Teachers of Math have for many years focused on teaching learners to solve Mathematical problems by following steps rigidly and memorizing numbers combinations. Whilst there is a place for rigor and memorization in learning, effective teaching that would lead to meaningful learning should focus on helping children develop understanding of concepts and procedures through problem solving, reasoning and discourse.

There are young learners (ages 4-5) who can recite and “write” 1-1000 but cannot successfully represent “55” in quantity. According to Bloom’s Taxonomy there are six levels of learning behavior; remembering, understanding, applying, analyzing, evaluating, and creating (Bloom, 1956) . Memorization leaves children operating at the lowest level – remembering. Meaningful learning of Math should start with remembering facts and then develop to the highest level (creating). It should move children from recall of memorized facts to number sense. Number sense reflects a deep understanding of mathematics which comes about through a mathematical mindset that is focused on making sense of numbers and quantities. (Boaler, 2016)

Kilpatrick et al. ( 2001, Pg115-116) in “Adding it up – Helping Children Learn Mathematics” having analysed the Math to be learned and findings of research in Cognitive Psychology and Mathematics Education recognized that no term captures completely all aspects of expertise , competence, and knowledge in mathematics. Thus, they chose Mathematical Proficiency to capture what they believe is necessary for anyone to learn Mathematics successfully.

In this module, we will examine these Math Proficiency Strands and how they can be integrated into the teaching
and learning of Math. It is important to note that the five proficiency strands are interwoven and interdependent in the development of proficiency in Math. They provide a framework for discussing the knowledge, skills, abilities, and beliefs that constitute mathematical proficiency. Please see diagram