​Professorial Inaugural address: Caroline Long

Reform Mathematics Education over the past 50 years has brought the human and creative element into the learning and teaching of mathematics, has privileged the experience that children bring with them from their out-of-school environments, and sought to develop their mathematical thinking.

According to Caroline Long, a professor in Childhood Education, at the Faculty of Education, University of Johannesburg (UJ), the expression “mathematics as a human activity” aligns with the idea that mathematics has its roots in everyday situations; it is then from the generalisation of principles emerging from these situations that more abstract mathematics is developed.

Professor Long pointed out that the idea that mathematics should be creative and enjoyable is supported by both highly respected mathematicians and educational philosophers in this movement. “How is it that when we have had a movement for reforming mathematics education since the 1970s, almost 50 years, we still have the perception of mathematics as boring or of no relevance for the majority of people?” Prof Long posed this question when she delivered her professorial inauguration address, “Mathematics as a creative activity: mapping a conceptual field for mathematics teacher education”. Prof Long’s inaugural address took place in the University’s Council Chambers, Madibeng Building, Auckland Park Kingsway Campus on Wednesday, 19 September 2018.

Prof Long argued that doing mathematics is a creative activity, and if doing mathematics is a creative activity, then the teaching of mathematics, and the teaching of prospective mathematics teachers must certainly be. She focused on the topic good education, then made the link to teacher education. Against this broad focus she positioned reform mathematics education, focusing mainly on Gérard Vergnaud’s theory of conceptual fields.

In attempting to map a conceptual field for mathematics teacher education, Prof Long proposed that there are many domains and constructs (personal competence, social values, mathematical proficiency, pedagogical knowledge, assessment skills and knowledge of research design) that require attention in order to prepare the student teachers for the education environments in which they will work.

Prof Long explained that one of the challenges for mathematics education is that mathematical concepts are rooted in situations and problems. Consequently from a conceptual perspective, a single concept may be applied in many different problem situations, and one situation or problem may require many distinct concepts. Another reality that must be faced from a cognitive perspective is that a single concept does not develop in isolation but invariably develops in relationship with other concepts. It is important therefore to consider a conceptual field made up of situations, concepts and representations for both the teaching and researching of mathematics.

“The role of the teacher, is to transform the learner’s intuitive and localised conceptions of students that can be applied to a single problem. into generalised and explicit concepts that can be applied to a class of problems, thereby developing more powerful mathematics.”

The notion of good education, teacher empowerment and agency, reform mathematics, assessment and measurement, and a research approach, all combine to contribute to mathematics teacher education, essentially a creative activity, where the first stages involve play, but then lead on to precision and generalization,” concluded Prof Long.

Professor Caroline Long has served on the Qualifications Standards Committee for Umalusi since 2013, the South African Mathematics Olympiad committee from 2013, and the SAERA Special Interest Group for Assessment, from 2015. She has a C2 research rating from the National Research Foundation.

She is currently a member of the Psychology of Mathematics Education (PME) 2019 organising committee, and a co-chair for the International Congress of Mathematics Education (ICME 14), Topic Specific Group on Assessment in Mathematics Education, taking place China in 2020.