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.