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This is known as diagnostic prescriptive instruction.
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Attention Deficit Hyperactivity Disorder or ADHD is a complex condition that is often complicated by poor Working Memory.
In the math classroom, students with good working memory are able to stay on the task at hand because their working memory tells them to stay focused. It helps them to ignore distractions and manage their behaviour as they complete each question or assignment.
Students with ADHD may be ready to explore and take on a new math concept, but it often appears as if they are working against themselves. Their motor cortex is overactive, so they need to keep moving. They may attempt to keep focused by tapping the desk, doodling on paper or talking out in class if they don’t understand a concept.
It isn’t difficult to understand how these disruptions interfere with their working memory. It cannot do double duty and manage behaviour as it tries to learn a new math concept, so the student may tire and slip into daydreaming in the middle of a lesson. The result of this confusion is that the math student with ADHD has a working memory that cannot clearly learn or recall math facts and concepts let alone apply them in math homework.
In short, the students’ lack of focus due to ADHD results in gaps in their learning that inhibits them from being successful.
Rethinking the way we instruct these students and gearing instruction to foster permanent learning will assist these students in overcoming their difficulties.
In the last post we were exploring the important, positive tasks that working memory allows each of us to do on a daily basis. We will explore these positive aspects of working memory in following articles as well as how working memory is disadvantaged in life and in math particularly.
So to set the stage, let’s start by solving this math problem:
Now many of you have solved it in your mind already, but for a young student it may be challenging because it involves several steps that rely on working memory. If you can remember ever having difficulty with horizontal math problems, the steps listed below will show you it is much more complex than you think. Let’s take a look at each step in the addition process.
Step 1. Take the 7 and the 8 and use you mind to calculate the first part of the answer.
Step 2. Put the answer 15 in your working memory and hold it there.
Step 3. Remember the 5 and use your working memory to regroup or carry the 1 (from 15) and prepare to add it to the 2 (from 27).
Step 4. Update your working memory with 2. Combine 2 with 1 (from 15) to get the answer 3.
Step 5. Recall the 5 held in working memory.
Step 6. Organize the numbers with the 5 in the ones place of value and 3 in the tens place of value for the answer 35.
This problem is tricky because it is presented horizontally rather then vertically. Children frequently solve it by writing down 125 because their working memory is not up to the task of keeping track of where they are in the problem. They are left to puzzle about what to do with the 1 that is carried over.
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Working memory is a key factor in keeping numerical knowledge in the correct order to solve problems such as these.
(adapted from Working Memory by Tracey and Ross Alloway)
Next – positive aspects and disadvantages impacting working memory.
Resources:
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Many bright students have a difficulty with math that puzzles their parents and teachers.
These students are bright enough and appear to understand the math concepts as they are practiced in class.
But for some reason this information is not recognized the next time the concept is presented.
The problem could be a difficulty with working memory.
We’ll be exploring the many facets of working memory in further posts, but first let’s look at what working memory is and what its role is in our lives.
Working memory gives you the advantage of managing information in your day to day life from birth to old age.
Simply put Working Memory is our ability to work with information. More precisely it is the conscious processing of information while simultaneously keeping us on task and blocking out distracting information
For example, a student in math class needs his working memory to hold on to new instructional information and apply it while screening out distractions such as other students moving in and out of the room, people chatting, the intercom buzzing or managing the fear that he isn’t going to get it and keep up in class.
In summary Working Memory enables us to do the following important tasks:
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The list is a great reminder of how much we take our working memory for granted when it is working well for us.
We’ll explore these positive aspects of working memory in following articles as well as how working memory is disadvantaged in life, and of course in math.
Suggested Reading:
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When you look at the learning experience, the higher the degree of interaction or activity, the higher the degree of retention. Earl Robertson, Quota Corporate Training.
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Significant errors in public school math textbooks may be negatively affecting students’ abilities to understand the subject, says a senior lecturer in mathematics at Simon Fraser University. Malgorzata Dubiel spent the last year studying the textbooks and determined “errors in terminology, definitions and presentation of mathematical concepts” may be contributing to students’ difficulties in understanding concepts. She found many such errors in Math Makes Sense, the most popular kindergarten-to-Grade 9 math textbook series in B.C
“I don’t want to say that they are truly bad, because they are based on sound methodology and so on, but they were written just by teachers and no mathematician was ever consulted either in reviewing them or writing,” Dubiel said. “There are some issues which can make learning more difficult for students and for teachers. There are things that are, mathematically, totally incorrect.”
As an example, Dubiel cited a Grade 7 math textbook that defined the term “average” as “the number that represents all numbers in a set,” which may or may not be equal to a mean.
“In statistics, those words are used interchangeably, and average means exactly the same as the mean, but we’re telling students that it isn’t,” she said.
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The textbook, however, states this is impossible: “[Pi] never terminates or repeats. So, the circumference will never be a whole number.”
She has contacted both the publisher of the textbooks and the Ministry of Education to little effect to date.
In response to a detailed report on Dubiel’s findings, the ministry told Dubiel in a letter the public school system is in the early stages of transformation and her findings would be shared with ministry staff working with document references.
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