walking around and as soon as I see something that I did not anticipate, I'm writing that down because I'm gonna use that next time I'm teaching this lesson."
 Level of effort to evaluate "Sometimes eighth graders were a little bit more reluctant to want to engage and that was a frustrating piece for her. So we worked on trying to get students to engage a little bit more by setting those expectations."  Absence "The students failing are the ones with their head down and skipping class."  Playful cold calling "When I cold call students, they have to explain their thinking verbally. I push them to use precise vocabulary when they discuss it as well. They're required to write first before they speak. So that way the kids are able to share and build off each other's thinking."
 Discomfort with control reduction "Letting go of control was uncomfortable."  Story/Lesson verbal reflection "We just reviewed equations today. While listening, if I hear them say “Balancing” “undue”, etc. I know they are on track. I hear them talking about the stories I taught them to help them understand problems."  Purposeful seat charting "I design my seating plans purposefully with a high student between 2 children that struggle."
     Facial signals "I can see it in your face that you are not understanding."  Community of support building "Building a community of culture in classroom to support each other. Lots of group work. Community building to help with homework outside of school. Really effective. As the year progressed, we did small group intervention." 
     Transformations "Students that never wanted to be called on now are attempting to learn the math. I have kids trying. That gives me confidence this curriculum this working. They are trying with other students. I think kids feel safe in being wrong because of our discussion based classroom."  Augmented notes "It did take him a while to get engaged. He likes to draw so I gave him annotated notes every day. He has a sketchbook and he starts drawing."
     Error recognition "I think it's important for students to pick out mistakes and not just answer the question."  Partition absentees  "I don’t pay attention to the scores of the absent students all the time. They are included in the intervention of the kids struggling."
     Talking/Discourse "The more I see discourse with the students talking, the better they do."  Interesting/Relevant/Fun problems "I ask them different things related to their background: asked them about cooking rice with ratios and proportions. How much rice will they make with amount of people."
     Expressed joy "I have teachers right now, in seventh grade statistics and probability, and the kids are like, “This is so much fun.”"  Embedded errors "Sometimes I put incorrect answers on the homework and see if they tell me I’ve made a mistake."
     Hand raising "Some teachers only call on kids who have their hand raised. It's a matter of how the teacher wants to do it. But it's also very much a matter of the context of that class. Once you start seeing what kids are producing, whether it be from paper and a pencil, talking, etc., you can start to get to know what they know and don't know."  Encourage writing "They're required to write first before they speak. So that way the kids are able to share and build off each other's thinking."
     Providing answers "Some teachers go over all the homework  answers. I think about the kids who didn't do their homework. And they're sitting there, and I'm like, what are they doing? Are they copying down the answers? I want them to take some ownership of checking their work. I'll post the answers. They can ask questions so I could either post it during the period right after their warm up, or I post it on my webpage, where they could check it on their own and ask questions."  Independent work "We followed a led model. Start off with critical thinking and explore together. 80% of class working independently and pull the 5 students to another part of the room. We could dive down into the learning."
         Class leader role "Class leader role - anyone who applies gets the position. Make sure they have supplies. Go around supporting."
         Encourage student evaluation/critiquing "We've started with sharing a student’s work and we have a hand signal if you want to build on to what somebody else is saying and if you agree."
         Peer discussion "Before we discuss the opening task, students can share their work with their teammate to be able to build upon or revise their work. It gets everybody kind of thinking about it. I check to see if a student is showing their work and either explain it or can justify it as well."
         Warm up/Non-math start "Agenda on the board. Learning target and upcoming important dates. I’ll put on the board a warm up. Could be an opinion type question to get their brains moving. No wrong answer question. “Low floor, high ceiling” - all students can feel successful in the beginning of class. Gives them opportunities for a response. I ask them different things related to their background: asked them about cooking rice with ratios and proportions. How much rice will they make with amount of people."
         Alternating between abstract and hands-on activities "Hands on is how they learn. Bouncing back and forth between abstract and concrete."
Expert      Excitement about math The students had to convert the gallons to teaspoons. Then, they measured the water in a measuring cup. If the measurement was correct and the water filled the cup perfectly to the top, you could see the kids’ excitement.   Prompting to share breakthroughs "While circulating, you realize a student group makes a good point. Ask them to repeat for the entire class."
     Distracted focus, technologies "Students have their phones out and aren't paying attention."  Continuous observation "For a teacher to succeed, you have to observe what’s going on in the classroom." 
     Task focus "The students would help each other because they had a task to do, so they were attentive to the lesson."  Encourage error sharing "The openness in the classroom encouraged students to volunteer and share their mistakes and different strategies, unprompted. The goal was to get better and for the whole class community to get better."
     Asking to share mistakes "A student raised his hand and said, “Can I share a mistake I made?” Another kid’s hand went up and asked if he could show the teacher another strategy. My students refused to be taught and just spoken to. I was like, “My kids have arrived.” I was proud of them. They created space for themselves."  Encourage writing and revision "Look for students to jot down what they are thinking, so when it’s time to turn and talk, they have something to say, and they have something tangible to refer back to. It’s also important to have opportunities for students to revise their work."
         Circulating, with evidence gathering "I’ll do walk-throughs of the classroom and collect feedback: cognitive load, student discussion, etc."
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Monitoring: Progress
Novice/ Advanced Beginner  Analyzing data    "For new teachers, data is 100% overwhelming. They don't know where to look or what to filter."   Internal assessments  "We can see her students' scores progressing via internal assessments."     
Data tracking   "Data tracking was a whole other ball game to being a teacher. It was difficult the first year."         
