Tag Archives: task analysis

CTSPEDMATHDUDE Approach to Teaching Math

The purpose for having this website is to share my approach to teaching math. The approach is the use of special ed principles brought to bear on math. Specifically, I use a task analysis approach to break down a math topic into “bite-sized” pieces and to use a variety of instructional strategies and reinforcement to move the student through the individual tasks towards mastery of the math topic (including conceptual understanding).

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Making Slope Less Complicated


Slope is the rate of change associated with a line. This is a challenging topic especially when presented in the context of a real life application like the one shown in the photo. The graphed function has different sections each with a respective slope.

One aspect of slope problems that is challenging is the different contexts of the numbers:

  • The yellow numbers represent time
  • The orange numbers represent altitude
  • The pink numbers represent the slopes of the lines (the one on the far right is missing a negative)

Before having students find or compute slope I present the problem as shown in the photo above and discuss the meaning of the different numbers. What I find is that students get the different numbers confused and teachers often overlook this challenge. This approach is part of a task analysis approach in which the math topic is broken into smaller, manageable parts for the student to consume. Once the different types of numbers are established for the students we can focus on actually computing and interpreting the slope.

This instructional strategy is useful for all grade levels and all math topics.


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Documents for Task Analysis Presentation – DADD 2017 Conference



Here is a link to a Dropbox folder with the documents I will address in my presentation. (Note: documents will not be uploaded until Jan 19, 2017.)

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Documents for Webinars on Supporting Students with Autism in Math


Link to Drop Box folder for webinar on Task Analysis

Link to Drop Box folder for webinar on Making Math Meaningful (note: the folder is not populated with handouts with excerpts shown on the video. These documents will be available in the folder by Oct 16.

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Targeting Gaps in a Math Topic

percent vs monetary value

A key to intervention for math is to drill down into a topic to see which step is causing a student problems. This is a big reason why ongoing progress monitoring is vital to intervention.

In this case a student in a previous session had occasionally added the percent to the dollar amounts – the step that was problematic. He conceptually wasn’t thinking about the meaning of the values but just added or subtracted numbers he saw. In response the next session focused on helping the student discern between the percent rate and the monetary values.

In the photo above is the work of the student as review of the previous session. This was followed by highlighting the dollar amounts in green and the percent amount in yellow. It was emphasized that the yellow was not used in the calculation in the bottom row.

This was followed by the task seen in the photo below. The focus is strictly on the one step that was problematic. This was followed by work on IXL.com (2nd photo below) with the student writing in values on the handout shown on the  bottom photo to help the student focus on this tep

percent vs monetary value 2

percent vs monetary value 3

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Assessment for General Curriculum Math Topics

In special education there is a tool called a task analysis. It is a formal approach of identifying the steps taken to demonstrate mastery of a skill. For example, putting on shoes with Velcro straps involves the following steps: get shoes, sit on chair, match shoes with feet (right to right), insert foot into respective shoe etc.

I have applied this approach to general curriculum math topics from counting money to solving using the Quadratic Formula. Below are the iterations of my task analysis for the objective count TENs, a FIVE and ONES (dollar bills) to pay a given price. The first shows a rough draft of notes I took as I actually counted out the money, going through each little step. The second shows the steps written out on a task analysis table I created. The third shows the final, typed version.

paying price with bills task analysis rough draft

paying price with bills task analysis rough draft on table

paying price with bills task analysis final

The table is used for assessment, collection of data and progress monitoring. The steps that are problematic can be targeted individually, e.g. skip counting by 10s.

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Shaping Behavior

Shaping is a term in special ed which basically means to train a student to incrementally follow through on a sequence of substeps to accomplish a task. B.F. Skinner coined a different name for this which he called operant conditioning. The top photo below shows “Skinner’s box.” The pigeon was placed in the box and when it pecked at the metal wall a pellet of food was presented to it. Eventually the reward was given as the pigeon pecked closer and closer to the disk in the wall where its beak is in the photo. Finally, it learned that by pecking this disk was the only means of getting the pellet.

In special education, this shaping is used to train a student to achieve specific outcomes. In the bottom photo below my son Gabriel is playing with his favorite all time toy, Legos. As is the case with many with autism, he would not look at people in the eye. His therapists trained him to make eye contact by first holding his Legos in the air until he requested them. Eventually the Legos were held incrementally closer to the therapist’s eyes. The second to last step was to hold them next to the eyes and finally he had to look into the therapist’s eyes before getting the Legos.

This same approach can be used to train students to attempt problems, think critically, follow classroom norms such as the appropriate steps for starting classs and any other desired behavior.

skinner box

lucas and Legos

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Homework as a Challenge Part 1

In another post  I describe a former 7th grade student of mine who was classified as having asperger’s and tested at a 1st grade or kindergarten math and reading level. He was not doing his homework. His science teacher explained that he was prompting the student to copy the homework. The student’s guardian explained that she asks to see his homework but he didn’t have any. I set out to research why.

The first photo below shows what he copied for his science homework in his agenda. Immediately apparent is the problem with writing, spelling and simply making sense of the assignment. I took his agenda to the science classroom and found what he had copied (2nd photo below). It was not even the assignment but the key sections for a lab report.

My takeaway from this is as follows:

  • A problem with homework completion can be the result of a variety of causes.
  • The most common approach to supporting homework completion that I have seen in 17 years is to prompt the student to copy homework.
  • General ed teachers can easily overlook the complexity of completing homework that a child with a disability can encounter.
  • Even the act of completing homework is a skill with numerous steps that can be broken down by a task analysis (see my post about homework and reading).
  • As Dr. Molteni, one of my professors overseeing autism studies at the University of Saint Joseph often stated, students with autism who find success usually have an individual who takes a personal and direct role in helping the student. That is certainly what this student needed.

I.C. copy of hw from board into agenga

science report outline on board

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Shaping Critical Thinking and Self-help Skills

Below is an example of a puzzle I use to train students to make an effort and to think about problems. I have found that many students not only have a learned helplessness when it comes to math but they have been trained to follow steps mindlessly. Following a task analysis approach the first step is for students to find an entry point to a problem. They also need to feel comfortable taking risks. Slowly moving the students towards solving more complicated problems is called shaping.

Below you can see that the student made a more simplistic attempt. Given that this was done the first day of school I was very pleased with the effort.

How many squares problem

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