I'm looking for some working definitions and operationalisation of mathematical problem solving and mathematical word problems to support this section of my literature review. Do word problems sit within problem solving or are they interrelated?
This is a very good question.
The penultimate source of ideas on problem solving in mathematics is G. Polya's little book:
https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pdf
nicely summarized in
https://math.berkeley.edu/~gmelvin/polya.pdf
and fully available at
https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X
In a more advanced setting in which plausible reasoning takes center stage in solving problems (including word problems), Polya's two volume work on analogy is source of helpful ideas and methods:
https://uberty.org/wp-content/uploads/2016/01/Polya_Mathematics_and_Plausible_Reasoning1.pdf
A book by Terence Tao
Solving mathematical problems. A personal perspective.
could be helpful too.
All the books listed above are truly wise works. But if in a few words ... One famous German mathematician once said: "Mathematics is a language." Further, respectively.
I just now found a recent Springer volume:
A. Engel, Problem-Solving Strategies, downloadable from
http://gimnazija-izdijankoveckoga-kc.skole.hr/upload/gimnazija-izdijankoveckoga-kc/multistatic/748/Problem-Solving_Strategies_Engel.pdf
This is an excellent book with many helpful examples and problem-solving methods.
My book, "The Language of Mathematics: Utilizing Math in Practice", deals with this subject, in particular, "translating" a natural language description into a mathematical model. See http://www.language-of-mathematics.eu and the link there to the publisher's (Wiley's) web page for the book.
- Badges
- Science topic
- Similar topics
- Mathematics