How can we d
eve
reasoning in m lop
aths?
Concept Cartoons
One very powerful way to
promote reasoning and kick-start
maths learning conversations is
the use of concept cartoons.
Concept cartoons are drawings which showcase a
collection of viewpoints about an idea that children debate
together. Cartoon-style characters are presented engaging
in a conversation using speech bubbles.
How can you use concept cartoons?
Have children complete a Reasoning Board where they attempt
to justify their group’s thinking and provide evidence for each
speech bubble statement.
Here is an example:
pull out and keep!
Statement
We agree/disagree
“I think multiplying
always makes a
number bigger”
We disagree with
this statement
1. We tried
2.
3.
Concept cartoons can be used in a variety of ways throughout
the maths curriculum. Let’s take multiplication as an example,
and tackle the common misconception that “multiplication
makes bigger.”
“If you multiply
by zero, the
product is zero”
We disagree with
this statement
1.
2.
3.
Hint: You can find templates for this at
www.doodlemaths.com/concept-cartoons
“Multiplying by a
fraction makes a
smaller number”
We think this
statement depends
1.
2.
3.
The cartoons are normally used in group settings where children
benefit from the opportunities to meaningfully debate with and
challenge their peers. They can be used at the beginning of a
topic or part way through to extract children’s ideas, pinpoint
areas of uncertainty and, crucially, identify misconceptions.
Evidence
Multiplication upgrade
Ask children to consider the following statements:
“I think multiplying
always makes a
bigger number”
“If you multiply
by zero, the
product is zero”
“Multiplying by a
fraction makes a
smaller number”
Divide children into small groups of three to share their ideas.
Make it very clear to children that the focus of the task is on
understanding, and that understanding is a team effort involving
different ways of thinking.
Available on Windows
Available on Mac
The statements definitely promote cognitive conflict and you can
see within these responses that there are rich opportunities for
deeper thinking. Children may agree, disagree, or offer a new
way of looking at the concept under discussion in a way that no
one else has thought of.
This is also the time to open up the debate to the whole class in
order to show particular examples such as multiplying by
negative numbers, proper fractions, or improper fractions.
By discussing ideas together in this way, children will enrich
their understanding and come to realise that multiplication
doesn’t always make things bigger. Concept cartoons are a
flexible classroom tool for engaging and generating high quality
talk for learning across the maths curriculum.
Take a look at
www.doodlemaths.com/concept-cartoons
to find all you need to start using these
with your class.
NEXT ISSUE - MARCH 2017
TEACHING TOOLS: Concept Cartoons
Concept Cartoons
“I think multiplying
always makes a
“If you multiply
bigger number”
by zero, the
product is zero”
“Multiplying by a
fraction makes a
smaller number”
Reasoning Board
Statement
“I think multiplying
always makes a
number bigger”
“If you multiply by
zero, the product is
zero”
“Multiplying by a
fraction makes a
smaller number”
Available on Windows
Available on Mac
We agree/disagree
Evidence
1
2.
3.
1
2.
3.
1
2.
3.
TEACHING TOOLS: Concept Cartoons
Concept Cartoons
Reasoning Board
Statement
We agree/disagree
Evidence
1
2.
3.
1
2.
3.
1
2.
3.
Available on Windows
Available on Mac