Huang - Math in Scratch

I thought I was good at math until I got to multivariable calculus and suddenly, nothing made sense anymore. I feel like having some sort of computational model or program in that class could’ve been really helpful. But anyway, for grade school math, one of the things that I always found difficult was those word problems that ask you to figure out the speed of some moving transportation device given a certain time or distance, etc.

Like this problem from this website: http://purplemath.com/modules/distance.htm.

A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in three hours.

Or this problem (http://www.shelovesmath.com/algebra/intermediate-algebra/systems-of-linear-equations/):

Lia walks to the mall from her house at 5 mph.  10 minutes later, Lia’s sister Megan starts riding her bike at 15 mph (from the same house) to the mall to meet Lia.  They arrive at the mall the same time.  How far is the mall from the sisters’ house?  How long did it take Megan to get there?

I don’t know what it was, maybe it was just too many words for me to read or that I didn’t really understand the concept of or relationship between speed, time, and distance, but I always found these problems challenging. Maybe it would be helpful for learners to better understand these problems if they could use programming to work through it. I’m not exactly sure what that would look like in terms of the actual program that we would ask students to write. It would be great to represent this visually, though. And maybe someone else will have an idea.

After this past week with the USN kids, one thing that I have been struggling with is how to present concepts to learners who are programming. Programming seems new enough to them that there are many challenges in just the language; how can you entice a learner to also care about the concepts? Is it enough to just provide them with the intuition or do we actually need to show learners that this concept we are teaching them plays out in their program in this way? I am afraid just giving them intuition would provide too superficial an understanding, like the concerns raised in the article that looked at different collision scenarios (Simpson, 2005). What can we do to make sure that these concepts are getting through to our learners while they are programming?