teaching fractions through instructional design

I'm helping some home schooling parents teach their kids fractions - using the Idit Harel Instructional Software Design Project (ISDP) method. It's the best way I know to teach fractions, which is acknowledged to be one of the worst taught things in primary school ("a weeping sore" article by Ellerton and Clements)

For an overview read this article on my website --> Educational Software: Designed by Kids for Kids. This time around we're using Scratch rather than LogoWriter.

It is available as a book - Children Designers: Interdisciplinary Constructions for Learning and Knowing (some extracts available from this link)

Today I took the parents through the pretest and the general approach. The pretest contains questions like this:




The way I explained this is that we are learning the deep structure of fractions, in contrast to a worksheet algorithm approach made up of questions like what is 3/4 of 16. The problem with the worksheet alogorithms is that the children might be able to get the correct answer but still not have a clear understanding of what a fraction is.

By the deep structure of fractions I mean the ability to transform between picture, word and symbolic representations:


We discussed the questions after the adults had done the test. Naturally, this focused mainly on the questions that someone had got wrong. This is modelling the process the parents will go through with their children.

The next step is to pose these questions to your kids:

• What do you or your siblings find difficult about fractions?
• Make up your own multiple choice questions to test your sibling with, something that will improve their understanding.

There is a lot of meta learning involved in this process - asking and assisting the kids to finding the zone of proximal development for themselves and their siblings.

I then showed the parents how to represent such a question on the screen using Scratch

That's where we got up to. After I went home I looked up Idit Harel's thesis and realised I had missed out her "What is a fraction?" interview, which is another good way to start. This isn't completely represented in her thesis but I'll quote part of what she says here, so the parents can work this into their approach as well.

PURPOSE OF INTERVIEW IS TO INVESTIGATE THE CHILD'S CONCEPT OF WHAT FRACTION IS, their "favourite" representations of fractions, their way of "talking about" fractions and their ability to link or translate representations. Add to these questions if you want, whatever comes to mind.

General questions:
What is a fraction?
Can you describe anything in this room as a fraction?

Activities:
Use this set of pegs (or play dough, paper, blocks etc.) to show an example of the fraction 2/3

Probing questions:
One child told me that this red block and this yellow block together equal one-half. What do you think?
If this yellow block is the unit, what are these two yellow blocks and three red blocks together (the red blocks being half the size of the yellow blocks)?
Then probe further depending on what they come up with

Related: Questioning Research