Pi Day (with minimal mention of digits)

Posted on March 15, 2017 by Andrew

Today, we celebrated our belated Pi Day! It was delayed due to inclement weather…

Though my #MTBoS friends were there to comfort me in my time of need!

@bkdidact that’s the rounded up version anyway, none of this truncated 3/14 crap
— Jonathan (@rawrdimus) March 13, 2017

Our spring trimester focus is always financial literacy. So, we spent most of last week researching recipes, planning for a shopping trip, going to the bank, shopping for ingredients, and making pies. Yes, I said it. We made pies for Pi Day, sue me! Now, finally the time had come to eat our pies, but first…we had to do some more math!

First we reviewed of some of the digits of Pi, highlighting that when rounded to the nearest hundredth it matches the numerical date of March 14th, which is subsequently known as “Pi Day” for this reason. I also wore my Pi shirt, which gives the students an opportunity to see that there are A LOT of digits in this number known as Pi and that I’m a nerd. We did, however, skip the traditional digit memorization activity for several reasons including working memory and tedious boredom.

Instead we estimated, explored, and discovered the circumference formula with our pies and some string.

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An Instructional Routine for “Which One Doesn’t Belong?”

Posted on January 17, 2017 by Andrew

We are currently studying geometry. The standards for geometry list one important understanding to develop before 4th grade, “Reason with shapes and their attributes.” If you click through the link you can read more about the specifics, but the activity that gets students reasoning about shapes and their attributes the most, in my opinion, is Which One Doesn’t Belong? This activity allows students to share their thinking about shapes and their properties without the fear of being wrong. Why? Because every answer is correct as long as you can justify your reasoning! You can read more about how I implement “Which One Doesn’t Belong?” in my class and you can use it for more than just geometry.

But this post is about how I used this activity as a basis for an instructional routine. Continue reading →

An Inch Wide and An Inch Deep: A Call To Action

Posted on March 23, 2016 by Andrew

One of the most popular ways to critically describe mathematics education in the United States is “a mile wide and an inch deep.” The TL;DR is that most mathematics education focuses on too broad an array of topics with a lack of emphasis on conceptual understanding and critical thinking.

My worry is that most special education math classes are an inch wide and an inch deep. I ran across this chart from Browder, Spooner, Ahlgrim-Delzell, Harris, Wakeman (2008).

Demonstrated here is a clear focus on an extremely small amount of topics and the only one investigated in any kind of depth is financial literacy, which admittedly is an extremely important topic for students with disabilities. For students with disabilities to be successful members of their communities they need to be financially literate. But this need should not preclude students with disabilities from exploring other mathematical topics.

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Simple Prompts Can Lead to Complex Mathematical Thinking

Posted on March 3, 2015 by Andrew

This post is inspired by chapter 8 of Steve Leinwand’s book Accessible Mathematics. If you haven’t read this book, do it! Leinwand is a leading voice in the push for math instruction that makes sense to students and will lead to longer lasting mathematical understanding. Chapter 8 is entitled, “How Big, How Far, How Much?” and in it Leinwand encourages this instructional shift:

Tie the math to such questions as How big? How much? How far? to increase the natural use of measurement throughout the curriculum.

He goes on to say that measurement as a mathematical skill is often a “skipped chapter,” but is also one of the most pervasive life skills in the mathematics curriculum. Leinwand goes on to encourage teachers to incorporate measurement as “an ongoing part of daily instruction and the entry point for a larger chunk of the curriculum” (p. 46).

The game shelf!

Now you may be saying, “But I have a million other goals and standards and expectations and test prepping and whatnot that I have to do before I teach the kids to use a ruler!”

Well, lucky for you the Standards for Mathematical Practice also have you covered.

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There’s More Than One Way to Skin a Task

Posted on February 23, 2015 by Andrew

Teaching is really only as valuable as the learning experiences and opportunities created for the students. Crafting and choosing which experiences and opportunities are available to students should be at the forefront of any teacher’s mindset when planning lessons or units. So let’s delve a little deeper into crafting and choosing learning experiences.

One of my classes has been using the geometric study of area in order to practice and apply multiplicative thinking. Crafting and choosing specifically rich tasks that engage the students has been one of my major goals for this unit. So I’d like to just investigate different iterations of reasonably similar tasks that apply multiplicative thinking in the geometric context of area.

You could just start and end your search with:

Draw a rectangle with an area of 56 units.

This certainly gets the job done. Students have to think about factors of 56 and which make the most sense. The great thing about this task and others like it (check out Open Middle for more) is that there are a multitude of correct answers. Having many “right answers” leads to deeper group work and richer class discussions. The drawbacks to this task are the lack of visual support and the separation from a concrete representation or real world context. Also the language processing comprehension of this task is high, so students who struggle in this area would require additional supports.

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Humans vs. Zombies! (or How We Learned About the Coordinate Plane)

Posted on February 4, 2015 by Andrew

This week began our study of the coordinate plane. I used the first lesson of Transition to Algebra’s unit 6 as a pre-assessment. It proved that I needed to take a couple steps back and address many of the basic concepts relating to the coordinate plane (axes, integers, ordered pairs, quadrants, etc…) in a more direct way. Our class goals are pulled from the Common Core State Standards Initiative:

First, I used this game as an anchor for plotting ordered pairs, then the students did some individual practice on worksheets. Today we played another game…

Humans vs. Zombies!

My very crafty assistant teacher, Ms. Avellino, took a game from a website and turned it into this… Continue reading →

A Tale of Two Tasks

Posted on January 29, 2015 by Andrew

Differentiation is a widely accepted (and debated) strategy for meeting the needs of a diverse range of learners, especially in special education classrooms. According to Carol Tomlinson, “a differentiated classroom provides different avenues to acquiring content, to processing or making sense of ideas, and to developing products so that each student can learn effectively.”

But what does it look like in practice?

First, let me describe our class setting to give you some background. I teach at a self-contained special education high school in Manhattan. The learners at our school range from students with learning disabilities or speech and language delays (which effect academic performance, but do not generally effect their physical appearance or how they react in social situations) to those with autism spectrum disorders or down syndrome (which effect socialization and communication as well as academic levels.) Our math classes are mixed grade (9th graders with 10th graders and 11th graders with 12th graders) in order to create groupings that can best meet each student’s academic and social/emotional needs. There are three concurrent math classes, which means our class groupings are no bigger than 8 students with a head teacher and an assistant teacher. This leads to collaborative in-class groups that can be as small as 4 students to 1 teacher.

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A Better Shapes Class

Posted on January 27, 2015 by Andrew

Christopher Danielson recently released “A Better Shapes Book” for free on his blog. Before you read on, go take a look at it, download it, and enjoy!

Our Hallway Display

Since some of my classes are studying geometry this trimester this was a fortuitous release. My students, who are in self-contained special ed classes, can identify benchmark shapes (squares, rectangles, triangles and circles), but we are currently investigating how squares and rectangles relate as quadrilaterals. This book was the best way for our students to explore shape properties without having to read, write and remember a lot of vocabulary. We were able to discuss what they saw and critique the arguments of classmates in a safe space, because all arguments were valid for one reason or another. The elimination of the potential to be flat out “wrong” created a safe space for my student population. As long as there was some semblance of justification, you were “right.” The students liked that!

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