Category Archives: special education in general

Math Rulz

Screenshot 2017-03-23 at 11.45.11 AM

Math is challenging for various reasons:

  • It involves numbers and not just words that we use on a regular basis to communicate.
  • It is a language all of its own so students have to learn the language as well as the concepts.
  • We teachers sometimes make learning the math more challenging.

I want to elaborate on this last reason. The photo above speaks to this. We present a topic. If the students struggle there is a tendency to “dumb down” the topic to rote memorization of a meaningless set of steps. Below is 1 of dozens of examples of memorization tricks we use. I call these Math Rulz.

Integer opreations for Math Rulz

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Zone of Proximal Development


The photo above shows 3 levels of task demands for children based on Vygotsky’s levels of development.

  • On the left is a level in which the student can readily perform the task independently, i.e. he is doing something he already knows how to do.
  • On the right is a level that is too challenging for the student to accomplish independently. It is something he cannot do and does not know how to do.
  • In the middle is a sweet spot. The level involves tasks that are accessible to the student but with support – scaffolding.

In reading this is known as the “instructional level” – see photo below. Reading material is evaluated by determining how challenging it is for a student. Material that the student can read independently allows for some growth in reading ability. Material that the student finds too challenging would not allow for substantive growth. In the middle is the sweet spot – the Zone of Proximal Development.

Instructional Level

We can do the same with math using scaffolding. In the photo below is work performed by a former 7th grade student of mine with Asperger’s who tested at a 1st grade math level. I used colored pencils and 2 sided tokens to support his work with integers (red for negative and yellow for positive) in a CRA approach. The color coding and tokens were like the swimmies in the photo above of the child in the ZPD. Eventually these supports were faded. Throughout this process I was constantly pressing him to do more with a little less assistance.

adding integers chips and colored pencils

I want to emphasize 2 major points regarding this.

  • Substantive learning occurs when a student has to step beyond his or her current ability level – the ZPD.
  • Often in schools educators avoid this, especially for students with special needs, because we want students to be engaged and successful (in the short term). We often confuse being active with learning. The guy on the tricycle in the top photo was performing a task but was he learning? (Note: this is not a student with special needs but a guy having some fun.)

Here’s are a video that fleshes out this idea.

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Stratford SEPTA Presentation: Making Math Accessible for All Students


Presentation by Randy Ewart at Feb 27, 2017 SEPTA meeting

Link to Drop Box folder with documents to share.

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List of Performance Points



Painting the letters on the ground is a performance point for the person responsible for this task. The task was discussed at some other time and location. Performance points, as explained in another post, are the situations or locations or times that a person has to perform a task. For students with special needs this is where special education gets real. It is where the supports play out. For students with more severe disabilities, e.g. ADHD, Autism or Down Syndrome, most if not all performance points require some support so identifying these points is important and often overlooked.

Below are a list of performance points students encounter in k-12 education.

  • transition between classes
  • using a hall pass
  • arriving or leaving school
  • riding a school bus
  • transition to and from lunch
  • transition to and from specials
  • gym
  • playground/recess
  • entering and starting class
  • packing up and leaving class
  • transition between activities during class
  • choice or down time during class
  • following directions given in class
  • retrieving, using and returning class materials
  • sharpening pencil
  • asking permission to use a pass
  • identifying appropriate reasons to use a pass or to ask a question
  • responding to questions or participating in class discussion
  • paying attention to presentations
  • group work
  • individual work
  • homework
  • studying for an assessment
  • long-range projects
  • bringing materials to class
  • organizing notebook and book bag
  • using a notebook effectively, e.g. finding and following examples
  • interacting with classmates in a socially appropriate manner (during classwork, free time, down time, in the hallway, at lunch, at recess) – note: socially appropriate would need to be defined with observable behaviors
  • empathizing with others
  • reciprocating in a social conversation
  • curtailing behavior when presented with negative feedback
  • initiating conversation
  • greeting others appropriately – initiating and responding
  • identifying non-verbal cues and communication

Certainly there are more. Please comment below if you want me to add anything to the list.

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Standards vs Deficits and Long Range Plans


I’ve had discussions with multiple caregivers and parents recently about IEP objectives and evaluation/assessment. I think this is not only an important issue but is an issue that is a foundation for special education.

The purpose of special education, as established in IDEA, is outcome based. The focus is on the future life of the student. Decision making and services are made in this context. With this in mind I believe evaluation/assessment and the development of the IEP, especially objectives, fall under this context. There should be an alignment to the long range future of the student.

Often the focus of special education is on deficits. Evaluations identify deficits and the programming is developed to address the deficits. Certainly many or most educators are conscientious of long range outcomes but the deficits are the priority. Contrasting this is a standards based approach. I do not mean every student working towards grade level work as this would be entirely inappropriate for severely impacted students (like my son). I mean more of an outcome based focus with long range goals as the priority. If the purpose of special education is to prepare students for life after K-12 education then the standards or outcome based approach is necessary. A deficits based approach can result in progress but progress that does not translate into necessary preparation for the future.

