Inquiry-based learning and teaching of calculus in continuing education for in-service teachers.

Inquiry-based learning and teaching of calculus in continuing education for in-service teachers.

The project aims to investigate how inquiry-based practices in calculus can support teachers’, students’, and teacher educators’ development of mathematical competencies and inquiring habits of mind.



The Norwegian government invests approximately 1,5 billion NOK yearly in continuing education for in-service teachers (Ministry of Education and Research 2019) to promote their competency building, as formal requirements of ECTS-credits for teaching a subject are implemented in 2025. Considering the high investments in continuing education and its important aim, research on didactical processes supporting students’ learning, is important. Calculus is the first course that the students meet at the continuing education program in mathematics at NMBU. The course has been given as a traditional calculus course, covering single variable calculus as well as some basic multivariate calculus. We see that many students primarily obtain an instrumental understanding (Skemp 1976) of the mathematics without understanding the core ideas of calculus.


Over the last decade, there has been an increased focus on developing competences for sustainable and life-long learning (Artigue and Blomhøj 2013, Safford-Ramus, Misra et al. 2016). Creative problem-solving and critical thinking are core areas in this respect, and are also prominent in the new curriculum that is being introduced in Norwegian schools (The Norwegian Directorate for Education and Training 2019). There is a broad consensus in mathematics education literature that providing students with the opportunity to engage in student-centered and inquiry-based ways of learning is highly beneficial for in-depth learning of mathematical concepts and ideas, and for the ability to apply the knowledge critically through evaluation, reflection, and metacognitive awareness (e.g. Jaworski 2004, Artigue and Blomhøj 2013, Maaz and Artigue 2013, Dorier and Mass 2014). Inquiry-based learning and teaching emphasize classroom practices in which students inquire and pose questions, explore and evaluate. Learning is driven by open questions and multiple-solution strategies. Teachers support and challenge all students. Promoting a shared sense of ownership is highlighted, so is the development of inquiring minds (Artigue and Blomhøj 2013). This project aims at studying how inquiry-based teaching approaches can promote in-depth learning of calculus for students participating in a continuing education program for secondary school teachers at NMBU. The overarching project question is: How can inquiry-based practices in calculus support teachers’, students’, and teacher educators’ development of competencies (e.g. problem-solving abilities, conceptual understanding, reasoning abilities) and inquiring habits of mind?

More about the project

The project uses a design-based research methodology approach (Barab and Squire 2004, Anderson and Shattuck 2012), where our primary goal is, through cycles of planning, implementation, and reflection, to develop our teaching in ways that promote life-long and in-depth learning of calculus, as well as developing inquiring minds, amongst the students. The teaching sequences emphasize problem-solving and multiple-solution strategies, explorations, discussions, and mathematical reasoning, and both students’ learning and teachers’ ways of using inquiry are objects of study in order to develop several layers (Jaworski 2004) of the teaching of mathematics. The data collection consists of video observation and audio recorded conversations, following school teachers both in their role as students in the continuing education course, and mathematics teachers and facilitators in their own classroom. 



Anderson, T. and J. Shattuck (2012). "Design-based research: A decade of progress in education research?" Educational researcher 41(1): 16-25.  

Artigue, M. and M. Blomhøj (2013). "Conceptualizing inquiry-based education in mathematics." ZDM Mathematics Education 45: 797-810.        

Barab, S. and K. Squire (2004). "Design-based research: Putting a stake in the ground." The journal of learning sciences 13(1): 1-14.          

Dorier, J. and K. Mass (2014). Inquiry-based mathematics education. Dordrecht, Heidelberg, London, New-York, Springer.          

Jaworski, B. (2004). Grappling with complexity: Co-learning in inquiry communities in mathematics teaching development. Proceedings of the 28th conference of the international group for the psychology of mathematics education. Bergen, Bergen University College. 1: 17-36.

Maaz, K. and M. Artigue (2013). "Implementation of inquiry-based learning in day-to-day teaching: a synthesis." ZDM Mathematics Education 45(6): 779-795. 

Safford-Ramus, K., et al. (2016). The troika of adult learners, lifelong learning, and mathematics. Switzerland, Springer Nature.

Skemp, R. R. (1976). "Relational Understanding and Instrumental Understanding." Mathematics Teaching 77: 20-26.