There are a lot of quotes (maybe as many as there are teachers) that begin something like this: “The goal of education is…” For example,
“The one real goal of education is to leave a person asking questions.” –Max Beerhohm
Undoubtedly, many of these are spoken in a hyperbolic manner, and should be interpreted as such. (Myself, I would be wary of anyone who believed that there are precisely N goals of education, true for all places and at all times.) Nevertheless, this sentiment came to my mind last week, the first week of school.
This semester, I am teaching one Grade 10 and two Grade 9 math classes, and I am happy to be teaching many of my Grade 9 students from last year in Grade 10 this year. I knew we would have another good semester when, on the first day of class (only 15 minutes long), the students skipped formalities and picked up right where we had left off in January. Although I had planned a team-building activity for the brief period, a student asked, almost immediately after class had started: “So anyway, is 0.999… = 1?” The other students jumped right in, arguing vehemently yes! or no!, trying to articulate some deep concepts that are, technically speaking, beyond the Grade 10 curriculum; this led us to other questions, such as the meaning of 00, 0, 0/a, and a/0. I noticed that some students had changed their mind about certain issues from last year, especially regarding the question of whether 0 is, in fact, a number (in particular, more were leaning towards yes, and were able to articulate why). I am sure they know by now that these kinds of questions are a great way to get me off track from my lesson plan, but there also seemed to be genuine curiosity in their questions, and genuine emotion in their responses.
“Have patience with everything that remains unsolved in your heart. Try to love the questions themselves, like locked rooms and like books written in a foreign language.” –Rainer Maria Rilke
The students’ responses during this discussion were interesting in and of themselves, but what struck me most was simply that they had remembered these questions and debates from our time together last year, which were not part of the curriculum and had certainly not been on any homework assignment, quiz, or unit exam. Presumably, they had learned some mathematical content in my class, but what seemed to stick with them was the questions – and, in particular, questions that can’t be answered using a rule or algorithm, questions to which the answer may not be black or white. They had also remembered that my classroom was a space for mathematical curiosity, where they could, and would, wrestle with such tough questions – even if they didn’t immediately get answered, and even if they technically didn’t “count.”
I left school that day with my heart full. Fostering and supporting (mathematical) curiosity is one of my main goals as a mathematics teacher, and it was heartening to see that I was able to at least nourish, if not spark, an inquiring attitude about mathematics among this group of students. It is my greatest hope that when I see my current Grade 9 students in Grade 10 next year, they, too, remember the questions, and are eager to tackle them anew.
And so the work begins again. Next week, my Grade 9 students will be tackling the following problem, sparked by an interesting question a student posed last week regarding the possibility of “stacked” exponents: “Which is bigger: 2710 or 2710?” I can’t wait to see what other questions we wrestle with this term.