Towards a conceptual framework for understanding and developing mathematical competence: A multi-dual perspective

ABSTRACT

Possessing the mathematical competence to encounter the challenges under globalisation and the ubiquity of digital technology is an important goal of education. Herein, we propose a broad conceptual framework for understanding and developing mathematical competence. The framework comprises four non-overlapping but interlinked cores: learning, knowing, applying, and viewing. Our framework encompasses ontological, epistemological, and pedagogical dimensions based on a multi-dual perspective. The proposed framework serves as a foundation for generating different learning paths to develop mathematical competence. Examples of learning paths are provided to illustrate the correlative and complementary relationships among the cores of mathematical competence.

KEYWORDS:

• Applying
• knowing
• mathematical competence
• learning
• viewing

Acknowledgments

The authors gratefully acknowledge the financial support of the Ministry of Science and Technology, R.O.C. (MOST 104-2511-S-003-006-MY3).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Ministry of Science and Technology, Taiwan [104-2511-S-003-006-MY3].

Notes on contributors

Kai-Lin Yang

Kai-Lin Yang is a professor at the Department of Mathematics, National Taiwan Normal University. Her research interests include reading comprehension and reading strategies for learning mathematics, mathematics textbook analysis based on abstraction as well as teachers’ reasoning on pedagogical problems.

Tai-Yih Tso

Tai-Yih Tso is a professor at the Department of Mathematics, National Taiwan Normal University. His research interests include geometry learning, mathematical reasoning and argumentation, mathematical modelling, dynamic geometry teaching, and e-learning in mathematics.

Ching-Shu Chen

Ching-Shu Chen is an associate professor at the Centre of Education Tainan University of Technology. Her research expert in childhood mathematics instruction and learning. Her topic of mathematics interests includes combination of literacy and mathematics to promote children’s competency of mathematics and mathematics reasoning as well.

Yuan-Horng Lin

Yuan-Horng Lin is a professor at the Department of Mathematics Education, National Taichung University of Education. His research interests include mathematics instruction and assessment, mathematics literacy as well as students’ performance in mathematical language and reading.

Shiang-Tung Liu

Shiang-Tung Liu is a professor at the Graduate Institute of Mathematics and Science Education, National Chiayi University. His research interests include problem solving and problem posing performance of gifted students, as well as the professional development of mathematics teachers for teaching their gifted students.

Su-Wei Lin

Su-Wei Lin is a professor at the Department of Education, National University of Tainan, Taiwan. Her research interests include the development and implication of assessments in mathematics education, primarily related to computerised adaptive testing, dynamic assessment, and large-scale assessment.

Kin Hang Lei

Kin Hang Lei completes her doctorate degree at the Department of Mathematics, National Taiwan Normal University. Her research focuses on students’ geometrical reasoning using dynamic geometry environment, multimedia instruction, instructional materials design and textbook analysis.