Creative ways of generating discussion with your students
We often traditionally think of number talks as involving numbers and operations, but they can be anything. For this reason, I think that the term 'Maths Talks' can sometimes be more a more accurate representation of these types of tasks. A maths talk encompasses every strand of maths and allows for a more creative and open definition of a task that you are working with. It could be a traditional 18 x 5 problem or a WODB task. The world is your oyster with a maths talk.
In the maths talk given above, a set of cuisenaire rods is shown and the question is asked about the whole. The reason that I decided on this activity is because often the whole or 'unit' in a fraction is misunderstood, leading to a very fragile understanding of fraction concepts. Hearing students' different points of view on what they perceive to be the whole, can lead to some very interesting discussion. When doing one of these maths talks, I'm interested in a students thinking and whether they are able to justify it. In this particular activity, there clearly is no single answer to the question which is the whole point. I don't want to know the answer, I want to know your thinking.
The idea of a maths talk is that it generates discussion. Some of my favourite, are Fraction Talks by Dan Finkel. Dan presented the one below at the Mathematics Association of Victoria (MAV) annual conference in 2017 and it was an instant hit.
Fraction Talks - Math for Love
Once again in this activity, the question can be anything. 'What fraction of the whole is blue and how did you arrive at your answer?' for example. Like in the cuisenaire activity, we always want to ask about the 'how'. This ability for students to be able to justify their answers is one of the most difficult to teach and learn in my opinion, so it is important to practice, practice, practice.
My favourite thing about doing any maths talk is hearing all of the creative and unusual ways that students use to solve a problem. In more cases than not, I will walk away having learned something new as well and I love it.
If you have some interesting and creative maths talks I'd love to hear about them so either post them in the comments below, post it on my facebook or twitter page, or simply send me an email via my contacts page.