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Math + Art + Desmos… Connections.

“I love math and art, and I’m glad that I was introduced to Desmos, a way to use both subjects at the same time.” – Marianna, Grade 10

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Callisto, Grade 10

Drawing with graphs has been a powerful way to motivate students’ interest in understanding how equations relate to functions, and how manipulations of equations lead to transformations from a parent function.  I jumped on to Fawn Nguyen’s Des-Man project as soon as I saw the idea, and have done some incarnation of this work each year.  Each time I’ve guided students through this process, it’s gotten better and deeper, both through the development of my own approach, and from improved tools like the Desmos Des-Man interface (…which I’ve heard is currently “in the shop” undergoing some improvements) and more recently tweaks to this idea like the “Winking Boy” challenge, created by Chris Shore (@MathProjects), and posted on the Desmos Activity Builder by Andrew Stadel.

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Amit, Grade 10

This year’s work was definitely the strongest yet, and I owe the major improvements to my reading of  Nat Banting’s post, which extended this project to another level for my students. In the past, I have asked students to create a graph, which had features of a face or a building or a plant.  This year, I asked my grade 10 students to choose a graphic, photo, or work of art, which they had to replicate using only equations.  I asked that they choose an image that was meaningful to them for some reason, and then helped to guide them to something that was challenging, but that they could accomplish – a natural moment for differentiation, built in to the process.  In the earlier versions of this project, students had been motivated by trying to make their face look angry or happy or sad, but they didn’t have a specific place where their equations had to end up. Asking kids to commit to re-creating something forced them to be purposeful and deliberate in every choice.

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Ilyas, Grade 10

They took the responsibility of recreating their chosen image seriously, and honestly, their work exceeded my expectations. There were regular exclamations of satisfaction echoing around the room as we worked on this. They persevered. They definitely attended to precision. They argued with each other about the best equations to use. They reflected about how to make the best use of Desmos. They practiced the habits of mind of successful mathematicians.

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Anastasia, Grade 10

When we shared the in-progress work for some peer feedback, kids were actually applauding each other when their work came up on the screen.  Not because I reminded them to be a supportive audience, but spontaneously.  Seriously.  And when they saw the staff creative picks at Desmos, they asked me whether they might be able to submit their work.  The whole class was taking pride in creative math work.

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Karim, Grade 10

I asked that students reflect in writing on their learning during and at the end of the project.  I haven’t asked for students to do enough writing in math so far this year, so when they seemed to be really struggling with this, I made a fill-in-the-blank “reflection assistant” to scaffold their thinking and writing, and to give them some ideas about what to include in their written analysis.

A few highlights from their reflections:

  • “I was quite surprised that I could replicate a drawing by using graphing.  If somebody asked me to do it last year, I would say that it is a “mission impossible.”   However I was able to do it.”
  • “As my piece of art, I chose the logo of the football club Barcelona because I am a big football fan and FC Barcelona is a club worthy to be recreated through the use of quadratic equations in vertex form. In addition, the logo was an appropriate challenge for me, containing easy and smooth curves but also difficult shapes, like letters or circles. When the project was assigned, I was skeptical that it was possible to recreate an artwork, just by using equations. But now that I am done and a proud owner of a recreated art piece, I strongly believe that it is possible (obviously).”
  • “I found out that desmos is a really good tool to practice and sharpen your understanding on any equation and in my case it was the vertex form of a quadratic. Desmos allows you to experiment and find new ways to fix the problems or even work more efficient in order to surpass the problems in the first place. I am proud of the detail and sharpness of my work in general. I tried really hard to make the whole piece smooth and detailed. In order to do so, I zoomed in a lot and by doing so, I identified minor mistakes and was able to fix them.”
  • I chose “Pumpkin Pepe” as the subject of my project because it provided the right level of challenge for me and it was really fun to do. Overall, I really liked this project because it solidified my knowledge of graphing equations and has made me more comfortable using parabolas. I found that my understanding of quadratic equations really improved while I worked on this project because before, I wasn’t sure which variable shifted the parabola which way, but now I understand.
  • “I found that my understanding of parabolas and linear equations really helped me improve, and made me more confident during my work on this project. At first parabolas seemed to not make any sense to me, but now I feel like I really understand the way they work. Now I have the capability make connections with all these equations in the real world.”
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Marianna, Grade 10

