Traditional pedagogy has focused on rote memorization of facts and skills with little attention paid to the conceptual relationships involved in mathematics. As passionate educators of mathematics, many want to encourage a shift in pedagogy by framing the content and skills of mathematics with conceptual understandings. Table 4 illustrates an example of an overarching generalization and a topical generalization that I have from my book.
Statements of conceptual understandings are intended for teachers’ reference only as in a concept-based model we do not tell students what they need to understand; we draw these conceptual understandings from students through inductive, inquiry based learning environments.
Research has shown that a concept-based model for curriculum and instruction will:
Increase motivation for learning as this model addresses the “why” we are learning what we are learning
Require deeper intellectual engagement as students are encouraged to form their own conceptual understandings through inquiry based learning
Provide opportunities for social constructivist learning where students are given opportunities for personal meaning making through collaborative learning engagements
Increase academic achievement. Gao and Bao (2012) found that adopting a concept-based learning environment ultimately results in increased understanding and therefore increased academic achievement.
The new IB diploma mathematics courses have been designed to support the evolution in pedagogy and encourage teachers to develop conceptual understanding using the content and skills of mathematics. A concept-based framework will allow students to think more deeply, critically and develop skills necessary for the 21st Century and future success.
About the Author
Jennifer Chang Wathall is an independent educational consultant with over 25 years’ experience in the education field. She is author of “Concept-based Mathematics Teaching for Deep Understanding in Secondary Schools” and travels the world delivering keynote addresses and facilitating professional development workshops. She majored in mathematics at the University of Sydney and utilizes her Masters of Arts in Educational Technology to support schools with technology integration and innovation. https://www.jenniferchangwathall.com/