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As I read the report I came across a reference to “reasoned discovery” and had to pause and attempt to understand what the authors meant by this term. I got this nagging feeling that they didn't mean it in the constructivist definition of "discovery" per se.
This term only appears once in the entire report in this particular passage:
In Japan, by contrast, closely supervised, collaborative work among students is the norm. Teachers begin by presenting students with a mathematics problem employing principles they have not yet learned. They then work alone or in small groups to devise a solution. After a few minutes, students are called on to present their answers; the whole class works through the problems and solutions, uncovering the related mathematical concepts and reasoning. The students learn through reasoned discovery, not lecture alone.The first thing I did was google “reasoned discovery” assuming I’d find so many articles that I’d have to do some serious sifting. That’s not what happened at all. I found some references to reasoned discovery in some scientific articles and research but I struggled to find a clear definition of it as a type of discovery.
So why the adjective, "reasoned"?
I don’t believe “discovery” in the implementation carried out by most proponents of constructivism is what the Glenn Commission authors were referring to when they articulated “reasoned discovery”. I think that they had a very specific idea in mind and chose their words very carefully. In another passage they referred to “mathematics as the language of scientific reasoning” which suggests that they used the adjective “reasoned” to distinguish it from “discovery” in and of itself.
By dissecting the passage, I tried to come to a better understanding of what these 25 collaborators had in mind.
1. The collaborative work is closely supervised. The teacher plays an active role in the learning.
2. The group presents the answer after only “a few minutes”. There is no prolonged “struggle”.
3. Immediately thereafter, the whole class works through the problems and solutions presumably under the careful direction of a teacher “uncovering the related mathematical concepts and reasoning.”
4. The students “learn through reasoned discovery, not lecture alone” which means that lecture (direct instruction) is a tandem component and is assumed to be part of the teaching/learning process.
After staying up and thinking about this for much too long, I'm still wondering what “reasoned discovery” means.
10 comments:
The Glenn Commission's characterization of how math is taught in Japan was taken head on in a paper by Alan Siegal of NYU's Courant Institute. Siegal is also a founding member of NYC HOLD which has a link to his paper. You can find it at:
http://www.cs.nyu.edu/faculty/siegel/siegel.pdf
He starts the paper with the quote you provided from the Glenn Commission and then proceeds to describe a lesson in a Japanese classroom that was captured on a videotape. Interestingly, others like Stigler have viewed the same tape and taken away a completely different impression. I go with Siegel's interpretation.
"The group presents the answer after only “a few minutes”. There is no prolonged 'struggle'."
I have had many teachers use this sort of tactic. They want the kids to achieve the light bulb effect. They ask questions that slowly lead to the correct answer. But even in groups, only one or two will achieve the light bulb effect. The rest get no benefit over direct instruction. But I don't think there is anything special about the light-bulb effect.
I have also seen teachers get quite frustrated when they have to practically tell them the correct answer. I have nothing against this approach unless the curriculum is built around this process. It is neither necessary or sufficient.
"The students “learn through reasoned discovery, not lecture alone” which means that lecture (direct instruction) is a tandem component and is assumed to be part of the teaching/learning process."
Most kids will learn (or not) either from direct instruction from the teacher or direct instruction from another member of their group. And why does this always have to happen in class with groups? Why can't they do it as individual homework? At least that way it forces all kids to do some discovery work and not be a passive participant of the student group. Group class discovery is too wasteful of time, and if they don't spend enough time, then why bother breaking into groups. Just use teacher-lead discovery.
I want to know the exact brain mechanism for the light-bulb effect. Is it the excitement that motivates them? What if their light-bulb idea is wrong? Is there some better sort of brain wiring that goes on? I've been pretty excited at times with direct instruction. Good direct instruction is like being led toward discovery by someone who knows what they are doing. When I taught and when I teach my son, my explanations are all about a very clear path to understanding. I put a lot of thought into it. How is this any less of a discovery process? It's also a whole lot more efficient.
When I taught and when I teach my son, my explanations are all about a very clear path to understanding. I put a lot of thought into it. How is this any less of a discovery process? It's also a whole lot more efficient.
Absolutely! It is NOT any less of a discovery process it's just a much better one. All learning is "discovery", if you didn't "discover" it then you must have already known it.
Just because an experienced teacher carefully guides you to find your way to the answer doesn't make it any less of your own. Unless of course you are passively sitting in a group, waiting for a classmate to discover the answer for you.
Most kids will learn (or not) either from direct instruction from the teacher or direct instruction from another member of their group.
Or their tutor, or their parents,....
Steve, you always hit the nail on the head.
As Siegal's paper discusses, the Japanese students discover nothing on their own, despite perceptions otherwise. In fact, the instructor in the Japanese classroom gives them explicit information essentially to solving the problem, gives them prompts and guides them.
Thank you for reminding me about the Siegel paper. Reading it again in the context of the Glenn report certainly paints a detailed and very different picture of Japanese math instruction than one might imagine from observing a "discovery" classroom in the constructivist sense here in our own country today. If the dynamic of the Japanese classroom was the goal, we've really missed the point.
What the Glenn report did get right, however, is that a profound understanding of mathematics on behalf of the educators was the key to a student's success in math and science. The Siegel paper doesn't mince words about this either. The instructor in the Japanese classroom is able give explicit information essential to solving and understanding the problem because he/she understands the subject matter deeply enough to do so.
The instructor in the Japanese classroom is able give explicit information essential to solving and understanding the problem because he/she understands the subject matter deeply enough to do so.
Which raises an interesting point. Is the reason "problem based learning" aka "discovery learning" aka "inquiry based learning" aka "constructing knowledge" is so popular in this country because teachers are unable to provide direct instruction?
Which raises an interesting point. Is the reason "problem based learning" aka "discovery learning" aka "inquiry based learning" aka "constructing knowledge" is so popular in this country because teachers are unable to provide direct instruction?
I not only think it's possible, particularly as it pertains to math and science, I fear it's likely the case at most K-8 public schools in this country. I would like to hope that in high school there is a greater understanding of subject matter.... please tell me there is.
I would like to hope that in high school there is a greater understanding of subject matter.... please tell me there is.
I believe so. In Virginia where I live, (and I believe this is true for most states), in order to get a teaching credential to teach in secondary school (defined as 6th through 12th grade in VA), you have to show proficiency in the discipline you wish to teach. For math, that means having a degree in math, as well as passing the Praxis II in math, which tests algebra through calculus.
In K-5, teachers are not specialized, and only need to pass Praxis I which tests both verbal and math. The math on Praxis I is basic arithmetic.
Despite this, I've seen some horrendous teaching of geometry in some of the classes I've observed. Mastery of proofs is not a requirement and Praxis II doesn't cover that very deeply.
Clarification to above: To teach math in VA, you have to have taken certain core math courses. Generally these are fulfilled through majors in math, engineering or science. Those who are missing one or more core courses would have to take them as part of the process of getting teacher certification.
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