Concrete-Representation-Abstract
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Place Value Representation
Here is an easy way to create and implement strategy to unpack place value for students (created by one of my former graduate students). I suggest using this after manipulatives and visual representations (drawing on paper) in a CRA sequence. It is hands on but it includes the symbolic representation (numbers). Hence is another step…
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The I in Instruction can be the same I in IEP and IDEA.
I am consistently surprised by the reliance on canned items for students who struggle. There are different reasons students struggle but we know that there are secondary characteristics and factors that inhibit effective information processing that can be addressed with some Individualization. In a math intervention graduate course I teach at the University of Saint Joseph,…
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More Than: Concept and Symbol
The alligator eats the bigger number is the common approach for student to use inequality symbols (< > < > ). I find that students remember the sentence but many do not retain the concept or use the symbols correctly, even in high school. This post presents an alternative approach. Alligator Method The reason, I believe, is…
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Sausage Fractions – Real Life Example
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Common Denominator – Why?
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Concepts vs Skills – Need Both
In general math is taught by focusing on the steps. Conduct a Google search for solving equations and you will see the steps presented (below). You need a video to help your student understand solving and you typically get a presenter standing at the board talking through the examples. (I’ve posted on my approach to…
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Simplifying Expressions (Combine Like Terms)
Simplifying expressions (see photo below) is one of the most challenging algebra tasks for many students receiving special education services. A major problem is that it is typically presented as symbol manipulation…addressed in very symbolic form. My approach is to make math relevant and more concrete. Below is a scaffolded handout I use to help…
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Authentic Activities – Money and Prices
Below is a photo of a typical worksheet for money. I worked with a parent of a high school student severely impacted by autism and she explained that her son worked on nothing but worksheets when he worked on math. For students with more severe disabilities the worksheet may not be real or meaningful as…
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Introduction to Solving Equations
I introduce solving equations by building off of the visual presentation used to introduce equations. The two photos below show an example of handouts I use. Below these two photos I offer an explanation of how I use these handouts. First I develop an understanding of a balanced equation vis-a-vis an unbalance equation using the…
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Basic Skills Older Students
A widespread problem at the secondary level is addressing basic skills deficiencies – gaps from elementary school. For example, I often encounter students in algebra 1 or even higher level math who cannot compute problems like 5÷2. Often the challenges arise from learned helplessness developed over time. How do we address this in the time…