Author: deborah.rebhuhn

When I first started this blog, I was trying to tell regular classroom teachers what was different about special education.  I wanted to explain what special education teachers had to do differently and why.  What I have figured out since I started many years ago, is that it was all much more complicated than I thought it would be and that I don’t have all of the answers.  I now realize that I need to share my questions and my failures in addition to my answers.  I did my best while actively teaching, but I sometimes shudder at the “obvious” things that I missed.

One of my classroom failures was Susanna[1], although at the time I thought I was successful with her.  Susannah really tried, but she was easily frustrated.  When she didn’t understand by the 4th try at an explanation, she would rage in frustration. “You’re not explaining!  Why don’t you explain!?”  The explosions happened several times per month.  After an explosion, she was totally unable to focus on learning. (The other students in the class tended to sigh, keep working, and ignore her.)

Susannah was normally a polite and conscientious child who did her best, but succeeding at understanding mathematics was really important to her.  When she had trouble, she became anxious and, when anxious, she sometimes exploded.  Anger or punishment from me would just stoke her anxiety.  In fact, she had been moved between classes in another subject because her parents had expressed a concern that Susanna’s original teacher made Susannah feel too anxious to be able to learn.  

Susannah also needed every minute of class time to move forward.  She learned at her own pace, and every time she blew up, we lost productive class time to allow her to cool down.

In the end, I learned to anticipate the situation.  If I was explaining something to Susannah and she did not understand what I was telling her after 3 tries, I would say, “Susanna, I have tried all of the explanations I can think of right now.  They didn’t work for you.  I need time to think up some new explanations.  Do you mind practicing something else and I will come up with some new explanations for tomorrow?”  It worked like a charm.  We did not lose more class time for temper tantrums.  

Susannah would agree to work on something else and I would have alternative work available for her.  The next day, Susannah was much calmer, and my explanations (often the same ones as I made the day before) would take.

I had resolved my classroom dilemmas.  I was not losing 10 or 15 minutes of class time to temper tantrums from Susannah, I was not increasing her anxiety and interfering with her ability to learn mathematics.  Even so, when I reflect on the situation many years later, my short cut did not really provide the most important help for Susannah.

Someday, Susannah was going out into the world of work.  Someday, she would be working for someone and get frustrated.  If she lashed out at her boss and criticized her boss for not explaining, Susannah was unlikely to keep her future job.  I had solved my immediate classroom problem, but for Susannah, the longer term problem was more important.  She needed to be able to explain what she needed respectfully.

Behavioral interventions in the special education classroom are often more important than course content.  I could have taught her to recognize her feelings before the explosion and then to ask for a break to calm down.  I could have shared my feelings and suggested more respectful ways to let me know hers or I could have shared the problem with her counselor and her counselor could have provided more intensive interventions.  Either way, Susannah would have had a chance to learn how to share her frustrations without alienating other people. 

By keeping my eye on the narrow goal of teaching mathematics, I missed the opportunity to make a major difference in Susannah’s life.

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[1] The students I describe are composites of the students I taught.  The incidents described did all happen in my classrooms.

Why I Had to Modify Number Talks

I have many students who are afraid of arithmetic and who solve problems mechanically using whatever method they have been taught without thinking about what they are doing.  After reading about number talks, I thought, “What a terrific way of introducing flexibility in problem solving!”  “But, what do I do with an entire class of students with anxiety disorders?”    If I ask them to multiply a pair of 2 digit numbers in their heads without using a pencil and paper, will they try it or will they shut down and refuse to try anything else in my classroom for the rest of the school year?

If I have only five (or two or three) students in a class, can I do number talks or will I get too few ideas to help students understand different approaches?   Will I get enough different ideas to really help them see that there are different ways to do problems and they can use the one that makes most sense to them?  More about my number talk experiences in a future blog post.

Why I Had to Modify Group Work

The consensus among people who educate teachers seems to be that it helps to have students work together in groups.  I thought about some of the classes that I and my colleagues have taught.  There was the really competitive class in which students would make fun of anyone who made a mistake. There was the class with the two noisy students who couldn’t be allowed near each other because they would hit each other with book bags and knock papers off each other’s desks. The third student was sensitive to loud sounds and kept asking to work outside by himself where things were quieter.  

