Pro Tip

Anytime anybody asserts anything disparaging (or affirming) about contextual problem solving in mathematics, it’s helpful to ask “what representation of problem solving are you talking about?” Because a) unless the student is actually outside the classroom in the context, you (or more likely your textbook’s publisher) have had to represent that context somehow for use in the classroom, and b) not all representations are created equal. Also, not to get too big for my first-year PhD student britches either but this seems like a blind spot in the existing research.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. You might be interested in contributing to Richard Lesh’s work on mathematical modeling. He and an expanding group of colleagues have done a lot of excellent work in this area. Beyond Constructivsm (with Helen Doerr) outlines his key ideas and provides several sample problems.

    In a nutshell:
    “One of the most significant characteristics that make model-eliciting activities different than most traditional textbook word problems is that, for the latter, the main thing that’s problematic (beyond difficulties associated with computational skills that such problems generally emphasize) is that students must make meaning out of a symbolically described situation. Whereas, for model-eliciting activities, what’s most problematic is that students must make productive symbolic descriptions of meaningful situations.”
    (from article @; also includes a number of sample problems)

  2. You might want to do some research on developmental learning theory. Also, seek out some articles by Dan Willingham, Joanne Olson and myself about representation types. This might be a hole in the math ed research, but not the greater education literature. That said, finding your niche is key to success in academia!

  3. Sorry for the repeated comments, but I found this reference that will be up your alley for representational types:

    Olson, J.K. (2008). The Science Representation Continium. Science and Children, 46 (1), 52-55.