Category Archives: special education in general

Levels of Learning

Learning is not a singular threshold to be met. There are different levels of learning – a continuum (see photo below taken from the book Teaching Mathematics Meaningfully).

continuum of learning

A student demonstrating proficiency (fluency) is far different from a student simply showing some level of understanding (acquisition). I remember learning to drive a car with a stick shift. During acquisition (initial understanding) I was looking down at the pedals and the stick shift as I thought through the steps. It is not surprising that many students who only show acquisition of a math topic soon forget it. Despite this, the acquisition stage is often were math in schools resides.

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This extends beyond math fact fluency to all math topics and the students should take the next step and demonstrate maintenance. To do this, I recommend that a curricular based assessment be given a couple of weeks after a student initially showed what is considered mastery – the student successfully performing problems aligned with a given math objective.

Below is a excerpt from the book with an explanation of the topics. I use this text in the math for special ed courses I teach at different universities.

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Meeting Needs Part 2

In the past year I have helped two 7th grade students who are categorized as twice exceptional (2e). Both had more severe math anxiety that impacted their performance and masked their ability. When we started both were working on elementary school level math. Within a couple of months both were working on algebra. (Both had gaps but I was testing their ability by test running higher level math with them.)

As I shared in a previous post my approach is to focus on meeting needs. I want to elaborate on this. My secret is I listen to the student… In other words, the student drives the instruction.

Here’s an analogy. You go to a frozen yogurt or ice cream store and they offer you a sample. You try a couple then go with the one you like. That’s what I do. I try out different types of instruction (samples of the ice cream) and the student tells me (verbally or by the response to the instruction) which one they want. That is the I in IDEA and in IEP.

icecream samples

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Submit Questions for the Daily Mailbag

If you have questions about math support, services or strategies share them using comment bar below or email me. I will answer as many questions as I can get to.

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Mailbag Jan 26, 2019

Are you a parent of a student with special needs who is struggling with a math topic? Are you a teacher figuring out how to differentiate for a particular student on a math topic? Pose your question and I will offer suggestions. Share your question via email or in a comment below. I will respond to as many as I can in future mailbag posts.

Here is a topic multiple educators and parents ask about:

I don’t want my child to be stuck in a room. He needs to be around other students.

Randy:

Often we view situations in a dichotomous perspective. Inclusion in special education is much more nuanced.

Image result for for in the road

In math if a student cannot access the general curriculum or if learning in the general ed math classroom is overly challenging then the student likely will not experience full inclusion (below) but integration (proximity).

For example, I had an algebra 1 part 1 class that included a student with autism. He was capable of higher level algebra skills but he would sit in the classroom away from the other students with a para assisting him.  Below is a math problem the students were tasked with completing.  Below that is a revised version of the problem that I, as the math teacher created, extemporaneously for this student because the original types of math problems were not accessible to him (he would not attend to them).

mapping traditional

comic book mapping

I certainly believe in providing students access to “non-disabled peers” but for students who are more severely impacted I believe this must be implemented strategically and thoughtfully. Math class does not lend itself to social interaction as well as other classes. If the goal is to provide social interaction perhaps the student is provided math in a pull-out setting and provided push-in services in other classes, e.g. music or art.

Here are the details of example of a push-in model I witnessed that had mixed effectiveness.  A 1st grader with autism needed opportunities for social interaction as her social skills were a major issue. She was brought into the general ed classroom during math time and sat with a peer model to play a math game with a para providing support. The game format, as is true with most games, involved turn-taking and social interaction. The idea is excellent but the para over prompted which took away the student initiative. After the game the general ed teacher reviewed the day’s math lesson with a 5-8 minute verbal discussion. The student with autism was clearly not engaged as she stared off at something else.

Inclusion is not proximity.

 

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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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Retaining Information

Below is a model for information processing (retention and retrieval). Here are a couple key points I want to highlight:

  • A lot of information is filtered out so what gets through? Information that is interesting or relevant.
  • Information that is connected to prior knowledge, is relevant or that is organized has a better change of being stored effectively for retrieval.
  • Working memory has a limited capacity. Consider what happens to your computer when you have a lot of apps open. Your computer may start to buffer which is basically what happens to our kiddos if instruction involves opening too many apps in their brains.
  • Long term memory is basically retrieval of information. Think a student’s book bag with a ton of papers crammed in it. How well can he or she find homework? Compare this to a well maintained file cabinet that has a folder labeled homework with the homework assignment in question stored in this folder. That paper is much easier to retrieve. This is analogous to long-term memory. If the information is relevant or meaningful it will be stored in the file cabinet folder and more easily retrieved. In contrast, rote memorization like the rules teachers present students are papers crammed into an overflowing bookbag.

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Overlooked Skills for Success

Ask employers what skills are desired in graduates and you will not see academic competence at the top of the list. In schools we talk about creating life long learners and similar qualities but the major focus in the 7+ K-12 schools in which I have served is academics, or more appropriately grades as a proxy for academic mastery.  Add to this the focus on exit exams for graduation and you see major disconnect between the desired outcomes and the focus.

I have taught math at 5 colleges or universities and have seen first hand students struggle with content but also with independent study skills. Manchester Community College in Connecticut conducted a survey of students and asked students to cite reasons why students struggle in their classes. The second most commonly cited responses by students themselves is that students don’t know how to study (see below). In high school we talk about study skills. Teachers will share they expect students to be independent but often the focus is on academic mastery and not the study skills.

MCC survey

At Manchester Community College I serve as an instructor at a highly successful (based on objective outcomes) bridge program for first generation students. A major emphasis is a focus on student academic discipline with a mantra that discipline is the bridge between goals and accomplishment (see below). Learning how to BE a good math student, especially academic discipline, is as important as developing the prerequisite skills to be successful. This could be a major focus in the IEP for students who have a goal of college or post-secondary training..

discipline bridge

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Graduation, Now What?!

I believe that the high school diploma is widely viewed as the end game of K-12 education. The purpose of special education focuses on life AFTER the diploma. The focus of our collective efforts should be on NOW WHAT?

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I have posted on this topic and want to circle back to it. If the purpose of special ed is to prepare students for life after K-12 education then I believe we should use backwards planning to guide services. I stumbled across a website on LinkedIn that can be very useful. This site (see below) provides detailed information about requirements for various occupations – useful for backwards planning. For example, I worked with a student in 7th grade with a more severe disability who was interested in working with cars. The math needed for this occupation was largely measurement and that was the focus for his math – a modification.

career one stop

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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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Busy Engagement vs Intellectual Engagement

Owls are symbols of intelligence but the purported reasons are based on the appearance of awareness and the deft hunting skills. It is claimed that the appearance and skill sets are confused with actual wisdom.

owl

I find a parallel between the perceived wisdom of the owls and the perceived learning of students. Through my years in education I have seen teachers praised for their student centered activities. The students may be energetic and on task by an activity which is often considered a touchstone for learning. What is often missing is independent assessment to determine actual learning.

Once I was covering a class for a teacher widely praised for his activities and multimedia activities. In the class I covered the students were taking a test. It was clear that the majority of the students were hesitant about their performance. Several were looking around, one pulled out a phone and a couple looked at other people’s paper. Very few were locked in on completing their test.

I am not suggesting that multimedia or student centered activities are ineffective. My point is that there is a perception that such activities are inherently effective and reflective of actual learning. There is a difference between being intellectually engaged and being busy. The owl deftly executes action and skill but that does not indicate higher level functioning. Conceptual understanding requires more than simply being engaged by activity. Hopefully this is food for thought.

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