Naomi Ingram, University of Otago From Brussels Sprouts …

Naomi Ingram, University of OtagoNaomi Ingram, University of Otago

From Brussels Sprouts …


… to Summer Strawberries


Engagement

…involvement in the activity of the classroom.

mathematical?


Relationship with mathematics

Views of maths Feelings about maths Perception of ability Mathematical knowledge Habits of engagement


Engagement in mathematics is important because of the nature of the subject.

There’s so much in maths. If I get behind in maths, it would probably be the worst subject to try and catch

up on (Debbie).

I am aware that I need to try my hardest. I am more attentive than in other classes. I know we need to

know this (Sean).


Tensions …

I didn’t work to the depth required because I was bored with it (Jason).

I work hard in other subjects. I talk the most in maths. In other subjects I’m quiet the whole time because I’m doing

it (Tracey)

It’s easier to talk than making my brain hurt (Bridget).


Students develop habits of engagement.

Homework Getting ready to learn

How much they socialise

How they ask questions

How they listen

How they engage in each mathematical task

How much they get involved in class discussions


A mathematics problem:

A machine prints four books in 10 minutes.•How many will it print in two hours?•How many hours would it take to print 390 books?

48

16 and ¼ hours .. or is it?

g


Reflect on your feelings and engagement

• How did you feel before you saw the problem?• How did you feel after you saw the problem?• How aware were you of others doing the

problem?

• Did these feelings affecting your doing of the problem?


Reflect on your feelings and engagement

Imagine the problem was given to a class of mixed-achievement Year 10 students as a starter. What range of behaviours would you observe?


Relationship with mathematics

5. Habits of engagement

Context ofthe moment

Engagement in a mathematical task

Unique learning experience and outcomes


Context of the moment

When students engage in a mathematical task, they are each situated in a unique context of the moment.


Teacher

classroom hot

classroom cold

too bright

social awareness

seating arrangements

Who I sit next to totally affects me

(Moira)

All Blacks

romantic relationships

issues with friends

after-school jobs parents’ divorcing

other subjects

lack of vegetables

family illness

Relationship with maths

Engagement in a mathematical task

Students have habitual pathways of engagement

when doing a mathematics task

Avoidance

Full engagement

Superficial engagement


Pathway of Engagement - Avoidance

Some things I just don’t attempt (Debbie).

Look at what I did today. No maths (Mark).

Going to the toilet, ruling up pages in their exercise book, organising their equipment, programming their

calculator, eating, daydreaming, writing notes to each other, writing poetry, doodling, talking socially,

writing out the problem as neatly as possible …


Pathway of Engagement - Superficial

I try and figure the problem out. After a wee while if I really can’t do it at all, I just give up (Bridget).

I kind of get frustrated when I can’t do something. I just give up (Paul)

Unprepared to think deeply about a problem.


Pathway of Engagement – Full engagement

I’ll read it a couple of times and think about it logically and sort of see what it actually means. I talk

to some other people about it … see what their methods are (Katrina).

When fully engaged, students think about the processes of solving problems, they persevere, use a variety of strategies and discuss mathematics with

others.


Asking for helpI need the teacher to go over answers I get

wrong.

The way I learn is by the teacher

explaining it to me and helping me

understand on my level.

Is this an indication that a student is engaged?

I get frustrated. Can’t you just tell me what it is?

Maths is like a silent movie because you either

understand the storyline by following the action and

another person explaining it, or you sit back,

bewildered.

Students have a set of engagement skills that operate at different levels of

effectiveness.


Perseverance

Integrity

Intimacy

Independence

Concentration

Utilisation of feelings

Cooperation

Reflection


The skill of continuing to do a mathematical task, despite experiencing difficulty.

Perseverance


Perseverance

IntegrityCommitment to searching for mathematical truth and understanding


Perseverance

Integrity

IntimacyEmotional engagement with mathematics


Perseverance

Integrity

Intimacy

Independence The skill of solving problems autonomously.


Perseverance

Integrity

Intimacy

Independence

Concentration The skill of remaining focussed, despite disruption.


Perseverance

Integrity

Intimacy

Independence

Concentration


The skill of being resilient to negative feelings felt during a task, and instead using them as a signal to persevere or change strategy.


Perseverance

Integrity

Intimacy

Independence

Concentration


Cooperation The skill of discussing mathematics, solving the tasks cooperatively, and to ask for help as a strategy, rather than as a form of disengagement or dependence.


Keep going

Integrity

Intimacy

Independence

Concentration


Cooperation

Reflection Being self-aware. Reflecting on own and others’ engagement.


What can we doto enhance engagement?

• Help students to recognise and act on feelings of confusion and worry when working on mathematical tasks.

• Encourage students to develop effective engagement skills.

Hmmmmmmm …….


Some ideas …1. Be explicit about the importance of doing mathematics to learn.

2. Get to know students’ engagement.

3. Wait until everyone is ready to learn before revealing the problem.

4. Give students a variety of problems of different contexts, difficulty, depth, and length.

5. Make sure ALL students have the opportunity to experience confusion.

6. Talk about your own engagement and/or the engagement of a tame mathematician. Normalise and EMBRACE confusion.

7. Ask students to try a problem by themselves for a time before talking to a friend or asking for help.

8. Ask students to reflect on how they solve problems.

9. Report formally on engagement skills to school and parents.


• Try the problem yourself before asking for help.

• Don’t give up when you are stuck.

• Seek understanding as well as an answer.

• Expect confusion

• Concentrate. Maths is thinky.

• Remember that mistakes are windows into your thinking.

• Cooperate with others.

• Be proud of your progress.

• Reflect on your doing.

When doing maths …


Naomi IngramUniversity of Otago, College of [email protected]

Naomi Ingram, University of Otago From Brussels Sprouts …

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