Priscilla Allan26th November 2015

In 2015 I completed aMasters of Professional Studies in Mathematics Education.

MProfStudsWhich is not yet fully marked.

I also graduated with a Post Graduate Diploma in Education with Distinction.

PGDipEd

This presentation is about the research component of the MProfStuds.

Engagement

Motivation

Flow

TaskSelection

Maths

My concern with

emotions led to

the im

portance of ta

sk selection.

The artists muse, or in the zone.

• Flow • Mathematical Flow• Group Flow• Group Mathematical Flow

Flow is optimal engagement.

How can we tell the differencebetween flow and engagement?

Students in flow have to be kicked out of the room when the bell goes.

A high level of challenge AND skill is required

.M

odel

bas

ed o

n em

otion

al re

spon

ses.

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 flow @ 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

http://2015byod.wikispaces.com/Flow+Course

Focus Not focused. Sometimes focused.

Focused Half the time. Mostly focused. Completely

focused.

Score: 1 2 3 4 5Comment on Focus:

Time I was clock watching.

Time moved slowly.

Time passed normally. Time flew past. I was unaware of

time.

Score: 1 2 3 4 5Comment 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: 1 2 3 4 5Comment 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: 1 2 3 4 5Comment on Effort:

Challenge It did not challenge me.

It was a little challenging. It was challenging. It was very

challenging.Extremely

challenging.

Score: 1 2 3 4 5Comment 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: 1 2 3 4 5

How did I promote flow?• Tasks: low entry – high ceiling.• Provide the space and time for flow.• Write on walls and desks. Food. • Social atmosphere. No pressure.• Relaxed self selected groups.• 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)

So what have I gained from all of this?A mathematical flow experience can

open a pathway to success.Mixing mathematics and socialization

is important.Free-style mathematics could hook

students into math.Stretching wider and higher might

make it easier?

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¢.