You are given four separate pieces of chain that are each three links in length. It costs 2¢ to open a link and 3¢ to close a link. All links are closed.

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Presentation transcript:

You are given four separate pieces of chain that are each three links in length. It costs 2¢ to open a link and 3¢ to close a link. All links are closed at the beginning of the problem. Your goal is to join all 12 links of chain into a single circle at a cost of no more than 15¢.

Flow is optimal engagement. How can we tell the difference between flow and engagement? Students in flow have to be kicked out of the room when the bell goes.

The artists muse, or in the zone. Flow (Emotions drive goals) Mathematical Flow Group Flow Group Mathematical Flow

A high level of challenge AND skill is required. Model based on emotional responses.

Anthony Harradine: gaming-mathematical-flow?

Research Preliminary Study Interviews (8 people)

Mathematical Flow: luxurious, divine, beautiful, enjoyable. I got into it as well. I just enjoyed it immensely. They’re stupid little problems. No one takes them seriously anymore. They have been cut out of every curriculum, everywhere. They are fun, mathematical recreations. And so when I took that, and when I got so interested in it, that’s what turned me on, into math. [interview 4]

Mathematical Flow: luxurious, divine, beautiful, enjoyable. Oh yes, there is something there, there is something really beautiful, something really fundamental [interview 5] Oh yes, I have experienced group flow many times, and it is a divine feeling. [interview 5]

Mathematical Flow: luxurious, divine, beautiful, enjoyable...that it sort of, felt luxurious to be allowed, [interview 1] …and then I eventually understood why it wasn’t working and ah so that was a very nice moment. I understood, everything sort of clicked together at once, if you know what I mean, [interview 3] I could do that all day, it was such an enjoyable thing to do. [interview 4]

Mathematical Uni …what I am trying to say is that when we started doing proof based stuff rather than just rote method based stuff that’s when I actually started to become engaged in learning maths. [interview 8]

Research Intervention Inducing flow (6 sessions) 48 Data collection Sheets

Focus Not focused. Sometimes focused. Focused Half the time. Mostly focused. Completely focused. Score: Comment on Focus: Time I was clock watching. Time moved slowly. Time passed normally. Time flew past. I was unaware of time. Score: Comment on Time: Attention I was looking for distractions. I was easily distracted. I sometimes got distracted. I was only distracted once. I was not distracted. Score: Comment on Attention: Effort Could not be bothered. I tried at times. I tried half the time. I tried most of the time. 100% effort. Score: Comment on Effort: Challenge It did not challenge me. It was a little challenging. It was challenging. It was very challenging. Extremely challenging. Score: Comment on Challenge: Compared school math class Similar. Nothing special. More fun than a typical math class. As much fun as the best math classes. More fun than all my math classes this year. That was the best fun I have ever had doing math. Score: 12345

How did I promote flow? Provide the space and time for flow. Write on walls and desks. Food. Social atmosphere. No pressure. Relaxed self selected groups. Tasks: low entry – high ceiling. Elements of choice and surprise. Minimal teaching, lots of doing.

Comparison: (4) More fun than all my math classes this year (25 selections) (5) That was the best fun I have had doing math (6 selections)

Engagement Motivation Flow Task Selection Maths My concern with emotions led to the importance of task selection.

Designing and using mathematical tasks. John Mason and Sue Johnston-Wilder. The Open University Page 39. Responsibility for learning. To ignore totally ‘where the learners are’ is to invite disaster – who would attempt to teach Quantum mechanics to a four-year-old? But when the claim is that teachers need to know ‘what the learners know’ and to appreciate the learners’ motivations, intentions, desires and propensities and so on, the request is absurd. What could a teacher do with that information even if it could be gathered? With only one learner it would be difficult to use; with thirty or more it would be quite impossible.

So what have I gained from all of this? The curriculum is like a straight jacket sucking the soul out of mathematics? Perhaps by occasionally ignoring the straight jacket and simply enjoying some free-style mathematics we can hook students into math? Stretching wider and higher might make it easier?