Cling to the main vine, not the loose one.
Kei hopu tōu ringa kei te aka tāepa, engari kia mau te aka matua

123Thoughts on Teaching and Learning of Mathematics
Engagement and Lesson #12
Engagement and the measure of engagement is a puzzling problem.

What is engagement? How does one measure it?

Does engagement lead to student achievement? How do you know?

It turns out that this is a global puzzle. Engagement appears to be in four parts.
a. Behavioural
b. Emotional
c. Cognitive
d. Social

Behavioural is about being self managed and making the effort and giving the respect to be part of the group.
Emotional is about being relaxed and mentally resilient, being supported as a person and not having any great emotional dilemmas dominating your existence.
Cognitive is about being mentally prepared, interested and keen to learn more. All with relevant contexts.
Social is about connecting with your peers and being accepted, participating and contributing.

Measuring all this is even more problematic. More later.

I do know as a teacher when my class or "most of" is engaged. It is buzzing or busy, I am not required, I am noticing and watching. I may as well walk away. Thsi has happened a few times in my 30 years of being a maths and physics teacher. It can be scary and is so when it first happens.

For me, it first happened in a physics class 1981, 3rd year teaching,  when I was trying to create an experiment using a builders plank and making a ballistic pendulum to measure the speed of an airgun pellet. I needed the weight and casually asked a couple of students to weigh the plank. They came back to me a few minutes later saying the scales only measured to 5 kg and the plank must be heavier than that because the scales bottomed out.

I said "Well just weigh one end and double it." I was solving the problem and did not expect the response.

The class erupted in uncertain laughter and confusion.
"That won't work. There will be some of the plank you are not measuring!"
"You will get an incorrect answer"
"Weight does not work like that"
"Hogan, you are all sh..!

So I said "Well, weigh each end and add them up!"
The class started rolling around the floor laughing and was absolutely convinced I was a crazy man. I started to enjoy this response. My experiment had been destroyed. Goodbye ballistic pendulum and welcome cognitive dilemma and engagement. These students became one of my better classes.

They argued, debated, reasoned, pondered, wrestled, twisted truth, falsified truth, ignored fact, embraced hysterical crowd behaviour, fought, resisted and eventually just before the 1 hr period ended decided that perhaps I was right and decided to test my idea on a lighter object. What an astonishing thing to witness. Learning happening before my eyes.

The students found something they did not agree with and could not assimilate the suggestion.  It did not fit their world view or understanding. They resisted as all conservative humans do to change and dilemma. They pondered and created a way to test the hypothesis. They discovered new truth. They created new knowledge. They learned that the "up" forces equaled the "down" forces. They then figured out that for a symmetrical plank weighing one end and doubling the answer would give the exact weight of the whole plank.

Hence Lesson 12

Some questions...
Can everyone become a team player?
Is there still a place for individuals in the modern world?
Adult literacy and numeracy website for rubrics on listening etc.
What mathematical content knowledge does a teacher need to inform team development?

Teacher TASK
Try Team based work in your classroom.
Try Problem Based learning.
Can you assess a group rather than an individual?
How do you measure ENGAGEMENT?

This is to help look around my pages. I have tried to make it consistent in all chapters. The Planned chapters are only ideas at the moment.
1. Intro and Relationships, L#1
2. The Main Vine, L#2
3. Beginning a Year, L#3
4. Number and Algebra, L#4
5. Geometry and Measurement L#5
6. Probability and Statistics L#6
7. Problem Solving L#7
8. Investigations L#8
9. Visual Mathematics L#9
10. Assessment and Learning L#10
11. Team and Problem Based Learning L#11
12. Engagement L#12
13. The Classroom L#13
14. Being a Teacher L#14
15. Being a Leader L#15
16. Managing the Principal L#16
17. The Importance of Whanau (Family)L#17
18. The Importance of the Student L#18
19. Math Topic A - Squares
20. Teacher Tools
22. Math Phobia