Information Processing Analogy – Big Picture

Effective instruction is effective because it addresses the key elements of how the brain processes information. I share an analogy to help adults (parents and educators) fully appreciate this.

Information Processing Model

Below is a model of information processing first introduced to me in a master’s course at UCONN.

Here is a summary of what is shown in the model.

  1. Human senses are bombarded by external stimuli: smells, images, sounds, textures and flavors.
  2. We have a filter that allows only some of these stimuli in. We focus on the ones that are most interesting or relevant to us.
  3. Our working memory works to make sense of the stimuli and to package it for storage. It is like a computer, if there is too much going on, working memory will buffer.
  4. The information will be stored in long term memory.
    • Either it will be dropped off in some random location and our brain will forget the location (like losing our keys)
    • Or it will be stored in a file cabinet in a drawer with other information just like it. This information is easier to find.

Analogy to Classroom Learning

Here is an analogy to what happens during school instruction. You are driving down the street, like the one shown below.

There is a lot of visual stimuli. The priority is for you to pay attention to the arrows for the lanes, the red light and the cars in front of you. You have to process your intended direction and choose the lane.

Other present stimuli may be filtered out because it is not pertinent to your task: a car parked off to the right, the herbie curbies (trash bins), the little white arrows at the bottom of the photo. There is extraneous info you may allow to pass through your filter because it catches your eye: the ladder on the right or the cloud formation in the middle.

Maybe you are anxious because you are running late or had a bad experience that you are mulling over. This is using up band width in your working memory. Maybe you are a relatively new driver and simple driving tasks eat up the bandwidth as well.

Impact on Students

For students with a disability that impacts processing or attention, the task demands described above are even more challenging. A student with ADHD has a filter that is less effective. One with autism (a rule follower type) may not understand social settings such as a driver that will run a red light that just turned red. Another with visual processing issues may struggle with picking out the turn arrows. Their brain may start to buffer, like a computer.

What is Buffering? — Causes and How to Stop It - Dignited

Specific Disabilities

Effective instruction would address these challenges proactively. Here is a video regarding learning disabilities (LD) that summarizes the need in general for teachers to be highly responsive to student needs. This link is for a great video that helps makes sense of what autism in terms of how stimuli can be received by those with autism (look for the street scene). Another is a video of a researcher explaining how ADHD responds to sensory input (he gets to a scenario that shows how impulsiveness can be a factor).

What to Do

To address these challenges:

  • Reduce the amount of information presented in a lesson segment, i.e., chunk the lesson.
  • Use color, e.g. highlighters – this helps students see the different parts of a problem
  • Use hands on and visual representations in lieu of words – words are symbolic and abstract, start with forms of information easier to process.
  • Connect information to prior knowledge or make it relevant.
  • Scaffold the work to provide supports for unpacking the concept, following the steps, or identifying the parts.
  • Relevant situations – learn by doing. Have the instructional setting mirror the real life setting as much as possible. Better yet, conduct instruction in the real life setting.

Adding ones digits in 2 digit numbers with carrying

A major obstacle in math for many students with special needs is carrying in addition problems. Below is a task analysis approach.

First, I target the step of identifying the ONES and TENS place in the 2 digit sum in the ONES column (below it is 12). In a scaffolded handout I create a box to for the sum with the ONES and TENS separated. At first I give the sum and simply have the student carry the one.

sum of ones given.jpg

Then I have the student find the sum and write it in the box (14 below). Once mastered I have the student write the sum and carry the 1.

sum of ones given

They would have mastered adding single digit numbers before this lesson. I revert back to single digit numbers to allow them to get comfortable with writing the sum off to the side without the scaffolding. (In the example below I modeled this by writing 13.)

sum of ones with color no scaffolding

The last step is to add the TENS digits with the carried 1. I use Base 10 manipulatives to work through all the steps (larger space on the right is for the manipulatives) and have the student write out each step as it is completed with the manipulatives.

sum of ones with carrying with base 10 blocks first

Finally, the student attempts to add without the scaffolding. I continue with color but then fade it.

adding 2 digit numbers with carrying with color no scaffold

Color – Easy to Implement Strategy

When my son was in preschool I asked him who was in his class. He replied, ” Natalie, she’s the yellow heart.” Children learn color before they learn words because it is easier to process.

preschool shapes and colors

This is found in children’s toys with color used to guide use of toys.

keyboard for childrens book

The obvious use of color in real life in traffic lights. The colors represent different concepts with red being used universally in the U.S. as representing stop. Color is used to partition an object into sections, as often seen in maps of areas with different sections. Think of how many highlighters are sold to college students to help them highlight key passages in textbooks.

traffic lightsFenway Park, Boston Red Sox's Ballpark - Ballparks Of Baseball in Miller Park Seating Chart With Seat Numbers Image

The use of color help convey information, especially sections of a whole is an effective and easy to use instructional or support strategy.

The top two images below show my earliest attempts to use color. The student for whom this was used was a 7th grade student with asperger’s who tested in math and reading at a 1st grade level.

