“ADHD makes it sound like I have a lack of focus, but I think of it more like a mismanagement of focus.” -student with ADHD

Here are the first few pages of a recent calculus midterm of one of my students who has been diagnosed with ADHD. I’ll let you take a peek at what you see before I give my reflection.

Now, I want you to go back and take a look at the first page, where question #1 ii required the knowledge of the derivative of *log_{3}(x)*. You can see that the student set up the equation* log_{3}(x) = b* in order to help him determine the derivative using the quotient rule. But the giant “*?*” beside *b’* caught my interest. (Of course, if there is anything else of interest to you please leave a comment!)

Now, he begins playing around at the top of the page, recalling rules for how to deal with logarithms. There is a *y = 3^x* and a *y = log_{3}(x)* indicating to me that he was thinking about potentially finding the derivative using inverse functions or implicit differentiation. However, not much happens here, so we will catch up in a few pages.

The next page is nothing special, in that he tackles the next couple derivative questions without making any more thoughts on the log base three problem he is having. But check out the top of the third page. Here, he correctly gets the relationship between exponentials and logarithms: *3^x = b* means *log_{3}(b) = x* (or vice versa). Then there is a little bit of play at the bottom of the page trying to re-write this relationship in various ways to potentially get a nice equation to differentiate. Aside from now having the inverse relationship solidified, not much headway is gained on the initial problem.

Finally, on the last page, we see one last attempt to think about *3^x = u*, perhaps a nod to the variables I use when doing the chain rule (*dy/dx = dy/du * du/dx*). This is the final attempt to determine the solution to the log base three problem, and the rest of the test continues in a normal fashion.

The most interesting thing from my perspective is embedding what I see in a cognitive load theory setting. We know that the working memory has limited capacity to hold and synthesize information. This information can come from either environmental stimuli, or as schema entering from long-term memory. I was always under the impression that trying to cut back environmental stimuli for students with ADHD was a must, as this allows the working memory to focus more on the task at hand. However, seeing this test had me thinking a bit deeper.

At the college level, we are typically good at minimizing outside distractions; doors are closed, rooms are quiet and I cross my fingers that maintenance has fixed any lights that are in strobe-mode. However, as I do not have ADHD myself, I cannot comment on what outside stimuli might still be entering the working memory. Perhaps a song that was heard earlier that morning? Whether or not he forgot his lunch at home? What plans are for after school? So let’s assume that some working memory space has been allocated to this.

Now it’s test time. Since this particular student is quite adept at mathematics, most schema enter the working memory quite effortlessly. We can see this demonstrated on page 2, where some complex derivatives are handled. From my perspective, it is actually the snag of not knowing the derivative of *log_{3}(x)* that pushes the working memory over its capacity. Look at how often he returns back to the problem – at the top of page 1, the top & bottom of page 3, and at the top of page 4.

Just how taxing is it on the working memory to be subconsciously processing this log base three problem over the course of four test questions? How debilitating would this be if there were not well-developed schema to draw from when writing this test? How much more success would there have been if he was able to dislocate this log base three problem from his working memory, instead of it continually returning back to occupy his focus? I find these questions super interesting, and I have thoughts, but no particular answers. If there are any readers who have studied cognitive load theory from the perspective of individuals with ADHD, I’d love to read a bit more on this topic.

## Leave a Reply