Tag Archives: chunking

Cutting Up the Math Into Bite-sized Pieces

When I train new math and special education teachers I explain that teaching math should be like feeding a hot dog to a baby in a high chair. Cut up the hot dog into bite-sized pieces. The baby will still consumer the entire hot dog. Same with math. Our students can consume the entire math topic being presented but in smaller chunks.

bite sized pieces

My approach to doing this is through a task analysis. This is very similar to chunking. It is a method to cut up the math into bite-sized pieces just as we would break up a common task for students with special needs.

Image result for task analysis

While waiting for my coffee order at a Burger King I saw on the wall a different version of a task analysis. It was a step by step set of directions using photos on how to pour a soft cream ice-cream cone. I thought it was amazing that Burger King can do such a good job training its employees by breaking the task down yet in education we often fall short in terms of breaking a math topic down.

soft cream icecream cone task analysis

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Scaffolding Higher Level Math Topics

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The graph shown involves derivatives – a calculus level topic. Before getting into this heavier mathy stuff, consider the title of this post and the other content presented on this blog. Making math accessible to all students is not a special ed or a low level math thing. It is a learning thing. This artifact is what I drew to explain the math concept to a student in calculus to help her grasp the concept as well as the steps. The following are strategies used.

  • color coding – each of the 4 sections written in different color
  • connecting to prior knowledge – the concept of velocity was presented in terms of a car’s speed and direction (forward or backing up)
  • chunking – the problem was broken into parts and presented as parts before exploring the whole
  • multiple representations – the function was represented with a graph, data (1, 2, 3, 4, 5) and a picture (at the bottom)

As for the mathy stuff, the concept of velocity was address by its two parts: speed (increasing or decreasing) and direction (positive or negative). The graph was broken into the following parts: decreasing positive, decreasing negative, increasing negative and increasing positive. Each part was presented with possible y-values (data) and the sign. The most intuitive part is increasing positive which is a car going forward and speeding up.

I find that when I provide intervention, this approach especially by addressing conceptual understanding is effective as the students respond well.

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Chunking a Lesson

Chunky peanut butter means you there are pieces or chunks of peanuts. The peanut butter is broken into distinct parts. Chunking in teaching means breaking a concept or lesson into distinct, smaller parts. This makes it easier for students to process the lesson and the concept. They focus on less content at one time which is important given that working memory has a limited capacity, especially for many students with disabilities.

Here is an example of how it can play out. On a lesson on slope (compute slope of a line given two points from the line) the steps are as follows for (1, 5) and (4, 11):

  • write the formula y2-y1/x2-x1 (rise over run)
  • plug in the ordered pairs (11-5)/(4-1)
  • compute 6/3 = 2

But there is also the conceptual understanding that is often lost on the students. These steps do little to help with conceptual understanding.

In the photo below the teacher is presenting a conceptual piece as a chunk of her lesson before she gets to the steps listed above.  She has drawn a triangle to represent going downhill, another going uphill and a horizontal line segment representing no hill. The rise and run are listed for each (the horizontal line segment has no rise). The students wrote a rise over run ratio showing the slope for each then practiced this before the teacher moved onto to the steps listed above.

kristen lesson on slope

Upon completion of this chunk the teacher can give a practice or pop quiz to help students fill in the gaps individual students may have before moving on to the next chunk.

The next chunk would not yet involve the formula. A slope triangle would be drawn under the line to visually represent the rise and run. Students would practice finding slope using this approach with the next step bringing in ordered pairs and the formula listed above.

slope.14

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