There were the classes of extremely distractible students who regularly got into conversations with each other and totally forgot the mathematics.  (Of course I redirected them.  It would only last for a minute or two.)  There were the classes with a scapegoat who was put down by everyone else in the class if he even tried to participate in a conversation.  How could I try group work if it subjected a student to bullying and harassment?

 I go to conferences and ask other teachers how they handle similar problems.  I have had other teachers tell me that I just need to get my students together to talk to each other to resolve the problems.  I do see change and improved behavior for some of my students over a period of several years.  I rarely see that type of change over a few weeks or a few months.    If weekly group therapy and counseling can’t fix it in under a year, I don’t believe that I, as a mathematics teacher, can fix a destructive behavior pattern in under a year either.  As a result, in some classes, I try to find ways to help my students share information without actually having to work together.  More about that in another blog post.

When the Ability Gap is Too Large to Bridge

Current orthodoxy is that mathematics students should not be grouped by ability.  Everyone should be in a class together.   Since the range of abilities among my students is wider than in a typical classroom, I cringe at the thought.   If I try problems with a low entry threshold and a high upper bound on what students can achieve, will I still be able to do group work that includes students who forget by the next day along with students who have more typical memories?   What about grouping students who don’t understand whether they should multiply or divide two numbers to calculate take home pay with students who can read the same word problem and write an equation to describe the problem situation?    Students at a 1^st, 2^nd or 3^rd grade math level with students who can write and solve equations at an 8th grade level? 

The students who forget by the next day are used to being embarrassed in mathematics classes and they are already in the habit of shutting down at the first idea they don’t understand.  They would rather be accused of laziness than be accused of stupidity and stupid is how they see themselves.  If I include them in groups working with more neurotypical students, will I destroy their confidence? 

Do I Really Believe What the Experts Say?

I know that Jo Boaler grouped students of many levels together in her summer camp math program (If you haven’t taken her online Methods and Materials class, I highly recommend it.)  On the other hand, I did see one child in her videos almost screaming with frustration after another student tried to explain something to her.  I wonder how that particular child felt about mathematics by the end of the summer program?    If I try the group work for my students without Jo Boaler’s experience and level of skill, will that work for my students?  More about my experiences with one of Jo Boaler’s weeks of inspirational math in another blog post.  (See www.youcubed.org  for information about her week of inspirational math.) I do know that if even one student is lost in my class, I can’t just teach the others and allow that child to flounder.  I need to reach every student as best I can.

Please Share Your Own Experiences and Ideas

I am hoping this blog will connect me to other teachers who work with special needs students.  I want to share some of the things that worked for me.  I am hoping that others of you will chime in and share what worked for you.  I will be happy to share your ideas and stories with the world as well as my own.  In fact, I will be happy to have you write a guest blog if you are willing to share your ideas and approaches.

If you have worked with special needs children and you have wondered whether information from the experts will work for your students, please share your doubts and questions.  I get tired of being the only person at an NCTM or AMTNJ meeting that says,” Does that work when . . .?”  and have everyone look at me as if they had never come across a similar situation. 

For those of you who do not have a lot of experience with special needs students, I hope that I can supply some approaches that may be of use to you as well as an attitude check for you.  Those students who never do homework,  who try to skip school, who have an attitude about doing math (“When will I ever need this?) are doing their best.  They are not necessarily careless or lazy, but they may have given up trying because they are so discouraged.  It is our job to meet them where they are, not to write them off.

What You See in the Classroom

For about a year and a half, I had a colleague who insisted on teaching students by explaining how to do problems at the blackboard.  He was a bright man, but he came to our daily staff meetings with a smouldering sense of frustration.  His students would not pay attention when he explained things at the board.  He complained bitterly that there was no sense of discipline at our school, and no consequences for students who did not follow teacher direction.  Eventually, he left in the middle of a school year having accepted a position at a public school where, presumably, discipline (and pay) would be better.

I remember one day when he let us know that he told his students he gave up on explaining to them because no one paid attention when he was at the blackboard.  He then lost it when one of those students asked for help with a worksheet problem.  Since the student hadn’t paid attention when he explained at the board, my colleague refused to answer the student’s questions.

If I had not felt so unwelcome when I tried to talk to my colleague outside of a  staff meeting, I might have been able to tell him that many of his students were unable to  follow blackboard explanations of mathematics.

