Friendly Critic Observations

This year is only my second year in my current school & my second year choosing “informal” observations only. These are “drive-by” observations where my principal and AP stop by for about 15 minutes before passing on to another class. They send me a write-up with some feedback – but they rarely discuss these lessons in person – or in detail. On the one hand, getting all highly effective ratings makes a person feel like their hard work pays off – on the other hand, it doesn’t actually help me grow!

On Monday this week, I had someone come in to observe me and coach me a bit. She’s a former teacher who’s been out of the classroom only a few years, and is currently working on PD for teachers through the DOE. She followed me around when I conferenced with students, and we had a really good lens for her to view my class with; our lens for the day was balancing student independence with interdependence and how problem content, context and teacher questions can support this balance. I think that needs to continue to be my lens again next year because I felt like I was just scratching the surface in listening to her feedback.

Because she was not evaluating me – in fact, had absolutely NO POWER over me at all, I was able to listen and be present with her feedback. I felt like I knew she wasn’t judging me, but was supporting me to become a better teacher, so I could explain without getting defensive. Next year, she offered to come visit my classroom earlier in the year, and try to get in more frequently, so she can really provide me with some coaching – and I felt really good about that idea.

To this end, we asked, “What are some ways to increase student accountability for listening to each other during the whole group share (and not only to you to reiterate or confirm, implicitly or explicitly)?” And “how do you transfer some of the responsibility for moderating the group share conversation to them?”

We brainstormed a few ideas of what to do differently in the future, such as:

Turn-and-talks for vocab refreshers

Co-creating what they share out as per team vs. per individual (and thinking about how to encourage diverse voices when sharing on behalf of the teams)

Accountability for actually turning and talking (had one boy in a group of 3 who was totally silent all class)

Asking “What did you team notice/wonder?” vs what did YOU notice/wonder and building accountability around truly having a team response.

Clarifying questions and answers can be team based (at least as a 1st pass) to free me up to ask conceptual questions when I conference with students (which also means I need to have better conceptual questions planned)

Instead of answering the clarifying questions myself, ask the students,”Review your worksheet. What questions do you have about what to do?” and then direct them to spend the first 2-3 minutes of the explore portion of the class clarifying those questions with their table mates and asking, “Have you asked your partner?” Then, when I circulate, just listen in, instead of answering.

Follow Yvonne Grant’s advice of think of “What question can I ask” when students ask a question (instead of providing an answer).

Cultivating my “Kara face” (i.e. my poker face) when students say something incorrect. (I’m usually better about that, but in this case, it was a tangental topic, and I felt rushed, so I didn’t spend as much time clarifying as I could have).

I wonder if I can also view the student feedback from this same lens of the tension between independence and interdependence. I think I have a longer post about that alone percolating in my brain, but it’s not ready to come out yet.


Soliciting Student Feedback

Angry about Guns

I’m angry. I’m furious indeed, about the debate that’s raging in our country right now. I’m angry that it was almost 20 years ago that the shooting at Columbine happened, and we’re still letting these events occur and pretending that it’s unavoidable. I still remember how when that happened, the WB postponed an episode of Buffy several months because it involved a character, Jonathan, bringing a gun into a school campus. They even postponed the season finale because it involved blowing up the school (to kill the demon mayor). Now, school shootings are common enough that politicians send their THOUGHTS & PRAYERS (TM) and move on to the next tragedy, without making any major changes.  In fact, they argue over what changes to make and they literally stand in the way of making the real changes and reforms that are needed. I am furious about the way this country seems to love its guns more than its children. And now the Florida law makers are deliberately ignoring the demands of students AND TEACHERS who are saying putting more guns into schools is NOT the answer. But let’s be honest: the politicians are being paid by the NRA, so they are bought and paid for by dirty money.

I’m also angry with the Mayor of NYC for his lack of guidance to schools about how to react on March 14th for the school walk out. Although he promised he would soon give guidance on 2/222/23, and this week, the Mayor has yet to provide guidance to schools. Today at lunch, my principal held a planning meeting with some students and teachers who are interested. Unfortunately, my GSA meeting was happening simultaneously, so I couldn’t attend, but two of my students stopped by after school to fill me in (and my principal sent out an email to us at the end of the day).

