What Do High School Teachers Mean by Saying “I Pose My Own Problems”?

Abstract

The aim of this chapter was to identify mathematics teachers’ conceptions of the notion of “problem posing.” The data were collected from a web-based survey, from about 150 high school mathematics teachers, followed by eight semi-structured interviews. An unexpected finding shows that more than 50% of the teachers see themselves as problem posers for their teaching. This finding is not in line with the literature, which gives the impression that not many mathematics teachers are active problem posers. In addition, we identified four types of teachers’ conceptions for “problem posing.” We found that the teachers tended to explain what problem posing meant to them in ways that would embrace their own practices. Our findings imply that most of the mathematics teachers are result-oriented—as opposed to being process-oriented—when they talk about problem posing. Moreover, many teachers who pose problems doubt the ability of their students to do so and consider problem-posing tasks inappropriate for their classrooms.

AppendixThe Survey

Selecting Problems to Be Used in Mathematics Teaching

This questionnaire is part of a research done in the Department of Education in Technology and Science at the Technion. The research aims at understanding how mathematics teachers select problems for their teaching. None of the questions has a “right” or “wrong” answer. It is very important that you will answer all the questions of this brief questionnaire.

We would like to thank you for the time you dedicated to answer this questionnaire.

• 1. The last three years I teach grades:

  7

  8

  9

  10

  11

  12

• 2. Usually I teach class levels

  Strong

  Medium

  Weak

• 3. Describe all your special teaching project if any ________________________

• 4. To what extent do you use the following resources for selecting mathematical problems for your teaching?

  	Almost always	Often	Sometimes	Rarely	Almost never
  Textbooks
  Other books
  Internet resources
  Professional development workshops
  Fellow teachers
  My prior academic study
  Pose my own problems
  Problem posed by students
  Others

  Point out any other resources that you use ______________________________

• 5. To what extent do the following situations occur in your teaching?

  	Almost always	Often	Sometimes	Rarely	Almost never
  Use my own problems
  Activate students in problem posing
  Promote class discussion
  Encourage group work

• 6. For what purposes do you pose your own problems?

  _______________________________________________________________

• 7. Seniority in mathematics teaching

  1–2 years

  3–5 years

  6–10 years

  More than 10 years

• 8. To what extent the following situations are in your responsibility:

  	Little	Much
  Planning the school year
  Planning the lessons
  Execute my planning
  Select the mathematical problems to be used

• 9. Education

  	Math	Math Ed.	Science Ed.	Computer science	Engineering	Biology	Physics	Others
  B.A./B.Sc.
  M.A./M.Sc.
  Ph.D.
  Other

• 10. Personal details (optional)

  • Name: ________________

  • Email: ________________

  • Phone: ________________

• 11. I am interested in receiving updates about the results of the study

  Yes

  No