Problems like the addition problem below are often viewed by adults as straight forward. This perception can make it difficult for adults, including teachers and even special education teachers to help students who struggle with it.
I find that the math teacher candidates and special education teacher candidates struggle with breaking down math topics, especially “easy” ones like the one below, into simple steps. To help students who struggle with math breaking down the math topic is imperative. The analogy I use is to break the topic down into bite-sized pieces like we cut up a hot dog for a baby in a high chair.
For new teachers I use a formal task analysis approach to teach candidates how to cut up the math into bite-sized pieces. A task analysis for the problem above was an assignment given to a group of graduate level special ed candidates. As is common, they overlooked many simple little steps hidden in the problem. These steps are hidden because they are so simple or so automatic in our brains that we don’t think about them. See below for how I break this topic into several pieces or steps. For example, before even starting the addition the person doing the problem has to identify that 43 is a 2-digit number with 4 in the TENS place and 3 in the ONES place. Understanding that the problem is addition which entails pulling the numbers together to get a total (sum) is an essential and overlooked step. If a student struggles with a step the step can be addressed in isolation, as I show in another blog post.
A reader asked about an algebra 2 problem and shared (below) his effort to cut up the math into bite-sized pieces. I greatly appreciate his effort because he is trying to meet student needs. While this post is very “mathy” I want to make a couple of points to the readers. First, I wrote out a detailed response (2nd photo below). Second, in both of our efforts we attempted unpack as much as possible. This is what our students need. Also, the reader is developing his ability to do this unpacking and if he continues he will become increasingly more adept at this skill (growth mindset). That means his future students will benefit!
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.
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.
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.
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).