Monday, October 09, 2006

How the Brain Looks with Visual vs. Symbolic Math

These researchers may have not found what they were looking for because the look of the brain solving math problems with a visual model vs. through algebraic symbols (x & y), looked largely the same:

From another perspective, though, it is interesting to see how much working memory is involved with algebraic problem solving. It might be also explain while young precocious math students may still prefer visual mathematical problem solving to more symbolic methods. It may not be that they aren't able to think symbolically, but rather their working memories are the limiting factor (remembering the Blessings and Burdens post?...the higher the IQ, the weaker the working memories in the early years).

Visual vs. Symbolic Math, Algebra, and fMRI
The Blessings and Burdens of High IQ


  1. Many many years after wrestling with algebra (and being defeated) I understood that I had severe problems with remembered any type of coding or non-contextual material. And more recently, I've learned about working memory and know that mine is definitely lacking. Why aren't educators taught to look for these problems in their students and find alternative teaching methods? That's a rhetorical question, of course. The sense of frustration still hasn't gone away.

  2. We can really understand where you're coming from. Working memory has really been underestimated in its importance for learning. It's often the "gatekeeper" for tasks (determining whether or not something will be mastered or learned to automaticity). But teachers have not been taught how to vary how subjects or principles are taught to minimize the demands on working memory. This is a basic teaching efficiency issue, that we hope will become a bigger theme in educational pedagogy.

  3. What really strikes me is how quickly Kerry Lee, Zee-Ying Lim and Stephanie Yeung jump to pedagogical recommendations.

    Also, I do not agree with your comment that

    "But teachers have not been taught how to vary how subjects or principles are taught to minimize the demands on working memory."

    Maybe, it is exactly the working memory that has to be trained and expanded?

    I would compare the model/symbolic method to pointing a finger / saying a sentence in a conversation. A finger frequently suffices, but we have to teach our children to speak.

  4. I understand your viewpoint. I guess I see that working memory is a great gatekeeper for many students in many that it would be helpful for teachers to be explicitly taught how to break down subjects to avoid working memory overload.

    An additional goal would be to strengthen the working memory of the student, but this is a situation where it would beneficial for everyone to be conscious of the fact that working memory is sometimes the weak link.

    There may be a limit for some people's working memories - so that they can only take in so much at one time...these folks may still be quite good learners. They may be more like hummingbirds who need to take multiple little sips at a time, rather one huge gulp.

    Please don't think that we are pointing fingers. It might be valuable to identify the source of different people's problems, and recognizing that teachers, students, and parents / tutors may have their own ways to help.

  5. Anonymous3:26 PM

    So, if I am understanding this correctly, this might explain why my 8 year old, with an age equivalant working memory of a teen ager, is flying thru algebra at this point? Is that correct?