Mathematical Mindsets“Everybody could rock through their multiplication tables and I could do my ones and my twos and my zeros and my tens, and that was about it.” – Jack Laws, naturalist

I’ve been enjoying a book, Mathematical Mindsets written by Stanford Professor Jo Boaler.

It’s great stuff. She’ll help a lot of dyslexic students if they adopt her approaches to teaching math.

The first concept is deceptively simple, but resonates with me after seeing over a decade of dyslexic students work math problems in our clinic. There is a high degree of overlap between dyscalculia and dyslexia although there is also a significant number of dyslexics who are solid or even outstanding mathematicians. The weak ones almost invariably struggle with basic math facts and require calculator accommodations as they advance in their schoolwork. One might expect that students with spatial talents might excel in certain types of math subjects like geometry, but what is the secret of success for math gifted dyslexic students?

More often than not, we see that these students have a flexibility with numbers and a strong enough working memory that allows them to keep the numbers being worked on ‘in mind’. Flexibility with numbers means being able to see the number 18 as 10 + 8 or 9 x 2 or 20 – 2, all the while proceeding to the solution of a math problems. These are kids who sometimes arrive at an answer before anyone else, but then get bogged down if they are required to ‘show their work.’

Dyslexic students learn well by patterns and flexible problem solving, that’s why Dr. Boalers approach can really help young math students. Listen to her explain then also listen to how many different ways Stanford math students try to solve the problem 18 x 5 in their heads:

 

Some of the students told me that they stumbled onto their own way of mental math themselves when they found they couldn’t remember them by rote like some of their classmates. In Jack Laws case, if he had been taught some of the pattern finding approaches of mental math, he might have been able to learn his multiplication tables…not by rote, but by strong knowledge of his 1’s, 2’s, and 10’s and pattern finding on a 100’s chart.

See below for a Mental Math Strategy Sheet. For Premium subscribers, we’ll also add a teacher’s ideas for teaching math patterns using a 100’s chart.

mental-math-strategies

Download HERE.

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math-pocket-chartFrom Jennifer Sisul’s Fostering Flexibility with Number in the Primary Grades (sorry – this is not open access, but I did find it in our public online library), a simple 100 pocket chart was used to teach number sense.

Sisul began by hanging up an empty chart to stimulate students’ curiosity. Then she adds in 3 numbers (14, 32, 64) in their appropriate spaces, then asks students why they thought they were placed in the ones she had chosen.

Then over the next days to weeks, she has students place in numbers of their choice in the correct location, explaining how they found their way of putting their number in the right spot. If a student chose the number 16, for instance, he could count up from zero or down from 16. As more numbers get added in, a student with the number 26, could choose to put it directly above the 16 after adding 10.

The activity can be varied by a teacher adding numbers (for instance all the numbers in one row or column), then asking about what the numbers have in common (e.g. same first digit or same second digit).

Additional suggested activities by Sisul include:

* Guess My Number Students ask questions to determine my (or other students’) secret number

* What’s the Pattern? I (and later, the students) document a pattern on the chart by flipping over cards to their blank side. Students try to discover the pattern, not by yelling out guesses but by flipping over
subsequent cards in the pattern. After a few additions, I ask them to describe the pattern.

* What’s My Rule? I flip over cards that fit my (and later, the other students’) sorting rule, such as all
numbers divisible by five. The students add cards that fit the rule, similar to the above game, by flipping
over numbers.

* What’s Different? Before the class arrives, I switch two numbers and see if the students can determine
the switch.

In an activity such as this, letting students work with the 0-100 chart in view will reinforce the patterns as well as provide a kinesthetic reminder of numbers and their relationships.  The strategy is strength-based for many dyslexic because it uses abilities in pattern recognition and spatial and personal memory more than pure rote memorization

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