Emergent modeling: discrete graphs to support the understanding of change and velocity

By L. M. Doorman, K.P.E. Gravemeijer. 2009

94 citations recorded by the source corpus.

In this paper we focus on an instructional sequence that aims at supporting students in their learning of the basic principles of rate of change and velocity. The conjectured process of teaching and learning is supposed to ensure that the mathematical and physical concepts will be rooted in students’ understanding of everyday-life situations. Students’ inventions are supported by carefully planned activities and tools that fit their reasoning. The central design heuristic of the instructional sequence is emergent modeling. We created an educational setting in three tenth grade classrooms to investigate students’ learning with this sequence. The design research is carried out in order to contribute to a local instruction theory on calculus. Classroom events and computer activities are video-taped, group work is audio-taped and student materials are collected. Qualitative analyses show that with the emergent modeling approach, the basic principles of calculus can be developed from students’ reasoning on motion, when they are supported by discrete graphs.

Subfields: Computer Science Applications, Developmental and Educational Psychology, Education

View Paper: https://www.semanticscholar.org/paper/7f03509136f12f390de00c177b3556e6803dfc51

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Developmental and Educational Psychology

1. C. Gurel
2. A. Abassian
3. Mahmut Kertil
4. J. Bostic
5. Sarah B. Bush
6. Farshid Safi

In Education

1. C. Gurel
2. A. Abassian
3. Mahmut Kertil
4. J. Bostic
5. Sarah B. Bush
6. Farshid Safi

Citations in the corpus

• Five different perspectives on mathematical modeling in mathematics education (2020, background): “…emergent modeling perspectives tend to investigate the teaching and learning of mathematical topics, such as calculus (Gravemeijer & Doorman, 1999; Doorman & Gravemeijer, 2009), data analysis (Gravemeijer, 2002), and functions (Doorman, Drijvers, Gravemeijer, Boon, & Reed, 2012), through the…”
• Mathematical Modeling: A Bridge to STEM Education (2016, background): “From the perspective of seeing modeling as vehicle to teach mathematics, mathematical modeling activities are considered to be meaningful problem solving situations for teaching mathematics in a meaningful way (e.g., Lesh & Doerr, 2003; Doorman & Gravemeijer, 2009).”