# Back to the future with discovery learning

### Will the new Australian curriculum, published tomorrow, promote teaching methods such as discovery learning?

*“Why is it, in spite of the fact that teaching by pouring in, learning by a passive absorption, are universally condemned, that they are still so entrenched in practice? That education is not an affair of ‘telling’ and being told, but an active and constructive process, is a principle almost as generally violated in practice as conceded in theory.” John Dewey, Democracy and Education, 1916*

I left yesterday’s *Age Schools Summit* before David de Carvalho’s speech on the imminent publication of the draft version of the new Australian Curriculum. Helpfully, he has now posted his speech online.

I’m not quite sure what to make of it. He focuses on maths and, at one point, enthuses about discovery learning.

*“A student might, for example, memorise the formula for calculating the length of the hypotenuse if given the length of the other two sides of a right-angle triangle, but do they understand why that formula, known as Pythagoras’ theorem, works every time? The process of discovering that for themselves, with the assistance of the teacher, is what makes learning exciting. And it’s what make teaching exciting. Seeing the look of excitement on the face of the student when they experience that “aha!” moment.”*

This is not a new idea. It embodies something that Richard Mayer describes as the ‘constructivist teaching fallacy’. This occurs when people take the largely uncontroversial constructivist theory of learning - that we relate new knowledge to stuff we already know - and assume it implies specific classroom practices. In maths, this typically involves people asserting that ‘rote memorisation’ of mathematical procedures is not enough and to gain ‘understanding’ students need to engage in discovery learning because reasons, as if nobody has ever been able to understand an explanation.

Despite being the fashion for at least 100 years, the track record of discovery learning is poor and you have to wonder why people repeatedly discover it. I am aware of no strong evidence that we learn something better if we discover it ourselves. The one study I do know to systematically investigate this hypothesis involved teaching the scientific principle of controlling variables to middle school students. One group were explicitly taught the principle. The other group were aided in discovering it. As we may perhaps expect, fewer students learnt the principle in the discovery condition. However, what is particularly interesting is that those students who *did* manage to discover the principle themselves were then no better at applying it to the evaluation of science fair posters than those students who had been explicitly taught.

Discovery learning is less effective than explicit teaching because it consumes cognitive resources in evaluating all the dead-ends and possibilities. It therefore drives a wedge between those students who are already advantaged by possessing greater cognitive resources and more prior knowledge and those who are disadvantaged. It is inequitable.

Is discovery learning to be in the new draft curriculum? To be fair, it already sits in the old curriculum under the guise of problem-solving and reasoning. What is maths, if *not *problem solving? All I do in class is teach students how to solve problems. I don’t teach them anything else. When people insist that we must make more time for problem-solving, I can only assume that they want students to spend more time solving problems they have not been taught how to solve, perhaps in the hope that this will develop supposed maths problem-solving ‘skills’ that always remain nebulous and underdefined.

De Carvalho explains that, up to now, the issue has been that pesky teachers have been ignoring these exhortations to ineffective practice:

*“It should be noted that the current Australian Curriculum in Mathematics already includes four Proficiency Strands: understanding, fluency, problem-solving and reasoning. The issue has been that these proficiencies have not been incorporated into the Content Descriptions, which is what teachers focus on.*

*So the major change we have made in the proposed revisions to Maths is to make these proficiencies more visible by incorporating them into the Content Descriptions.”*

Carvalho then gives the example of a Year 7 content descriptor that has been changed from, “Students will learn to calculate volumes of rectangular prisms” to, “Students will learn to establish the formula for the volume of a prism. Use formulas and appropriate units to solve problems involving the volume of prisms including rectangular and triangular prisms”.

The language is odd. Why are we suddenly talking about ‘formulas’? That’s a weird, reductive term for mathematical relationships. And what do we mean by, “learn to establish the formula”? This sounds like we don’t want teachers to teach this particular relationship, we want students to figure it out for themselves like in de Carvalho’s hypotenuse example.

But wait! No! Please nobody get the impression that teaching methods are going to be mandated:

*“It is also important to note that in proposing these revisions, ACARA is not making any recommendations about pedagogical approaches. How best to teach content is a matter for teachers who know their students best. But they [I think this refers to problem-solving ‘skills’] do need to be taught. Which is why as the five national Maths and Science organisations said in their joint statement that ongoing professional development is so important.”*

This doesn’t make any sense. Let’s see what tomorrow brings.

Establish the formula themselves sounds like, as you put it, they will be "guided" to figuring out what formula to use by trial and error, I assume. Weird.