Why it Happens

Children will try to do well if they can.  Acting out in mathematics class (or asking when I will ever have to use this) is a sign of frustration.  Although there are many more reasons that a student might not be able to follow a blackboard explanation, the major issues for my own students are

• slow processing,
• distractibility,
• working memory limitations,
• anxiety or depression, and
• difficulty with receptive language.   

Some of my students have a mixture of several of these issues.

Why doesn’t the blackboard work for students with these issues?  Let’s discuss them one at a time. 

Slow Processing

In my first years of teaching, I had one class of students who would take 20 minutes to solve two 2 step equations even after weeks of practicing similar problems in different contexts.  At the time, I was convinced that they were purposely working slowly to avoid doing more work.  One day, one of the students requested a favor from me.  I agreed, provided that his work got done promptly.  I watched him work.  His body and facial expressions said, “I am determined.  I am going to get this done fast.”  It still took him 20 minutes to solve two 2 step equations.  That was when I realized that my student was not avoiding work or purposely working slowly.  It really took him that long to think through anything. 

Describing a process or procedure on the board won’t work for these students.  They are still thinking about your first sentence or equation while you have moved on to say 3 more sentences.  By the time they are ready to hear another sentence, you have moved so far ahead, they have no way to figure out what you are sayiing.

Distractibility

Students who are easily distractible (with or without a diagnosis of ADD or ADHD) may not be able to follow a complex sentence, much less an explanation of how to solve a complex problem.   I have had many  students who would tune out while I was talking to them.  I learned to ask them  to repeat back what I said to make sure that they had heard me. 

Ocasionally, a student who actually had a diagnosis of ADHD was taken off medications for other health reasons.  In the past,  at least two of my students who were taken off medications went from sometimes understanding  to  always being lost in their own brains.  If my primary teaching style had been explaining at the blackboard, those students would never have been able to listen long enough to follow my explanations.

Working Memory Limitations

Working memory is temporary storage in the brain.  One day I suggested wording  for an answer to a student in my study skills class.  He was unable to remember the sentence long enough to write it down and had to ask me to break the sentence down into smaller phrases.  I realized that he did not have enough working memory to store a compound sentence in his brain.  If I had tried to explain a problem on the board, he would have forgotten the first sentence by the time I started on the second sentence.  There was no way he could have followed or understood a sequence of logical steps demonstrated at the board.

I had another student with a very limited working memory.  When he got into class, he would look at his work and spend 10 or 15 minutes just staring at it before he could start working.  He occasionally got into trouble with other teachers who accused him of wasting time instead of getting started on his work.  He really couldn’t just read a paragraph and remember what to do.  He did not have enough temporary storage in his brain to keep track of the numbers in a problem as well as the processes and procedures he needed to do to solve the problem.  That 10 to 15 minutes was required for him to be able to start work.  Several years later, when I tried working memory training and realized how difficult it is to try to remember more than your brain can hold in storage, I realized that this particular student was amazing.  He went through that torture every day without complaint to try to do what was asked of him.  He was probably exhausted by the end of my class every day.  (More on working memory training in another blog post).

For students with poor visual working memory, tracking what the teacher writes on the board is a problem.  If they move their eyes away from the board, they can’t find the spot they were just looking at.   While they try to find that spot on the board,   they will have lost track of what the teacher was saying.  Note taking is impossible for these students.  It is just an exercise in frustration.

Anxiety or Depression

Working memory is blocked for people who are feeling anxious.  Students with anxiety disorders often have the same problems as students who have limited working memory.  They are more likely to have variable working memory which works when they are calm, but does not work when they are anxious.  When they perform well on some days and badly on others, their teachers acuse them of failing to make an effort.  “I know you can do this,” the teacher says.  “You tried yesterday.  I see that you are not making an effort today.”  The trouble is that student is too anxious to be able to do the work today.

Although I have not read of any research that says students with depression have limited working memory,  I believe that many of my students with depression have similar problems.  They are not being lazy.  They can focus on some days and they can’t focus on others.

Problems Understanding Spoken Language

Even students without special needs may need to hear something more than once before it clicks and they understand it.  My daughter teaches college mathematics.  When she is in a lab or tutoring center helping students, she often gets thanked for helping them along with complaints that their regular teachers couldn’t explain it very well.  Her own students make the same complaints about her to others. Sometimes, even for a student who does not have special needs, it takes multiple explanations for a new idea to click.

