PES PD: DMIC 11 March 2019
The hardest part of learning something new is not embracing new ideas, but letting go of old ones.
Justifying and Arguing Mathematically:
-Require that students indicate agreement or disagreement with part
of an explanation or a whole explanation.
-”Do we agree? Does anyone not agree?”
-Ask the students to provide mathematically reasons for agreeing or
disagreeing with an explanation. Vary when this is required so that
the students consider situations when the answer is either right or
-”Why did you do that?”
-Ask the students to be prepared to justify sections of their solutions
in response to questions.
-”Can you explain why you (or your group) did that?”
-Everyone in the group presenting is held accountable for the solution.-Require that the students analyse their explanations and prepare collaborative responses to
sections they are going to need to justify
-Model ways to justify an explanation
-”I know 3+4=7 because 3+3=6 and one more makes 7”
-Structure activity which strengthens student ability to respond to challenge
-Expect that group members will support each other when explaining and justifying to a larger group
-Explicitly use wait time before requiring students to respond to questions or challenges
-Require that the students prepare to explain their thinking in different ways to justify it
Questions to support student justification/extension?
-Why did you….
-How did you know…
-What do you mean by…
-Why did you do this...and not this…
**Encourage “so” “if” “then” “because” to make justifications**
Questions to extend an explanation into a generalisation? (CONNECT to GENERALISE)
-Does that work for every number?
-Would this work for “X”?
-Can you make connections between…?
-Can you see any patterns?
-How is this the same/different to what we did before?
-Representing a mathematical relationship in more general terms
-Looking for rules and relationships
-Connecting, extending, reconciling
-Ask students to consider what steps they are doing over and over
again and begin to make predictions about what is changing and
what is staying the same.
-Ask the students to consider if the rule or solution they have used
will work for other numbers
-Consider if they can use the same process for a more general case
-”What happens if you multiply the number by 2?”
Revisiting how we Develop Proficient Mathematical Learners
-Attend to classroom culture
-Choose high-level, problematic tasks
-Launch tasks in contextual ways
-Anticipate strategies and monitor group work
-Select and sequence the sharing
-Allow student thinking to shape the direction of discussions
-Plan for anticipations and how the connect could look
Revisiting the Launch
-First focus on the context. The problem should be in front of each
group of students. Let Y3 up read it themselves.
-Use Talk Moves to help students with lower literacy levels to
access the information of the problem
-”What is happening in this story?” Ask for others to add on or
repeat and revoice until you know they all understand the
-20% Teacher Talk 80% Student Talk
-”What do we need to find out?” Do not let them say an
operation, focus their attention on concepts not how to do it
-5 minutes work time (Jr School) 15 minutes (MAX!! Seniors)
-Think through grouping carefully, think social grouping or
what individuals can bring to the group work
-Never ‘High Half’/”Low Half’
-Keep groups close together to work on the mat
-Teacher role: roving, monitoring, etc
Connecting and Summarising
-Draw connections between solutions
-End with a summary of key maths ideas so students leave with
a “residue” from the lesson. This provides a way of talking about
the understanding that remains