Reasoning is an important element in mathematics learning, whether the learner is in Kindergarten or in Grade 12. Visuals, either with or without accompanying words, can be extremely powerful tools for reasoning and explaining; they are powerful not only because they help us understand more quickly, but also because sometimes they lead us to be more general than when we use specific numerical examples. This can be true at any grade level.
Here is a mathematical concept captured in a visual.
The picture may evoke any of the following ideas:
- equal groups of 2 could be created by splitting the icebergs with 4 penguins into two mini-icebergs
- equal groups of 4 could be created by combining pairs of icebergs with 2 penguins
- you can show any amount as a multiplication if one factor is 1 (e.g. 32 = 32 x 1 or 1 x 32)
Resist telling students what to look for.Rather, ask simple open questions about the visuals, such as:
When do we use multiplication?
Are all of the groups of penguins the same size? Does that matter?
Could the penguins be rearranged into equal groups?
Is it easier to use multiplication for this picture than if there had been 5 icebergs with 2 penguins on them?
This powerful concept enables students of all ability levels to share what they see.
What math concepts can you think of where the use of an image would help your students understand?
Marian Small is a Canadian mathematics educator and a regular speaker on K–12 mathematics throughout Canada and the US. Marian is the former Dean of Education at the University of New Brunswick, and has been a classroom teacher and professor of mathematics education for over 30 years.
In her latest resource, Eyes on Math, Dr. Small provides an extendable strategy. Teachers are provided with examples so that they might think of their own simple drawings for other math concepts. For more information on Eyes on Math click here.