Tag Archives: color coding

Inclusion vs Proximity

Some educators and parents of students with special needs are unclear about what is meant by the term inclusion. Some think it is having the student with a disability in the same location as “nondisabled peers.” Some think it involves doing the same exact tasks or academic work.

Sesame Street figured this question out years ago. The girl in the red shirt in the video below (video set to start with her) was experiencing inclusion, not because she was next to the other kids. She was not jumping rope but was most certainly included and appeared to love it! (Note: “inclusion” is not defined in IDEA, so formally this issue would be one of least restrictive environment.)

Below is a genius representation of inclusion (not my idea).

It appears that inclusion is sometimes viewed as a dichotomous choice. For example, I observed the student in a school who was the most severely impacted by a disability sitting in a grade level history class during a lesson communism. This was an effort to provide inclusion but was he was experiencing proximity.

Below is an example of inclusion for a student with autism in an algebra 1 class. Below left is a typical math problem. To the right is one I created for the student with autism. It was designed to help him understand the concept of matching inputs and outputs without using a lot of the math terminology. In his case, the focus in math was on concepts.

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Plotting Points Introduction

Plotting points is surprisingly challenging for some students. Here is an approach originated by one of my former math teacher candidates in a methods class I taught. This approach uses the analogy of setting up a ladder.

First, determine where to position the ladder, then climb the ladder. (brilliant and not my idea). Plot the point on the ladder, then pull the ladder away. The context includes green grass for the x and yellow for y because the y axis extends to the sun. This is shown on a Google Jamboard with moveable objects (you can make a copy to edit and use on your own).

Next, fade the ladder but keep the color – note the color of the numbers in the ordered pair. 3 is green so move along the grass to the 3. Then yellow 5 so move up 5, towards the sun.

Now, keep the the colored numbers and still refer to the green grass (faded) and sun (faded).

Finally, on a handout students can use highlighters as necessary to replicate the grass and sun numbers. The highlighters can be faded to result in a regular plotting a point problem.

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Simplifying not so Simple Equation Solving

Several special ed teachers identified solving multi-step equations as the most challenging math topic to teach in middle school math. Here is my approach to teaching multi-step equations like 3m + 4m + 1 = 15. .

First, I use a task analysis approach to break down the math topic like we cut up a hotdog for a baby in a high chair. MOST of the steps involved are prior knowledge or prerequisites skills. I present these in a Do Now (warm up, bell ringer, initiation) – see image below. This allows me to fill in the gaps and to lay the foundation for the lesson. The prerequisite skills include simplifying expressions and solving 2 step equations. I also present meaning for the equation with a relevant real life problem that is modeled by this equation. By attempting the walkathon problem without the “mathy” approach, the students will more likely understand the equation and why they add 3m and 4m.

After reviewing the Do Now I use Graspable Math, which is a free online application that allows users to enter their own expressions and equations. These can be manually simplified and solved by moving parts around. Here is a tutorial on how to do this. This allows them to manually work with the simplifying and the equation before working on the handout, in a concrete-representational-abstract approach.

This is followed by a scaffolded handout with the use of color coding. I have student work on the first step in isolation as that is the new step (the other steps are prior knowledge and were addressed in the Do Now). This avoids all the work on the other steps that can result in sensory overload and allows me to address mistakes in the new content immediately.

This handout can have the equations removed and be used as a blank template to follow. In turn this would be followed with regular solving worksheets.

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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

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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.

 

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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.

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Corresponding Angles in Stain Glass

corresponding-angles-in-glass

Found this (above) cool example of corresponding angles (see photo below for explanation). This window photo could be a nice introduction to this type of problem by printing it out on paper and having students match angles as the teacher shows the photo on the Smart Board or screen.

screenshot-2017-02-28-at-8-56-25-am

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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.

 

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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

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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

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