Essentially, my school is allowing middle school students to walk out to the yard during third period (when 10AM happens in our schedule). After attendance is taken in third period, students will go to the yard where some students will give speeches. At 10AM, there will be 17 minutes of silence observed. Then there will some sort of post-it note reflection that students may complete and they will return to third period. Attendance will be taken again (to ensure students are accounted for) and then fourth period will be shortened to account for the extra 15 minutes.

One of my two students who came to share about this with me said she didn’t feel like it was enough, and she was angry that she couldn’t walk out of the school “for real.” When I prodded her for why she was feeling that way, she said she felt like adults had failed to keep kids safe and this protest was still being supported by the adults in the building. She felt like it was important to make the statement that students are rejecting the adult rules because the adults aren’t doing enough to keep them safe. She said “No offense to you, Mr. G” when she made her comment about the adults, and I realized she sees me as one of “them” – the adults who have failed to protect students. And it made me even angrier that I didn’t feel comfortable (and protected) for agreeing with her and sharing with her my own anger and frustration about the gun control laws in this country. I was only a year older than she was the first time (Columbine), and yet nothing significant has changed – at least, not where it matters! We spent more money putting security officers in schools – and it didn’t help at all! Her friend who was with her (both at the meeting at lunch and today after school) said she thought they would have more impact this way (because they would be able to communicate with other students at the school) and that she was worried her friend would get in trouble/suspended if she did walk out for real.

According to the ACLU and the Supreme Court’s decision is Tinker v. Des Moines, students (AND TEACHERS!) do not give up their right to free speech in the school building as long as it’s not considered disruptive to the educational process. And in fact, schools are prohibited from punishing a student more harshly due to political beliefs motivating their actions than anyone else committing the same infraction.

According to the NYC DOE’s discipline code:

Screenshot 2018-03-07 21.07.26Screenshot 2018-03-07 21.07.18Screenshot 2018-03-07 21.07.09

So that means, at worst, a student can be admonished, have a conference with a teacher or AP/principal, have a parent conference, or have in-school disciplinary action.

I volunteer as tribute! Any students who are in trouble for “walking out” or doing something beyond/outside of the “official” program – I’ll host a captive lunch – and we can spend the lunch period writing letters to Congress! We can talk about what their next actions will be!

It gets a little bit trickier when it comes to “political” speech as a TEACHER – the rules are a little unclear. I wrote a facebook post about two weeks ago about my feelings about arming teachers: (needless to say, I’m vehemently against it!).

But I haven’t decided what I’m going to do on March 14th – Pi Day. Is there some sort of math that I can connect to do a teach-in during ALL of my classes that day? Even if I just do it for the warm-up in class, it will make me feel more like we’re talking about the important things. I KNOW my students – and they’re very well behaved and they respect me. They will do the lesson I tell them to do. So what kind of message will it send to them if I say nothing? It will tell them that I don’t care enough about this, when it couldn’t be farther from the truth. Mayor Di Blasio – I want reassurance that teachers won’t get in trouble for speaking up too!

Any other math teachers planning a teach-in?

ABC+M of Motivation (From @RhondaBondie1)

In coaching Rhonda’s online course, I’ve also purchased her new book. I’ve been reading chapter 1 and going along with the course’s assignment, so I can better give feedback to students. Much of it (so far) is review for me because of all of the ALL-ED courses I’ve taken with Rhonda at Math for America (probably part of why she asked me to coach!).

In chapter 1, I’ve been reading about motivation: both the ten facts about it and the “ABCs+M” of it. Here’s one video that I think should tell you why we should NEVER award “merit” pay for teachers who increase their student scores.

In the ten facts about motivation, the first one is dispelling the myth that motivation is a personality trait – something you either have or DON’T have. I wish I could convey this one better to my colleagues. So often, I hear my co-workers complain about “unmotivated students” and how their students don’t do anything for themselves – and I wonder to myself “Do your students feel autonomous? Do they feel a sense of belonging? Do they feel competent? What’s their self-efficacy for this task like? Do they find it to be a meaningful use of their time and energy?” If not, NO WONDER they’re not motivated! Sadly, rather than being self-reflective, I think sometimes teachers just feel too overwhelmed with the day-to-day and don’t question these premised – What can we do as educators to create an environment where our students feel ABC+M of motivation daily?

