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In my home province Discovery Learning is getting a substantial amount of pushback.

I've been trying to follow the discussions, but have been struggling because I can't seem to get a clear answer as to what exactly is meant by Discovery Learning. The wiki page ends with me more confused than I came in.

My understanding is that the teaching is based on attempting to have children understand why mathematical properties hold through 'discovery'. Yet parents seem to be very upset, and it seems to be more than just their children not knowing their multiplication-tables.

So what it is discovery learning, and why so controversial?

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School Mathematics Project was doing this in the UK when I was a child in the 80s. –  Ian Mar 26 at 21:27

3 Answers 3

I have been keeping up with the Canadian mathematics education battles from the last few years, especially in how the media discusses it. In fact, my last graduate assignment had everything to do with this issue.

I know that the "Math Wars" in Canada and in the United States are closely related. The debate has to do with a "traditional" vs, a "reform" mathematics education, and stems from an even longer history of mathematics education which Schoenfeld describes very well in his paper, Math Wars: http://www.math.cornell.edu/~henderson/courses/EdMath-F04/MathWars.pdf

As presented by the media, discovery learning seems to be a method of student-centered teaching and learning, coupled together with a corresponding style of assessment and evaluation. The prevailing media image is that given a problem, a student can "discover" a mathematical concept on their own, with very minimal guidance from the teacher, and be able to extend their abstractions to solve other problems. The motivation behind this method is to have students take initiative in their own learning and gain experiential knowledge. Dr. Jawaharlal explains guided discovery learning in this blog post: http://www.huffingtonpost.com/dr-mariappan-jawaharlal/teaching-discovery-learning_b_856463.html

The pushback from parents is from a misguided notion of what this looks like. Parents see "new math" homework and don't understand what they are looking at because it is unlike their own educational experience. The idea that their children are not getting direct instruction and might end up "discovering" a wrong understanding of concepts leads to more confusion and backlash.

However, the missing element in this misunderstanding of discovery learning is the teacher. This is where classroom design has to be done very carefully - the teacher is supposed to challenge understanding and correct reasoning. Parents' notions that traditional teacher-centered learning would prevent this from happening is also misguided - it is easy to just assume that dispensing correct information from the source would allow students to get it right and move on. Follow-up in both situations is essential.

Since most parents don't get to see or understand current educational research, their only sources come from what they hear in the media. As you might imagine, media is not very good at delivering a balanced message about this because they often rely on the loudest voices to inform them, and anti-reform advocacy groups will be the one to take up the pitchforks and torches.

EDIT: I neglected to give the journal reference to Schoenfeld's paper: Schoenfeld, A. H. (2004). The Math Wars. Educational Policy, 18(1), 253-286.

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It would seem that the promoters of new educational methods for children would see the need to communicate the concept of the instruction to parents. It seems much of the problem is the parents don't understand the mathematical exploratory exercises are to help understand the structure of numbers rather than replace an algorithm. On the other hand, if the exploratory methods are to replace, then the parents are right. It is certainly true that conventional methods of computation beat the experiments... this comment based on a number line example of the method I saw last week –  James S. Cook Mar 26 at 2:31

Discovery learning has each child build his or her own individual understanding of a concept. The teacher is there to guide and reinforce this process.

This stands in contrast to the traditional model for teaching, in which the teacher knows a secret, reveals it to the students, and the students recite it back verbatim.

Discovery learning has been demonstrated more effective not only at conveying understanding and motivating students, but building meta-understanding (i.e. knowing what you know). However, letting students build their own understandings comes with risk -- they way they understand things might not be the same way that their parents understood them. This becomes a problem when parents see how the children are doing arithmetic and complain that the algorithms that they, the parents, were taught to memorize do not have the same emphasis (or are even missing). And indeed if taken to excess discovery learning risks rediscovering the wheel; some amount of secret-sharing is necessary.

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I'm not sure that this is a widely accepted definition of discovery learning, or even of traditional teaching methods. I imagine a continuum of different levels of discovery from "Here are some tools, invent all of math yourself" to "Here are the steps to every math problem you may ever encounter" and everything in between. –  David Wees Mar 26 at 2:34
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surely at some point it is worth knowing methods. I'm all for creativity and such, but not at the cost of losing long division as a shared concept of the math community. Standing on the shoulders of giants is worthwhile tradition. –  James S. Cook Mar 26 at 2:35
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I find it a bit uncharitable to suggest that parents' adverse reactions to "discovery learning" is based, essentially, on an irrational fear of the unknown. In the long history of education reforms, not every new and shiny technique has lived up to expectations (to put it mildly---my wife attended a school that experimented with limiting windows on the theory that it would decrease distractions). I'd say that parents (and, perhaps even more so, teachers) are wise to hold on to some skepticism at first. And the politicization of this particular issue makes such skepticism doubly recommended. –  Adam Bjorndahl Mar 27 at 16:29
    
It is not a fear of unknown, but the fear that the educational reforms are not effective enough for the current conditions of the workplace, society, and the world. The question is really what do we want students to learn and why? Do we hold on to rote and memorization techniques because our society requires it? Do we want to work in a collaborative, creative problem solving environment? These are not easy questions to answer, so reactionary responses are going to come up more than philosophizing about mathematics education. –  Extrametrica Mar 27 at 17:37
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Such teaching techniques can be very valuable, but require teachers that rise way above the "I know the secret, I tell you, and I can see if you are able to recite it back" level. I'm not so sure most/many are up to the task... –  vonbrand Jun 2 at 17:01

I have some experience using discovery-based learning at the college level, with gen ed students. I liked it, and I think it succeeded better than other modes of instruction in building deep understanding and critical thinking skills. But there were several significant disadvantages:

(1) Some students didn't buy in to it, and some students had trouble with the intellectual challenges.

(2) The rate at which we could cover material was much lower than with traditional instruction.

(3) At some point you need the students to consolidate what they've figured out. The method I used was to have them maintain a file of notes online (in a system similar to google docs), which I corrected, commented on, and graded once or twice a week. This worked, but it was a huge amount of work for me. The role of a textbook becomes awkward in a course like this. Students deserve some kind of organized source of information that isn't just their own notes.

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