Category Archives: special education in general

College Preparation and Retests

In a recent Facebook group for high school math teachers, an interesting discussion arose about retests and how to respond to students who have a low score on a given test. A common perspective that I shared for a time is that we should eschew retests as we are preparing students for college. In this post I offer counter points to this argument, and attempt to unpack the college preparation issue. The focus is on math.

It appears that colleges universally have placement tests. Below are excerpts from universities in Florida, Texas, California, Washington, Nebraska, and Connecticut, along with a sprinkling of 2 year schools from some of these states. If a student makes an A in precalculus in high school, that does not qualify the student to take calculus or even to retake precalculus! A test score is required, whether it is the SAT or the college’s placement test. Indirectly, this appears to show that the colleges are not taking high school results at face value. Whether the student took a retest or not, or didn’t need one he or she still must prove content mastery to some degree.

Then consider what is happening at colleges. Dr. S.A. Miller of Hamilton College wrote an essay about grades in college (excerpt below left). In it, she cites Dr. Stuart Rojstaczer‘s article in the Christian Science Monitor about grade inflation in college. The focus here is not on how the grades are inflated, e.g., with a retest, but the evidence shows grades skewed towards the higher end and has increasingly become more pronounced over the past few decades. The rigor and accountability cited in the argument against retests is not what it appears.

Given the need to demonstrate content mastery through placement tests, and college academic expectations that are not quite what they seem, it makes sense to focus on mastery of content. This is illustrated by what is happening in Connecticut, a state that ranked 3rd in US News and World Report state K-12 education rankings and 2nd in Wallet Hub’s rankings of state school systems.

In a Connecticut State Board of Education report, over 40% of students entering a state community college or state university (not including UCONN) needed to take a remedial course.

If this is happening in Connecticut, it may shed light on what is happening in other states. It certainly appears that there is something not working in terms of content mastery in math. I am not attempting to place blame and certainly do not suggest that the problem is a lack of retests. Another issue is self-help study skills and how well students are playing their part of the learning process. A report of a survey conducted by Manchester Community College in Connecticut included the most common reason people struggle in their classes. The 2nd most cited response, by 60% of faculty and 61% of students, was that the students do not know how to study effectively.

It appears the issue of retests is more an issue of why is there a need for retests to be considered and the implications of not filling in the content knowledge gaps. I will conclude with a bit of irony. UCONN is ranked as the 23rd best public university. Students are allowed 3 attempts on the math placement test.

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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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Counting Money at the Store

The way a student counts money in school on a school desk or table (top photo) is the way he or she will attempt count at the register as seen in the 2nd photo in which the student pulled all bills from his wallet then counted, with some bills folded. (Bonus if you can identify the woman in the photo!!!)

In the top photo (below) I had the student pull bills out from his wallet, with the bills unfolded and in order in his wallet (you can see he pulled a $20 bill first). In the next photo you can see that he is counting out the bills from the wallet as he did in practice.

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What is a math topic you want more information about?

I am asked by individuals, sometimes out of the blue, to provide insight about math for special education topics. I make an ongoing effort to share what I have and continuing to learn to help students. What is a math topic you want more information about? I will respond to general or even specific situations. 

Enter your request in a comment.

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“They Will Never Need This Math”

As a parent of a child with a disability and as a math educator, I am repeatedly struck by the fact that a group of adults (educators and professionals) convene to discuss and plan how to help a child. A great deal of time, resources, and money is concentrated on that child. Awesome! Unfortunately, in math education I frequently encounter situations in which this collective energy is concentrated on math that is more about boxes to check than engaging the student in math that he or she will need in post-secondary life.

IDEA enumerates the purpose of special education, with the transition goals aligned with employment, living skills, and future education that are desired for each individual student. This is explicit and aligns with the goal most teachers likely have, to make a difference in the lives of their students.

Despite this, when I am called in to help with math programming for a student I often find the math being presented to the student is not aligned with the post-secondary goals and often appear to the result of following the general ed curriculum, by default. Here are some examples.

  • I co-taught an algebra 1 class with a student impacted by autism to the point that he needed a paraprofessional guiding him through the daily work. He worked in isolation with the para and struggled with the basic elements of the course. It was not until his junior year that he was moved to a consumer math class. 
  • A senior was in a consumer math course I taught. The course was for students who could not access the general curriculum, yet her transition goal for education was to attend a community college. This setting likely require a math course (that did not have consumer math topics) and a placement test.
  • I was called in by a district to help a 10th grader who was not grasping the basic math or pre-algebra that was presented for months. He was showing significant task avoidance. The postsecondary education goal was for him to attend a community college. I started algebra work with him immediately and he was grasping it.
  • Over 25 years of teaching math I have periodically heard educators minimize the struggles of students with math with the rationalization “they will never need this math.” My response is to ask why “then we are presenting this math to them?!”

So what math do they need? Here is a list of blog posts that address this question. In short, here is what I share with IEP teams, educators, parents, and special ed teacher candidates I teach.

