The Case for Constructivism in Mathematics Cassrooms

I recently had some feedback on my post criticising Minster for Education Christopher Pyne (Pyne a Pain for Education in Australia).The comment suggested that many schools had taken the constructivist approach to teaching and learning too far, as a result, students were not spending enough time learning facts and were instead building too many dioramas and other meaningless inquiry-based projects. The comments prompted me to reflect on why exactly I am a proponent of constructivism: this article will address the case for constructivism in mathematics classrooms. Whilst I argue this from a mathematics background, I am sure many (if not all) arguments apply equally across other KLAs: we are discussing fundamental skills for 21st century learners, and these do not apply exclusively to mathematics.

Constructivism has emerged from mathematics reform in the 1980s and 1990s to be cemented as the fundamental approach to teaching and learning in the twenty-first century. However, its roots lie in the earlier work of psychologists such as Piaget, Bruner and Vygotsky who challenged the traditional understanding of knowledge as the transmission of facts, instead considering learning as an adaptive function that required active engagement by students in order to be effective.

Constructivist approaches to education are supported by many mathematics and science teachers and are present in curriculum documents (see NSW BOS, ACARA, Victoria). The constructivist philosophy is driven by the premise that meaningful learning occurs when learners actively strive to make sense of new information, and consolidate new learning with an existing knowledge base. What exactly does this mean? Constructivism is not a pedagogical approach: but it is a model for learning. It is based on three core principles:

  1. That learning is active and reflective
  2. That learning is continuous, and learners should understand new experiences in the light of prior knowledge, and,
  3. That learning is social and requires interaction to develop deep conceptual understanding.

This theory is present in classes around the world: from kindergarten through to tertiary-level study.

Constructivism moves away from the notion that you can teach a person directly, instead seeing the ‘teacher’ as a facilitator of the learning process. The constructivist perspective posits that knowledge cannot simply be transferred from one individual to another: the learner must be actively, cognitively engaged in the learning process. As a facilitator, the teacher provides opportunities to engage with concepts, rather than instructing how to perform procedures. This means fundamentally changing one’s classroom perspective: favouring mastery and understanding over rote learning; valuing discourse; and promoting self-reflection.

Constructivsm ensures that current instruction is anchored within an existing body of knowledge. Predominating education until the 1960s and 1970s was the metaphor of a human mind as an empty bucket, with the role of learning being to fill it. Following this metaphor, one would consider the acquisition of new knowledge to be teachers handing students books (information), which were to be stored in a library (brain) and called on at will (‘knowledge’). In fact this is in no way true of education. Advances in modern cognitive science have highlighted the associative structure of memory as being its most important feature (Gijselaers, 1996). We refer to the structure of related concepts as semantic networks. The process of learning new knowledge involves its integration into existing networks: if new knowledge is better connected to existing structures it will be recalled and used more easily, whether its for solving problems, critical analysis, or basic factual information.

Vygotsky’s theory of socio-cultural development is key to the third principal of constructivism. Shared knowledge is a powerful learning environment. No man is an island and learning should not occur in ‘isolation’: solitary book-work, at desks, in silence. Verbal discourse forces learners to be adept communicators, and develop their capacity to reason and explain their thinking process: fundamental skills in the mathematics curriculum.

Constructivism is learner-centred: it considers the individual learner’s needs, ideals, cognitive abilities and perspectives. Student-centred learning accepts that students learn at different rates. By empowering students with tools in metacognition and reflection we can support them to develop autonomy over their learning, rather than forcing students to progress at the same rate. Students’ that participate in student-centred learning tend to have higher intrinsic motivation and superior critical-thinking and problem-solving schools compared to students learning in content-centred models (Zain, Rasidi & Abidin, 2012).

Traditional approaches such as lectures and rote memorisation are inadequate pedagogy. Whilst these methods may have their place, they approaches fail to equip students with adequate skills required for 21st century thinkers. As we move through the 21st century we are in an increasingly information-heavy society. I have access to far more information in my smart-phone than I did in any library when I was at school (less than ten years ago!). Skills in problem solving, critical thinking, reasoning and communication, and a capacity to be a responsible decision-maker. These skills are highly prized by universities and employers alike. Students need to be flexible, dynamic thinkers: this cannot be developed through pedagogy that emphasises the regurgitation of facts.

It is essential to know that constructivism is not synonymous with inquiry learning, problem-based learning or discovery learning. Constructivist approaches do no seek to deny the importance of basic mathematical knowledge, or base knowledge in any field. As a mathematics teacher I understand the importance of basic mathematical facts and procedural fluency: these skills are the lynchpin for learning. I emphasise the importance of students knowing their times-tables, of being able to quickly add and subtract, of having proficiency in algebra. I appreciate the time and place for repetition, for practice. However, in doing so, I acknowledge the constructivist philosophy. I strive to anchor new learning within an existing body of knowledge. I emphasise the importance of social interaction in generating understanding.

To segregate mathematics teachers as traditionalists versus constructivists, is to do students an injustice. The world is not black and white, and teaching is not black and white. It is important that we can incorporate the ‘shades of grey’ into classroom practice: to accept the time and place of different pedagogical strategies. There is no ‘one size fits all’ model for teaching, there is no silver bullet, and there never will be. However, by accepting the strengths of different educational philosophies and pedagogies, we can ensure that our teaching practice best suits our own needs as educators, as well as the needs of our students.

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About madelinebevs

Mathematics teacher and researcher. Runner. I'm excited by mathematics education. Having taught high-school mathematics for several years I am currently studying a Master of Education (Honours) in mathematics education, with the aim to ‘upgrade’ to a PhD later this year. My research is addressing how the constructivist epistemology (more specifically explicit instruction in metacognitive and self-reflective strategies) influences students’ affective domain. Mathematics education and research excites me greatly. I’m thrilled that I have the opportunity to write and work in this area. This blog will be (mostly) a collection of opinion pieces published several times a week on contemporary issues in mathematics education, with an Australian focus. More often than not topics will be generated from recent news headlines.
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3 Responses to The Case for Constructivism in Mathematics Cassrooms

  1. Fantastic summary, Madeline. I love your blog – you bring such an intelligent, research based perspective to broad educational issues, but so grounded in practical, day to day classroom practice. Absolutely brilliant!

    • madelinebevs says:

      Oh wow, thank you so much Corinne. It means a lot to me to have such well-respected and experienced educators comment so positively on my work – especially as I’m so early in my career! Hope you have a wonderful day!
      Madeline

  2. Pingback: The Case for Constructivism in Mathematics Cass...

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