Mrs Baliqis Olawunmi Banjo lecture
Good evening colleagues. Thank you for having me here.
My name is Balqis Olawumi Banjo.
It is an honour to present my view before you, the Creative Minded Educators. I specially thank Mr Odetola for the opportunity.
As a Mathematics Educator and a Researcher, I have keen interest in learning about essential knowledge that educator should possess in order to teach mathematics effectively.
“Life is good for only two things: discovering mathematics and teaching mathematics”
My topic here today is: The teaching of mathematics. Presently, I’m most familiar with Mathematics National Curriculum Statement (NCS) of South Africa: The Curriculum and Assessment Policy Statements (CAPS) Grades R-12. However, the context of my presentation is neither limited to mathematics, nor South Africa.
Colleagues, let’s do this together. What kinds of understanding (in general) will you suggest that an educator should possess in order to TEACH?
Different names have been used to describe the necessary knowledge that the educator needs to know to teach mathematics. Poor or insufficient educator’s knowledge of teaching among other factors has been identified to negatively impact on mathematics curriculum implementation.
Educator’s pedagogical content knowledge (PCK) is no more a new terminology in the teaching field, but I believe there is a need to explore its basic-essential-elements that can be assessed in the teaching of mathematics.
Lee Shulman, the original author of PCK, used it to signify a special kind of educator’s knowledge that differentiates an educator of any given discipline from an expert of that discipline. It is a specialized knowledge possessed by experienced educators and used to make understanding of a topic accessible to learners.
PCK is the ways of representing and formulating a concept, that makes it comprehensible to learners, including an understanding of what makes a specific mathematics topic easy or difficult to learn.
Today, I will like to focus on PCK for teaching mathematical concept as comprising of:
• the educator’s content knowledge;
• the curriculum knowledge that he/ she uses in the teaching of this concept;
• educator’s knowledge of learners and how he/she applies it during the teaching of this concept;
• the educator’s knowledge of appropriate instructional strategies for teaching this particular concept.
Shulman says, “To teach is first to understand”
This simply implies that no educator will successfully teach what he or she does not understand. The quote also highlights the significance of the educator’s subject matter knowledge, otherwise known as the content knowledge, as a prerequisite for educator’s PCK.
It is important that educators teach mathematics effectively to ensure that learners gain understanding of the concept and the relevant curriculum outcomes. This can only be possible if the educator possesses the knowledge required for teaching.
In order to develop learners’ problem-solving and cognitive skills, teaching of mathematical concept should not be limited to “what” but should rather feature the “how” “when” and “why” of problem types; learning procedures and proofs without a good understanding of why they are important will leave learners ill-equipped to use their knowledge in later life.
“Mathematics is not about numbers, equations, computations, or algorithms: it is about conceptual understanding”
Educator’s content knowledge should be an in-depth knowledge about the concept that he/ she wants to teach, that is, an educator must know far beyond what is in the curriculum of a class/ grade, in order to positively influence his/ her instruction during the teaching.
An educator’s content knowledge should at least be in the same level with that of his/ her colleagues.
Knowledge of the curriculum demands that the educator understands the structures of the content; understand how a particular concept links with others, within the subject, across the subjects, and across the grades. It is high time educator understood that mathematical concepts are connected and should be taught as such.
Curricular approaches, for example in South Africa (may be also in Nigeria) have changed from transmission-based teaching or, even from learner-centered approach to learning-centered approach. The focus is no more on people; it is now on conceptual understanding that we want our learners to gain. Unless an educator understands the curriculum demands of the subject that he/ she teaches, the little that person can do to achieve the curriculum goals. Let us study our subject curriculum in detail, and with special interest.
It is important to understand how learners learn mathematics.
“If kids come to us from strong, healthy functioning families, it makes our job easier. If otherwise, it make our job MORE IMPORTANT”
I believe we all underwent introduction to psychology of education, and some other courses that exposed us to the psychology of learning. Let us go a bit further, on our own, to update this knowledge. I often tell colleagues, it’s not always about what you know as an educator, but how best you can impact the knowledge to the learners.
One researcher reveals that learners conceive mathematical concept in two ways: operationally – when learners see concept as a process; and/ or structurally – when learner see mathematics concept as an object. All these studies are important to our teaching, and we should endeavour to incorporate them where necessary.
Mathematics educators need to be more sensitive to learners’ prior knowledge and learners’ individual differences. Identifying and using learners’ prior knowledge is an integral part of PCK. It enhances effective teaching and learning of mathematics.
Understanding of mathematical concept is closely connected with learners’ experiences, this implies that learners gained conceptual understanding of the concept when they can draw inferences from their prior knowledge or recognise relationships between the prior knowledge and the new experience.
Research also shows the importance of error analysis, as it forms integral aspect of educator knowledge. Learners often hold and express incomplete mathematical knowledge. This calls upon the educator’s pedagogic skills to scrutinize, interpret, correct and extend this knowledge.
Constructivist approaches are still considered most appropriate to the teaching of mathematics; they allow learners to take responsibility of their own learning. Its theory underpins the aspects of PCK.
Learner-centered method, modeling, and problem-solving were commonly considered suitable teaching strategies for mathematics. They are said to foster active participation among learners. I am of the opinion that every society needs its own framework for teaching mathematics; a framework where education stakeholders have common views and practices of ensuring quality of teaching.
In the beginning of this presentation, I asked: what kinds of understanding (in general) will you suggest that an educator should possess in order to TEACH? Here are my own suggestions:
- It is important that educator identifies and understands the key ideas to be taught in every given topic, with respect to a given class.
- Understand what other topic (within or/ and outside the subject) can be related to the concept at hand.
- Understand various ways in which a particular concept can be represented during your teaching. For example, if you are teaching function in mathematics, you should illustrate an example in different ways: graph, word, table, flow chat and formula.
- An educator must understand the purpose of a particular topic in the curriculum. This will enhance his/ her understanding of teaching it. It is also important that educator exposes learners to the purpose of learning a topic from the beginning.
- Mathematics’ topics are interrelated and usually cut across the grades. Hence, at the beginning of a topic educator should identify learners’ readiness by assessing them on the prerequisites which they are supposed to know.
- I usually urge educators to keep record (in every topic) of the concept the learners find difficult and what they find very easy. This record will facilitate effective planning subsequently and of course constructive instruction. This also goes to ‘keeping records of common errors’ that learners usually make in mathematics. Colleagues, we create most of these misconceptions (unknowingly), and we have to facilitate learners to “un-learn and re-learn”
- Educator should use variety of representations which include analogies, illustrations, real-life examples and demonstrations, in their teachings.
- Educator should allow learners to be independent; take responsibility of their own learning. Give them opportunity to investigate theories, explain their findings and make generalization.
- Educator should use an inclusive approach that ensures active participation of all learners.
- Most importantly, educator should plan and be adequately prepared for every lesson. A good educator should reflect on his/her instruction, think and make note of what went well, what went wrong; how can I make it better?
Dear colleagues, let me use this opportunity to remind you that better Africa depends greatly on the quality of education she provides to her citizens. Quality education implies quality teaching and learning in our various communities; and it is a function of our own teaching knowledge.
As mathematics’ educator, I believe I am charged with responsibility of its quality teaching, most especially in my communities. I take my inspiration from the words of Andre du Plessis, who says, ‘Can I improve my mathematics teaching? Educator Action Research holds the key to how!’
I thank you.🙌🏻