Competent Persisting errors "You don’t want students to think they got an answer in a different way and think they are wrong."  Assessments "Data driven or re-teaching. Exit tickets, homework (can’t observe what's going on), controlled environment (in class), exams/benchmarks. Look at data and what they produced."  Exit tickets on paper "I have an exit ticket tracker. Labeled by date and score."
     Preponderance of achievement "I look for 90-95% of students getting it."  Individual question/problem tracker "Use a spreadsheet to mark off if kids are getting the question. Some people will use a tally system. Have an exemplar from the day and tally how many kids got it right or wrong."
     Exit tickets "I wanted 65% or better on his exit tickets. That's the only quantitative piece I was tracking."  Individual student tracker "I'm not looking at his work everyday but I know who I need to look out for."
     Future performance "On the big exam she scored a high 2. Up from the 1 she did receive previously. Significant move. In further years she was in the 3s and maybe 4s."  Cross-class data comparison "Compare data across other classes."
     Perceptions of demeanor "Looking for his demeanor and the excitement he would show like “hey i got this”."  Behavior tracking "If he didn't have a good day the day before, I would check in with his behavior before the pre teach."
     Shown work "The work I see on their paper is what matters the most. Seeing their steps. If I see that, I know learning is happening."  Spiraling on specific, complimentary skills "I'll pick a skill or 2 that compliment each other. I'll plan to integrate it into my lesson. I can do a quick re-teach and assess again. I'll do it over a few days until I see 80% showing mastery."
     Verbal expression  "I’m listening to how he's explaining what he's thinking to his peers. That's how I'd know if he's making progress or not."  Track learning rates as scores/time "I look at the scores over time. I would define it as how quick students are mastering a skill. Multiplying multi digit numbers can take 2-3 weeks to master. If a kid can show mastery of that, i would say that's an accelerated rate. If they can't pass that time, it's a slow learning rate."
     Perceptions of independence "After a while she didn't seem like a project. Same person as before. Feeling more responsible for what she produced instead of a team effort."  Habits of discussion "I teach students to have good habits of discussion."
     Behavioral observations "The rest was qualitative. Bathroom trips slightly decreased. He would go less frequently and not spend a lot of time."    
Proficient  Perceived erosion of potential "Wasn't a surprise that one child didn't pass. Had behavior issues/lack of confidence. Spent time outside of classroom. Suspended a lot. Missing first 5 mins of my class is the recall/retention part. Child was a repeat offender. Wasn't first time he wasn't successful. He struggled. Had potential eroded from him."  Software packages "If I want to look at the questions that were missed the most, I'm gonna to look at illuminate. If I want to look at how much the kids are practicing, I'm gonna look at IXL."  Software packages "I decided we would use a high level curriculum (IM). Rated one of the best research based math curriculum. I can compare her students vs students at a different school with the same curriculum."
 Budget constraints "It's a subscription based platform. Schools decide if it’s in their budget."  Group performance "End result: improve the outcomes of the 5 students. Only one child did not receive a passing grade on the exam."  Comparative datasets analysis "We would then together look at the data. Is there a theme in those hiccups for students? What piece or part of math do we need to re-teach?"
 Data literacy "Some people don’t understand the data."  Broader datasets "So besides our state testing, the county has recently, in the last 6-7 years, done progress checks which are created at the county level."  Segmented performance analysis "I look if the students that participate everyday are getting it (70% or higher). Then I look at the students struggling. Are they at least passing or almost?"
 Data volume "Data is really overwhelming unless you know what to look at."  Verbalized cross-unit connections "I’ve had students making connections between different units. Before, they would say “I don’t remember this.”"  Extensive individual tracking "The last conversation she and I had with this student was, “You can do this. You are going to take longer. You might be the last one done. We may need to call mom and get mom to pick you up. The teacher has talked to her. We're prepared to do this as a community but we need you to do your part and take your time. If you need a walk break, take a walk break. If you need more scratch paper, we got it for you.” That young man passed his SOL."
 Test quality "The county progress check assessments were terrible in terms of just accessibility. The reading levels of them. So we feel constrained in that we take them 2 times. It's too much testing."      Warm-ups "I would use warm ups throughout the year to ask questions on units we’ve already done to keep it fresh."
 Nonlinear performance "Could also see kids not understanding during the unit and then perform well on the summative. They are usually doing a lot of work behind the scenes."       Rework "It’s hard to fail my class because if you don’t get it the first time, we can keep trying. I allow them to re-do homework and classroom assignments."
 Perceived memory challenges "When it came to reviewing a lot of content at the end of the year, they couldn’t remember. It’s a long term memory issue."       Misconception tracking "I will keep track of misconceptions being made my students. I track that and tally how many kids have each misconception."
         Continous check for understanding; "Piggy Questions" "“Piggy questions' ' - something you learned 3 days ao, 3 weeks ago, and 3 months ago. Keeps fresh in mind. Pre canned stuff is good as a base but I use things based on trends. Creates everyday. I would typically use state test questions." 
         Question analysis "What question did most of the kids miss on the test? Which subset of kids got it right and what's the distractor?"
         Spiraling: Cross-topics "Activity - 3 questions are from a state exam and where they've struggled before. If they struggle with negative numbers, they are going to struggle with future topics. Making sure they are constantly getting these topics."
Expert  Perceived impermanence "They were learning, but it was not internalized."  Perceptions of insights "It’s really cool when a kid thinks of something and it’s mathematically sound."  Practice "We also have two spiral workbooks that have 10-15 problems basic problems for different topics (multiplication, addition, graphing, and story problems). The students do those every day." 
