Become the Subject

My Speech is now live on youtube! For those of you who missed me talking at MfA’s MT-squared, here it is: Become the Subject.

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Goal Setting in Math (part 2)

Tonight, I was talking with Rhonda Bondie about Goal Setting in math classes. I was sharing with her my observations from the previous post that most student goals either focused on their grades, their HW completion, or their participation in class discussions. It rarely focused on their actual math “skills” or strategies or thinking. I acknowledged that it was harder in math class because there was a tension in thinking classrooms between revealing too much information by revealing the topic of study too early (i.e. telling students that we’re going to discover the Pythagorean Theorem might ruin the discovery if a student has been introduced to the formula already in SHSAT prep or Saturday School, whereas telling students we’re looking for a pattern in the areas of the squares doesn’t give it away, but might make it a bit harder to set a goal).

Except, maybe it wouldn’t make it harder! Maybe THAT was the key to setting the goals. I realized that vague “we’re looking for a pattern” connected to what it is mathematicians do (look for, study and analyze patterns), and that maybe the Math Practices were a better way to set up our student goals. And then I made a connection to my absolute favorite diagram from from Amy Lucenta’s and Grace Kelemanik’s book, Routines for Reasoning.

avenuesfrombook

In the book, they argue that the 8 Math Practices are not actually created equal, but instead, there is a hierarchy.

“MP 1: Make Sense of Problems and Persevere in Solving them is an overarching goal.” MP2: reason abstractly and quantitatively, MP7: look for and make use of structure, and MP8: look for and express regularity in repeated reasoning “describe three avenues for mathematical thinking” that allow you to solve problems. The remaining practices, MP3: construct viable arguments and critique the reasoning of others, MP4: model with mathematics, MP5: Use appropriate tools strategically, and MP6: attend to precision, all describe important ways to navigate those three avenues of thinking and play an important role in problem solving, no matter which avenue of thinking you choose. (I’ve paraphrased/summarized/quoted various ideas from pages 3 – 10 in their book in this paragraph)

This made me think about introducing the following ideas to my students at the beginning of the year.

“In this class, our goal is to think like mathematicians. One thing mathematicians do is make sense of problems and persevere in solving them. The way they solve them is by following a particular avenue of thinking. Our goal is to get good at all three avenues, because sometimes we might find a particular type of problem is more easily solved using one type of reasoning than another. We might start using one avenue that we’re typically more comfortable with, and then get stuck as we start to solve the problem. We might have to try a different avenue of thinking to get unstuck. Other times, we might successfully solve a problem using one avenue of thinking, but it doesn’t give us sufficient evidence to convince a skeptic, so we might need to solve a problem using multiple avenues of thinking to convince the skeptics.

As we navigate these three avenues for thinking, there are some important things to keep in mind. We need to be able to construct arguments using our reasoning and critique the reasoning of others, we need to be able to model with mathematics, to use tools strategically, and to attend to precision.

So these eight ideas set our goals for the year. A student who has mastered all 8 has achieved our goal for thinking like mathematicians. They’ve grown in a way that’s more comparable to the previous year as well – for example, maybe in 6th grade, they were struggling with looking for structure and making use of it, so in 7th grade, they’re going to focus on that avenue of thinking. And maybe by the end of 7th grade, they’ve started to master looking for and noticing structure, but they’re still not quite sure how to actually make use of it, so in 8th grade, they’re going to focus on using the structures they notice to solve the problems.

Now, in Grace & Amy’s book, they have an appendix with the following chart:

Screenshot 2018-07-18 02.19.52

You’ll notice that there’s clear questions to “ask yourself” for each avenue and there’s clear “actions” to take when solving problems using each avenue. Let’s focus in on what the rubric might look like now. I’m going to choose just MP7 about Structure to focus on, because I’m most familiar with that practice.

Here’s the CC’s text:

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

The Ask Yourself Questions: The Actions:
·       What type of problem is this?

·       Does this remind me of another problem situation?

·       How is this (situation, object, process, etc.) behaving? Can I connect it to something else I know?

·       What are the parts (chunks) of the process?

·       How can I get the answer without doing all the calculations?

·       How can I use properties to uncover structure?

·       How can I change the form of this (number, expression, shape) to surface the underlying structure?