When a student has trouble understanding what they are hearing, whether the problem is trouble understanding words, trouble distinguishing sounds,  or trouble understanding full sentences, the explanations will take even longer to sink in.  These students  have a hard time understanding anything in real time.  Words, spoken or written on the blackboard, won’t sink in as you are saying them.  These students can be hard to distinguish from the distractible students, but it helps to treat them the same way.  Don’t use the board (or anything else that requires them to understand what you are writing or saying in real time), and if you have said something to them, ask them to paraphrase so you can tell if they understood the words.

So How Do We Teach Math to Students Who Cannot Learn From Blackboard Explanations?

Those of you in special education probably already recognize the issues I have described.  If you have techniques that you use instead of presenting procedures at the blackboard, please share them.  I will be happy to give you a forum for your ideas.  All of these issues (and many others which are not listed here) can interfere with a student’s ability to follow a blackboard presentation.  In my next blog, I will share some of the approaches that have worked for me and for some of my colleagues.  Please feel free to chip in and share any techniques that worked for you.

When the blackboard presentation doesn’t work, how can we reach students with special needs?  The techniques that my colleagues and I have been using are:

• use a good discovery method curriculum and provide just in time answers when my students get stuck (Just in Time Delivery)
• provide insight (Visual  Models)
• come back to the same ideas and techniques in many different guises  – mathematical logic may be deductive, but my students appear to develop insight from inductive logic (figure out a pattern after Many, Many Examples, perceptual learning) . 
• use graphing software  (Algebra as an Experimental Science, Visual Models, Many Many Examples in one small package)
• use videos so the students can rewind
• include worked out examples for the students to look at.

This post discusses just-in-time delivery.  The other techniques will be discussed in subsequent blog posts.

Just in Time Delivery

Early in my teaching career, I worked at a school that was using the Carnegie Learning algebra 1 curriculum (before common core).  When I first looked at the algebra 1 text, I was blown away by the content.  The text started with simple questions:  If you make $8 an hour and you work for 2 hours, how much will you earn?  For 3 hours?  For 10 hours?  The questions made sense to students with a knowledge of arithmetic, but the text eventually snuck in tables, equations, and graphs as different ways of looking at the same problem.  The questions were broken into tiny parts that my students could often (but not always) answer.    Many of my students, unable to follow an explanation at the board, were able to progress by working through the examples.  If I was able to supply answers just as they were needed, my students, who would have been lost with blackboard explanations,  were able to continue work.  Better yet, the breakdown of questions into tiny parts allowed me to figure out the exact point at which my students got confused.

I have successfully taught algebra to many students with learning disabilities by giving them Carnegie Learning texts and coming over to supply help just as they need it.  If you have students who can work together and help each other out, the approach is probably even more effective.  I have been at a number of AMTNJ meetings where the speakers mentioned supplying information just as students need it as an effective way to help the students learn.    For students in grades 1-6 or students who need to relearn topics from grades 1-6 math, I really like the JUMP math common core textbooks.  You can see sample grade level materials by going to the JUMP math website.

In addition, for those of you who have read Make It Stick (the science of teaching to help students remember), the authors claim that students will remember mathematics better if the students  attempt to figure the material out before they get help.  A discovery method curriculum with just-in-time help allows the students some time to try to figure it out on their own before before you supply the help.

I live in mortal fear that Carnegie Learning  will stop publishing their original textbooks.  Although they told me that they plan to stop, there are clearly other fans at other schools that are still ordering the original (pre common core) books because  those original books are still being printed.  The original text incorporates what is now 8^th grade math (which I need to teach to many of my algebra 1 students before I can actually teach algebra 1), and progresses to include the content of a regular common core algebra 1. 

 If you have a good discovery method program that you are using, please share the information with the rest of us.  There are probably many programs that support just in time delivery to students who are struggling.  If you have another way of doing just-in-time delivery to students who cannot follow presentations made at the blackboard, please share that with us as well.  Sample lessons are also welcome.

Are there other techniques that work for you when students cannot understand from blackboard presentations?

I will discuss visual models, many-many examples, and algebra as an experimental science in subsequent blog posts.