 Completion focus "Math wasn’t the emphasis at this one school, I guess. It was just about getting through some textbook series."  Student question quality "If a student isn't scoring well, then they’re not asking questions. They have to keep asking questions until they understand it."  Spiraling "I prepared the entire year’s sequence and spiraled these standards across classrooms, so the students wouldn’t forget what they learned. They saw problems every week, so it wasn’t lost to them (i.e., Pythagorean Theorem problems every Monday). Use it or lose it."
 Premature placement "I’m disappointed when high schools are pushing kids to get to AP Calculus or BC Calculus. They’re looking at what’s going on the resume as opposed to becoming mathematicians."  Developmental models "If you watch kids develop, there is developmental staging that children go through. When they’re ready, they’re ready. If you race through just by doing more, they’re not going to know it any better until they’re ready for it."  Comparative data analysis "We were really data driven. We would look at the data and reteach what we needed to."
     Achievement against new problems "Students started using their toolbox and stopped following a step-by-step recipe. They were thinking on their own and unpacked never-before-seen problems and made sense of them."   Student self-monitoring "We had the students monitor their progress with a monitoring sheet. In their notebook, each student had a protected sheet with the date of the test, their score, and a space for reflection, including their goals, what they needed to do to get better, and if they were satisfied. They could see which areas they needed to work on. If they struggled in a certain area, they were encouraged to come to Saturday school. It was up to the students to keep track of their own data."
     Frequencies of surprise "Students stopped saying, “You haven’t taught us this before.” In the past, the students used to say, “We’ve never done anything like this before” when the only thing I did was switch the variable or make it a vertical versus horizontal table."   Progress communication "The philosophy is, yes, we are beholden to this progression, but we are really trying to communicate how we are figuring things out. Communication is key."
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Novice/ Advanced Beginner  Time / effort constraints  "I would go to sleep at 2am writing lessons. I was spending so much of my time to figure out what I'm teaching the next day." Provided curriculum    "I knew of some open source curriculum and use them as sources."  Mark up lesson plans      "During the work time, one of my teachers marked up the entire lesson plan and how she would teach it. I saw the level of effort and engagement." 
Content development    "She would have to compile resources on her own and teach that and hope it aligns."         
Limited preparation "A lot of teachers try to build a car while driving. A lof of the practical issues should be finalized by the beginning of the school year."         
Dated materials / resources    "Some teachers use old materials, but it's kind of frowned upon."         
Curriculum disagreement  "Other teachers will tell me IM and Amplify are not good. They want to write the curriculum because they can 'do it better.'"        
Surprises     "I was surprised by ways kids figure out how to solve a problem that I've never seen before."         
Pacing    "They have to hit certain lessons and specific times so kids have exposure."        
Competent  Evolving rosters "I found out I had 45 students in my classroom. I didn't have enough seats for the kids. Kids were being added and subracted from the roster daily."   Prior assessments "We know questions on previous state exams."  Classroom organization "It's important for me to have a well-organized classroom. I needed places to remind me what to do." 
 Evolving standards and/or emphasis "We are figuring out what lessons we can throw away or less stress about as teachers. It changes every year. We have to align with the network standards as well."   Administrative guidance and mandates "Discipline and classroom management was very charter school-like, but the curriculum was public school based."   Built-in flex days "I have flex days in my calendar so I can go back to units. If my class didn't understand equivalent ratios, I can use a flex day to tap into a previous unit based on data I have of the students." 
 Holistic requirements "If there aren't routines set in place within 6 weeks, it will derail the lessons set in place."      Student familiarization "Put a lot of emphasis on learning names the first day. Knowing their names and where they sit is important. They knew they couldn’t get away with a lot." 
 Adminstrative restrictions "Charter schools give certain instructions to follow. District schools have more flexibility. If i was in district, i could adjust to my students learning rate. Now I have to stay within these perimeters."  "Public schools have less flexibility with making curriculum decisions. They don't have the same vertical alignment, and it's more difficult to have those types of conversations."      Routine establishment "Setting clear expectations. Silent during solo time. Setting a timer on the board. Kids knew what to expect." 
         Prior and future assessment reviews "If I see there are multiple questions in an assessment, I’m going to heavily focus on that topic. It’s important for us to look through assessments. You’re planning ahead on which gap to close based on questions being asked more."
         Vocabulary "I don’t like to introduce a topic without figuring out what the word means."
Proficient  Time and effort constraints "It takes me a while to create the scripts and give them to teachers at the other schools. Showing them the misconceptions."   Provided curricula and/or materials "Teaching math is best when you’re already using high quality materials. I was able to become the expert because those high quality materials freed up my space."  Include classroom management "We have protocols and routines and procedures. Kids know what is expected. Students walking in and knowing what to expect helps me with my management. I don't let things slide. If you want to go to the bathroom, you better have your work done. They can't throw anything away until it's independent time. Less distractions while learning math." 
 Pacing pressure "My principal sees the scores, the district sees the scores, etc. Pressure to complete the curriculum to 90% brings pressure with the pacing guide."  Prior materials "As I got closer to the state exam, I knew I needed to teach functions. I didn’t have time to use the longer drawn out approach. I did fall back on other resources I used in the past."  Data-informed revision "Manipulate the curriculum based on how the current students are performing and where the gaps are."
 Professional development variability and volume "Amplify Math is the only support we get. It’s been a struggle ensuring that the professional development sessions have been useful for us. They have consistently chosen to not share the agenda/activities of the sessions. They say it’s information they can’t share ahead of time but can give the objective. I go in blind. I have no idea how it’s going to go/help my teachers. I don’t know the nuts and bolts about how they are going to teach it. It hasn’t been that successful. They aren’t tailored to my school - it's one size fits all. That contract was signed prior to me coming in."   Misconceptions "You have to anticipate the misconceptions and that sort of thing while making the curriculum."  Just-in-time vocabulary "Now, they say to not introduce vocabulary until it comes up in the lesson. Using the word when they need to make the connection, not beforehand."