·       Chunk complicated mathematical objects (expressions, shapes, etc.).

·       Connect representations.

·       Change the form of the number, expression, space, e.g., create equivalent expressions.

·       Recall and use properties, rules of operations, and geometric relationships

The Ask Yourself Questions:

  • What type of problem is this?
  • Does this remind me of another problem situation?
  • How is this (situation, object, process, etc.) behaving? Can I connect it to something else I know?
  • What are the parts (chunks) of the process?
  • How can I get the answer without doing all the calculations?
  • How can I use properties to uncover structure?
  • How can I change the form of this (number, expression, shape) to surface the underlying structure?

The Actions:

  • Chunk complicated mathematical objects (expressions, shapes, etc.).
  • Connect representations.
  • Change the form of the number, expression, space, e.g., create equivalent expressions.
  • Recall and use properties, rules of operations, and geometric relationships

Now, I’m currently envisioning a few different ways students could assess themselves about how well they’re using this avenue for thinking.

One, you could put it into the same four-point mastery scale from my last post, though I do find the “above grade level” to be a bit challenging here. One thing we haven’t specified is that deploying this practice looks different at different grade levels (in part because of the types of content the students are exploring), but also because their level of independence with this may vary.

1: Below Mastery 2: Approaching Mastery 3: Proficient(At grade level) 4: Mastery (above grade level)
Rarely uses the ask yourself questions OR cannot make sense of the math problem through asking the questions.

Cannot see chunks or ways to change the form. Does not make connections between representations.

Does not recall or use relevant properties or relationships.

Does not result in successful solution NOR do they switch to a more successful avenue.

Sometimes uses the ask yourself questions to make sense of math problems.

Is sometimes able to successfully chunk, connect, or change the form to solve problems.

Recalls and uses only some of the relevant properties or relationships.

May or may not result in successful solution.

Regularly uses most of the 7 “ask yourself” questions to make sense of math problems.

Chunks, connects, or changes the form to solve problems.

Recalls and uses relevant properties and relationships.

Results in successful solution.

Regularly uses all 7 “ask yourself” questions to make sense of math problems.

Chunks, connects, AND changes the form to solve problems.

Recalls and uses relevant properties and relationships.

Results in successful solution that student can verify using a second avenue for thinking.

Gradeless Gradeless Gradeless Gradeless

Another way I could see assessing it is by using Rhonda Bondie’s “Must Have” and “Amazing” criteria. For example (and I’m not sure I’m in love with this way yet – it’s my first draft still):

Must Have Amazing
·      Ask yourself at least 2 of the “ask yourself” questions to make sense of the problem.

·      Chunks, changes, or connects.

·      Valid mathematical thinking shown that begins the problem.

·      Ask yourself at least 5 of the “ask yourself” questions to make sense of the problem.

·      Does at least two: chunk, change, or connect

·      Can justify why it makes sense to chunk, change, or connect in the way that they did

·      Recalls and uses properties, rules of operations and geometric relationships

·      Can use another avenue for thinking to solve the problem and verify answer.

If you needed to use a 4-point mastery scale, you could do something like:

1: Most of the Must-haves

2: all of the Must-Haves

3: All of the Must-Haves and some of the Amazing

4: All of the Must-Haves and ALL of the Amazing (or MOST, depending)

I’m not sure which of these two ways I like better yet, but I recognize they’re not quite equivalent. Either way, I can now see much more specific goal setting around mathematical thinking if students become comfortable with the math practices as avenues for thinking.

They might say “My goal is to use structure to solve at least two problems in the next unit.” or they might say “My goal is to use two avenues for thinking to solve every problem.” or they might say “My goal is to get better at asking myself these questions when I use this avenue.” or they might focus even more narrowly on something like, “I’m going to improve my ability to chunk problems, and I’m going to use that strategy on at least two problems.”

Now it even makes sense for a teacher to share from one year to the next a student’s goals. Well, Kit was very strong at using MP7: make use of structure, but he really struggled with reasoning abstractly and quantitatively. Encourage him to develop goals around MP2 next year.

I want to do more fleshing these ideas out over the course of the summer. This connect came organically out of a conversation I was having with Rhonda this evening.

