Teaching mathematics: Activity 2. Sequencing material - Part 2

In sequencing concepts and activities to enhance student learning relating directly to the current topic, it is important to take the opportunity to simultaneously develop transferable mathematical skills, including:

  • logical presentation;
  • critical and analytical thinking;
  • mathematical communication; and
  • problem solving.

Knowledge of mathematical concepts and the development of mathematical skills are an integral part of mature mathematical thinking and cannot be taught in isolation; they should be each interwoven in any lesson planning. Moreover, such skills, though here being developed in the mathematics context, have value for students and should transfer to their whole education and their development as professionals. Institutions now expect that disciplines can describe and document the development of transferable skills in their units and programs; this development begins by building them into your lessons.

In relation to a lesson on differentiation from first principles, one could develop skills as follows:

  • logical presentation and mathematical communication can be enhanced through a clear explanation of the steps involved, such as the writing down of the definition, the substitution of the specific function into the definition, the simplification techniques and the taking of limits to obtain a solution. Remember that graphical aids can be used to facilitate understanding.
  • analytical thinking can be facilitated by assembling known information, both generic (definition) and specific (given function), by substituting the specific information into the generic information, and by manipulating and applying known techniques to approximate a solution (algebraic manipulation, including concepts such as multiplying by a conjugate).
  • problem solving can be enabled by collecting and organising relevant information, abstracting into the theory especially for complicated functions, by identifying difficult or complex elements of the problem (the step at which you cannot easily go forward) and using known techniques to simplify and reorganise material, moving closer to the final solution.