Wading through the world of twitter and academic articles was particularly enriching for me this week.

First off, I learnt what a ‘Threshold Concept’ is. And I’m all the better for it.

Secondly I went a bit further down the rabbit hole I’ve been exploring recently. Trying to work out why, when I give my class the same resources, some of them manage to successfully learn, and other seem to really struggle. I give some key takeaways from a paper by Alexander Renkl exploring this question.

Thirdly (would have been first in another week as it’s so good!) a must read article on group work. Only a couple of pages too. Has inspired me to incorporate group work into my classes next term. Watch this space.

For the remainder, have a read if:
4, You’re keen to know more about how teacher intuition can get in the way of effective instruction
5, You want some interesting resources and reflections about increasing the amount of talk in the mathematics classroom
6, You’re a high school science teacher
7, You’re a high school science teacher
8, You teach maths
9, You're keen for a look inside a ResearchEd event
10, You think you’re invincible (or you know someone who does…)

Enjoy : )

(all past TOTs here), sign up to get these articles emailed to you each week here.

What is a ‘Threshold Concept'?

What is a threshold concept? (new term to me, I was intrigued…) , Glynis Cousin (ecu.edu/cs-acad/writin…)

Maybe they’re one way to move away from a stuffed curriculum that’s a mile wide and an inch thick?

Apparently they’re hard to forget

Reminds me of my bio primary/sec discussion with @mrbartonmaths . Perhaps a threshold concept epiphany signals the beginning of the transition from ‘slow, effortful, complex and explicit/conscious’ to ‘fast, frugal, simple and implicit’ processing w.r.t a given concept.

The 2-pager’s language then starts sounding a bit postmodernistic… watch this liminal space (as an aside, check this out: ). None-the-less, it makes some interesting points about the difference between mimicry and learning. (en.wikipedia.org/wiki/Sokal_aff…)

FYI.

An interesting link is then made between such mimicry and building a ‘culture of error’ in your classroom (my interpretation of their words). Makes sense.

I like the idea of ‘threshold concepts’. They add a layer of depth to a ‘core question's approach, which I already love (see via @adamboxer1). Here's a pic from the post that introduced me to threshold concepts (achemicalorthodoxy.wordpress.com/2018/03/02/fix…)(thescienceteacher.co.uk/structuring-st…)

What's the difference between what goes on in the minds of more and less successful learners?

You give 36 students sdts a set of worked examples and tell them to start learning. At the end of 25 mins you test them on some near and medium transfer Qs. After controlling for prior knowledge, 1/3 of the group demonstrates significantly more learning than the other 2/3. Why? Alexander Renkl tries to work out what the heck is going on in the minds of these learners, and what’s the difference between the more-successful, and less-successful ones. – Renkl, A. (1997). Learning from worked-out examples: A study on individual differences. Building on the research of Chi and colleagues (1989), Renkl aims to dissect the self-explaining that successful learners do.

Subjects were asked to verbalise their thinking processes (think aloud) whilst studying the worked examples (relating to learning probability) and their verbalisations were coded in relation to seven categories.

Renkl then analysed the data to see if any patterns of response emerged. He found that, based how often each person exhibited instances of each of the self-explanation categories, the participants fell into four clusters (see image). These are taken as ‘self-explanation styles'.

An odd-even analysis (regressing responses to even numbered qs against those to odd) suggested that each individual’s self-explanation style was relatively consistent, independent of the worked-example being studied. (but not-so for ‘noticing coherence’).

Interestingly, results suggest that we would be unjustified to reduce these self-explanation characteristics to a single construct (such as we do with intelligence), as correlations between them were insufficient. This has implications for instruction.

The next question to ask is whether these clusters differentially achieved. The below table (edited) shows achievement (scores standardised and adjusted for prior achievement) on the post test. Principle-based and Anticipative reasoners learnt significantly more.

Correlation or causation?

Prior knowledge didn’t seem to be a pre-requisite for applying these strategies. To me this suggests that perhaps there’s a significantly domain-general aspect to ‘learning to learn’, and thus, it’s possible to teach students to learn better. (Note thw caveat @ the bottom though)

Next I’ll be exploring papers that try to determine whether we can teach students to move from passive or superficial learning approaches, to more principle-based or anticipatory strategies. Watch this space!

The best, most actionable article on group work I've ever read

The curse of knowledge for teachers

Talk in the mathematics classroom, one teacher's reflections, via @rhwave2004

Resources for high school science teachers. Well worth a look, via @sci_challenge

More on high school science, using ‘the bar model', via @Benneypenyrheol

Collection of multiple choice quizzes for maths

What happened at ResearchEd Blackpool? via @mathsmrgordon

Anxiety, it can happen to the best of us

This piece reminded me of a great quote that I found in Alain de Botton's Religion for Atheists a few years back.

“While for long stretches of our lives we can believe in our maturity, we never succeed in insulating ourselves against the kind of catastrophic events that sweep away our ability to reason, our courage and our resourcefulness at putting dramas in perspective and throw us back into a state of primordial helplessness.”

Related