I am looking for classifications of algebra story problems. I have read the work of R.E. Mayer:
Mayer, R.E. (1981). Frecuency norms and structural analysis of algebra story problems into families, categories, and template. Instructional Science, 10, 135-175.
My first objective is to design a base of algebra problems, as complete as possible, and then work on solving these problems with an intelligent tutor.
It sounds like you're looking for functional forms, in addition to more generic features? One classification from Koedinger and Nathan is start-unknown versus end-unknown. I'll look into the Mayer.
Dear Haiwen,
The classification start-unknown versus end-unknown is interesting, but my objective is very different from the study of Koedinger.
I am interested in the design of an instructional program for the learning of algebra story problems. If you try that your students learn and practice algebra problems, you will think first what kind of problems you want your students solve. I am in this first stage.
Regards,
Carlos
So you mean functional form? At the elementary operation this is an issue of "what's the operation", and later on this goes to linear/quadratic/exponential, etc. The best treatment of story problems that I've read is the Verschaffel book, "Words and Worlds"
If you talk about story problems that can be solved with a linear ecuation, do they have all the same level of dificulty? I think this is not the case. I'm looking for a finer classification, perhaps depending on the form of the linear equation.
I know the work of Verschaffel. In arithmetic problems, semantic classification is a good option to me. I do not find something similar in algebra story problems, but I am not expert in this domain.
Thank you for your help.
Regards,
Carlos
And are you restricting within a single functional form? So, for all linear equations, those which are best modeled by, say, slope-intercept, two-intercepts, standard form etc?
I started sorting within linear equations, according to the form. For example, algebra story problems that can be modeled by an equation:
ax + b = c, ax + b = cx + d, and so on. All are linear equations, but I guess it will be more difficult to translate from the story problem and solve the equation in the second case.
But I find it very strange not easily found some literature on the subject. I see a lot of research on problems of algebra, but not an attempt to classify problems. For example, if you want to write a textbook of mathematics and include algebra problems, what is your reference for the field of algebra problems? How do you know that the sample of problems that you choose for your textbook is representative of the kinds of problems students must solve?
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