This week's TOT is Shorter on the links because I spent more time reading and summarising papers than I did on Twitter.

To start off I've got some news that I'm very excited to share. A link to my 3 hour and 33 minute long interview with Mr Barton of the Mr Barton maths podcast (he interviewed me, so I got a chance in the hot seat for a change!). Craig asked me all about my current approach to teaching mathematics, experiences from my first year running the senior maths department at Sunshine College, and cognitive load theory. It was a really stimulating discussion, I hope you enjoy it!

Second up is a quick and amusing tweet from Dan Willingham.

Third is my takeaways from a really interesting paper on the reciprocal relationship between students justifying their thinking, and developing that thinking in the first place.

Takeaway four is a summary of wot-I-got from reading a great article on effective use of mathematical manipulatives in the classroom.

Following that we've got a link to another podcast, an interesting reflective piece on priming prior knowledge, and a taster of some of what is to come in future TOTs.

Enjoy : )

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Craig Barton interviews me on the Mr. Barton Maths podcast

Schools for making worker, then and now. An amusing observation

The understanding or the justification, which comes first?

(This was originally posted as a twitter thread here)

I’ve always been of the mind that an individual’s ability to justify their reasoning about a physical situation, such as the balance scales questions below (will it balance, fall left, or fall right?) depends on their understanding of the physical situation. Little did I know

That the relationship is actually a reciprocal one. The development of an individual’s understanding of a physical situation is, in part, dependent upon the ways in which we encourage them to justify their thinking about the situation. In ‘ Schwartz, D. L., Martin, T., & Pfaffman, J. (2005). How mathematics propels the development of physical knowledge.’, Schwarz and colleagues presented 9yo participants with puzzles similar to the one above, got them to make a prediction, then justify their thinking. The only difference between conditions was that one group was told to use math to justify their decision as to whether the scale would fall left, fall right, or balance. The other group was told to use justify their decision using words. Let’s digress for a moment to see how student responses were ranked. Student responses were placed on a developmental continuum based upon which rule they applied.

And their responses can be compared to the distribution of rules used by individuals from the broader population

In this experiment, the simple difference of prompts of ‘use math’ vs. ‘use words’ to justify thinking encouraged a larger number of the ‘use math’ group to consider both mass and distance, as was required.

Whilst this difference wasn’t significant, in another experiment related in the same study, instead of students just being told to ‘use math’ they had some key features pointed out to them.

In this experiment, the difference was even more pronounced.

Experimenters explored the ‘ecological validity’ of this approach by accompanying it with a lesson on the same topic.

Takeaway: It isn’t just our understanding of a situation that allows us to justify it using maths. Reciprocally, the support we’re afforded in the use of maths to justify our thinking can actually contribute to our understanding of physical phenomena in the first place!

A summary of Dan Willingham's article on manipulatives

(This was originally posted as a twitter thread here)

Unsurprisingly enlightening (i.e., it’s unsurprising that it’s enlightening) article from @DTWillingham on the ins and outs of using manipulatives to build student understanding. (aft.org/sites/default/…) Turns out, sometimes really small changes in the way we treat manipulatives/analogies/representations can have big effects

A particularly fascinating point is that perceptually rich (often realistic) materials often lead to quicker learning, but more limited transfer.

(sounds to me like another case of the ‘transfer paradox’, ) (ollielovell.com/tot/038/#The_t…)

The cool idea of ‘concreteness fading’ can apparently help us to get around this challenge, plus, using manipulatives consistently.

As always, we must include the fact what students think about is what they learn. Thus, it’s crucial for us to draw our students’ attention to the feature/s of the manipulative that’s relevant!

But interestingly, this can be done in different ways, AND, other small changes like counting on rather than counting up again (not sure if that’s the correct terminology?) can have substantive impacts to learning.

In closing, don't be lulled into a false sense of security. It’s not a given that students will link the manipulatives you’re encouraging them to use with the written maths you’re trying to convey to them. Even after a year. 

Manipulate that!

Leading with less ego, via @hbarvardbiz

Activating relevant prerequisite knowledge before a problem solving task, via @rhwave2004

Struggling with promoting student understanding

This paper has sent me down a rabbit hole. But it's a taster to a series of papers that I'll definitely be summarising soon : )

Related

2 Replies to “TOT039: Mr Barton interviews me, reciprocal relationships between learning and justifying, + more Twitter Takeaways”

  • Thanks for a really engaging discussion. You’ve really got me thinking about how I teach. I tried setting up backgrounds via youtube to each maths topic – history, interesting developments etc. I thought they’d really help the kids and get them engaged, but they did not really work for the older kids. But do you think they are still useful for younger kids in the exploration stage when you don’t have to rush through skills like in senior years?

    But, your explanation of cognitive load theory seems to explain that I’m doing too much and need to concentrate just on the simple skills.

    Ollie’s point about the most important things is to create a situation where students experience success as it also creates strong positive emotions in the students really makes sense to me.

    • Glad you’ve found some of this stuff stimulating George : ) I highly recommend Craig’s book, it goes into a heap more depth on a lot of this stuff. Look forward to continuing the conversation. Ollie.

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