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.

One of my 9th and 10th grade classes is studying geometry.  The goals of the unit are pulled from the Common Core State Standards Initiative:

geometry goals

Tomlinson says differentiation allows for multiple ways for students to access content, process the information, and produce evidence of understanding.  So let’s first analyze the content of my class.  Our content focus is area.  The students are using the study of area to practice and solidify the multiplicative skills introduced during our first trimester which focused on number sense.  Now this, unto itself, is not an example of differentiated instruction.  Every student in the class has the same geometric content goals, to be able to apply their understanding of multiplication and addition to solve problems involving area. But the differentiation is apparent when the computation goals for each student are analyzed in conjunction with the geometric goals.  The geometric context is the same, but the computation content is differentiated.

Group ONE is working on this goal:

multiplication goal 1

Group TWO is working on this goal:

multiplication goal 2

Now on to process.  During a lesson we will use the same tools, manipulatives and models which allow students to simultaneously work on the topic of area, while mastering two different computation goals at the same time.

Here’s what I mean: I gave the two groups different tasks about the same thing.

Based on work with cuisenaire rods done by Simon Gregg, our class has been using these manipulatives to model the groupings inherent in multiplicative thinking as it relates to the area model.

Group ONE was asked to use cuisenaire rods to make and draw quadrilaterals representing the following expressions (3×10, 7×3, 6×4, 3×8, 4×9) then find the area of each quadrilateral.

Group TWO was asked to make as many quadrilaterals as they could with the following areas (24, 30, 16).

Group ONE at work…



All of the students worked to understand the concept of area, but the way it was presented was different for each group.  Group ONE was asked to use the very basic multiplicative idea of multiple groupings to find the area of certain quadrilaterals.  While Group TWO was asked to use flexible thinking about factors and products to construct quadrilaterals of varying areas.

The products, however, ended up being very similar and not differentiated at all.  This could be because the tools, manipulatives and materials provided to represent the student’s thinking were all the same.  It could be because as I guided the students to show their thinking, I guided them all in the same direction.  It could be both of these things.  In special education math classes I am finding that it is harder to differentiate the product since most students require scaffolding and prompting throughout the process of working on a larger project or even the classwork of a single period.  If you have strategies for differentiating products in special education classes, please leave them in the comments.

Anyway, here’s some Group ONE work…



Here is some work from Group TWO



We are planning to differentiate the next steps for each group as well.  Group ONE will gradually move to finding side lengths (read: factors) for given areas (read: products), but the grid and cuisenaire rods will remain as scaffolds.  Group TWO will move from counting unit squares to finding area by multiplying given side lengths as well as finding missing side lengths with given areas without a grid.

What do you think would be appropriate next steps for both groups? Are they truly differentiated? Let me know in the comments!

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