Category Archives: IEP

“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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Prerequisites for Algebra – An Illusion

The orange circle on the right looks bigger, but in fact both are the same size. The deception is based on the additional sensory input.

Similarly, the prerequisites for taking algebra are often considered to be basic skills. This is largely an illusion. I routinely encounter students who are referred to me for help as they have been caught in an infinite loop of working on basic math such as number operations (adding, subtracting, multiplication, and division) before moving on to algebra, with limited progress. I am not suggesting basic math skills are not important but am focused on the context of prerequisites needed to engage algebra. Many of the students I have helped who were in this situation. We worked to quickly move them into algebra where they were successful.

One student worked on half a year of 4th grade math during her 7th grade year. During the spring of that 7th grade year and the subsequent summer, I worked with her on algebraic thinking and algebra topics. She successfully completed algebra 1 during her 8th grade year.

The Common Core of State Standards (CCSS) for Math maps out the prerequisites as seen in the CCSS math domains (below). Throughout elementary school, Operations and Algebraic Thinking topics are covered. The Algebraic Thinking standards establish for the students a foundation for algebra taught in middle and high school. A focus of algebra is to model or represent patterns or relationships in real life situations using equations, tables, and graphs. These include quantities modeled by variables.

Below is a break down of this foundation in elementary school. If you are supporting a student in middle or high school who is taking algebra and has major gaps in his or her math education, look to these standards for the essential prerequisite skills.

First Grade: represent situations in word problems by adding or subtracting, and introduce equations (and equal sign).

Second Grade: Represent, solve word problems, introduce multiplication as groups of objects.

Third Grade: represent, solve word problems, explain patterns

Fourth Grade: Solve word problems, generate and analyze patterns

Fifth Grade: Write expressions (equations are 2 expressions with an = in between), analyze patterns and relationships

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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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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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Stratford SEPTA Presentation: Making Math Accessible for All Students

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Presentation by Randy Ewart at Feb 27, 2017 SEPTA meeting

Link to Drop Box folder with documents to share.

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Standards vs Deficits and Long Range Plans

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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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Evaluating the Effectiveness of Math Objectives

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The math objectives present in the photos on this post were written for former students of mine. These types of objectives are ineffective and ubiquitous. When I have sat in IEP meetings the majority of the time I am the only person who is capable of evaluating IEP math objectives. This post provides some guidance for others to evaluate these objectives.

In the photo above the objective has 3 major flaws.

  • “Using tools” is ambiguous. A 4 year old can use a calculator even if he does not know what he is doing.
  • “Problem solving skills” is a broad term that needs to be defined.
  • “Improve” can mean a student increases a success rate from 0% to 1%. That speaks for itself.

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In the objective above there are 2 major problems.

  • “Multi-step word problems” is very broad. If a student shows she can solve a problem that requires addition and then subtraction but no multiplication or division is this mastery?
  • Often the accommodations are built into the objective and therefore the assessment. I have repeatedly had educators tell me this is what the student needs. That is valid if there is no intention for the student to do the work independently but often that point is overlooked.

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The objective above is similar to the previous example. The examples in the objective include “solving” and “graphing.” Is the student supposed to demonstrate mastery in all the different types of algebra concepts? Or, if he can solve equations is the objective mastered?

How can caregivers evaluate these objectives? 

The language of an effective objective can be used, almost verbatim, as  problem. For example

  • Objective: Billy will add fractions with like denominators.
  • Problem: Add the following fractions (with like denominators).

Have the person writing the objectives provide an example problem that can be used to assess mastery of the objective. If the problem includes additional information or language beyond what is written in the objective then the objective is ineffective. For example:

  • In objective 1 above (the first one) the objective is to use tools to improve problem solving skills.
  • Below is a possible problem (from LearnZillion.com) that could be used. I would ask the author of the objective to explain what problem solving skills should be demonstrated and to explain what constitutes improvement. Neither of these terms is explicitly stated in this problem. It is very likely that valid responses to these questions is not possible and hence the objective needs to be revised.

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Solve the word problem above using a calculator.

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Standards Based IEP Math Objectives

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In my 21 years in working as a math teacher (with 6 that focused on special education) I have rarely seen IEP objectives for math that are directly aligned with the math curriculum that is to be accessed by the respective student for whom the objectives are written (see photo below).  The photo above shows an excerpt from an OSERS letter regarding IEP goals that are standards based.

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“improve” and “problem solving skills” are entirely too obscure

Below is a list of IEP objectives I have written for use in an IEP. They are directly aligned with the math content to be covered. Some educators insist on including the specialized instruction as part of the setting of the objective. I have no qualms with this as long as the student ultimately will demonstrate mastery of the objective without the supports (unless the supports are to be permanent or lead to subsequent objectives that will not have the supports included). NOTE: If you would like suggestions for IEP objectives please use form below and I will add them to this post.

Pre-Algebra and Algebra 1

  • Goal 1: Xxxx will accurately simplify expressions and solve 1 variable linear equations.
    • Objective 1: Xxxx will simplify a given algebraic expression 8 out of 10 times with only minor algebraic mistakes (e.g. arithmetic error).
    • Objective 2: Xxxx will solve a given 1 variable linear equation by simplifying first 8 out of 10 times with only minor algebraic mistakes (e.g. arithmetic error).
    • Objective 3: Xxxx will solve a given 1 variable linear equation with a variable on both sides 8 out of 10 times with only minor algebraic mistakes (e.g. arithmetic error).
  • Goal 2: Xxxx will accurately complete linear function problems by identifying and using slope and intercepts.
    • Objective 1: Xxxx will identify and interpret slope given various representations (equation, graph or table) 8 out of 10 times with only minor algebraic mistakes (e.g. arithmetic error).
    • Objective 2: Xxxx will identify and interpret y-intercept given various representations (equation, graph or table) 8 out of 10 times with only minor algebraic mistakes (e.g. arithmetic error).
    • Objective 3: Xxxx will convert between various forms of a linear function 8 out of 10 times with only minor algebraic mistakes (e.g. arithmetic error).

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