Here’s an analogy. A person gets up in the morning and has to go to work. She has a range of tasks from the essential, e.g. getting dressed, to the desired but not essential, e.g. send an email to a friend or make a cup of coffee to go. As is often the case with me, she runs out of time. Maybe she can try to send the email but then has no time for the coffee. Maybe she needed to print a report for work but overlooked it because she was preoccupied with all the other tasks. At some point she has no choice and has to leave regardless if the coffee is ready or the report is printed.

Our kids have a limited amount of time in special education. Like the person going to work, at some point our kids are exited from IDEA regardless if they are prepared. We know a great many of our kids are not prepared. A deficits approach prioritizes urgency at the expense of important. The email is sent but the report was overlooked. A standards/outcome based approach focuses on importance not urgency. This doesn’t mean deficits are overlooked but they are prioritized.

In my experience in school and in working with many different parents I have found a focus on deficits.

  • A sophomore in high school spent an entire year on arithmetic (doing this by hand) and basic pre-algebra skills because these were deficits. The goal is for him to go to a community college where he would qualify under ADA for use of a calculator.
  • A junior moderately impacted by autism was taking a basis algebra class. His postsecondary plans focused on some level of independence and maybe a supported work placement. He couldn’t count money but he was being taught how to simplify 3x + 2x.
  • Often, accommodations, e.g. teacher prompts, are included in assessment of IEP objectives “because the student needs this to be successful.” I’ve heard this in multiple situations.

Contrast this with another situation. I helped a family with a middle school student with autism. His mother explained to me that they had a goal of him having some type of job and some level of independence. He was very much interested in cars and working with cars in some capacity for his job. The math needed for auto repair is mostly measurement. We mapped out a muti-year plan for his math to focus on measurement and consumer math. He was not going to learn to simplify 3x + 2x but would focus on what a 5/16 inch wrench is and what is meant by 5/16 of an inch.

The first student I ever helped when I began my work in special education was a sophomore with aspergers. He received ineffective special education support and entered community college with the same challenges and gaps in math as he had his sophomore year. I served as a kind of case manager for him as he worked through community college. He needed help with study skills, math content, stress, completing work etc. This semester he is likely to graduate from community college and plans on transferring to a university.

Again, I am not proposing that deficits be marginalized. The deficits can be prioritized based on long range goals and addressed accordingly. The photo of the table above shows 3 categories of post-secondary outcomes and the level of focus on standards and curriculum.

  • Some level of independence – no formal vocational training or college course work
  • Some vocational training or college course work or a community college certificate or degree.
  • 4 year college

My position is that the current student work and support should be aligned with the appropriate outcome.

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Address Challenges at Performance Points


In the photo above you see a contrast between how children learn and how educators often teach necessary skills. Children learn to ride a bike by actually performing the target skills. This is a performance point – the setting in which the child actually performs. In school students are often taught necessary skills in isolation, away from the performance points. Imagine teaching a child to ride a bike by having him sit at a desk while the parent points out all the steps for riding a bike.

Often accommodations and supports are provided in isolation or out of context. Students with autism have lunch buddies in a contrived setting with an educator leading conversation. Students with ADHD have a weekly time to organize their notebooks. Students who have trouble functioning in a general ed classroom may be pulled out as a result.

Below are a couple of examples of how support can be provided at the points of performance. The photo below shows a checklist I used for a students with autism in my algebra class. They would follow the checklist and self-evaluate by checking off each step as it was completed. They were learning how to perform necessary skills at the point of performance.


Another overlooked point of performance is in organizing a notebook. Students should organize a notebook while IN CLASS and on a DAILY basis. I use the rubric below to help support students with this task.


Dr. Russell Barkley, an expert on ADHD, talks about performance points for students with ADHD in his book and in his ADHD Report. This focus at the “points of performance” can and should apply to any student with a disability (and students in general).

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Math Rulz

math rulz

Despite Common Core for State Standards, a multitude of initiatives, best practices, differentiation etc. math is challenging for most students. A major reason is that math is often taught in piecemeal fashion with an attempt at rote memorization of an overabundance of rules. I compiled many of these rules into a single document.

Imagine our kiddos receiving special education services who already have trouble grasping various topics having to memorize all these facts.

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Standards Based IEPs

At the turn of the century education has seen a standards based reform movement, e.g NCLB. IDEA 2004 reflects this with a change in the focus of an IEP towards curriculum standards. What does this mean? The focus of academic based IEP goals and objectives should be strictly aligned with the curriculum standards. This helps to make the general curriculum accessible for all students – to the extent possible.

For example, in the past a math IEP objective may be written based on weaknesses found in psychological tests regardless if this was in the curriculum covered in the life of the new IEP. Maybe a student had trouble with calculations with fractions on the testing so an objective would focus on improving these types of calculations even if the class was not going to cover calculations with fractions.

These new types of IEPs are called Standards Based IEPs. Here are a couple of links.

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Purpose of Special Education

purspose of special educationAfter taking a course in special education law I have come to realize that most parents and educators, including many special education teachers, do not know the purpose of special education. I am not an expert but have researched the issue beyond simply reading IDEA. Here is a file with slides (including the one in the photo above) from a presentation I give on this topic.

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