 Perceived differences in requirements "But again, the curriculum had to be a school based decision, and our principal had to know  what we were doing. He had to approve it, but it was not something that the county wanted. It was something we did."  Audits "TNTP came in and did an extensive audit on our systems. They found that our lessons were falling below grade standards. Because of that report, I decided we would use a new curriculum. They observed the lessons in the classrooms."   Personal and/or provided pacing guides "I keep my own personal track of the pace that I’m going at. We do a planning calendar each week. And then we get a daily pacing calendar for each course, and it goes up to high school."
 Misaligned mental models about curriculum "I’m very Type A follow rules person. I didn’t understand some of the reasons in the curriculum so I wouldn’t do them. Throughout training, I am now seeing where those pieces are fitting in. I’m not doing as much tailoring anymore. When I design my own lesson plans, it’s easier. Using someone else’s curriculum, it’s difficult to see the connections."      Include potential strategies "When the teacher is preparing their lesson, they have to understand the other ways to solve a problem. Possible representations." 
 Provided material variability "Within the modules, we have “The launch” website. It has the student work = aim, “please do now”, opening task, stamp (main things they need to know), practice problems, “we do”, independent practice (2 rounds, 5-6 questions each), challenge problems (1-2 questions), “exit ticket” (2-3 questions at the end of class, set up with exceeding requirements), homework."      Include potential misconceptions "I prepare my lesson and anticipate the strategy. Possible strategies and misconceptions because I want to address those. As soon as I see a misconception, I go up on the board and take one student's work up."
 Tedium of (re)formatting "So you are doing the same thing every year, you're just doing it in a different format, essentially."      Design for flexibility "Nowadays, there is more flexibility with teachers. For the teachers that show strong results, they can make modifications as needed. Swapping in and out their own lessons as needed. They are encouraged to swap problems in an out based on data trends they are showing." 
         Target standards "Not sharing results but strategizing. About 4 big topics that account for 50% of the grade." 
         Consider prior and future grade level requirements "It’s best for teachers to know the standards below their grade level so they know their journey. And the grade levels ahead so you can make strategic plans if things are important for them in the future. The more you know about the other grade levels, will help you be a stronger teacher." 
         Intervention focus "So I'm planning for a 60 min math class and I'm also planning for a 30 min math intervention. What are we learning this week? What's the response to intervention? What fluency are we gonna do? Because our intervention starts off with like 3 to 5 min of math fluency. Are we going to work on multiplication?"
         Include concrete and abstract activities "You start with a concrete manipulator, go to a pictorial representation of some kind that could also be a virtual representation, and then move into an abstract idea of students working with mathematics."
         Curriculum professional development "I was responsible for the rollout of it, teaching and training. Helping them understand the curriculum." 
         Teacher-authored curriculum "Because our curriculum is written for us, teachers just rely on that. They  don’t have to predict as much. There isn’t as deep intellectual thinking going on. We write our own curriculum. It’s not from one textbook or research. For the most part, it’s positively received. They like that they don’t have to write the problems themselves."
         Provided curriculum "IM is a free curriculum. We also use Amplify Math. We have a contract with them. I do get to see a free vs paid curriculum. I track that as we go. I get to interact with their digital platform since it’s hybrid. Anything students or teachers do on Amplify Math, we can see the data. It tracks each individual and spits out a report for the teacher." 
         Weekly lesson planning "We have a competition with students, our weekly goals, and have our lesson plans submitted."
         Teacher-authored assessments "I get the SOL questions about 48 hours after the students take the exam. I’ll choose about 6 students and look at their scores. I’m looking at how many questions a topic were asked. Thats how I know where to put my focus strategically. I will make a spreadsheet by hand."
         Teacher-generated keys "My elementary teachers in particular always ask me, “Where's the key?” No, create the key. Because when you create the key, you have done the math. You have probably done the math twice to check yourself cause you don't wanna make a mistake in front of the students." 
         Vendor research "I cross referenced the data with other curricula out there. I did research. While I was waiting to hear from vendors, I did research with all of NY state data. I mapped out which charter networks were doing better based on math scores. I tried to find what math curriculum they were using. I cared about the data. I wanted their success of their curriculum."
Expert  Domain complexity "Education is uber complex and there isn't a simple solution."  Guiding principles and common topics "Our guiding principles are still the common core topics."   Flexible pacing "We had to have flexibility with students and teachers. It needed to make sense, so it did not always work out that the entire school from 6th to 8th grade was doing a project at the same time." 
     Current performance "Project timing depends on sequencing and how the students were doing."   Flexible projects "I love my projects, but sometimes I’ll have to shorten those or take out parts or it based on how fast or slow we are moving. I may make it a one-day project, or a Friday afternoon project as opposed to a three-day project." 
     Future grade level requirements "One of our missions is to get students ready for high school."   Grade-level strategies "In fourth grade, the philosophy is: How do you, the child, think? What works for you? Try to articulate and communicate how you are thinking. If you have a way to solve a problem, we can work with that." 
     Prior insights "As you teach more, then you’ll realize stuff like, “Oh, that’s an interesting question” or “if I use this number, they might do this," but it's hard to predict what students are going to say."   Summer work "I spent the summer working on my personal projects. A day before school started, I asked my principal if we could meet. I showed her what I had been working on, and she was excited like me." 
         Cross-grade-level projects "I created a hands-on project sequenced for 6th, 7th, and 8th grade, so each grade they experienced a project. The rigor increased each grade, and the standards matched the grade-level standards. The projects were pretty fantastic." 
         Cross-grade-level alignment "I spent the summer thinking about the alignment between 6th, 7th and 8th grade, and certain hands-on projects we need all of our students to do." 