Here are the project guidelines, the rubric, some peer editing forms, the “reflection assistant,” and a .pdf, which has a range of student work.  My rubric borrows from the I.B. Math Internal Assessment Guidelines, as one of my tasks as a grade 10 teacher at my school is to do some specific preparation for the I.B. program in grade 11.  Thanks in advance for any feedback on this project, and on the guidelines and rubric.

Desmos Drawing Project Guidelines and Rubric

Desmos Peer Feedback

Desmos Drawing Project Reflection Assistant

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Put Your Marks Where Your Mouth Is

I was struck recently when reading Robert Kaplinsky’s post, Why Are You Using That Problem?.  In this piece, he articulates 3 different reasons that we might choose to use a particular problem: to introduce a concept, for productive struggle, or for problem completion – each of which has its own value.  Kaplinsky convincingly argues that we should be purposeful not just in which problems we choose, but in why we choose a particular problem.  I have been considering his thoughts in reference to productive struggle, and specifically in how to best to support students when we choose a problem with this as our goal.

I have always talked about encouraging and nurturing a classroom culture in which it is safe to take risks, and to experiment.  When I introduce a novel problem, I tell students that my expectation is that they try – that making an attempt is what I value.  My marking scheme always always includes credit for getting started, and for each step of a problem.  But in some ways, my marking scheme has been generally geared toward a sequence of steps leading toward a correct answer.  In awarding credit for specific answers, I have been communicating to students that I value those answers.  If I want students to put value on productive struggle, I need to demonstrate that that is what I value – and by extension, that is how they can earn marks.  (For now, I’ll leave the question of whether earning marks in general is productive at all…)

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I worked with Dr. Andreas(@DrAecon), my excellent colleague in the chemistry department, to create a set of guidelines and a rubric to support students in becoming independent and confident problem solvers.  In our guidelines, we tried to give students some explicit ideas to try when they are presented with a novel situation, and in our rubric, we tried to express criteria that values the process more than the answer.  We want students to make valid arguments, to justify their reasoning, to persevere in problem-solving,  and to feel that they can take risks, including taking a path that might not lead to a correct solution.  I hope that our guidelines and materials communicate these values.  I want to be explicit and transparent with students about this.  We’ll need to set aside time where we are not focused on learning specific content, but instead are focused on becoming strong and reflective problem solvers who know that they can earn respect and grades with this focus.  I want to put my marks where my mouth is.

Here are the rubric and problem-solving guidelines, based on Polya’s four steps.  I’ve included both Word and PDF versions, and a blank version, which is intended for students to use as an organizer for their work.  These are written with 10th grade students in mind, but I plan to create simplified versions of these for middle and elementary school students.  Please let me know if you can use these, and if you have any suggestions for improvement.

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PDF: Problem_Solving_Rubric_Grade_10

Problem Solving Protocol_Grade 10

PDF: Problem Solving Protocol_Grade 10

Problem Solving Protocol_Grade 10_Blank

PDF: Problem Solving Protocol_Grade 10_Blank

There Can Be Only One (Marker)

Observing a student working on a whiteboard is the best way that I’ve found to get immediate insight into his or her thought processes.  Perhaps because of the impermanence of the medium, students act much more freely than when working on paper.  They are more willing to take risks and to potentially make mistakes.  Even when writing in pencil on paper, the act of erasing is slower than it is on a whiteboard – it seems like they can think more quickly and freely on the whiteboard, which leads to a more fluid thought process, and less barriers between their thinking and their writing.

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I’ve been a huge advocate of students’ use of whiteboards since I began teaching.  One of the very first things I do when I move to a new classroom, is to cover as many surfaces as possible with whiteboards.  Asking students to stand up and work in a visible way has the immediate effect of increasing sharing of ideas and showing thinking in a public way.   And it’s fun and they just really like it.