What do other people think about these ideas? I’d love to hear from you on here or on twitter/FB!

Goal Setting in Math vs. ELA (Part 1)

A few years ago, I was in a meeting to discuss vertical alignment among the math departments at my middle school. We were looking to trace how the skills and standards built from 6th grade to 8th grade in our math classes. One of the members of the meeting was a special educator who worked with both the math and ELA departments, and she introduced us to a document that the ELA department had been working on where they looked at how the standards built vertically as well. In that moment, I was suddenly even more jealous of ELA teachers than I already was (sometimes, I think I should’ve become an ELA teacher – but that’s a different post!).

If you look at the ELA common core standards across the domains and grade levels, they build on each other very directly. I randomly chose Reading: Literature to look at across the three grades. I chose the first standard within that strand, and I followed it from 4th grade through 10th grade.

CCSS.ELA-LITERACY.RL.4.1
Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.

CCSS.ELA-LITERACY.RL.5.1
Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.

CCSS.ELA-LITERACY.RL.6.1
Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

CCSS.ELA-LITERACY.RL.7.1
Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

CCSS.ELA-LITERACY.RL.8.1
Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.

CCSS.ELA-LITERACY.RL.9-10.1
Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Look at how connected these 6 standards are. In all of them, they reference using textual evidence, but they do so in more and less sophisticated ways across the grade levels. At first, kids are expected to just refer to details, then be able to quote specifics, and eventually they’re citing evidence – first any evidence, then several pieces of evidence, then choosing the strongest evidence, and ultimately, being strong and thorough in their citations. All of the standards mention both what the text says explicitly as well as drawing inferences from the text.

This makes vertical alignment pretty easy and it makes it more obvious when a student is above or below grade level in this standard – for example, if a student is only citing one piece of evidence and they’re in 7th grade, you can see they might be operating at a 6th grade level, whereas if a 7th grade student is citing the strongest piece of evidence, then they might be operating above grade level. I confess there seem to be some degree of subjectiveness on the part of the teacher about assessing whether the evidence cited is the “strongest possible…” But there’s no question in my mind that these 6 standards are linked directly, and that there is a growth in the student.

If I’m a middle school student, I can even do a self-evaluation, rating myself on a four-point mastery scale relatively easily. Let’s say I’m a 7th grade student. I might consider my skills along the following rubric:

1: Below Mastery 2: Approaching Mastery 3: Proficient

(At grade level)

4: Mastery (above grade level)
Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.

 

Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

 

Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

 

Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.

 

Grade 5 Grade 6 Grade 7 Grade 8

Now, admittedly, it’s possible that even as a 7th grade student, if I’m below grade level, I might not even be quoting accurately from the text. But, there’s definitely a progression of the skill, where I can self-assess “Where am I now?” and then “What’s my goal?” And this goal even hints at the above-grade level work for the following year, allowing a student to push themselves. If I’m struggling with the current work, I can even see perhaps where I should have been developing it – if I’m not able to cite several pieces, am I at least citing one? Am I at least quoting something accurately? If not, then I can set a SMART goal: “In the next book club chat, I will cite at least two pieces of textual evidence to support my inference.”

Let’s contrast that with mathematics for a moment. First off, it’s practically impossible to trace a domain by code the same way I did with ELA – from elementary to middle school, the domains change names, and in 8th grade, one domain is replaced with another! I chose to look at Numbers &  Operations in Base ten in Elementary and the Number System in Middle school, as they seemed to flow together. Again, I chose just the first standard in each grade level at this domain. You can see for yourself how much less clear the thread is connecting these.

CCSS.MATH.CONTENT.4.NBT.A.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

CCSS.MATH.CONTENT.5.NBT.A.1
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

CCSS.MATH.CONTENT.6.NS.A.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

CCSS.MATH.CONTENT.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

CCSS.MATH.CONTENT.8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

CCSS.MATH.CONTENT.HSN.RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

What the heck?? It’s practically impossible to see how knowing there are numbers that are not rational is even connected to adding and subtracting integers or how either of those ideas are connected to fraction quotients. Other than the use of the words rational and integer in the RN.A.1 (which comes from the high-school “Number System” standards), I’m not sure that you can see how this standard builds on the middle school ones either.

