Six Subtypes and a Stream

I enjoy walking the trails in a park not far from my house. 

When I want to get the lay of the land or plan out my trip, I bring a map. When I want to simply wander letting my interest guide my path, I don't. 

There are times I focus on the animals: the sounds they make, how they move, where they rest. There are times I focus on the trees: some have interesting shapes, others have fallen from a recent storm. 

I go for as long as my mood or my body can take me. It means that every time I walk, I encounter a different place, even if I had taken that particular trail a dozen times before. 

I realize I encounter ideas much the same way. 

This week I set out to explore what different researchers have found regarding subtypes of dyscalculia. And although I came out of that trail with more understanding of the science, I also observed how my approach quietly changed.

Hikes begin with something: whether it be a map tucked into a pocket, or simply a general sense of where to go and a water bottle. My intellectual hike this week began with a map.

My Map

• There are many different "ways" to struggle with math. Some people call that dyscalculia, others call it Specific Learning Difficulty in Math (SLD), or even Mathematics Learning Difficulty (MLD).

• Researchers have proposed different profiles of dyscalculia and have classified them into subtypes. 

• Even though it is agreed that there are different subtypes, it hasn't been agreed upon as to what those subtypes are. 

• Dr Giannis Karagiannakis, in 2014, proposed 4 subtypes. Thus far, I find them easiest to work with in my classroom.

• Dr Steven Feifer, in 2013, proposed 3 subtypes based on the areas of the brain used in math learning. He developed a standardized assessment based on his work. It's very interesting, but so far I have found it difficult to connect its implications to my classroom practice.

  
  

A few weeks ago, I had a thrilling conversation with Rob Jennings, cofounder of The Dyscalculia Network. He mentioned a few names, one of which was Daniel Ansari. I'd heard his name before from other educators I respect (thanks, Dawn Frank Cohen). So when he also recommended I read some of his work I finally admitted that it was time to move Ansari's name to the top of my reading list. 

Google Scholar is very helpful, by the way. If you haven't perused it yet, you might want to. That's where I found one of Dr Ansari's papers on his own proposed subtypes of dyscalculia. I knew I had uncovered a trail on my map that I hadn't encountered before.

Let's add that to the map, shall we? 

What is Dr Ansari saying about dyscalculia subtypes? 

I started with the abstract and introduction to get a sense of whether or not the paper could potentially connect to my teaching. Let's be clear, I always start there when reading research papers, but in this case, everything else seemed to be behind a paywall. Apparently, one of the perks of being affiliated with an institution is access to research papers. I guess there's not much of a market for us "civilians."

The first thing that caught my attention was that Ansari proposed more subtypes than I had encountered before. Six, to be exact. Feifer proposed three subtypes, while Karagiannakis proposed four. I realized that I wasn't looking for the "one correct trail" anymore. I was looking for why each cartographer drew the forest a little bit differently. 

I paused on this trail for a moment. I'd never seen that stream before. Was it always there? What made Ansari determine six? A clue appeared in the form of a phrase I had only encountered once before: a priori. 

A priori simply means beforehand. In other words, categories are determined before data are analyzed. It's like saying: When I go on this hike today, I'm going to look for these four types of trees.  Lots of research starts that way. But Ansari didn't. He collected data first, then allowed patterns to emerge. The patterns revealed clusters, which he then labeled as subtypes. 

Ansari's six subtypes weren't the starting point of the investigation; they were the result of it. His work gave names to six different patterns he observed in learners. 

Weak Mental Number Line Subtype

Weak ANS Subtype

Spatial Difficulties Subtype

Access Deficit Subtype

No Numerical Cognitive Deficit Subtype

Garden Variety Subtype (I'm serious that's what he called it.)

At first, I was tempted to spend the rest of the afternoon unpacking each one. But the more I read, the more I realized that wasn't the trail that interested me the most. I wanted to understand what each subtype might look in the classroom. I wanted the part of the paper where I could giggle and think, "Yep, that's Sonia," or "I've seen Ibrahim do that same thing." 

The trouble was, I was looking for the answer to a question that Dr Ansari and his colleagues never set out to answer. 

The paper shifted away from identifying the different patterns and toward explaining why those patterns might exist. The discussion began weighing competing theories, debating which underlying cognitive mechanisms best explained the clusters, and suggesting directions for future research. It was fascinating, but I realized I was venturing down a different path than the one I'd intended. I hadn't brought my bug spray today. 

I didn't end this hike with the answer I'd set out to find. I didn't find the classroom portraits I hoped for either. But then again, that's how ideas work. We don't discover something entirely new. Sometimes we simply notice a stream we've walked past on that very same trail. 

I wonder where it goes. 

But that's all for another day.