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John Orr’s whiteboarding protocol in his recent “My Favorite” post (Week 2 of the MTBoS 2016 blogging initiative), has filled in a piece that was missing from the work in my classroom.  When he groups kids at the whiteboard, he gives each group only one marker.  Every few minutes, he calls “marker switch” and whoever has the marker has to give it up to someone else in their group.  Sounds simple, and I know that I have read about this somewhere before (I think maybe in Henri Picciotto‘s blog but I couldn’t find the reference), but I never thought that it would have the profound effect that I observed when we tried this.  When the kids all had markers, some would inevitably be drawing instead of  mathing,  most would be doing their own thing, and they would occasionally talk to each other.  Providing only one marker forced communication and collaboration in a way that I just hadn’t anticipated.  If they wanted to express their idea but it wasn’t their turn to draw, they had to argue for it verbally.  I can’t recommend this strategy highly enough, and it has had a very positive effect in my class.

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A related, but maybe non-mathy aside: I was an art teacher, both at the college and the community level for years before I got into math teaching, and have continued that work along with teaching math.  Most of my life as an artist has been focused on making sculpture, but I did some animation and installation work for a couple of years, which involved a technique I learned from studying the South African artist, William Kentridge.  The process involved making a charcoal drawing and taking a photograph of the drawing.  The drawing would then be erased and/or altered slightly, and then photographed again.  This process was iterated again and again and again (this must be related to my interest in fractals…).  The photographs could be played in a sequence, which gave the illusion of motion.  Here is an example of an animation of some flying bats, which I used as a projected component of an installation piece.

For me, this process of animation was extremely freeing.  I was not afraid to make marks on the page because I knew that whatever I did would be erased soon.  There would be a record of the act of making the drawing, and all of the pieces would come together to form a whole, but each individual drawing would only be seen for fraction of a second.  I think that kids experience something similar to this when white-boarding.  They are more inclined to take risks and just try things because there is no danger of permanence.

Try giving them only one marker!  And let me know how it goes.

Generating questions

MTBoS blogging initiative, week 3!  This week’s prompt focuses on questioning.

betterquestionsMy colleague, who teaches the grade 6 and grade 7 math courses at my school is in training to run a marathon.  He has put together a training program for himself, which includes a schedule of endurance-building, and he has been collecting data with a GPS watch.  As he examined the data, he thought that this might make a rich exploration for his students and we have been working together to set up a project  for them.

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Here is what the raw data looks like

We started with the driving question: How long will Mr. Feutz take to complete the Limassol marathon? and then we began by brainstorming questions together.

  • How long will Mr. Feutz take to complete the marathon?
  • How many steps will he take to complete the marathon?
  • How many calories will he burn during the run?
  • What percentage of his overall time will be spent moving?  (Compared to taking breaks)
  • What will his average heart rate be during the marathon (In B.P.M.)?
  • What will be the shortest/longest mile time, and what is the range between these?

We tried to analyse which questions are actually interesting, and what might we be able to ask kids to do with them.  While running, he found that he was constantly doing math of one sort or another.  How much further will I run today? When will I arrive back at home?  Things that he had genuine curiosity about, and questions that math gives us the power to answer.

We set up a graphic organizer, and decided to ask our driving question directly.  Here are some of the kids’ initial responses.

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They always manage to think of something that we haven’t anticipated (…which is why we love kids!).  “Will you be listening to music, because if it’s like… Taylor Swift, you wouldn’t be as inspired as if it was like… hard rock.”  Students were given a graphic organizer and asked to write their first guesses.   As they acquire more information, they will refine their estimates.  Part of the beauty of this work is that they will get to actually test their prediction, and compare their answer to what actually happens.

Students will revisit this project over the next weeks, and will be asked to refine their work.  They have already studied unit rates, and are moving into work on ratio and proportion next.  We are hoping that more questions will arise as we continue this work.  My favorite so far is, “Given a start time, time spent running so far, and a map of the run, can you figure out where Mr. Feutz is now?”