They do a much better job at connecting the two from elementary school, but maybe that was because of the different domain name? 5.NBT.1 builds clearly on 4.NBT.1, because now in addition to recognizing that a digit in one place of a multi-digit number represents ten times as much as the place to its right, students will also understand that it represents 1/10 of what it represents in the place to its left.

There are other planning documents that show the progression of standards, as you can find here: http://ime.math.arizona.edu/progressions/

And Randall Charles does a great job at summarizing big ideas in mathematics which you can link to the standards: http://www.authenticeducation.org/bigideas/sample_units/math_samples/BigIdeas_NCSM_Spr05v7.pdf

Cathy Fosnot has place big ideas in the landscape for learning which also includes models and strategies.

All of this tells me there seems to be an extra layer to understanding the way math content is connected to the big picture that doesn’t seem to exist in the ELA standards. It has always made me wonder how helpful information from previous year teachers was in math, especially in middle school – for example, does a student’s understanding of how to add and subtract integers impact their ability to identify a number as rational or irrational? I think not. That’s not to say that the skills for identifying a number as rational or irrational aren’t laid down in earlier grades or carried through to later grades. Quite the contrary – you just have to know which skills are related and how this is all connected. No easy task for a teacher who’s busy mastering their own grade’s standards – hence the progressions, and this other ideas I shared here.

This brings me back to the meeting I was sitting in: vertical alignment within the math department. It’s harder to identify when a student is above or below grade level if you don’t know what your grade-level standard looks like in earlier/later grade levels. It’s harder to differentiate for a student if you don’t know or understand how the math builds over the years. And the arrangement of the standards in math does nothing to shed light on it.

I also couldn’t help but notice the common core’s website is differently arranged for math vs ELA – in the math section, you must click on a grade first (K – 8) and then on the domain, and then on individual standards, whereas in ELA, you needed to choose a domain FIRST, then a grade! That speaks to the idea of vertical alignment more than the discrete topics and standards arrangement that pervade the math standards structure – which also seems to indicate the way that many people seem to consider ELA skills to build on each other whereas many people often view mathematics as discrete topics or skills that are to be memorized (but are seemingly disconnected from each other).

Recognizing this challenge of the math standards made the idea of goal setting challenging. How can you set a goal and see where you were, where you are, and where you’re going without giving away some of the story in mathematics? If I want to develop a conceptual understanding of the Pythagorean Theorem using the areas of tilted squares on grid paper (thanks Betina Zolkower and CMP3 and MAP), then I need to know if the student understands how to find the area of rectangles, triangles, and tilted squares. I need to know if they have already heard of the formula a^2 + b^2 = c^2. I need to know what they know about triangles, specifically right triangles. Understanding the triangle inequality theorem may be helpful, though it’s not necessary. Once they know what it is, they may learn the converse of it, how to use it to find missing side lengths, and how to expand it to work in three dimensions. This connects to their work with exponents (what does that symbol mean? How do you “undo” it? etc.) as well as with solving equations (if you push them to work algebraically vs. working arithmetically).  Eventually, they should understand that the Pythagorean Theorem is generalized for non-right triangles as the law of cosines. They will learn about trig for right triangles eventually as well, and they might study special cases of right triangles. The Pythagorean Theorem is also connected to similar triangles and what they may know about angles of a triangle (including that the sum of the interior angles is 180 degrees). This theorem might also help them as they find the areas and perimeters of composite shapes involving triangles and/or inscribed and circumscribed triangles. They will also eventually learn how to prove the theorem – and they may be introduced to any of the 2000+ proofs that exist.

I bring all of these ideas up to illustrate that it’s much more difficult for a student to self assess where they are in terms of their prior knowledge, their current understanding, and what their goals should be in mathematics class. If I’m a student who is in middle school, just learning about the Pythagorean Theorem, how do I assess which aspect I’m struggling with, or how to go above grade level, or how to set a goal? I don’t have nearly as clear of an idea just based on looking at the standard or even if I looked at a rubric. I’m not sure I could even think about what a rubric would look like for this topic in the same way.

