Important paper at SIGCSE 2015: Transferring Skills at Solving Word Problems from Computing to Algebra Through Bootstrap

May 11, 2015 at 7:44 am 8 comments

I was surprised that this paper didn’t get more attention at SIGCSE 2015.  The Bootstrap folks are seeing evidence of transfer from the computing and programming activities into mathematics performance.  There are caveats on the result, so these are only suggestive results at this time.

What I’d like to see in follow-up studies is more analysis of the students.  The paper cited below describes the design of Bootstrap and why they predict impact on mathematics learning, and describes the pre-test/post-test evidence of impact on mathematics.  When Sharon Carver showed impact of programming on problem-solving performance (mentioned here), she looked at what the students did — she showed that her predictions were met.  Lauren Margulieux did think-aloud protocols to show that students were really saying subgoal labels to themselves when transferring knowledge (see subgoal labeling post).  When Pea & Kurland looked for transfer, they found that students didn’t really learn CS well enough to expect anything to transfer — so we need to demonstrate that they learned the CS, too.

Most significant bit: Really cool that we have new work showing potential transfer from CS learning into other disciplines.

Many educators have tried to leverage computing or programming to help improve students’ achievement in mathematics. However, several hopes of performance gains—particularly in algebra—have come up short. In part, these efforts fail to align the computing and mathematical concepts at the level of detail typically required to achieve transfer of learning. This paper describes Bootstrap, an early-programming curriculum that is designed to teach key algebra topics as students build their own videogames. We discuss the curriculum, explain how it aligns with algebra, and present initial data showing student performance gains on standard algebra problems after completing Bootstrap.

via Transferring Skills at Solving Word Problems from Computing to Algebra Through Bootstrap.

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8 Comments Add your own

  • 1. Bonnie  |  May 11, 2015 at 10:55 am

    Two thoughts… First, why do we need to prove ourselves by worrying if learning computing transfers to math? Isn’t the acquisition of computational thinking skills enough? It seems to be that algorithms and computing have become really important in all kinds of areas.

    Secondly, I have never been convinced that there is much relationship between skill at programming and skill at math. I have seen too many strong math students utterly fail at their first programming course, and too many really good programmers (and I don’t mean people who could just sling out code, but people who really understood the algorithms) who were not that great at math. This was particularly true of many of the best software engineers I met in college.

    What I have noticed in years of teaching is that many of the best computer science students are also strong analytical writers. They are the kind of people who can really dig in and analyze something, and then write up their conclusions in an organized way. I think the fact that we have so many non native speakers of English in our field obscures this. I often suspect that in their own languages, the awesome CS students from China or Russia can also write well.

    So, maybe we should be studying whether learning to program improves ones writing skills….

    • 2. Mark Guzdial  |  May 11, 2015 at 11:11 am

      I completely agree that acquisition of computational thinking skills are enough, Bonnie. Many people suspect that there is transfer from programming skills to other areas of STEM — and maybe even writing, as you suggest. Investigating those questions is interesting and worthwhile. It may make learning computing more valuable. My own research is just focused at making computing education available, not showing that it influences other learning, but kudos to those who are working that hard path!

      • 3. gasstationwithoutpumps  |  May 11, 2015 at 12:24 pm

        Transfer to improved writing seems somewhat unlikely to me. I think that what Bonnie is seeing is that smart people with good skills in both analysis and synthesis are both good writers and good programmers. It isn’t clear how much those skills are developed by a programming class and how much they are simply exposed.

    • 4. Kathi Fisler  |  May 11, 2015 at 8:36 pm

      I’m one of the authors of the cited paper (thanks for the plug, Mark!). We care about transfer from programming to math because we are trying to argue for using Bootstrap to embed computing into middle/high-school math classes. Having computing transfer to math is important to argue for this approach (given the already full math curricula).

      Why the embedding approach? All schools require math. Embedding computing into math becomes a strategy for broadening participation. This strategy requires training math teachers to teach some computing. If the approach to computing aligns with math, it becomes more feasible that math teachers could do this. Yes, we need to study this teacher-transfer question formally (and are beginning to do so). Seeing whether the skills transfer in the students, though, is the first step in the chain.


    • 5. KDecker  |  May 12, 2015 at 11:57 am

      “skill at math” (and general “skill at programming”) may be too broad a statement here. My observation is more like “being able to solve word problems/use/apply math (especially algebra)” relates to “being able to setup/design and solve problems using a computer program”.

      I too know many students who struggle with intro programming, but are “good at math”, but “good at math” for them just means they got A’s in trig, pre-calc, and calc 1, so they know how to solve simultaneous equations, integrate, differentiate, and graph things, but they typically can’t USE those skills to solve a (pure math) application problem—they can’t write/setup the equation(s) to solve/differentiate/graph/etc.

    • 6. shriramkrishnamurthi  |  May 23, 2015 at 11:46 am

      I’m a different author of this paper (like my co-author, I should say, thanks for the plug, Mark!) and I’ll present yet another take on this.

      Kathi Fisler gave the pragmatic one about broadening participation, an argument that Matthias Felleisen and I made back in 2008 ( But there is another, much more important, reason: Using computing, we can potentially change the way math is taught. Surely getting more people to become comfortable mathematically is a valuable end in its own right. But to demonstrate that, we have to show transfer. That’s an end in itself, not just a justification for teaching computing.

      Bootstrap helps students progress in their understanding of algebra: rather than just viewing it as a symbol manipulation activity, they can start to appreciate it through physical interpretations. The same approach leads (I believe) to potentially new and (if the evaluation holds) better ways to understand topics like calculus, which are currently an even bigger miasma of symbol manipulation without understanding.

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