         Teacher trialing "Have teachers preview the questions they give kids as an assignment. Look at the questions, and don’t just go online and get a worksheet and hand them a worksheet." 
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Managing: Collaborating
Novice/ Advanced Beginner  Veteran inflexbility    "Veteran teachers are used to teaching math a certain way. They are comfortable in it. The math they are teaching isn't aligned with how students currently learn math." Co-teachers  "I learned a lot from my co-teachers and what I wouldn't do."  Meetings "We meet on a weekly basis. We have weekly planning and data meetings to make sure they are on pace."
Professional differences  "It bothered me that the experienced teacher took the curruclum change so personally. It took away from the kids."      Discuss learning gaps  "I will talk to co-teachers and special ed teachers based on how to close the learning gaps." 
        Observation  "We have one formal observation and two random observations from our principal."
        Feedback / notes   "She would teach one class, I would teach the next, and she would give me feedback and notes." 
        Active mentoring   " Since I'm a first year teacher, they set me up with a mentor who will come watch and tell me what I should do differently."
Competent  Perceived senior teacher control "The lead teacher doesn't like it when I help the students one on one. Her view is that she taught the lesson and they should've been paying attention."  Administration "My Vice Principal gave me help with classroom management."  Practicing with others "During internalization meetings, teachers will solve a problem with the misconceptions so they know what to do in the moment." 
 Feedback timeliness "You can miss the bigger picture when you intervene with feedback too quickly."  Education/certification programs "My Masters program helped me the most. The professor helped me with lesson plans and practice."  Active monitoring "We sometimes do "active monitoring" with veteran teachers."
 Public speaking "There is the occassional person who is uncomfortable and doesn't want to participate in teaching in front of others."      Rubric-based evaluations "When evaluating teachers, we have a rubric that we share with the teachers. We let them know that they will be working on goals for 6 week cycles."  
 Lack of veteran teachers "Not a lot of veteran teachers reach out to help."       Co-teaching "At the beginning of the year I was doing pull out groups but it wasn't working. It was more beneficial for me to go into the classroom and circulate to target students in the class. We transition in oct or nov. i asked her how i can best do my job. Co-teacher was never fleshed out. I'll pull them out of specials. We never sat down to discuss teaching styles. I try to fill in any gaps that are needed in the class."
 Artificial training "I wish we had more training on realistic situations in a tough environment."      Veteran teacher feedback "We value feedback and constant learning. We will have veteran teachers provide feedback so everyone is involved." 
         Cross-school coordination, especially in high school "We collaborate with high school to make sure they get the content when they leave 8th grade." 
         Misconception sharing "Teachers hop on a Zoom call and we will lead them through the content of the unit. We will talk about common misconceptions of the unit." 
         Student information sharing "We will collect student data and compare with teachers to see if they are collecting data accurately."
         Gesture and nonverbal feedback "I was in the classroom where the teacher missed a key question that would be useful to ask at the time. I passed a note of the question. He asked in the moment. It worked well to push the rigor. Doesn’t completely derail the lesson."
         Coaching "We think of coaching as falling into 3 components: “The coherence cycle”. 1. Coaches meet with teachers to have lesson internalization meetings. The goal is for teachers to fully understand the math they are teaching, strategies to teach, clear lesson plan, peak questions to ask, coherence of how lesson builds and going towards. Teachers will practice and get feedback from instructional coach. Usually around a core topic for the unit. 2. Observation feedback. Coaches observe for 15-20 mins. Catering observation towards goal of the teacher. They can debrief lesson afterwards or real time coaching to slip teacher a note or hand signal to improve in the moment. New teachers can forget what happened in practice the lesson days later. 3. Data meetings. After the lesson, the teachers collect quiz or exit ticket data and bring into meeting with coach. They help them analyze data and what needs to be re-taught. Another practice component in that meeting as well."
         Evaluation meetings "Student outcomes is a component as well. We track a lot of data across schools. In evaluation meetings, teachers present their data."
Proficient  Perceived mentor resistance "My mentor didn't share anything with me. She thought it was important that I learned how to create all of my own material. After the first year, it’s much easier."  Coaches "A lot comes from coaching. If a math coach can help you with the common errors, that helps. They can help through their own experience."  Supervision "We have our assistant principals that come in and they come to observe us. They have some short observations and one observation that's longer. They fill out the rubric, which is the instructional excellency, and we fill out ours at the beginning of the year. We have a meeting where we sit down and we talk about. We also talk about the strengths and the areas of improvement."
     Mentors "But then she also allowed me to come in so much more that second year and it was nice to get to know her, her teaching style, seeing her interaction with the kids, helping to reframe questions she was asking and getting to some of the rich math content. Are you asking why? Are you having kids reflect on how you are going to use this?"  Facilitated professional learning communities "We do Professional Learning Community (PLC) meetings. We share resources. We care about how the entire grade level is performing. We align with each other. A new teacher will ask how to teach a standard. It's a collaborative space. We have to have a facilitator."
         Error sharing "We also share lesson plans that can include common errors. Also getting teachers involved in the different ways students can attack the problem. Getting teacher buy-in. Anticipate different correct opportunities." 
         Pre-unit meetings "Before we start the unit, we get on Zoom and have an hour long meeting with the other teachers. We break down the standards into skills. Coherent map and connect from previous years. How the standard is going to help in future grades. Look at the assessments and what students need to do to get the correct answer. Other resources we need (number line, anchor chart in the room, etc.) It’s usually about 2 weeks before every module starts." 
         TikTok "I use TikTok for ideas and send to other teachers."
         Modeling "I went into her classroom and had to model the learning so she could see how to run her classroom." 