The standards about this theorem exist in 8th grade:

CCSS.MATH.CONTENT.8.G.B.6
Explain a proof of the Pythagorean Theorem and its converse.
CCSS.MATH.CONTENT.8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
CCSS.MATH.CONTENT.8.G.B.8
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
It’s talked about explicitly again here:
CCSS.MATH.CONTENT.HSG.SRT.B.4
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
CCSS.MATH.CONTENT.HSG.SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
It’s the underpinnings for these two standards, but you need to already know the law of cosines is connected to PT to know that:
CCSS.MATH.CONTENT.HSG.SRT.D.10
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
CCSS.MATH.CONTENT.HSG.SRT.D.11
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
So let’s see: if I was an 8th grader, learning about the Pythagorean theorem, would I necessarily be able to use a rubric to understand where I was in my understanding? I’m not sure. Here’s one attempt at making a rubric for it…
1: Below Mastery 2: Approaching Mastery 3: Proficient (At grade level) 4: Mastery (above grade level)
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in mathematical problems in two and dimensions. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two dimensions. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

(NOTE: Big jump to understand what trigonometric ratios are!)

Grade 8 modified Grade 8 modified Grade 8 HS Geometry
When you look at this rubric, I tried to modify the 8th grade standard a bit to show partial understanding. I figure if grade level requires using it in both 2D and 3D contexts, then only being able to use it in the 2D context would be one example of approaching grade level. For level 1, I struggled with what to write, ultimately eliminating the real world problems, thinking this is basically a student who is just plugging and chugging numbers, but doesn’t necessarily understand what they’re doing or how to apply it to a context. (Though, I fully admit that a student who is below grade level in this standard actually might have even bigger challenges – they might not know how to square numbers or how to follow the order of operations or how to solve an equation with exponents – any of those skills could be preventing them from being able to apply this formula). For the above grade level, I tried to pull in the related HS geometry standard – but it mentions trig ratios, and those aren’t something that a student is going to be able to just “push themselves to do” based on what they know so far – in 8th grade, they may never have even heard of trig yet! (depends on their teacher, their school, etc.).  An alternate possibility in the above grade level section could be applying the formula on composite figures, inscribed/circumscribed triangles, or finding patterns in special right triangles.
This means it’s pretty hard to set goals and self-assess. How do I recognize if my difficulty is that I’m forgetting to square the numbers first, and I’m adding a + b and then squaring it? How do I notice that needs to be my fix? If I can use it in two dimensions but not three, I feel like that might be easier to recognize and set a goal around, but I (as a student) might not be sure HOW to figure out how to use it in three dimensions without outside support, whereas I feel like a student who already knows how to cite one piece of evidence can more easily push themselves to cite at least two (or even to choose the BEST evidence) relatively individually.
Today, in my conversation with Rhonda Bondie about goal setting in math, I had an epiphany. All this time, I’ve been trying to wrap my mind around having students set goals related to the math content standards. But they don’t flow well from grade level to grade level, and it’s not always super obvious how they’re connected. It’s hard to set a goal when you don’t have a clear idea about where you are, what your struggles or, or what your goals are. Feedback (from peers and teachers) also plays a role in goal-setting, as the feedback may cue you in on your strengths and struggles. But how do you give each student specific feedback every day in every content standard during the unit? So often, it feels like student goals (when I’ve had them set them before) are either focused on the “wrong” numbers – their grades (I’m going to earn a 90 on all of my quizzes, or on my exams, or on my report card), their HW completion (I’m going to do my HW every day), or their participation in class (I’m going to raise my hand more, or participate in class discussions more). I rarely hear/see my students set goals like “I’m going to learn how to solve problems with the Pythagorean Theorem in 3 dimensions,” – though occasionally, especially at the start of the year, I’ll hear a student set a goal related to math content from the previous year, like my student who said “I want to master long division because I don’t really feel comfortable dividing.” Sometimes, these content goals from the previous year are good goals (in this case, it was a sixth grader, so it was relevant!), but other times, those goals aren’t directly related to the new skills of the grade level (i.e. if an 8th grader said “I’m going to master how to do integer operations” – it’s an important skill for 8th grade standards, but it’s not in-and-of-itself related to any 8th grade standards!).
And then, in the course of my conversation with Rhonda, I had an epiphany about goal setting in math class. I’ll share that in my next post, so stay tuned!

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:

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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!).

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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!