Teaching via Problem-Solving or Teacher-Centric Access: Teachers’ Views and Beliefs

  • Anne MöllerEmail author
  • Benjamin Rott


This paper reports on an exploratory study, which investigates teachers’ preferences about the implementation of teaching via discovery learning and problem-solving. This discovery way of teaching is compared to receptive learning and a teacher-centric access in mathematics lessons. As most teachers seem to choose the latter way of teaching, we want to get to know, what reasons teachers name for using or not using discovery methods. Therefore, semi-standardized interviews with five teachers were conducted, analysed, and interpreted. This sample encompasses two teachers who prefer a receptive way of teaching, one teacher who uses discovery learning a lot and another two teachers who use both methods. A comparison of two selected teachers reveals that even if teachers prefer a different way of teaching, they may mention the same concerns about discovery learning. They do, however, differ in the number of advantages of discovery learning they mention in the interview. Teaching time and students’ performance in mathematics are mentioned as important decision-making factors. As expected, the teacher who uses discovery learning mentions a lot more profits than his colleague.


Teachers’ view Beliefs Problem-solving Teachers’ preferences Discovery learning 


  1. Ausubel, D. P. (1968). Educational psychology, a cognitive view. New York: Holt. Rinehart & Winston.Google Scholar
  2. Bruner, J. (1974). Toward a theory of instruction. Berlin: Berlin-Verlag.Google Scholar
  3. Cai, J. (2003). What research tells us about teaching mathematics through problem solving. In F. K. Lester Jr. (Ed.), Research and issues in teaching mathematics through problem solving (pp. 241–254). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  4. Hofer, B. K. (2002). Epistemological world views of teachers: From beliefs to practice. Issues in Education, 8(2), 167–173.Google Scholar
  5. Lorenz, J. H. (1991). Reviewed Work: Entdeckendes Lernen im Mathematikunterricht. Einblicke in die Ideengeschichte und ihre Bedeutung für die Pädagogik by Heinrich Winter. Educational Studies in Mathematics, 22(1), 87–93.CrossRefGoogle Scholar
  6. Mayring, P. (2015). Qualitative Inhaltsanalyse. Grundlagen und Techniken (12. Auflage). Weinheim & Basel: Beltz.Google Scholar
  7. Neber, H. (1981). Neuere Entwicklungen zum entdeckenden Lernen. In H. Neber (Ed.), Entdeckendes Lernen (pp. 45–92). Weinheim: Beltz.Google Scholar
  8. Pehkonen, E. (1994). On teachers’ beliefs and changing mathematics teaching. Journal für Mathematik-Didaktik, 15(3/4), 177–209.CrossRefGoogle Scholar
  9. Rott, B. (2016). Problem solving in the classroom: The role of beliefs in the organization of lessons with the subject problem solving. In T. Fritzlar, D. Assmus, K. Bräuning, A. Kuzle, & B. Rott (Eds.), Problem solving in mathematics education. Proceedings of the 2015 joint conference of ProMath and the GDM working group on problem solving (pp. 201–213). Münster: WTM.Google Scholar
  10. Sawada, T. (1997). Developing lesson plan. In J. P. Becker & S. Shimada (Eds.), The open-ended approach: A new proposal for teaching mathematics (pp. 23–35). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  11. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.Google Scholar
  12. Winter, H. (2016). Entdeckendes Lernen im Mathematikunterricht. Einblicke in die Ideengeschichte und ihre Bedeutung für die Pädagogik (3rd ed.). Wiesbaden: Springer Spektrum.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of Duisburg-EssenEssenGermany
  2. 2.University of CologneKölnGermany

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