Welcome back! In today's blog, we are continuing our look into how dyslexia impacts math. Our focus for today is on Sequencing.
What is sequencing? Simply put, a sequence is a specific order of numbers based on a pattern or rule. The sequence can start at any specific number. For example, 1, 2, 3, 4, 5, 6, and so forth is a sequence of numbers. We started at 1 and then added 1 more to the previous number to get the next number in the sequence. Most children are very familiar with counting in sequences. In Arizona, we introduce sequencing in preschool. Kids practice rote counting up to 10 and counting objects in a set. When kids enter kindergarten, they are counting well into the hundreds place and practicing sequences starting at numbers other than 1 (such as, counting by 1s up to 20 starting at the number 4). In first and second grade, our kids are extending their sequencing knowledge by creating sequences with 2s, 5s, 10s, and 100s. Again, the challenge put to the kids is to start the sequences at numbers other than 1, 2, 5, 10, or 100. Backward sequences are also introduced to students as well as sequences with missing numbers (i.e., 6, 8, ___, 12, ____, 16, _____, 20...).
In order to sequence, a person needs to be able to recall names of digits, compare quantities, identify the value of digits based on place value, recall the names of the place values, and so forth. When we thinking about it, sequencing is quite complex!
How does dyslexia impact a person's ability to sequence and why is it important to understand the effects of dyslexia on sequencing?
To start, sequencing requires automaticity. Automaticity refers to the ability to quickly, or automatically, see a digit, recall the name of the digit, determine the value of the digit, and read the entire number. As it turns out, the portion of the brain that is responsible for automaticity is also the part of the brain that is not functioning properly in people with dyslexia called the Visual-Word Form Area. So, it makes sense that people with dyslexia might have trouble with instantaneously recognizing letters, patterns, and numbers. Of course, the ability, or lack of ability, to automatize varies from person to person.
Practically speaking, this means that our kids with dyslexia might struggle with being able to automatically extend patterns or sequences. For example, our kids might quickly recognize the pattern and extend the pattern when we count 10, 20, 30, 40...etc. If we ask kids to use the same pattern to extend the following sequence 14, 24, 34...they might not be able to automatically say that 44 is the next number in the sequence. It is even harder if we ask kids to start at 3 and recite the sequence of numbers when they are increasing by 8. Try it. Was that easy for you? Did you quickly arrive at the sequence 3, 11, 19, 27, 35, 43, 51, etc.? Now, think about how hard it might be for a child with dyslexia whose brain is not using the Visual-Word Form Area to complete that task.
When working on sequencing, we also require children to count backward. Let's try a quick task. Start at the number 133 and count backward by 4s until you get to the number 89...Great! Was that easy? Hard? Did you have any trouble when you got to the teens or when passing through 100? Now, try this task:
Fill in the blanks.
40, 33, ______, 26, _____, 12, _____, -2, -9, ______
Was this task easy or harder for you than the previous one? What was the most difficult aspect? Was it figuring out the rule to the sequence? Was it remembering the order of numbers going backward? Was it crossing into negative numbers? Maybe seeing the numbers written down made the task easier for you because you had reference points! Did you figure out the rule to the sequence by counting up instead of going backward?
For people with dyslexia, counting backward can be extremely difficult! First, we are asking people to reverse a sequence or pattern. This reversal assumes one can make a mental number line and can flexibly use a mental number line. Second, counting backward requires a lot of memory work, recall, the ability to hold a mental number line in one's head, and flexibility when using the mental number line. Often time, our kids will quit when asked to do a task where they have to count backward. The automaticity is just not there for them.
Dyslexia can impact sequencing in a few other areas, as well. For example, many of our children have difficulty with one-to-one correspondence and frequently miscount because of it. One-to-one correspondence means being able to match numbers to objects. So, if a child is asked to count a set of objects, the child with one-to-one correspondence will know that each counter they touch aligns with one specific number. Often times, our children with dyslexia have a very hard time with this task because they struggle with their motor skills and/or have executive functioning issues. I witnessed a fourth grade child arrive at an incorrect answer when counting a large pile of popcorn kernels because she counted two pieces of popcorn for numbers like thirteen, twenty-one, thirty-two, etc. She counted the syllables or words that she was saying without recognizing that each number she said corresponded with one and only one piece of popcorn. Other children rotely count, while arbitrarily touching the objects being counted without any recognition that the numbers correspond to one and only one object.
These examples also show that the children did not understand the concept of cardinality (the understanding that when counting items, the "number word" applied to the last object represents the total amount in the set). Understanding of one-to-one correspondence and cardinality are crucial elements of sequencing.
In day-to-day life, sequencing occurs frequently. People are asked to follow a sequence of directions when getting from place to place. We follow a sequence when getting ready for our days in the morning - like showering or bathing before we put on our clothes! In school, teachers provide students with a list of things to complete before the bell rings at the end of the day, such as figuring out what is for homework, putting said homework in a folder, putting the folder in a backpack, putting a chair on top of the desk, etc.
People with dyslexia often have difficulty remembering the entire sequence of steps to follow in a task or they might remember the sequence out of order. Misremembering or confusing steps in a sequence frequently leads to great difficulty with task completion or even getting in trouble with a teacher! I've heard countless stories of my students getting in trouble with their teacher because they forgot all of the things they were supposed to do, so the child filled the time with something else, something that was important to him or her, instead of abiding by the teacher's list. The child did not mean to disrespect the teacher's wishes; he or she just simply forgot the entirety of the list. Poor child!
As you can see, sequencing can be very tough for people with dyslexia, both in the world of mathematics and in daily life. In my next blog, I will look at how working memory (or short-term memory) can make learning mathematics difficult for people with dyslexia. Thanks again for joining me this week! Until next time...