How much guidance for learning mathematics is optimal?

It may depend on the interaction between limited memory resource, expertise in the maths domain and the complexity of maths materials.

This project aims to investigate when guidance should be provided and when it should not, for primary and secondary students learning mathematics.

Students with different levels of expertise were recruited and materials with different levels of complexity were used.

Mathematics learning is always challenging for most students. Some students may struggle with solving a problem and some struggle to memorise maths formulas. Therefore, how should we teach students solve maths problems and how should we teach students maths formulas? The same approach for both or should different approaches be used?

Cognitive Load Theory suggests that instructional designs should not overload working memory capacity, which is very limited when processing novel information. Also, learning materials could be estimated by the number of interactive elements, such as x and y could be treated as two individual elements, but x + 5 = 7 which contains 5 interactive elements which could not be separated for learning.

Learning maths facts which contain fewer interactive elements compared to learning maths procedures: based on research, guidance should be provided for learning maths procedures which has more interactive elements, but students should be encouraged to generate maths facts with cues. However, learners’ expertise would be considered too, as materials with more interactive elements (i.e., complex) would turn into being materials with fewer interactive elements (i.e., simple), so when should guidance be provided?

Categorising learning materials with considering learners’ expertise would be a way to distinguish how to learn maths facts and how to learn maths procedures.

Ouhao Chen

Lecturer in Mathematical Cognition

Related information

  • Chen, O., Kalyuga, S., & Sweller, J. (2015). The worked example effect, the generation effect, and element interactivity. Journal of Educational Psychology107, 689-704.
  • Chen, O., Kalyuga, S., & Sweller, J. (2016). Relations between the worked example and generation effects on immediate and delayed tests. Learning and Instruction45, 20-30.
  • Chen, O., Kalyuga, S., & Sweller, J. (2016). When instructional guidance is needed. The Educational and Developmental Psychologist33, 149-162.