I think it’s funny, actually, because we often say that we can’t motivate anyone to do something, and while I think that’s true in many respects, I think that if we create opportunities for students to feel autonomous, belonging, competence, and meaning in the work we ask them to do, we create an environment that is conducive to motivation!

Specific Quality Criteria from @RhondaBondie1

As a teacher, I sometimes feel like I am a slow implementer. When I am exposed to a new idea, I need to spend a lot of time reflecting on it, analyzing it, often seeing it in action before I’m ready to implement it in my own class. The more extensive it is (or the better/more detailed I want to do it), the longer it’s likely to take me.

A few years ago, I was doing an ALL-ED course at MfA with Rhonda Bondie. She introduced me to the notion of giving students “specific quality criteria” or as I’ve begun to call it, “success criteria.” I wasn’t sure what that would look like in my own classroom yet, so I have been reflecting on how to do it. Then, last week, I met with Marvin Gruszka, and he showed me how he implements these quality criteria into everything he does with the students – and suddenly something clicked into place for me. I realized that all of the written work I have my students do in math class could “easily” be graded with his rubric (a “4 point mastery scale” that was also correlated to a “points” scale for grading).

Screenshot 2018-03-01 16.28.24.png

And then Marvin had different Must Haves and Amazing criteria, depending on the task itself. Here’s one example:

Screenshot 2018-03-01 16.28.33

This was for a written response students did in answer to the focus question of the day.

Yesterday, I used Connecting Representations with my sixth graders and I gave them some “success criteria” for the metacognitive reflections they wrote at the end of class.

My Must-Haves:

Complete sentences

Specific details from class


Cite a specific person by name.

Quote something someone else said.


Then, today, I had a double period with one of my classes, so I asked them for the success criteria! And they were way more detailed and came up with MUCH better criteria than I did!Screenshot 2018-03-01 16.42.32.png

I thought this was so awesome, I not only decided to share it with you here, but I think I’m going to actually use this criteria on their reflections from now on! Especially on their HW reflections (called My Understandings)!

Once we brainstormed these criteria, I had them write their reflections to the three prompts for the connecting representations we had just done. I asked my students to try to make it amazing, and gave them about five minutes of writing time (which is longer than a typical reflection, but we had a double, and I wanted them to focus on upping the quality of their reflections now, before we keep using this routine, because I’ve been disappointed by some of their previous reflections). Then they read their reflections to their elbow partners.

Then I decided to have them give each other feedback on their writing, so I had them swap notebooks with their mirror partners. I had them UNDERLINE examples of the student using the “must have” criteria in their response and STAR *examples* of the student using the “AMAZAING” criteria. Then they wrote each other feedback, using another routine I recently developed called “Positives and Deltas” They wrote two sentences: a + positive that the student should keep doing and a ∆ (delta, which means change): something you would recommend they change in the future.

I think it went really well, and I’m super excited to read their reflections the next time I collect them. I didn’t have an opportunity to read them today because the students wrote their reflections in their notebooks!

A New View of “Most Common Mistakes”

Lately, I’ve been thinking about the way we as teacher talk about students and their understandings and skills and their struggles. We often describe students as “low” or “high” depending on their performance on formal assessments (but we often fail to acknowledge that those are snapshots in time, informed by all of the students’ experiences). I’m sick of hearing teachers talk about “filling in the gaps” or how their students are always making the same mistakes. Maybe we need to stop viewing student mistakes and misconceptions as barriers to learning and start seeing them as the necessary rungs of the ladder to understanding instead. Some students can scale the ladder quickly, getting boosted up through certain misconceptions by prior/alternate experiences with math, whereas some students need to build up more muscles before they can move past a certain misconception. And sometimes, students appear to have passed a particular rung because they’re able to do other math, but then it later becomes apparent that the muscles needed to avoid falling on that rung (making that mistake) were underdeveloped and need more strengthening. So when we see students making “the same mistake” over and over again, we need to ask ourselves what experiences do they need that will create the kinds of cognitive dissonance that will unearth the limitations of their current understanding and grow their brains?

Right now, I’m focused on the “conceptual errors” students make in the predictable most common mistakes. I’m not concerned with the copying errors or rounding errors or even the computational errors (unless they’re related to the concept at hand).

