When the problem is not the question and the solution is not the answer…
In his 2008 paper(1) on Inquiry Teaching in the ATM, Andrew Blair(2) says that “knowledge comes pre-packed and is consumed in a way determined by the teacher.” Put that next to the OIS vision statement “We give our students the freedom to think, empower to be…” and you will notice why we have parted ways with teaching mathematics the traditional way.
Inquiry, in mathematics, is the experience of observing patterns, noticing connections and asking questions that challenge what is already known. When using this model in class, the teacher introduces an inquiry prompt (unlike a typical mathematical question) and provides students with opportunities to explore the prompt in several directions. During the process, students exchange their ideas about how to learn and why to learn about a given concept in a certain way. Allowing this type of socialization enables students negotiate their knowledge trajectory based on their ability and previous understanding.
When we decided to introduce this activity in Grade 8, our aim was to have a democratic approach to induce mathematical thinking and habits of mind. Students were given the inquiry prompt (Fig. 1) and set off to work in pairs to generate comments and/or pose questions about the prompt (Fig. 2). Their communication was mostly based on previous understanding of number theory concepts such as odd and even numbers, patterns in multiplication, rules of divisibility, patterns and sequences. (Figs. 3 and 4). They were required to examine the prompt and devise and test some conjectures based on their observations. Some of these conjectures could not be explained from the available information, which led them to the experience of not always reaching the solution for a given problem and keeping it open for further investigation.
The subtitle of this blog post, When the Problem Is Not the Question and the Solution Is Not the Answer:
Mathematical Knowing and Teaching, refers to a seminal academic research paper(3) from the 1990s that has discussed similar ideas on developing an inquiry culture in the mathematics classroom. It is a long but an interesting read to understand how students can develop this important thinking skill to become curious and inquisitive about their knowledge. It highlights how our traditional approach to perceive mathematics as a ‘perfect science’ of ‘accurate solutions’ is fundamentally wrong and rather needs to be replaced with efforts towards developing mathematical habits of mind.
“Give a man a fish and he eats for the day, teach him how to fish and he eats forever…” they say.
Welcome to our MYP blog. I feel very privileged, as a passionate MYP educator, to be the coordinator at OIS - JVLR. Feel free to visit our blog as we endeavour to make our learning more visible to you.