In lieu of referring to the “horizontal line” I can refer to the “yellow line” as in “find the yellow 3” for plotting the point (3, -2). Color, as in the aforementioned yellow heart, is much more intuitive for students, especially those with a disability.

coordinate plane

Color was used for the same student to represent positive and negative numbers, first with concrete tokens then with colored numbers on paper.

adding integers chips and colored pencils (2)

More examples are shown below. Color helps a student focus on the different parts of an equation or different parts of a ruler.

linear equationsruler

Color can also help organize a room into different parts. Each color represented different courses I taught, e.g. green was used for algebra 2. The room is more organized because of the sections outlined in color. Consider how this can help a student with ADHD, autism or an executive functioning disorder.

 

classroom

Mailbag Jan 26, 2019

Are you a parent of a student with special needs who is struggling with a math topic? Are you a teacher figuring out how to differentiate for a particular student on a math topic? Pose your question and I will offer suggestions. Share your question via email or in a comment below. I will respond to as many as I can in future mailbag posts.

Here is a topic multiple educators and parents ask about:

I don’t want my child to be stuck in a room. He needs to be around other students.

Randy:

Often we view situations in a dichotomous perspective. Inclusion in special education is much more nuanced.

Image result for for in the road

In math if a student cannot access the general curriculum or if learning in the general ed math classroom is overly challenging then the student likely will not experience full inclusion (below) but integration (proximity).

For example, I had an algebra 1 part 1 class that included a student with autism. He was capable of higher level algebra skills but he would sit in the classroom away from the other students with a para assisting him.  Below is a math problem the students were tasked with completing.  Below that is a revised version of the problem that I, as the math teacher created, extemporaneously for this student because the original types of math problems were not accessible to him (he would not attend to them).

mapping traditional

comic book mapping

I certainly believe in providing students access to “non-disabled peers” but for students who are more severely impacted I believe this must be implemented strategically and thoughtfully. Math class does not lend itself to social interaction as well as other classes. If the goal is to provide social interaction perhaps the student is provided math in a pull-out setting and provided push-in services in other classes, e.g. music or art.

Here are the details of example of a push-in model I witnessed that had mixed effectiveness.  A 1st grader with autism needed opportunities for social interaction as her social skills were a major issue. She was brought into the general ed classroom during math time and sat with a peer model to play a math game with a para providing support. The game format, as is true with most games, involved turn-taking and social interaction. The idea is excellent but the para over prompted which took away the student initiative. After the game the general ed teacher reviewed the day’s math lesson with a 5-8 minute verbal discussion. The student with autism was clearly not engaged as she stared off at something else.

Inclusion is not proximity.

 

Function Notation for Algebra

Below is a video of a lesson I recorded on function notation using the Explain Everything app. The lesson starts by addressing the concept of function notation by connecting it to the use of the notation “Dr.” as in Dr. Nick of Simpson’s fame. The lesson builds on prior knowledge throughout with a focus on color coding and multiple representations.

This videos shows an instructional approach to teaching function notation and concepts in general and video lessons can be used for students who miss class or who need differentiation.

Making Slope Less Complicated

slope-graph-real-life-application

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.

 

Introduction to Slope

which-jobSlope is one of the the most important topics in algebra and is often understood by students at a superficial level. I suggest introducing slope first by drawing upon prior knowledge and making the concept relevant (see photo above).  This includes presenting the topic using multiple representations: the original real life situation, rates (see photo above) and tables, visuals,  and hands on cutouts (see photos below).

10-dollars-per-hour-graphA key aspect of slope is that it represents a relationship between 2 variables. Color coding (red for hours, green for pay) can be used to highlight the 2 variables and how they interact –  see photo above and below.5-dollars-per-hour-graph

The photo below can be used either in initial instruction, especially for co-taught classes, or as an intervention for students who needs a more concrete representation of a rate (CRA). The clocks (representing hours) and bills can be left in the table for or cut out.cut-outs-hours-bills

Analyzing a Graph

analyze-graph-using-color

Students can hit a road block at the steps that appear to be very simple. For example, in the problem below the students are prompted to find the highest point on the graph. Many think the graph refers to the entire coordinate plane and they pick 5 as the high point. It is the highest point on the y-axis but not the graph. I introduce the problem by highlighting the actual graph in pink and explain that this highlighted line is what is meant by the graph.

Analyze Graph Using Color Coordinate Plane Only - Edited.jpg

The use of color also helps students distinguish between the x and y axes and what the variables x and y represent in the context of the problem (# minutes and # kilometers in this problem) – see photo above. This problem also involves plugging in a # for x (blue) IN the function (red). In the photo below you see how I use color to help emphasize this.

analyze-graph-using-color-function-notation-only-edited

Color Coding for Calculus

IMG_20160223_081145571

This is an example of color coding (highlighting) to help make a calculus problem accessible. You don’t have to know calculus to see that the yellow sections (left and right of the 0) are going up while the green section is going down. Color coding breaks a whole into parts that are easier to see and understand – works in preschool all through calculus!

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