A dry day at the office...

Developing Mathematical Inquiry ~ Session 3

Professional development certainly makes you appreciate what our children go through each day. Too much talking/death by slideshow can be painful and sends me straight to day-dream land. Today was certainly a full on day, with a lot to take in. I find this kaupapa really interesting, so there was no time for day dreaming! Keeping track of my thoughts here is a great way to stay focused. 

The jury is still out when it comes to DMIC at our kura. Here are my takings from the day...

Practise justification and argumentation 

88 / 4 = 44 / 2 + 44 / 2 

Look at the elements involved in solving the problem. In this case, there are 3. 

1. Understanding the meaning of the '='. Means, 'is the same as'.

2. BEDMAS - understanding the order of operations.

3. Knowing the divisor can not be halved, only the dividend can be divided.

When children are sharing their ideas, call a pause frequently and ask other groups to repeat, agree/disagree, ask a question...  

Justifying and Arguing Mathematically

What is the difference between an explanation and a justification? An explanation might be incorrect, there is room for error. A justification dives deeper and proves beyond doubt that the explanation is correct. 

Explicitly model ways to justify an explanation. Use 'because'.

Always call a pause after an explanation! 

Prepare students of justify and argue

Build the expectation that all children need to be able to prove with a why. Build resilience.  The whole group needs to function together.  Prepare collaborative responses. 

Stand back from groups - monitor. Ask yourself - if I have to go to that group, why am I? Ask a question that's going to stimulate thinking.

Pre-warning - make sure kids are clear with what they're going to share back to the group. "What will you say next? Then what? Then what?" Set them up for success! 

Encourage kids to unpack their thoughts. Can they use a visual representation? Can they explain it in another way? Can they number the steps in their process?

Strengthen students to respond the challenge

Explicitly use wait time. Encourage the use of so if, then, because.  Pre-warn, "I'm going to ask you to repeat just one idea." Know when the right time is to call on a child who might not usually contribute. If they're struggling with a response - "Do you want think time in order to revise your thinking?" Have a signal so a child knows when you're going to call on them.

What are the norms in the classroom? Have high expectations from the outset. "You will listen the first time so you don't need to ask for a repeat!"  

Good questions to ask 

• Can you convince us?
• How do you know it works?
• Why does it work like that?

Develop a generalisation

Big Idea - is like your Achievement Objective.

Generalisation - Success Criteria.  

Find your big idea, then look at what generalisations come out from that. 

Find teachable moments  - Know the difference between a misconception and a gap in foundations. Gaps can be parked and addressed as a group at a later time. I'm not going to use the words 'ability based groupings'...... but I just did. Misconceptions might be addressed at that moment.  

Think about the entry point of the task. Can each child enter at their own level? Low floor, high ceiling.  Is there a place for extension? Challenge more able learners to share in different way, eg. visual representation. If the task is solved too quickly, it's an issue with the task. 

Examples of questions - create a wall of questions. Add to one at a time, not all at once!

Developing Proficient Leaners

Attend to the culture

Choose high-level problematic tasks

Anticipate

Select and sequence

Allow student thinking to shape discussions

Plan for a connection

Intentionally lift the Status of the Tamariki

Point out the status of all kids, especially those who might not usually contribute. 

All kids need to see what 'smarts' they bring to their group.

Make the problems relevant to their lives (cultural context).

There are no passengers on the waka - everyone is paddling!

We make decisions about other people's ability on the basis of certain characteristics. Don't under estimate the impact of teacher body language/reaction to kids responses!

Conjecture ~ an opinion without sufficient proof. 

What does being smart mean? Ask the kids to tell you what they think!

- I'm good at asking questions?

- I never give up!

- I can explain my thinking?

My next steps

1. In planning - give more thought to relating the possible generalisations to the big idea

2. Refer to the framework more often.

3. Embed the norms - lift the status.