Here is our Graphic Organizer – totally open to your critique and suggestions.  What questions can you add to our list, and how do you come up with your project questions?  We would be most grateful if you share your curiosities or strategies in the comments.

Related:

Create Suspense – MTBoS Week Two: My Favorite

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For week two of our blogging challenge, we were asked to write about one of our favorite lessons, games, resources, tools or strategies. It was tough to pick one.  I have so many excellent resources and tools, that as I reflected on what to write about, it made me once again realize what a great time is it to be a math teacher and just how lucky I am.  What a hard but awesome job, and what a generous and sharing community we have.

I really like keeping students in suspense.  If I can set up a situation where students want to know what’s coming next, that often translates into engagement and the desire to learn.  When you watch your favorite TV show, and it ends on a cliff-hanger, you make predictions and you think about it in between episodes.  You are connected to and invested in the story, and you can’t wait to see what happens next.  I want my classes to have at least some of this kind of anticipation.

I also like to create some public presence for math in my school, and I try to create a bit of suspense around this as well.  Typically, a few days before we publish our work on the math wall, I will put up a provocative question, or something to generate interest. This week I just put up a funny title with a big question mark, and listened for the buzz..

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As a culminating activity of learning about graphing linear equations, I asked Algebra 1 students to create “math faces” through drawing with graphs. They used Desmos (…it was very tempting to write a series of “my favorite Desmos” posts – everything those guys do makes my classroom better!) to create their works of mathematical art, to practice transforming linear equations, and to solidify their understanding of domain and range.  I ask students to make sketches ahead of time to ensure that they are purposeful in manipulating their equations.  This is an activity
conceived of by the incomparable Fawn Nguyen, and one that I use every year.  I have written about it before as well.  This kind of task gives all students an easy entry point, but allows for real complexity for those who are ready. This low entry, high ceiling aspect of drawing with graphs makes it a rich and motivating activity that we can return to with students again and again.  Although the Des-Man activity is not currently available through the teacher dashboard at Desmos, I have heard that it is getting a make-over and that they will be bringing it back again.  Each time, I am amazed at how motivating this activity is for students.

After a couple of days, we published our process and our results on this year’s “Sweet Wall of Math!”

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How do you create suspense and anticipation in your classroom?

2016 MTBoS Blogging Initiative: The One Good Thing Glow

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As a math teacher, it’s really fun to work with students who come to my classes already loving the subject, students who have already mastered the content from last year’s course so they are ready to dig deeply into novel problems in our courses, and students who feel really good about themselves as math thinkers.  Doesn’t this describe most of our kiddos?

The reality is that a large part of my job ends up being working to alleviate the trauma that students bring with them to Algebra 1 or Algebra 2.  They have known since second grade that they are not a “math person.”  They feel that they are not as good at math or as fast at math as others around them.  Many of their mathematical experiences have left them feeling inadequate, and math has been a place where their self esteem has been eroded.  Not a big surprise that they have trouble accessing the beauty of the subject.

One of my grade 10 students showed up this year with all of the marks of earlier trauma.  She was reluctant to speak in class or even when I worked one-on-one with her.  When she did answer a question, it always sounded like she was asking rather than answering (…y’all know that “I have no idea if what I’m saying is right” tone of voice).

This week, she had a perfect score on her linear systems and inequalities assessment.

And this wasn’t an easy test.  I always include some questions that ask kids to synthesize and apply, and to recall ideas from earlier work – typically, I have very few 100%s.  In fact, hers was the only perfect score in the class.  Although I generally avoid comparing students to each other, I couldn’t resist sharing this with her.  You should have seen her trying to pretend that she wasn’t beaming!  I wrote a note the her mom, to share how proud I was of this effort and of her success.  When I saw her mom the next day in the school lobby, there were tears in her eyes while we spoke about this.  She said that her joy had nothing to do with the score.  She didn’t care about the test score, but she could see and feel the difference in her daughter’s confidence and sense of self.  I couldn’t agree more.

What a wonderful way to begin my Thursday.  The One Good Thing glow stuck with me all day!

