Abstract
The research presented in the article consists of two parts. Firstly, opinions on mathematical problem quality are explored within four groups of participants (novices, specialists and experts in problem posing; high school students who never posed their own problems). Secondly, self-reflections written by the participants who have some experience in problem posing (novices, specialists and experts) are explored and compared with the general view of problem quality received in the first part of the research. The more experienced problem posers have more requirements on problem quality (both as general requirements and within their own work on posing problems). There is a slight decrease in ability to notice important features of mathematical problem quality after the first experience in problem posing. Experts lay stress on mathematical features of the problem whilst novices and specialists more on problem – student interaction.
Highlights
In this article, the term “mathematical problem” means a word problem that is more difficult and more elaborated than a common exercise. Stehlíková (2000) says that the exercise becomes a problem if the solver does not immediately see the solving strategy and he / she has to search for it
The amount of their coded quotations is a bit lower (3.6 coded quotations per person). Their essays are shorter than the experts’ ones. Experts usually convey their statements in detail whilst specialists are often more concise. (Sometimes there are one-word quotations only – e.g. “Correctness”.) The least requirements on problem quality are observed by novices (1.6 coded quotations per person)
The research presented in this study shows that skilled problem posers have a more complex set of requirements on problem quality
Summary
The term “mathematical problem” means a word problem that is more difficult and more elaborated than a common exercise. Stehlíková (2000) says that the exercise becomes a problem if the solver does not immediately see the solving strategy and he / she has to search for it. The presented study is a part of research on the comparison of problem posing process by problem posers on various experience levels. A model of problem posing process of “skilled problem posers1” and novices has been made by Pelczer and Gamboa (2009). It includes the phases of Setup, Transformation, Formulation, Evaluation and Final assessment. The novices usually use a linear problem posing model (e.g. Setup – Formulation – Evaluation). (If a novice finds out that his / her suggested problem is not good, he / she does not transform it but drops it completely and starts from the beginning.) On the contrary, the model of problem posing process by skilled problem posers is cyclic. The wider research which is the source of presented study (e.g. Patáková, 2013b) deals with three categories of respondents: 1. Novices: Participants with nearly no experience in problem posing
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