Category Archives: Differentiation

Problems with Determining Math Grade Level for a Student

A common scenario involves a school official reporting out the grade level in math for a student. For example, a 7th grade student I was helping had tested at a 4th grade level. As a result, the student spent much of her 7th grade year working on 4th grade math.

There are a couple problems in establishing a grade level in math. First, unlike reading, math is not nearly as linear. The image below shows a breakdown of the Common Core of State Standards math categories, called domains. In a video, I use this graphic to unpack why it is more challenging to determine a single level of ability for math. In short, the reason is the student could be doing well in some categories and doing poorly in others. Second, the testing used to establish ability level can be problematic for the student. For example, the student may not have the stamina or attention span to endure a longer assessment.

If you are presented with a single grade level as an indicator of math ability, I recommend that you ask for a breakdown by category and how your student will be provided differentiation to address gaps. This is more appropriate than plowing through all of the math at a lower grade level.

 

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Wicked Cool Simulation Site

I used this site, Explorelearning, with a 7th grader with Aspergers who tested at a 1st grade math and reading level. We used the Photo Synthesis Lab (screen shot below) to gather experimental data on the hypothesis “what helps flowers grow?” He won at the school level and went on to district competition.

(As of April 2020 you can get free 60 day unlimited access.)

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IXL and Google Classroom

Here is what we are doing at home during school closure time. I created a Google Classroom (anyone with Google account can create a class on the Google Classroom app) and posted links to IXL topics (photo at bottom). (NOTE: this is one method I use to differentiate at school.) If the school is providing online work, you can enter this into the classroom as well.

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Worksheet Websites I Use and Recommend

The following are screen shots of online math worksheet websites I use. The variety and the options in the criteria you select for your worksheets for some of these sites allows for differentiation in the classroom.

 

I will start with my favorite site, Math-Aids.com. This site allows for dynamic selection of criteria for each handout (see 2nd photo below) such as choosing the types of coins in problems for counting out the total value. The coin images are outstanding! It also offers content up to Calculus.

 

 

Super Teacher Worksheets is often used elementary schools. It offers content in science and language arts as well. It requires a $25 annual subscription which I easily find to be worthwhile.

 

 

Common Core Sheets is very useful site if you want to find handouts for specific standards by grade level (see 2nd photo below). It offers multiple versions of each handout.

 

 

 

Dads Worksheets provides a large bank of worksheets – multiple versions of each worksheet.

 

 

Math Worksheets 4 Kids offers multiple versions of each worksheet and content in science and language arts. There are many worksheets that provide unique support in how the work is presented, e.g. the Ratio Slope worksheet shown in the 2nd photo below.

 

Visual Fractions – title speaks for itself.

 

Worksheet Works is my 2nd favorite. It offers options in the criteria you choose, e.g. difficulty level (2nd photo below). They also offer unique types of handouts such as a maze with math problems to solve to find the path (2nd photo).

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Counting Money as a Game

The Allowance Game is retail game tailored to students who are learning to count money.

 

I revised it to make it more authentic and more functional.

  • I changed some money amounts to necessitate the use of pennies (see below)
  • I use real dollars and cents to provide more opportunities to handle real money
  • I differentiate by creating different task demands. For example
    • I was using the modified version with 2 clients
    • One was learning to count out dimes and pennies only, but could manage ONES simultaneously
    • This student would also be provided a coin chart I use to teach students how to count with coins
    • The other was practicing with ONES, and all coins up to a quarter
    • I collected data on a data sheet – 1 per student

The students loved playing the game, it was engaging so they practiced the counting out money, I was able to collect data, and I was able to differentiate. When I co-taught a Consumer Math course, I would assign a para (instructional assistant) to facilitate the game with a couple students and to collect data.

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Asking for Examples of Mastery for IEP Objectives

To ensure the IEP team is on the same page as to what mastery of an objective looks like, the person writing the objective can take two steps:

  1. provide an example problem that would be used to assess mastery (and the example problem would have the same language as used in the objective)
  2. provide an example of a response to the example problem cited above that would be considered mastery level work

The graph below is not data. A graph is a representation of summary statistics. This summarizes the data.

The chart below does not show the actual prompts, e.g. what number was shown to Kate, but it does show the individual trials. This is data, with a summary statistics at the end of each row. Here is a link to more discussion about data, with an example of a data sheet I use.

 

The data shown below addresses the student’s effort to solve an equation. Problem 21 is checked as correct and the error in problem 22 is identified. I can use this data to identify where the student is struggling and how to help. NOTE: the math objective would use the same verb as the problem: solve the linear equation.

 

The excerpt of a data sheet, shown below shows trials in a student’s effort to compare numbers.

 

Data below shows a student’s effort to evaluate integer expressions.

 

This applies to all areas beyond math. The chart above or the data sheet I linked above show data sheets that indicate the prompt and the results, with notes. For example, if I am asking my son to put on his shoes, each row of the data sheet is a trial with the outcome and notes.

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Token Sheet to Address Target Behaviors

Perhaps the vast majority of students with disabilities need support with math. Their challenges with math can be directly related to their disability or can be the result the effects of an ongoing struggle with math. The later results in what is termed secondary characteristics.

When I work with students with a disability, I first seek out background information about the student to identify what interests them, what reinforcers (rewards) can be used to enhance their performance, and what challenges and behaviors need to be addressed. Upon gather this information, I often decide to use a token sheet that is personalized for each student.

Below is an image of such a token sheet. At the start of our work together I felt the student in question needed immediate reinforcement for work completed to get him into a groove. I was also targeting a behavior in which he would draw dots on each digit he wrote, which slowed him down considerably. He would earn a Scooby (I would circle it) in the middle column for completing his work and an extra Scooby in the right column if he wrote digits appropriately (no dots). After 2 sessions, his dot writing dropped significantly to the point that I was able to remove the column on the right. As you can see at the bottom, 5 Scoobies resulted in iPad time.

This can be particularly effective for students who have more severe math anxiety, a fear of failure, or have ADHD. Such a token sheet can be included in the accommodations page of the IEP.

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Meeting Needs Part 2

In the past year I have helped two 7th grade students who are categorized as twice exceptional (2e). Both had more severe math anxiety that impacted their performance and masked their ability. When we started both were working on elementary school level math. Within a couple of months both were working on algebra. (Both had gaps but I was testing their ability by test running higher level math with them.)

As I shared in a previous post my approach is to focus on meeting needs. I want to elaborate on this. My secret is I listen to the student… In other words, the student drives the instruction.

Here’s an analogy. You go to a frozen yogurt or ice cream store and they offer you a sample. You try a couple then go with the one you like. That’s what I do. I try out different types of instruction (samples of the ice cream) and the student tells me (verbally or by the response to the instruction) which one they want. That is the I in IDEA and in IEP.

icecream samples

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Twice Exceptional and Neurodiversity

In his 1992 trip to Australia, President HW Bush gave the backwards V for victory sign. That happens to be the middle finger in Australia.

hw and v for victory

This story parallels what we encounter in special education. Several people may encounter the same idea, image, curriculum objective, lesson etc. but have a totally different perspective (see photo below).

blind men and elephant

This is certainly true for individuals with autism and is true for students who are twice exceptional.

To meet the needs of such students we must work from their perspective and not ours. We must meet their needs. We must first take inventory of our bias and our subjectivity in how we perceive students, learning, doing math work etc. Here is a site, Different Brains, that I have not fully investigated but that looks interesting and important.

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