2016 Blogging Initiative

mtbos-blogging-initiative

I am participating in the 2016 MTBoS Blogging Initiative.  I am doing this in part in to open my classroom up and share my thoughts with other teachers. I hope to accomplish this goal by participating in the January Blogging Initiation hosted by Explore MTBoS

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I’ve just dusted off my “About Me” page to include the schools at which I’ve taught, and I’m excited for the next month.  You, too, could join in on this exciting adventure. All you have to do is dust off your blog and get ready for the first prompt to arrive January 10th!

Lies and Collaboration

I actually enjoy the puzzle-like aspect of exponent rules, and simplifying radicals.  For me, there is something satisfying about learning ways to manipulate numbers and letters – probably why I love algebra so much.  But I am tuned-in enough to my students to know that many of them don’t find the same satisfaction from doing this work just for the sake of intellectual exercise.   And since calculators came into vogue, it’s been harder to justify the need for rationalizing the denominator or expressing the square root of 50 as 5 times the square root of 2.  But we are tasked to follow standards that often include these kinds of skills and it has been helpful for me to turn this into exploration or game learning as much as possible.

IMG_4135I did some mining of the MTBoS for ideas to teach rules of exponent arithmetic and came across this post, which includes a nice exploratory worksheet from Andrew Stadel.  He describes a similar issue with contextualizing exponent rules for middle schoolers – one of the really great things about our online community are these moments where we are reminded that we are not alone.  He asks his students to find the mistakes in the equations, to explain where the author went wrong, and to find the correct solutions.  He used a bunch of the common misconceptions found on mathmistakes.org to help students to catch themselves in the common errors.  Very nicely done.  This would have been a good lesson as is.

IMG_4147Then I remembered the Bucket O Lies protocol from Nora Oswald at Simplify With Me.  Nora manages to gamify math like no one else that I’ve seen.  She manages to add entertainment even to potentially dry topics like this one.  I combined Andrew’s worksheet with Nora’s idea to make a bucket-o-exponent lies.  I printed the 3 worksheets, cut them out into individual problems, folded them up, and put them into buckets (or baskets).  Voila! Drama and Motivation.  In pairs or threes, learning happened.

IMG_2885Of course, I hammed it up with the students.  There’s nothing like telling teenagers that someone is trying to get one over on them to motivate them.  This has worked well for me in the past, especially when it came from advertisements.  I riled them up by acting outraged that someone had created this whole set of math material, which was full of mistakes!  (Actually, I blamed Andrew :) ) …Lies I tell you… these baskets are FULL OF LIES!  Let’s find the mistakes so we can write a self-righteous set of corrections back to this author who was deliberately spreading bad math.

They quickly saw through my act, but it was enough.  They were already motivated in spite of themselves.  Andrew’s worksheet was just enough for everyone.  I started by coaching the groups who needed help getting started and moved to pairs who were making mistakes with fractional exponents.  For my honors group, I added a few more examples with rational exponents.

Thanks Andrew!  Thanks Nora!  Our generous community is the Best!

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Revealing Learning Targets

DSC06230I am not always sure about how explicit to be about learning targets.  I have seen some convincing research, which seems to indicate that letting students know exactly what is expected of them for each lesson helps them to take ownership of their learning, and to make sure that they are getting what we think they are getting during each class session.  I agree with this practice in general, and I believe that it definitely has a positive impact on some students.  My current school, as well as the previous one have required that we post targets each day, and there are many educators who I respect who advocate for this practice.  But sometimes, I feel like a learning target can put a limit on where we can go as a class, and can feel a bit stifling, especially when we want a problem or exploration to feel open-ended.

Lately, I have adopted a practice of “Hidden Targets.”  I do post the learning target, but I often leave it covered up during class.

IMG_4121As part of our end of class routines, students make conjectures about what they think that today’s learning target was.  We reveal the target, assess how well the lesson matched the target, and whether the learning matched what was expected.  Although I think that I am good at starting class off, and generating enthusiasm, I sometimes am not as good at synthesizing and wrapping up.  Being conscious of synthesis and wrapping up class in a richer way has been one of my goals for this year, and this routine has been a good protocol for me and for my students.  It quickly reminds us about what we learned during class, and how this lesson fits in to the bigger picture.  Students have been highly engaged in figuring out the day’s learning goals; I hear students talking throughout the class period about what they think is under the flap for today – and you know that they remind me if I forget to do the “reveal!”