         Mock practice "We watched mock conversation videos during training and we practiced."
         Data analysis meetings "We had one of our content team meetings with the math teachers at school and our assistant principal would talk us through how you can look at information. Sometimes students will score differently on assessments than what you see in class. So then you have to look if they passed all the exit tickets."
         Formal observations "For formal observations, I have to have a conference before, plan for lessons, etc. I’ll do a formal write up with pre conversation and during. I’ll send the formal write up."
         Notes in curriculum "I’ll write in my comments how each lesson is connected."
         Curriculum planning "I work with people higher up writing curriculum. Gives your teacher goals, students goals, warm ups, what to look for in discussions.. Very comprehensive. It isn’t scripted." 
         Off-hour communication "I'm happy to respond and brainstorm with other teachers a little bit even if I'm on vacation because that's when they're thinking about it and that's what's in the best interest of students."
         Informal observations "Informal observations were an expectation from me. There is always room for improvement. I will tell the teachers my intentions: how long I’ll be in their classrooms and how often. I have “look fors” based on school plans. We develop a list as a dept so I’m not making things up. I’ll sit in the back of the classroom silently. Write evidence for the “look fors”. I’ll recommend things to the teacher."
         Team teaching "Other times we would sit down and plan and she needed to reteach 3 kids a concept and it wasn't necessarily as vital that I be in there as a second person to do direct instruction, but sometimes depending on what other activities I would push in to monitor and make sure that the other students were on task, doing what they needed to be doing."
         Document upload and administrative review and approval "I have to submit our work on our Google drop, we have something that's called “curriculum documents.”It has the different subjects and every teacher has a folder. And so in that folder, you have to submit your plans for the week for the assistant principals to look at. So my manager, the assistant principal of STEM, reviews it each week. He'll let me know whether or not it met the criteria or anything I need to fix."
Expert  Profession intensity "Teaching is pretty intense, and I expect a lot from people that I teach with. It’s sort of seven days a week. I’m hoping I don’t scare them off. I think math all the time."  Feedback from external observers "External observers came to see how our teaching styles matched up to the new curriculum. They said, “Nope, you’re still teaching the old-school way.” That feedback supported the shift in my teaching. I’m so grateful for it."   Practice teaching "Practice teaching in front of other teachers." 
 Professional enrichment "Not all the teachers felt the same way about changing the way things were run in the math department. They were like, “What? You want us to do what?” There were six of us. About half of the teachers were on board. The other half of teachers thought everything was good as it was."       Lesson planning "We were choosing and tweaking lessons—that’s when I got teachers from the other side excited about it because they were part of that assessment creation. They were enthusiastic about the questions." 
         Engaging department meetings "I changed our bi-weekly department meetings into real working meetings. We would bring in the data from the assessments and compare it. Then, we would think about it together and say things like, “What are you doing? What do your lessons look like?”" 
         Record and review "To get a glimpse inside of our classrooms, I did something called “Phone and Pocket.” Teachers recorded themselves on their cell phones and then shared a 3-minute clip in our meetings. We started a number of department meetings with this to work on our questioning."
         Open door observation "I asked to step out of the classroom for just one class period so I could observe, support, and provide feedback to the other teachers. I called myself the “Curriculum Implementation Specialist.”" 
         Cross-school observation, especially high school "I try to make the rounds and talk to other math departments in the area, mostly at the high school level, to see where they’re going and how our students who have gone there have done in math. I ask myself: "Is there anything that we should be doing differently or adding to our curriculum or emphasizing?""
         On-the-fly meetings "For fourth and fifth grade, our teachers have a quick meeting after every class." 
         Model "We had this new principal who was shifting things as well. She was trying to shift every department. The following year, she implemented the monitoring piece and sharing data with the students. It became a school-wide effort, rather than just me trying to do that in the math department. I’m so grateful to her, the timing, the school, and the student population." 
         Scaffold, guide, extend freedom to early teachers "I don't think you should demand new teachers to follow a script. They need more coaching and guidance. If they are going off a pathway, ask them why they are making those decisions."
         Partnership mindset with students "Our big goal is to have the students understand and accept that teachers are their partners in learning, so when they leave this school, they might not be the strongest students, but they know how to communicate with adults." 
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Managing: Dealing with Responsible Others (ROs)
Novice/ Advanced Beginner  Critiques   "I've had parents say, 'You aren't helping my child.'" Emails   "Parents would sometimes CC my co-teacher or principal. I was the target of the emails." Discuss student placement  "For IEP students, someone will refer them, and the teacher has to agree and talk to the parents to get the student into IEP." 
Demands   "Parents had a lot of demands and didn't trust my judgment. It was very hurtful, and I started to question myself.      Reach out to ROs for background information   "I could have called his caretakers and asked if they experienced (his behavior) at home. I just went straight to what I'm observing in the classroom at school. That's one thing I could have done differently." 
Variability within group: RO support    "There is a divide between kids that have support at home and those that don't. As much as I tell them to study or do homework, some don't. I can't control what happens outside of school."         
Competent  Uncertainty about necessity "I didn't share it with his mom. He's been opening up more since winter break."  Discuss learner traits "They gave me feedback on some of the things he likes and dislikes at home. Gave me insight on the type of person he is. They spoke about his confidence, especially in math. It grew over time. They witness that evident in him wanting to do his math homework. Previously he would neglect it or not do it. They saw him looking at videos I suggested."   Avoid high performers' ROs "I don't speak often to the parents in my high performing class. They are meeting the expectations for class. I'll call for students at risk of failing."