  • If the goal is a career that involves a 4 year degree, then boxes must be checked. The student will have to have the math courses needed to get into the college and to prepare for the math in his or her major. This is the “mathy math” that will be on a college placement test as well.
  • For a 2 year degree at a school with open admissions, the focus of the high school math can be narrowed to the math course required (if any) and on the placement test. Typically, this would involve a focus on algebra. For the aforementioned 10th grader, we did not cover geometry and prioritized the algebra topics to cover. 
  • For a vocation, cover the math needed for that vocation. For example, I worked out a long range plan for 7th grader whose mother shared that may work in an auto repair setting. The math needed for that vocation is measurement so the plan focused on measurement and life skills/consumer math. 
  • For another middle school student whose goal was to have a job and to be as independent as possible. He loved sports and his mother said he would love to work in a sports related store. For him I recommended data and statistics (not the mathy type but meaningful and applied stats and data) to help him make sense of and discuss sports stats. This was complemented by a recommendation for consumer math.

Students should be presented the math they NEED.

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Catching Up in Math is Often Akin to a Stuffing Suitcase

In working with students with special needs on math programming and services, a common and major issue is that the student is behind and there is a tension between filling in gaps and addressing grade level content. Let me unpack this (pun intended).

  • There is no single grade level for math, as is the case for reading. Math progression is more like a web, not a line. For example, if a student can do 5th grade geometry but only 3rd grade level fractions, do we average out the grade level math to be 4th grade? (No.) Do we identify the student as working at a 3rd grade level? (No.) 5th grade level? (No.)
  • Like a suitcase, there is a capacity to the daily time a student has for school services. I often encounter situations in which the services recommended involve the student working on grade level content and catching up on the gaps during support time. If the student has only been learning 75% of the math content each year, he or she needs that support time to help learn the new content to get closer to 100%. There is too much being stuffed into the suitcase. Something has to give.
  • The focus of the services and programming often shifts away from post-secondary plans, which has long term implications as I wrote previously using the falling dominoes analogy.

There are two recommendations I make in regards to addressing the gaps.

  1. Maximize the efficiency of the support time by having the support class focus on the prerequisite skills for current or upcoming topics.
  2. Use triage to shift focus to the priority topics. For example, the parents of a student in 7th grade but working on math from lower grade levels wanted to pursue a math track that would allow the student to go to community college. I mapped out a long range plan (image below) that focuses on algebra as that is the type of math most likely encountered in a math requirement. Here is another plan which was to prepare a student to possibly work in a field related to cars.
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Planning and Preparing for Math in the Fall

If you are reading this post, it is likely that you have a student or you teach students who struggle with math. Here are suggestions to help your students prepare for the math they will encounter in the fall.

Many students are behind in their math education. This has long term implications. The sooner you can address the gaps, the better chance your student has for post-secondary success or competence with math.

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Life Skills Math – Not So Easy

As I wrote previously, shopping is dense with math tasks as are grocery stores. Here are some division situations that are sneaky challenging and require a student to know when and why to divide before even reaching for the calculator. I will use these to help illustrate the fact that life skills math is not simply counting money or using a calculator to add up prices. There is a great deal of problem solving and thinking skills that need to be developed.

For example, if a student has $60 to spend on gifts for her 3 teachers the student needs to understand that she can spend up to $20 per teacher (before even talking about taxes).

An entry point for division can involve a dividing situation the students intuitively understand, e.g., sharing food. Start with 2 friends sharing 8 Buffalo wings evenly (below).

This can lead into the 3 teachers sharing the $60 evenly (below). In turn, this can be followed by the online shopping shown above.

This approach can be used to develop an understanding of unit cost (cited in the shopping is dense post). Start with a pack of items to allow the students to see the cost for a single item before getting into unit cost by ounces, for example.

I have had success with teaching these division related concepts using sheer repetition as much of our learning is experiential learning. Using a Google Jamboard as shown in the photos allows for the repetition.

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K-12 Math Education is a Line of Dominoes

Critical dominoes in math education start falling in 6th and 7th grade with the last ones falling in college. If you have a student who struggles with math and is entering or returning to middle school, now is the time to intervene to avoid more serious issues related to math education in the future. If your student is not going to college or is not accessing the general curriculum, I suggest you read this.)

Below is a chart showing the different categories of Common Core of State Standards (CCSS) math (called domains) at different grade levels. For the majority of students who will attend college, the traditional algebra based sequence (algebra 1, algebra 2, and maybe pre-calculus, calculus) is the path of math courses to be taken. Given this, for students who struggle in math but have a post-secondary education as a goal, the domains I emphasize in middle school are Expressions and Equations, Ratios and Proportional Relationships, and Functions. For high school, I emphasize Algebra and Functions.

Looking at the overviews for CCSS math standards (below) you can see the dominoes line up.

  • In 6th grade, Ratios and Proportions are an entry point for Functions in 8th grade which leads to Functions in high school.
  • In 6th grade, Expressions and Equations are the entry point for Expressions and Equations in 7th and 8th grade, which lead to Algebra in high school.

If your student is struggling with the middle school topics I cited and the gaps are not filled, the struggle will be carried with them into high school and into college.

I recommend the following:

  • Focus IEP math objectives on the priority units of the math curriculum, as cited above.
  • Ask for examples of mastery for the objectives to help you evaluate progress and mastery. Have this in place from day 1.
  • Focus on study skills, not just content mastery.

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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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