Inquiring Minds Don’t Want to Know

The National Council of Teachers of Mathematics, the guys that Jimmy Buffett pissed off, provide President’s Messages, monthly words of wisdom for the troops. This December’s message is titled,

Balancing Instructional Strategies in the Math Classroom

The message begins,

When you read inquiry-based instruction or direct explicit instruction, what feelings come to mind? Are they positive? Negative? Neutral? It often feels like an “either-or” debate, doesn’t it?

Well, yeah, because it usually is. But the President wants to be balanced:

However, there is a time and place for both methods of instruction, and our job as educators should be to use appropriate strategies at appropriate times.

Unfortunately, the President is unbalanced:

Inquiry-based instruction should be used most of the time as students begin to understand the concepts they are studying. Their curiosity is sparked, and they can begin to see the reason of learning the content, often increasing their desire to learn the material. Inquiry-based instruction centers on and is driven by students’ thinking as they develop a deeper understanding. …

Historically, and likely in many settings today, direct explicit instruction has been over-emphasized and overused, while inquiry-based instruction has been underutilized. … If we are genuinely interested in meeting the needs of all our students, we must continually work to increase the amount of inquiry-based instruction …

Where’s Jimmy Buffett when you need him?

14 Replies to “Inquiring Minds Don’t Want to Know”

  1. To be fair (but with no intention of being balanced, I’m not an equation!) there are some sensible messages in the lines of this speech.

    They are not the central argument though and in this case I think the central argument sucks (I took the central argument to be “more inquiry-based learning is needed with a teacher actively involved at almost every step”).

    The main reason I think the central argument sucks is that I cannot see the connection between inquiry-based learning and the “spark” the author writes of. Indeed, if direct instruction is used in the way the author advocates, I can imagine that providing a “spark” with equal probability.

    1. I have no intention of being “fair” to the guy. The title is a lie. The overwhelming message of the Message is that direct/explicit/whatever should play second fiddle. He’s taken a side: the stupid side.

      1. Yes. That much is quite clear and the point is not one I like.

        At least there is a proper acknowledgement of direct instruction and a hint that it is not what some “self discovery model” academics/commentators choose to claim it is.

        But as you say, sides have been taken and the “popular” side remains the loudest.

    1. I would say around the time “teaching” became “direct instruction”.

      And school leaders (who do very little actual teaching) would suggest that “educator” is a more inclusive term.


  2. The problem i see with “inquiry-based learning” is that it is hard for the teacher not to come in with a script about what is supposed to happen. So it just becomes a harder version of stand and deliver. In the traditional situation, there was a syllabus that was more or less taught in a standard way and it was the responsibility of the student to master it, and of the teacher to identify and try to remedy what inhibits this mastery.

    However, often the traditional model was not tolerant of student difficulties, often putting it down to the characteristics of the student (lack of interest, application, intelligence, etc.) rather than see the situation as trying to understand the perspective of the student and building a bridge between the student’s way of seeing the world and what is needed to secure the mathematical understanding and knowledge..

    I have found in my own teaching that the most productive times occur when a student asks about a difficulty, produces a situation that seems counterintuitive; handling this in class personalizes the situation — the explanation is no longer general or abstract, you are communicating with a particular student (one of them) about something he has problems with. It also often invites the class itself to participate in the discussion. Another useful thing is to sow seeds: just tell some interesting mathematical fact from time time or pose an interesting problem. A lot of the time, nothing comes of it, but occasionally it marinates, someone will pick it up and then nice things can happen.

    It is interesting that in places where education is curtailed in like Afghanistan, children and their parents seek education like water and the children see its purpose as more than fulfilling personal ambitions but in better contributing to their societies at large. i wonder how much of our educational problems in richer countries has to do with a lack of collective sense of welfare in many people, and see education in transactional terms which inhibits curiosity, exploration, and a desire to achieve a deeper understanding.

    1. Thanks. Ed. No question that there was a Sink Or Swim aspect to maths ed in the past. Now, it’s Wade. Or, more accurately, Wade And Then Sink Three Years Later. I’m not sure the change is totally a consequence of the Direct-Inquiry change, although of course it’s a decent part.

      Growing up, my public school primary classes had 35-40 students with, of course, zero teacher’s aids or, for better or worse, computers. What was a teacher to do, except aim for the declared target and do what they could with the outliers? Now, my daughters’ public school primary classes have 15-20 students, with human and inhuman aids here, there and everywhere. But, whatever is offered and however it is offered, there does not now appear to be any expectation of mastery. And so plenty of kids simply wade, until, three years later, they find the water is rising over their heads.

      Your last paragraph is depressingly worth pondering.

      1. A couple of points about traditional 1940s-1950s education. while there were NO government exams of any type until Grade 13, testing and assignments were woven into the regular regime – weekly arithmetic and spelling questions, writing of English compositions and book reports (kids were walked to the local public library every couple of months). The teachers had what must have been a huge marking task and kids in some subjects were expected to return their work with corrections. While there were no teachers aides, on occasion some kid would be asked to stay after school and help some other kid with trouble. While my public school teachers could mainly be described as spinsters of uncertain age, the atmosphere was certainly generally austere but with some instances of “tough love” (such as the Grade 8 teacher who told my brother that if he didn’t smarten he would not be going with his friends to high school).

        Remember that a lot of the kids of this generation were pretty independent, going to sporting events, riding the transit, some having paper routes, making deliveries for a pharmacy or small shop, or doing odd gardening jobs, so they needed and used arithmetic along with the adults, so having some skill in the subject was not just moot. A lot of the card and board games played also had mathematical features of one sort or another.

        There is always a risk of romanticizing the past, but I do feel that many children live in a world that has been artificially created for them rather than one where they can increasingly make choices, face their consequences and become responsible and resilient.

        1. Thanks, Ed. Frequent, semi-regular testing of the type you mention was a part of my primary education in the 60s. The disappearance of such testing has been a disaster.

          I think there’s a lot to your second paragraph.

          1. I agree that the second paragraph has a lot in it. But at the risk of sounding naive, sentimental or nostalgic (or all of the above), the generation referred to (from experience I’ll define it as the 60’s and 70’s) was a much ‘simpler time’ – way less traffic on the road, the neighbourhood milk bar was a social hub, there were evening newspapers (The Herald), black and white TV (and test patterns after midnight), shops shut at 5 PM, banks offered customer service etc. There were no mobile phones, social media etc. Universities weren’t commercial businesses (There were only two, and Monash was the new kid on the block). You could leave school at the end of Yr 10 (knowing the 3 R’s), get a job, work hard and be successful. The only existential crisis (that we knew of) was the bomb.

            Education is a product of the times. Today we live in complicated (and troubled) times and it’s no surprise to me that education reflects this. I know that nostalgia can make the past look rosier than it was. Nevertheless … (I hate to think what the future will be like if current times get fondly remembered as ‘simpler’).

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