Problem Solving in Mathematics Instruction and Teacher Professional Development pp 317-335 | Cite as

# Teacher Questioning in Problem Solving in Community College Algebra Classrooms

## Abstract

In this chapter, we focus on the ways two community college instructors worked with students to demonstrate the solution of contextualized algebra problems in their college algebra lessons. We use two classroom episodes to illustrate how they sought to elicit students’ mathematical ideas of algebraic topics, attending primarily to teachers’ questioning approaches. We found that the instructors mostly asked questions of lower cognitive demand and used a variety of approaches to elicit the mathematical ideas of the problems, such as using examples relevant to the students and dividing the problems into smaller tasks, that together help identify a solution. We conclude by offering considerations for instruction at community colleges and potential areas for professional development.

## Keywords

Questioning practices Algebra Community colleges## Notes

### Acknowledgments

We thank Linda Leckrone and Cody Michael for assistance with the analyses. Funding for this work was provided by the National Science Foundation (EHR #1561436). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

## References

- American Mathematical Association of Two-Year Colleges. (2018).
*IMPACI: Improving mathematical prowess and college teaching*. Memphis, TN: Author.Google Scholar - Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., et al. (Eds.). (2001).
*A taxonomy for learning, teaching, and assessing*. New York: Longman.Google Scholar - Blair, R., Kirkman, E. E., & Maxwell, J. W. (2018).
*Statistical abstract of undergraduate programs in the mathematical sciences in the United States. Fall 2015 CBMS Survey*. Providence, RI: American Mathematical Society. Document in production.CrossRefGoogle Scholar - Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more “real”?
*For the Learning of Mathematics, 13*(2), 12–17.Google Scholar - Brousseau, G. (1997).
*Theory of didactic situations in mathematics*(trans: Balacheff, N.). Dordrecht, The Netherlands: Kluwer.Google Scholar - Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning.
*Educational Researcher, 18*(1), 32–42.CrossRefGoogle Scholar - Bahr, P. R. (2010). Revisiting the efficacy of postsecondary remediation: The moderating effects of depth/breadth of deficiency.
*Review of Higher Education, 33*, 177–205.Google Scholar - Herbst, P. (2003). Using novel tasks in teaching mathematics: Three tensions affecting the work of the teacher.
*American Educational Research Journal, 40*, 197–238.CrossRefGoogle Scholar - Herbst, P., & Chazan, D. (2011). On creating and using representations of mathematics teaching in research and teacher development.
*ZDM Mathematics Education, 43*, 1–5.CrossRefGoogle Scholar - Jaworski, B., Mali, A., & Petropoulou, G. (2017). Critical theorising from studies of undergraduate mathematics teaching for students’ meaning making in mathematics.
*International Journal of Research in Undergraduate Mathematics Education, 3*(1), 168–197.CrossRefGoogle Scholar - Larson, L. R., & Lovelace, M. D. (2013). Evaluating the efficacy of questioning strategies in lecture-based classroom environments: Are we asking the right questions?
*Journal on Excellence in College Teaching, 24*(1), 105–122.Google Scholar - Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016).
*Problem solving in mathematics education, ICME-13 topical surveys*. Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-40730-2_1CrossRefGoogle Scholar - Mayer, R. E. (2003).
*Learning and instruction*. Upper Saddle River, NJ: Prentice Hall.Google Scholar - Mesa, V. (2010). Student participation in mathematics lessons taught by seven successful community college instructors.
*Adults Learning Mathematics, 5*(1), 64–88.Google Scholar - Mesa, V., Celis, S., & Lande, E. (2014). Teaching approaches of community college mathematics faculty: Do they relate to classroom practices?
*American Educational Research Journal, 51*(1), 117–151.CrossRefGoogle Scholar - Mesa, V., & Herbst, P. (2011). Designing representations of trigonometry instruction to study the rationality of community college teaching.
*ZDM The International Journal on Mathematics Education, 43*, 41–52.CrossRefGoogle Scholar - Mesa, V., & Lande, E. (2014). Methodological considerations in the analysis of classroom interaction in community college trigonometry. In
*Transforming mathematics instruction*(pp. 475–500). Cham, Switzerland: Springer.Google Scholar - Mesa, V., Ullah, A., Mali, A., & Diaz, L. (2018).
*Authenticity of instructor and student questions in algebra instruction at community colleges: An exploratory study*. Ann Arbor, MI: University of Michigan.Google Scholar - Mesa, V. (2017). Mathematics education at public two-year colleges. In J. Cai (Ed.), First compendium for research in mathematics education (pp. 949-967). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- National Council of Teachers of Mathematics. (2000).
*Principles and standards for school mathematics*. Reston, VA: Author.Google Scholar - Paoletti, T., Krupnik, V., Papadopoulos, D., Olsen, J., Fukawa-Connelly, T., & Weber, K. (2018). Teacher questioning and invitations to participate in advanced mathematics lectures.
*Educational Studies in Mathematics, 98*(1), 1–17.CrossRefGoogle Scholar - Perkins, D. (2000).
*Archimedes’ bathtub: The art of breakthrough thinking*. New York: W.W. Norton and Company.Google Scholar - Polya, G. (1971).
*How to solve it: A new aspect of mathematical method*(2nd ed.). Princeton, NJ: Princeton University Press.Google Scholar - Resnick, L., & Glaser, R. (1976). Problem solving and intelligence. In L. B. Resnick (Ed.),
*The nature of intelligence*(pp. 205–230). Hillsdale, NJ: Erlbaum.Google Scholar - Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.),
*Handbook of research on mathematics teaching and learning*(pp. 334–370). New York: Simon and Schuster.Google Scholar - Temple, C., & Doerr, H. M. (2012). Developing fluency in the mathematical register through conversation in a tenth-grade classroom.
*Educational Studies in Mathematics, 81*(3), 287–306.CrossRefGoogle Scholar - Viirman, O. (2015). Explanation, motivation and question posing routines in university mathematics teachers’ pedagogical discourse: A commognitive analysis.
*International Journal of Mathematical Education in Science and Technology, 46*(8), 1165–1181.CrossRefGoogle Scholar - Watkins, L., Duranczyk, I., Mesa, V., Ström, A., & Kohli, N. (2016). Algebra instruction at community colleges: Exploration of its relationship with student success: National Science Foundation (EHR #1561436).Google Scholar