Category Archives: Differentiation

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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Meeting Student Needs

One of my beliefs about the education is that teaching is built on a delivery based model. If teachers take certain steps the learning will happen – an educator’s version of Field of Dreams. Often the result is a focus on having students assimilate into the teacher’s class environment. 


I subscribe to the exact opposite approach. Teacher’s should accommodate student needs as the focus of the classroom environment.


Below is a quote from a parent whose child benefited from my effort to be hyper responsive to her daughter’s instructional needs. The child had veto power over any activity or strategy I attempted. If what I used didn’t work for her I would try something else.

“Working with Randy has been life changing for my daughter. 

Math was her biggest source of frustration and no matter how hard she worked it never made sense. Teachers would tell me she was ‘doing awesome’ but she was really just following steps without understanding any of it. I thought she was going to go through life unable to even buy a candy bar without being taken advantage of.

Randy changed all that. He is able to break math down in a way that makes sense. He is able to identify what is confusing her and find different ways to explain it. He makes it meaningful for her.”

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Strategy to Individualize Instruction

It is difficult to individualize instruction in a whole class or small group setting. I created and taught the curriculum for a Consumer Math course at the high school where I teach. For a class of 10-12 students, all with an IEP, I developed an approach that allowed me to individualize the instruction for each students.

In the photo below is an example of a folder set up I used with the students in Consumer Math. Each student would have a dedicated folder, kept in the room and updated daily. The smaller paper shows the individualized agenda. The other paper shows an example of how the folder can be used as a resource. Student computer login information, accommodations like a multiplication table or notes can be secured inside the folder. The agenda would be changed out each day. (In case you are wondering about the label in the agenda, “Math Group 4.” This particular folder was used in a special education training session for teacher candidates.)

individualized folder
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Basic Skills Older Students

A widespread problem at the secondary level is addressing basic skills deficiencies – gaps from elementary school. For example, I often encounter students in algebra 1 or even higher level math who cannot compute problems like 5÷2. Often the challenges arise from learned helplessness developed over time.

How do we address this in the time allotted to teach a full secondary level math course? We cannot devote class instruction time to teach division and decimals. If we simply allow calculator use we continue to reinforce the learned helplessness.

I offer a 2 part suggestion.

  1. Periodically use chunks of class time allocated for differentiation. I provide a manilla folder to each student (below left) with an individualized agenda (below right, which shows 3 s agendas with names redacted at the top). Students identified through assessment as having deficits in basic skills can be provided related instruction, as scheduled in their agenda. Other students can work on identified gaps in the current course or work on SAT problems or other enrichment type of activities.

  • Provide instruction on basic skills that is meaningful and is also provided in a timely fashion. For example, I had an algebra 2 student who had to compute 5÷2 in a problem and immediately reached for his calculator. I stopped him and presented the following on the board (below). In a 30 second conversation he quickly computed 4 ÷ 2 and then 1 ÷ 2. He appeared to understand the answer and this was largely because it was in a context he intuitively understood. This also provided him immediate feedback on how to address his deficit (likely partially a learned behavior). The initial instruction in a differentiation setting would be similar.
  • 2018-12-20 11.20.25
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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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    UDL Approach to Presenting Notes

    write equation given slope and point

    The photo above shows an excerpt from the presentation of notes in an algebra class using an UDL approach. The following strategies are implemented:

    • Graphic organizer
    • Color coding (notice that the slope, which is a rate of change, is green for go – movement and notice the consistent use of the colors for prior and new knowledge)
    • Connections to prior knowledge
    • Chunking (before attempting numbers the presentation focuses on the contrast between new and prior knowledge)

    This allows for Multiple Means of Representation as found in the UDL Guidelines.

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    Making Formative Assessment Formative

    strategic practice follow up to FA

    The photo at the top shows a portion of a cumulative formative assessment for a student in algebra 1 part 1. At the bottom is a handout with problems aligned with the formative assessment. A copy is made for each student and the student is assigned (using highlighting) problems on this follow up handout that are aligned with problems missed on the assessment. This allows for differentiation and formative assessment for the whole class – not an easy task.  (Note: in this post the samples are not for the same student.)

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    Streamlining Differentiation

    Photo below shows a grid I use to identify the daily activities for my 12 high school Consumer Math students (all with IEPs) in an 86 minute block.IMAG3910

    Our daily agenda is comprised of a warm up puzzle (to get them settled and to allow me to coordinate with the other adults – between 2 and 4) and two rounds of activities. Each column is used for a student. The “C” indicates computer use (we use IXL Math mostly and have 4 computers in the room) and the colors indicate the adult supervising.

    Each student has a manilla folder which contains all handouts needed, including the daily puzzle, and the IXL modules to complete taped to the inside front cover.


    In a given day we may have different students counting nickels and pennies, identifying coins, identifying bills needed to pay a given price, computing sales tax and total price and creating a monthly budget on Power Point, with photos. The system allows me to track the many details.

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