I have spent a lot of time analyzing student thinking closely by detailing what do students know and not know based on exit tickets (low-stakes problems solved at the end of class and collected. I give feedback, but no grades on these). I’m currently in my 8th year of teaching middle school math, and I always notice patterns in the kinds of mistakes students make. There are certain trends that I can tell students in class that I can predict the ways they might go wrong even before they start! I even draw their attention to the connection between these “most common mistakes” (MCMs) and the wrong multiple choice answers (the distractors) – those other options aren’t random! They’re usually carefully chosen to highlight a student that has chosen the incorrect strategy to solve a problem.

Lately, I’ve been rethinking the fact that we call these mistakes at all. If they’re so predictable, maybe they’re not the same as other kinds of mistakes. Maybe they’re actually a necessary phase of the learning process.

I first heard about the Landscape of Learning from Kara Imm, but my understanding is that Cathy Fosnot developed it.

When you look at it, it’s made up of big ideas, strategies, and models that build on each other. There’s no one linear path through the landscape, and sometimes students will have mastered some of the big ideas, strategies or models, but not others. While some of these build on others (i.e. you probably can’t use double and halve if you don’t know how to double), other strategies, big ideas, and models are independent of each other, and depending on a student’s prior experiences, they may each have different strengths than other students.

I’m now wondering if these predictable misconceptions also belong on the landscape for learning as stepping stones because they inform our recognition of student understanding (and misunderstanding). These predictable mistakes are often ways that students overgeneralize “rules” or mis-apply new ideas in the wrong contexts. For example, every teacher who’s taught fraction addition to students has probably seen someone take 1/4 + 1/3 and get 2/7. And we can see WHY students are getting that number! But by calling it a mistake, we’re not recognizing the way in which that misconception builds on addition of whole numbers; we’re just acknowledging how it falls short on recognition of fractions as numbers. I am proposing that we shift the conversation here from saying “What’s lacking in this student?” to “What can this student do?” and then build on where the student currently is. If we recognize these predictable mistakes as stepping stones that some students need to have access to the main roads through the landscape of learning, then we are better able to see the pathways that students need strengthened in order to master big ideas, strategies, and models.

We can better understand why students hold certain misconceptions (and thus what experiences they need to complete their understanding) by seeing which big ideas, strategies and model were only partially connected to this misconception.

Going back to my previous example of 1/4 + 1/3 = 2/7, we might recognize that students don’t seem to realize the big idea of needing a common whole to add or subtract fractions. We might see that the clock model might help students move through this misconception, because they know 1/4 of an hour is 15 minutes and 1/3 of an hour is 20 minutes, and they can see on the clock that the combination of that is 35 minutes (or 35/60) of 7/12 of an hour. (In this case, because of the numbers I chose, the clock model works better than the money model, but for other numbers such as 1/4 + 1/5, that model would work better). The connections between these ideas and the fraction bars model may be less obvious – but that’s another model that students might rely on when adding fractions with unlike denominators. Additionally, a student could use landmark fractions to help them estimate that 2/7 does not make sense, since the sum of 1/3 + 1/4 should be greater than 1/2. All of these different connections can provide possible pathways from the misconception (add numerators and add denominators separately) that might help guide students back onto the landscape of learning and away from this common mistake.

I also think that if we understand that students are having a difficult time with addition of fractions with unlike denominators, this might help us step back and question whether the student has mastered adding fractions with common denominators – whether they understand that they’re just counting up pieces or if they are still adding the denominators. For example, when they see 1/3 + 1/3, do they say 2/3 or do they say 2/6? That will inform where the disconnect in their landscape is and help a teacher figure out the necessary experience for the student to gain this understanding.

In thinking about the class discussions I facilitate, I often think posing the student mistakes, asking them to make sense of what someone might have been thinking if they made that, and then discussing where it falls apart in the reasoning or why we need to do something else – and then being able to convince our skeptics – results in a much richer classroom discussion where students are actually growing.

I think we need to reframe the way we discuss mistakes as wrong answers and see them through the lens of stepping stones on the learning journey. We need to honor their importance in growing our minds, and that without those mistakes, we never realize that there is more need to grow because we can’t see the limits of our own understanding. According to the definition of mistake, it is “an action or judgment that is misguided or wrong.” I think calling these ideas mistakes indicates that they’re wrong and misguided when in reality, they’re often necessary stepping stones that are pushing us on the trajectory of learning. I think it’s time we stop calling them mistakes, and start naming them as partial understandings and consider how they connect to the understandings we want to cultivate.