Friday, 13 April 2018


Through argumentation you get the generalizations from students to make their justifications.

Deeping Mathematical Explanations. 

Have students develop two or more ways to explain a solution which may include using materials (provided nearby the class...not given or suggested to the students to use)

Compare explanations and develop the norm of what makes that explanation acceptable. Reinforce what makes it mathematical.

15x3…..reinforce the story 15 what? 3 what?...remind students to label/record that to improve our explanation.

Have others ask questions….this is a from of mathematical reasoning

Reinforce the acceptability of multiple ways. Support them to make connections to other or previous problems. 

Be sure to explicitly note student behaviour that supports mathematical practices.

Reminding kids to ask how to make sense of what they are doing for themselves and for sharing with others.

-Be mindful of student body language especially with those who are generally withdrawn from learning. They are often the ones playing with the materials but they are actually able to use them and explain their thinking.
-Choosing the “visual” solving group to report first often allows for deeper understanding when hearing from those who have a higher level response.

What is my next step for Term 2? 

I want to be sure that my students are able to link back to and remember the context of the problem. It is about finding the solution to the story not solving a maths questions properly. I also want to focus on incorporating our norms into my classroom on a daily basis across subject areas.

These are a teaching tool.. They are not for the students to use on each other. There are many different talk moves but this set is a useful summary.

REPEATING: Always ask a student who has been listening and is confident to speak. This is used to provide understanding across the room for a point that has been made by one group.

Who can say that again? 

Who can put that into their own words? 

Who can restate what (name) said? 

Can anyone repeat what they heard (name) say? 

Tell us what your partner said. 

CLARIFYING: student thinking and thinking of others

Wait Time: ask the question and wait it out until that student is ready to report...used to provide “think time” to a student or group while reporting back to the class….Everyone (including teacher) is silent 

Turn and Talk (Circulate and listen) This is very powerful especially during the share back time 

Stop and Jot (circulate and observe) 

Will you share that with the class? 

Say more (who can say more; tell us more about what you are thinking; would you give an example?) 

So you are saying….? (Revoicing) 

DEEPENING: student understanding and reasoning

Why do you think that? 

What is your evidence? 

How did you get that answer? 

What convinced you that was the right answer? 

Why did you think that strategy would work? 

Can you prove that? What makes you think that? 

ENGAGING: with the reasoning of others

What do you think about that? 

Do you agree or disagree? Why? (BE EXPLICIT) 

Who can add on? 

What do other people think about that? 

Does anyone have a different way of looking at this? 

Does anyone have more evidence? 

Instructional activities (Quick Images) can be used and adapted at many levels. Good for visual representations and equations (excellent for moving into multiplying).

Steps in a Lesson

Anticipate: what will I expect to see from my students?

Predict and record different ways students will solve a problem

First, have the group discuss. Present the pen once everyone has shared in the small group and are ready to begin working it out on paper.

Set Norms/Launch: Norms then Launch

Monitor: make note of who is doing what

Close listening and noticing

Questioning to make thinking visible and to allow students to refine or revise their thinking

Pressing students to consider all aspects of the task

Select: which 2 groups will share back

Sequence: what order will they present in?

Connect: Circulate back to the BIG idea

DMIC Term 1 Reflection

The PES Staff spent the last day of the term with some members of the team from DMiC.  The first part of our morning was spent doing some personal reflection on how things are going so far.

Point to Remember:
Having children dig deep to work through the problem solving process is more valuable than actually solving the problem.

What has worked well? Why?
-Using mixed ability learning groups has provided such a different atmosphere of learning.  Students are able to work together and learn from each other. It has been fun watching students question each other and have to ‘defend’ their thinking process to their peers.

How do our children feel and act about learning maths this way?
-Although it has been a learning curve for them, they really enjoy the freedom to explore their own problem solving process and not have to use a scripted method.

What have been your struggles? Why?
Bringing in those kids who just refuse to participate. Engaging the students who are quite happy to sit back (or roll on the ground) and let the others solve the problem for them.