A Student’s Eye View

Ashli Black, over at Learning to Fold, recently posted this little bit of wit and whimsy.  The post essentially recounts her experience in algebra classes and compares it to the experience of contestants on an extremely confusing, quite vague, and thus hilarious math game show.  Ashli makes the point that, “As that kid without conceptual understanding in algebra, this skit is pretty much exactly what it was like in class for me. Confusing, almost no stated rules I understood, and at any moment the scene might change or I might be shoved in a box for not achieving Wangernumb.”  Ashli considers the difference between teaching for conceptual understanding and teaching for procedural understanding in her post, but it got me thinking about my own students.  I often think my students are holding their breath, waiting for me to tell them their answer was in fact “Numberwang.”

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My goal as a special educator is to communicate the day’s lesson or task so the students will be able to access, understand, and apply the mathematical content.  This often leads to accommodation, modification, and differentiation of everything for everyone.  When one thinks of accommodations the first things that come to mind are standardized testing accommodations.  The general list usually looks something like this:

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To Calculator, or Not To Calculator, That is a Question

When it comes to planning lessons in special education, or general education for that matter, the goal is for all students to be able to access, understand, and be able to successfully apply the content to show evidence of full understanding. The application can take many forms: performance assessments, formative assessments, summative assessments, teacher observations, etc…

But how do you get to that final assessment piece? This post is about the planning process that goes into successful lessons for all students.  Let’s begin with Universal Design for Learning (UDL). UDL is a model for planning lessons and units that creates access to the content for all students.  Here is a cartoon that embodies the philosophy of UDL.

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One major component of planning in special education math classes is prioritizing the mathematical goals and the needs of the students to access the mathematics in a lesson.  A Teaching Children Mathematics article from 2004 suggests the following steps for beginning to plan a successful math lesson for students with disabilities:

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

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:

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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

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

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!

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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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#10goodthings I’ve Learned This Year

First, I read @stoodle’s Exorcising Teacher Demons post.  In his post what stood out to me was that he took the “high road.”  Instead of actually venting for a whole blog post, which could be counter-productive, Matt chose to take his co-worker’s challenge:

If you were asked to come up with 10 things that you’re doing well this year, you could do it.

Then Meg Craig put out the call…

Here is my response to both Matt and Meg, but with a twist.  This year I have learned so much from the twitter/blog community known as #MTBoS (math twitter blogosphere) that I needed to show all of these wonderful educators just how important their impact is for educators across the country.  So, I decided to write 10 good things I’ve learned.

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If I Could Time Travel…

If I could time travel I would do one thing.  This post is about that one thing.

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Time And Relative Dimension In Space

Since everyone knows that when you travel back in time you can’t change anything because of the butterfly effect, this limits my choices to instances where I could simply be an observer.  What would I want to observe?  Would it be a famous event like the Gettysburg Address or the “I Have a Dream” speech?  Would it be something small like when my parents met or my first day of school?  No.

I decided I would want to observe myself as a first year teacher.  The reason for this comes from the advancements in technology that are making classroom filming more accessible and convenient, including this little gem.

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We Made a Math Game!

Well, to be more precise we made a puzzle-y, game-y type thing.

Let me explain.

If you follow me on twitter, then you saw this little bit of nerdiness…

I bought this dice bonanza bucket at Target during Christmas break.  I was very motivated to put the new dice to work for my students!

As I wrote about previously, one of my classes is studying algebra.  The contents of the dice bonanza varied between number dice, dot dice, color dice, and others it reminded me of Transition to Algebra like this:

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So my assistant teacher and I put the dice to work in this puzzle game we called Dice ID.  Here is the instruction booklet and here is the game board.

And here is how it went in our class last Friday…

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Algebra with a capital A!

I teach at a self-contained special education high school in SoHo in NYC.  Our math department does a good job of incorporating “algebraic thinking” into every problem we pose or task we assign.  Though, as they are in high school, our students are aware of what they “should be learning.”  In other words, they see what their peers without disabilities are doing in math class and generally it is not what they are doing.

So the desire to learn Algebra comes up quite frequently.  (The capital A is intentional in this case!)  Algebra is like our student’s white whale.  So, I try to be the boat to their Ahab.

My frustration, however, is that the typical approach to Algebra, with a capital A, is heavily language based. Vocabulary such as variable, dependent, independent, inverse, and substitute are very basic to capital A-lgebra, but they are also complex terms (and ones which have alternate meanings in everyday speech) that our students would require most of the year just committing to memory.

So I have been on a search for capital A-lgebra work that bypasses this vocabulary at least at the very beginning.  Cut to Fawn Nguyen’s Visual Patterns and Heinemann’s Transition to Algebra.

I began with a pre-assessment task about toothpicks

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Number Strings

This is a re-post from the Global Math Department Newsletter from 12/2/14

If you haven’t signed up for the GMD newsletter, please take a minute and do so by clicking the picture.

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Anyway, number strings are a classroom routine which I believe need to be highlighted more than they are currently. Rachel Lambert, an author of the number strings blog, was my school’s math consultant when I began my career. She has helped to shape who I am as a math teacher and my beliefs of what good math education is.  The following is an article from the GMD newsletter published on 12/2/14:

You may be aware of the Contexts for Learning Mathematics curriculum developed by Cathy Fosnot. A major component of the curriculum is a pedagogical technique designed to introduce and practice computational ideas and strategies called number strings. You may not be as aware of how to utilize this particular technique in your classroom. That’s where Rachel Lambert and Kara Imm’s blog called Number Strings comes to the rescue!

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