Dyslexia Math Issues: Directionality
Last week, Laura Busby and I attended two conferences on dyscalculia in London what an amazing experience. We got to listen to, and speak with, some of the leading researchers out of the United Kingdom about developmental dyscalculia, as well as instructional strategies for teaching math to kids who are dyslexic and dyscalculic. Over the next few months, I will blogging about three major takeaways from our trip:
1. How dyslexia impacts math
2. Developmental dyscalculia
3. Methodology of successful mathematics intervention
Dyslexia and Math
We know that dyslexia impacts the learning of mathematics, specifically in the areas of directionality, sequencing, working memory, and vocabulary or language of mathematics. In a four-week mini-blog series, I am going to explore these four issues with you. We will start with directionality.
When learning to read, we teach kids that the English language is read from the top of the page to the bottom and from left to right. In math class, however, we often hear our kids being taught to solve arithmetic problems from right to left. Haven't we all heard, "start with the ones" or "We always start with the ONES place"? This small change in direction can be extremely confusing to our children with dyslexia and dyscalculia. So, why do we make our children do this switch?
Mathematicians do not necessarily start with the ones place when solving arithmetic problems. Let's take the problem 543 + 251, for instance. Mathematicians will often start with the hundreds place to solve this problem. They will add 500 + 200, then 40 + 50, then 3 + 1. That will give them an answer of 700+90+4, or 794.
Let's make this a little more complex: 592 + 165. In this problem, there is a need for "regrouping" (some of you may have grown up with the word "carrying" instead of "regrouping". That is the same thing). If we start in the hundreds place, we add 500 + 100 to get 600. Then, 90 + 60 is 150. Lastly, 2 + 5 is 7. We now have 600+150+7. Again, 600+100 is 700 and 50+7 is 57. So, our answer is 757. No need to "carry a one" to get our answer (by the way, we regrouped a 100 in this problem, not a 1) and no need to start with the Ones. We started on the left side and worked our way to the right side. With less room for error, in fact. Oh! And, this same process works for subtraction. It is pretty awesome!
If mathematicians work from left to right and we read left to right, why do we force our kids, especially our dyslexic kids, to solve arithmetic problems the opposite way? Maybe our kids naturally work from left to right when solving arithmetic problems? Actually, when most kids use concrete manipulatives to solve arithmetic problems, they usually start with the largest place value. Kids stop this natural method when they get to school mathematics class and are taught that they "MUST start with the ones place". I am not sure why we make our children start with the ones, but I do know that it can cause a lot of frustration and computation error due to directionality issues.
Directionality also impacts our ability to write numbers. Our students with dyslexia often find consistency a comfort. This comfort with consistency stretches to mathematics. Kids learn to count rotely (i.e., 1, 2, 3, 4, 5...) at a very young age. Often times, they can count well into the hundreds before they can write down numbers on paper. It is when they get to school that we ask students to transfer their oral counting to written expression. This seems like a very simple task. But, there are difficulties with writing teen numbers (i.e., 13, 14, 15...). Dyslexic kids often transpose 13 to 31 or 17 to 71, for example. Let us examine a possible reason why this occurs.
To start, there is a very simple pattern that occurs when a person counts aloud by ones starting at the number 20. Try it...Start at 20 and count by ones until 40 or 50. By then, the pattern should be clear...
Okay, did you see that the pattern looks like this?
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43...
Do you see the pattern now? Oh, maybe you see a few patterns? Great! The one I would like to draw your attention to is related to place value. Look at the number 21. Did you read that number as "twenty-one" in your head? Good. The first digit in that number, when reading left to right, is the digit 2. That digit is not worth 2, though. It is in the tens place so it is actually 2 groups of 10. We call that value "twenty" (or "two-tens"). The digit in the ones place is 1, so it is 1 group of 1. We call that value "one". When we say, or read, the number 21, we say, "Twenty-one". That same pattern happens with every number that we say starting at 20, until we get to 111 (or any teen number). The pattern is to state the digit in the largest place value first, then the next largest, and so forth until we get to the smallest place value.
Teen numbers do not follow this pattern, however. One might be able to say that our teen numbers follow the exact opposite pattern as the one we just discussed. Think about the number 15. Say it aloud: FIFTEEN. Let's really examine this number...Fifteen can be broken into two syllables: fif tēn. "Fif-" refers to 5 and "tēn" infers 10. That is clearly opposite to the pattern we just discussed above! For the teen numbers, the first syllable refers to the value of the ones digit, while the second syllable refers to the value of the tens digit. How confusing!?! How inconsistent!?! Have you ever seen your dyslexic child write 51 for 15? It is quite possible that your child is having an issue with the inconsistent pattern in our numbers. The very one that we just explored! (Of course, 51 for 15 could be an issue with place value, but a skilled academic therapist or teacher will be able to discover if it is an issue with understanding place value or not.)
Directionality issues strike again when our kids enter 6th grade and are introduced to negative numbers. All throughout elementary school, we teach our kids that "we can't take the big number from the little number" when we are subtracting. Like in the problem, 73 - 45. We tell our kids to "line the numbers up. Then, start with the ones place." At that moment, our kids often hear, "We take 5 away from 3, so we have to go knock on our neighbor's door and borrow from the 7..."
This language of not being able to take the bigger number from the little number causes a great deal of issues for our kids. For 6 years of schooling, they have heard that they cannot take the bigger number from the smaller number and then in 6th grade we begin telling them that we can! Couple that new bombshell with asking a child to remember to "talk to the neighbor" on the left (the digit in the next largest place value) to get ten more and you are now facing a child who is mentally overloaded from too many directional switches in one problem.
Middle school math (and, then, high school math) possibility introduces a slew of new directionality issues for our dyslexic kids. From negative integers, x- and y-axis, coordinate graphing, inequalities, etc. there are multiple ways for our kids to make "simple mistakes" and get wrong answers just because someone is not aware of how the dyslexic brain works and how prevalent (and often problematic) directionality is in mathematics.
Next week, I will dive into how sequencing can cause issues for children with dyslexia when learning mathematics. Thanks for joining me today!