Category Archives: special education in general

Critical Thinking

Often we adults engage students with closed-ended questions and then consider this as having a conversation with the student. I witnessed this first hand in a high school consumer math course I co-taught. The adults sat with the students the first day after December break for a conversation about their break. The questions were consisted of and were similar to the following. “Did you have fun?” “Did you eat a lot?” For some, like my son, this is appropriate. For many others, we are offering low hanging fruit that does little to move them forward.

Ask open-ended questions that prompt the student to engage in critical thinking such as analyzing and evaluating – below, courtesy of Jessica Shabatura. Work this into IEPs and 504 to have teachers implement this. For example, I asked the students what they liked about break. Then I asked why they liked it. Here is an example of me questioning my son, who does not have a disability, when he was maybe 4.

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Curriculum Based Assessments

Most testing for IEPs involves standardized testing. As I wrote in a previous post, this is important testing but is not sufficient. A major focus of special education is to make the general education accessible as possible. Hence, curriculum based testing is an important complement to the standardized based testing. For example, the KeyMath3 assessment will speak to problem solving or geometry but those are broad categories. If I am working with a 3rd or 4th grade student, I would be interested in the student’s level of mastery in computing the perimeter of a rectangle.

Also, math is very different than reading because math has a variety of categories of math, aka domains. A student testing at a 4th grade level in math does not reveal much information, as I explain in this previous post.

When I conduct evaluations or assessments, I go to the Common Core Standards and assess each with curriculum based problems, see below. The photo shows my planning document and then I transfer the problems to a student handout for the student to complete.

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Secondary Characteristics: A Performance Factor

For students with a disability, performance does not align with ability.

In my view, there are 3 different categories of performance factors: the disability, gaps in achievement, and secondary characteristics. (Percents are contrived to provide a visual representation.)

To address these secondary characteristics, which manifest as a set of behaviors, I suggest a focus on shaping with a token board.

Here is a video explaining this.

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The Process of Learning

Often education and special education focuses solely on content. In turn, the content may focus only on steps and facts to memorize as opposed to ideas and concepts.

A challenge for many students during k-12 education then in post-secondary life is being an independent, self-sufficient learner. The adults supporting them often focus on short term success at the expense of long term success in terms of independence.

I propose shaping the independent learning process early and often. An activity I use is completing jigsaw puzzles.

With guidance, completing a puzzle can activate 3 processes of learning: critical thinking, mindfulness, and perseverance. By having a strategy of identifying the side pieces of the puzzle, the student is analyzing pieces which is critical thinking. Paying attention to the shapes of pieces in mindfulness. Continuing to try different pieces when pieces don’t fit is an act of perseverance. Start with fewer pieces and focus on the process, then use increasingly more pieces of the same puzzle before moving on to another puzzle.

Here is a link to a video of me explaining this.

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Math is a Language

The Gutenberg printing press was revolutionary because it provided a faster way to share words. In turn, these words and how they were structured were representations of ideas used to make sense of the world around us.

Math is a language with words and other symbols that also makes sense of the world around us. We consume and know more math than we realize or allow ourselves credit for.

When buying the latest iteration of an iPhone, we may call forth algebra. How much will you pay if you buy an iPhone for $1000 and pay $80 a month for service? Well, that depends on how many months you will use this iteration before moving on to the next iPhone. The number of months is unknown so algebra gives us a symbol to represent this unknown number of months, x (or n or whichever letter you want).

Just as there is formal and informal English (or other language), we can engage algebra formally or informally. You don’t need to write an equation such as y = 1000 + 80x to figure out how much you will pay. You can do this informally, compute 80 times 10 months + 1000 on the calculator. Then try 80 times 12 months etc.

Math provides us a means of organizing and communicating ideas that involve quantities like the total cost for buying an iPhone.

The difficulty in learning math is that it is often taught out of context, like a secret code. In contrast, a major emphasis in reading is comprehension through meaning, such as activating prior knowledge (see below).

In fact, math absolutely can and, in my view, should be taught by activating prior knowledge. My approach is to work from where the student is and move towards the “mathy” way of doing a problem.

Without meaning, students are mindlessly following steps, not closer to making sense of the aspects of the world that involve numbers.

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Karen Linder (advocate and parent of a son with a disability) and I are collaborating on a series of Parent User Guide materials for parents. The goal is to scaffold parent efforts to use the IEP. We are presenting documents in smaller chunks to make it easier for parents to understand the steps they can take without being overwhelmed with an already challenging endeavor of advocating for your child’s needs.

Our first installment is part 1 in understanding IEP objectives (see screen shot of front page above). There is a document with templates to use and an accompanying video to provide additional support in how to use the templates. Please share feedback so we can improve our efforts to help parents.

Please feel free to reach out to us if you think we can be of service or if you have questions.

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Real Life Math VS “Mathy” Math

In working with students, parents and IEP teams, I find that there is an assumption that math at some point, possibly beyond arithmetic, is simply a science fiction movie that is minimally related to real life. I hear from students as well as adults, statements like, “algebra, when are we ever going to use it?” My response is, ALL THE TIME!

The math we often present in school is a “mathy” version of the math we encounter in life. For example, the top photo below shows a pizza menu and a situation that is realistic. The calculator screen shot below the menu shows how we likely would solve the problem using a calculator on our phone.

Below is the same type of problem, but solved using “mathy” math. How many of us (besides me) are doing this at the pizzeria?

The point is, we engage in algebra but maybe do not use all the symbols and vocabulary of algebra, e.g. when we typed in 2.25 repeatedly in our calculator, we were working with the math term “slope.”

This has implications for secondary students whose post-secondary plans do not include college. If the math class is teaching “mathy” math but you want your student to learn math as it is used in real life, then an alternative math course is needed. This could be addressed through the IEP.

 

 

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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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Long Range Planning in Regards to Math for Students Receiving Special Ed Services

Below is a photo of a hyper-doc that I use to map out a long range plan for math services and academics for students receiving special education services. Here is a link to a video explaining how the document is organized and how it “works.” (Note, the image of the document on the video is not crisp, so I suggest you look at the handout while watching the video.)

The document contains several links to resources such as videos, websites and blog posts that provide additional information. Feel free to reach out to me using the Contact Form on this page if you have questions or would like input. I am happy to help.

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