IMG_4119…And it doesn’t hurt that we have created this sweet Appolonian Gasket on which to showcase the day’s targets.  Who doesn’t want to stare at this and contemplate infinity?!

First Week: Building Culture

The start of the school year is one of the most important moments for my classes.  Setting the right tone and attitude right from the beginning can mean buy-in from students right away – and conversely, a bad start can be really tough to recover from.  I had a pretty good start this year in my Algebra 1 and Algebra 2 classes.  I wanted to share some things that worked for me in case someone else might benefit, and to document the week, as I may repeat much of this work next year.

My students have been working on a pseudo-Appolonian gasket on the whiteboard. It makes a nice frame for our learning targets.

My students have been working on a pseudo-Appolonian gasket on the whiteboard. It makes a nice frame for our learning targets.

I have several goals for how I want my classroom to “be,” and the first week is a chance to work on some of the big picture ways that we will be working together this year.

  • It is important to me that as a group, we celebrate scholarship – and the struggles involved in becoming scholars
  • I want to nurture a love of learning and of curiosity
  • Our classroom has to be a safe place to take chances and to make mistakes
  • We need to be able to work collaboratively – even more than in other subjects, I believe that we really need to see how others think in order to understand math
  • To that end, we need to learn to be comfortable talking (and arguing!) about math
  • We need to work independently as well, and to trust and value our own ideas
  • We need to respect each other, and hopefully to love each other at least a little.  Of course I love all of them.

I used a series of activities (all sourced from the MTBoS of course) to try to help establish this culture.

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DAY 1: What does it take to do math?

Very first thing, I assigned each student a “secret partner” for the week, based on this idea from Origins.  Students are to observe their partner throughout the week, and are responsible to report back an acknowledgement of something positive that they observed at the end of the week.  The payoff for this happens on day 5.  Next, I introduced a version of Jasmine’s Tabletop Twitter.  I set up 5 stations around the room.  Each had chart paper with a question/prompt on it.  Students moved around the room in two minute rotations, and were asked to respond silently to each question.  I followed Jasmine’s lead in asking students to take a marker and write their name with that marker, so we could look back and see who had authored each comment.  My five prompts were:

  1. Why do we learn math?
  2. What will make our math class a good learning environment?
  3. What does it take to be a good math student?
  4. Respond to this quote: “Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.” – W. S. Anglin
  5. Add a song to our class playlists. Write a genre instead of a song if you prefer.

At the last station, I gave out this Capture your thoughts organizer, and asked students to synthesize and summarize the most important points from their station, to add anything they thought was missing, and then report back to the whole group.  We hung our new “posters” in the hall on this year’s “Sweet Wall Of Math,” to help establish that our work will be public this year and we are proud to show our thinking to the world.  I’ll use the ideas they shared to create our learning agreements for the year.  For anyone who would like more detailed plans for day 1, I’ve written them up just for you: Day 1 Plans. :)

Day 2: How can we create the questions?

I am totally convinced of the positive impact that Dan Meyer’s 3-Act format can have an a group of math students, so I was excited to introduce 3-Act math tasks right away on day 2.  Students are so used to arriving in math class, and just imitating the teacher that they often don’t know how to react when they are asked to think of a question themselves, and then asked to figure out what they actually need to do to solve their question.  The first tasks like this can be really tough and even painful, often for some of the “top” students.