 Anxiety "I don't like calling parents, it gives me anxiety. I'm a non confrontational person and don't want to tell them their kid is failing."   Discuss learner performance outside classroom "His mom is very on top of his grades. She follows up to make sure he's getting his work done."  Single purpose engagements "I had to get the parents involved. I had to call home and explain why it’s important for their child to use their voice." 
 Surprise "She and I will text about behavior. She is aware of that. Parent teacher conferences she was surprised his grade was so low."      Progress update "Later on in the year I tried to keep them updated with him and his progress. I didn't tap into them during the program. After that I decided to keep in touch with what he needs to work on." 
         Weekly calls "Our school is big on conversing with parents. I have weekly calls with parents whose kids are in danger of failing 5th grade."
         Surveys and Focus groups "Coming out of remote learning, we decided to re-think our schedules. We did surveys and focus groups with families. Families said they liked the longer school days. We also survey the students on the content and curriculum."
Proficient  Necessity "If you don't have the parents, you don't have them."  Relationship management "I feel if you have that partnership, then when you do have to make a phone call about a behavior or grade, it can lessen the blow a little bit."  Single purpose enagagements "On Zoom, the student would say, “You didn’t send the link.” The link is on the Google classroom under my class. It’s the same link every day. I called the mother and I said, “I was having a class and I was correcting your child because your child was being disrespectful. Your child is here to learn. Your child is not learning and disrupting the learning of others.” She said, “Okay, I understand.”"
 Additional effort "I had a love-hate relationship when I was a teacher at a parent conference night because it meant I didn't come home till 8:30 at night. I had to be up and at work at 7:00 clock the next morning. So that was not fun."   Collection contact information "In the beginning of the school year, we give a blue card. Contacts need to be added to it."   Newsletters "I know some teachers have had success with newsletters and sending things out."
 Under-engagement "My most difficult experience was a parent whose kid was doing remote learning during COVID. I was teaching from home. Which was the hardest thing to do. How can you engage your student, through a computer, right? And most of the parents were not helpful either but they understood how important teachers are right now. The student wasn’t even logging in."  Ensure support "Sometimes it can be with the student in the family depending on the family situation. Sometimes the family is very much looking for that support. Teachers have given that support and students will work for that teacher."  Celebratory calls "Most of the time when teachers call, the parents think that they are calling just to say something bad about their kids. But I’ll just give them a call, for example, “Melissa was good in class today. She got an A on her test.”" 
 Avoiding behaviors/Difficult people "The mom never showed up for the parent teacher conference last year in seventh grade. She would not even talk to us. She would curse us out."      Texts "I was calling her and sending text messages to her how well the child was doing."
 Disagreement about approaches "I hear from parents all the time that they learned it one way."      Sharing curriculum information "We have time in which parents come to meet us and we talk about the expectations for the class, what we are going to cover throughout the year, etc. Then we do parent issue conferences, but we are always in touch with our parents."
         Homework "The parents are a partner in their child’s education. I give details to the parents on what they should review at home." 
         Relationship management "I feel if you have that partnership, then when you do have to make a phone call about a behavior or grade, it can lessen the blow a little bit." 
         Learner traits "But engaging and talking to parents was so valuable. Getting their insight as to what they, you know, see as their students' strengths and weaknesses too."
Expert  Achievement goals "Parents are always worried about what college their kids go to."   Lack of RO support "We need to understand some kids might not have support at home or help."  Direct engagement with difficult RO "If there are difficult parents, we step in right away." 
 Critiques "If I had to speak to parents, they would say I’m not teaching well."  Placement discussions "One student moved from private school to my school, and she was ready for something higher than 8th grade math. She could’ve been in honors algebra. We talked to her family and moved her to a higher math class, and she was so happy."     
 Sanctioned non-performance "One student's mom told me my English wasn’t good enough, and her son didn’t want to do his school work. The mom gave her son the okay to not do his work, and he failed. I couldn’t do anything about it."         
  Difficulties Quotes Information Sources Quotes Strategies Quotes
Managing: Developing Self 
Novice/ Advanced Beginner  Lack of preparation   "I don't feel like college prepared me for this. We just practiced making lesson plans."  Feedback  "I've received feedback about being reflective."  Daily reflection   "He needs to reflect every day via email on what went well and what he needed to fix."
People pleasing   "Some teachers say I'm too nice… You want the kids to like you."     Student teaching  "I learned the most from student teaching. If I didn't have that, I don’t think I would be prepared." 
Student disconnect  "Some people know the content really well, bu they are socially awkward. They have trouble looking kids in the eye."         
Public speaking "My first year, I knew the content well, but I would freeze up asking the kids questions."         
Competent  Classroom management "It's difficult to manage a classroom and collect data. Practice is crucial."  Students "It was meaningful to me when he thanked me and actually learned something. I actually helped this person."  Showing vulnerability "I’m vulnerable with my students. I let them know if I’m having an off day."
 Social interaction "Some people know the content really well, but they are socially awkward. They have trouble looking kids in the eye."  Instructional videos "I did a lot of research on my own. I taught myself how to walk through instruction watching Khan Academy. I did this on the fly the first year."   Lesson content knowledge "Knowing the lesson well enough allows you to recover when there is a setback."
 Small talent pool "We are being placed in schools that are desparate for teachers. A lot of initial training was trial and error."  Graduate programs "I learned in a Masters class how to model for students and manipulate strategies-- "best practice.""   Journaling "I wrote in a journal little successes and lessons learned."
 Respect building "Kids wouldn't learn anything unless they knew me first. I focused on showing the kids who I am."  Characteristic lists "Characteristics of best teacher: 1. High expectations for kids and self. Doesn’t make excuses and won’t lower the bar. 2. Do whatever it takes. If I need to stay after school or work on the weekends, I am willing to do it. 3. Check for understanding. Consistently looking at data. Knows kids very well. 4. Engaging. Kids like to be there. Teacher shows their passion. 5. Overprepared. Fully internalizes lessons. Fully prepared to teach."   Observation and Coaching "I think the best training is being in front of kids and a coach giving rapid feedback. That's where I grew the most as a teacher."
