“Limited subject matter knowledge restricts a teacher’s capacity to promote conceptual learning among students. Even a strong belief of “teaching mathematics for understanding” cannot remedy or supplement a teacher’s disadvantage in subject matter knowledge. A few beginning teachers in the procedurally directed group wanted to “teach for understanding.” They intended to involve students in the learning process, and to promote conceptual learning that explained the rationale underlying the procedure. However, because of their own deficiency in subject matter knowledge, their conception of teaching could not be realized. Mr. Felix, Ms. Fiona, Ms Francine, and Ms. Felice intended to promote conceptual learning. Ironically, with a limited knowledge of the topic, their perspectives in defining the students’ mistake and their approach to dealing with the problem were both procedurally focused. In describing his ideas about teaching, Mr. Felix said: “I want them to really think about it and really use manipulatives and things where they can see what they are doing here, why it makes sense to move it over one column. Why do we do that? I think that kids are capable of understanding a lot more rationale for behavior and actions and so on than we really give them credit for a lot of times. I think it is easier for anybody to do something and remember it once they understand why they are doing it that way“.”
– Liping Ma, Knowing and Teaching Elementary Mathematics (2010, page 36)
The most important thing to remember when teaching maths – when teaching anything – as the teacher, the educator and the facilitator, is that you must understand what you are teaching. This is what Ma (2010, p. 36) is talking about here.
As a teacher and a professional educator, you are responsible for providing knowledge to your learners, not just passing it to them as information in a book or in the form of confusing statistics and facts, but as an understood conceptual view of the content. If you do not understand what you are teaching, this may invite opportunity for confidence to fall in your learners – you are the trusted educator in the classroom, on which your learners depend on to provide subject matter with an understanding you have thoroughly revised, in order to adapt the content to best explain it to them.
Outsmarted?… Imagine this. You are planning a lesson – a maths lesson. You have a vague and somewhat passive understanding of the content you intend to teach. And so you think your learners will trust that you understand what input they are going to receive, because, after all, you are the teacher. Right? That passive understanding you have, is only going to brush off onto your learners. Children are observant and will easily pick up on your mistakes, your struggles and perhaps your lack of confidence when you are teaching them. So, you plan your lesson, still intact with your passive understanding of the content you intend to teach. Then it comes to your lesson and your learner outsmarts you. Perhaps in the form of a question, that you cannot answer. Is this due to your negligence?
Your learners depend on you to know what you are talking about, and here, Ma, explains the profound importance to approach your intended learning content with a conceptual view – if you understand, you have more chance of your learners understanding!
Ma, L. (2010) Knowing and Teaching Elementary Mathematics – Teachers’ Understanding of Fundamental Mathematics in China and The United States. London: Routledge.