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The Super Bear was a nice one for both groups.  The math was easily accessible, which gave us room to learn the structure of how we should approach these kinds of tasks.  I made a new 3 Act handout for students to use, and guided them through the process.  I was strict about keeping silence in the room for the entirety of Act 1, except when they were asked to share their guesses and to establish a high/low range.  I stressed the importance of this “grappling” time, when they get to really think for themselves without the bias of hearing others’ ideas, and promised that they would get to work together for the rest of the task.  This is one of the important routines in my class, and is one of the few rules I impose on the group without their input.  Every group suggested weighing the bears, and several came up with ideas for how to measure volume (displacing in water, melting down the bears…).  Act 3 provided some rich discussion about the discrepancy between their solutions and the revealed answer, and the drama of the reveal of Act 3 can’t be beat!  Even reluctant students can’t look away as the gummy bears are weighed out.

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Day 3: Metaphors for perseverance.

We spent much of our class playing the Game About Squares.  I followed Annie Fetter’s suggestion to try this out with students, and read her post about this several times, so it was fresh in my head. She has a clarity about the importance of these tasks that I wanted to hold on to, emulate, and embody for this lesson.  This is a game that does everything that we want in our math classes.  It meets kids where they are, and little by little gives them slightly more challenging tasks to accomplish.  I (mostly)refused to help them at all, but made it clear that they were expected to figure out what to do.  After some initial discomfort with the whole idea that they were going to be playing an on screen game, and that I wouldn’t help, they dove in.  They grappled, made mistakes, started over, helped each other, groaned, and persevered.   They were competitive and proud when they solved each level.  We used the last 15-20 minutes to debrief the activity, to list the things that helped us succeed, and to respond to a short survey.  We talked about how these skills actually encompass just about everything that they need to be successful math thinkers.  Interesting that the number one thing they did that helped them to be successful in this game was to make mistakes.  I bet that we will be referring back to this often.

Annie Fetter is the best.  Just Saying.

G of Squares Survey results

Survey results after 30 student responses. Notice the top result!

Day 4: Number flexibility: You mean there’s more than one answer?

Day four, we worked on the four 4s.  This has been a favorite of mine since I began working with students.  It allows for multiple approaches and creativity in math thinking.  I’ve written about it further here and here.  This year, I decided to keep it to one class period.  In groups of 3, I challenged Algebra 1 students to create every number from 1-20, and Algebra 2 to shoot for 1-30.  We put their work out on our Sweet Wall, and they may go later to try to fill in any blanks.  Jo Boaler and the Youcubed team put together an excellent week of inspirational math, which began with this activity.  The rest of the inspirational week’s activities were tough to resist.  There are some good ones in there, along with great growth-mindset messages for students.  I may get back to the others later in the year if we have time.  I did play her day one video, and led a short discussion hinting at growth mindset to end Thursday’s class.  I was also especially tempted to jump on the explicit growth mindset work that Julie Reulbach has shared, but we can’t do everything.  I will be following Julie’s reflections closely to see how her implementation goes this year.

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Day 5: Assessing Numeracy + Mathematical Drama.

Trying to do Algebra without a solid understanding of arithmetic is rough.  I’ve seen students suffer through this, and it is not easy for me or for them, and there just isn’t the time during Algebra 2 to work on dividing fractions or operations with negative numbers.  So we’re implementing an after school numeracy workshop this year for grade 8, 9, and 10 students who need more support in this area.  We used this class to assess students’ arithmetic skills, and to identify those who might be most helped by the after school program.

I saved the last 20 minutes of class to follow up on the secret partners activity, and for a read-aloud.  Secret partners takes just a few minutes, but has a nice impact on student attitudes.  They act reluctant to speak nicely about each other, but they are grateful for this opportunity to celebrate each other’s good qualities.  Comments ranged from “I noticed A looking out for the new student at lunch” to “Y worked really hard on the science lab” to “X is really funny and cracked me up in English yesterday.”  I ended the week by reading the introduction to Zero: Biography of a Dangerous Idea.  This is an excellent book, and the introduction is high drama!  And kids just like to be read to.

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Although we didn’t get deep into new content this week, we did some valuable math together.  But equally important is the positive feeling that students left with on Friday afternoon.  With confidence in themselves from their successes, with trust in each other and the knowledge that their peers notice their positive behaviors, and with the assumption that their teacher cares about them, we are set up for the year.  Now we need to hold on to this feeling when the going gets rougher!