 Observed/Evidenced performance gap "A teacher looks good while they're being observed, but the students' performance data doesn't match that success."   Feedback "I implemented the feedback I was receiving based on classroom observations. If something wasn't working, I asked them to come back to observe and give more feedback."     
 Turnover "First year teaching is where you see the most turnover. It gets very overwhelming. I saw teachers get burned out."        
 Pay "First two years were at an independent charter school. Looked for somewhere that was paying more."         
 Mistake building "Learning to make mistakes. It shows kids I'm not just a robot teaching."         
 Gaps in content knowledge "If you’re not comfortable with different representations of numbers, then it can be a little intimidating when a child is looking at something and in their mind, they’re converting things to decimals, and you’re not understanding when they’ve made a mistake because they’ve done the conversion back wrong and you didn’t realize that they’ve converted to decimals in the first place because you’re so scared about rational numbers yourself."        
 Insufficient coaching "For first year teachers, they need to be willing to listen to students and be okay with not being able to answer a student’s question. They can answer the student tomorrow after talking to the other teachers."         
 Lack of training "We haven’t done an in-service training for the new teachers, so they’re learning as they go."        
 Apologizing "Learning to be able to say sorry to kids."        
Proficient  Effort "I was working 12 hour days for 6 years, including weekends."  Self-discretion "We don't expect teachers at our school to give the same homework. It's really teacher discretion."   Curriculum review and sensibility "If I think a different way would be better to teach, I have to use my professional judgment. If a lesson isn’t making sense to me, I won’t use that lesson. The approach is what matters. It’s what is driving the learning."
 Paperwork "The paperwork is so much work. Keeping up with their IEPs."  Veteran teachers "Veteran teachers have routines down."  Praise and/or Credit for mistake catching "I showed that I was human and capable of messing up. I loved when a student would correct me. “Thank you for catching that!” I would give extra credit for catching mistakes because they are paying attention."
 Performance pressure "Teachers will feel pressure and lack of trust that trickles down if they need specific scores. It’s a lot on state testing."  Visual representations "I'm very visual, so I need everything in front of me or on a piece of paper."  Expressions of joy for math "I convey my love of math to kids. It’s sincere and it is fun for me."
 Varying comfort with content "Some teachers don’t have the natural playfulness with the content. Or it’s fearful and scripted."  License requirements "There's a teacher licensure inquiry. The way the current license is, if there's through eighth grade math, you can get this algebra 1 add-on, which is pretty much an algebra 1 Praxis test and then you've passed it."  Teacher matching "Every first year teacher should be paired up with a co-teacher and watch a strong instruction."
 Lack of packing support "All they told me was, “Finish the book by the end of the year.” I didn’t know what a pacing guideline was. How do I get everything done? No systems were in place."  Self-reflection "My strength was the classroom management, structure, joy, that kind of thing. My area for improvement was making sure that I was putting the heavy lifting on kids."  Create answer keys " I like to do my own answer key."
 Self-doubt "I don’t always think I’m doing the right thing."      Pay "Pay teachers more so they have more reason to stay in the profession."
 Self-sufficiency "I was figuring out how to teach and pace material on my own."      Content studying "Content knowledge is a huge factor in effective teachers. Building time in teacher schedules to they can do deep dives into the content. Doing rigorous tasks as an adult so they are confident in the content."
 Lack of desired achievement "I need to be patient.  Students don’t build as quickly as I would like. It’s difficult with the pacing. I always feel that I want to keep moving forward. I have to listen while I walk around the room. Important points I want to bring to the class. As I facilitate, I need to give wait time."       Expressions of care "I’m also going to make one statement that hopefully sticks: “I care about you.”"
 Patience "A major shift is me being ok with them not knowing how to do something yet."      Teacher evaluation rubrics "Teacher evaluation rubrics: manage classroom, question techniques, responsive to data, strong classroom culture, engagement. Content knowledge also plays a roll. Demonstrated they have a strong knowledge of the content. How they speak about the math themselves. The way they plan/make adjustments to the curriculum. Can they unpack the common core standards? Are they showing their work on their moderator key (“teacher cheat sheet”)? I don’t think it’s a formal measure. More observation."
Expert  Reticence to change "Veteran teachers are more comfortable in their ways and difficult to shift. It’s a different approach with veteran teachers. You have to use the data so they can see it really works. It’s a slower shift."  Self-determination "The big shift in teacher turnaround was because, ultimately, teachers want to be successful, and they want their kids to succeed."  Adaptive practice "I started making shifts on my own."
     Student performance "What shifts teachers’ mindsets is when they see their students make gains."  Flexibility with content "There’s something so important about being flexible with your mind with the way children think."
     Experience "Teachers must have more expertise to be student centered. You have to have a stronger level of comfort with the content. These teachers feel more comfortable taking risks and having students challenge them."  Textbooks "The Investigations teacher book is good. At the back of each unit, it has a typical dialogue for each of the lessons with possible student questions and what to say. That was the most helpful for me. The program was good at opening your mind to accepting that students might say things that you’re not expecting, and that’s okay. It gave permission that it’s okay not to know the answer."
         Reflection "I thought to myself, “What are the things they need? What is a big task that I can create space for them to do what they learned?”"
         Visual reminders "I put big signs on my board to remind me and the students to think for themselves. One sign said, “Who is doing the thinking?” Another sign said, “Not the fast answer. The thoughtful answer.”"