A concept map is a visual way to organise information and to record links between known mathematical concepts and procedures, both within and between topics. The use of concept maps is a metacognitive strategy (HITS Strategy 9) that helps students to organise their thinking as an intermediate step, rather than an end-product in itself (Fisher, Frey and Hattie, 2016).
In mathematics, these kinds of visual representations require students to communicate information while supporting their learning (Armstrong, Ming & Helf, 2018). The following activity shows how students can be explicitly taught to create concept maps, so that students can later use them independently as a step in completing a problem.
Understanding this strategy
This strategy involves students reflecting on the key ideas of the current topic, linking new vocabulary and ideas to previously learnt vocabulary and ideas. In the first instance, teachers can introduce students to concept mapping for a mathematical topic by jointly constructing a map on the board. To do this:
- The teacher explains that concept maps are graphical representations that show relationships between ideas.
- The teacher asks students to brainstorm key ideas related to the topic and writes them in large font on the blackboard.
- The teacher leads a discussion, asking students how the key ideas are linked.
The teacher may explicitly explain how key ideas are linked if students are unable to provide sufficient details.
Alternatively, the teacher may press students until they clearly articulate the links between the ideas.
- As students explain how the ideas are linked, the teacher joins the related ideas with arrows. The teacher explains that the arrows indicate there is a relationship between the ideas. These relationships can be:
Unidirectional (single-headed arrow, ← or →)
Reciprocal (dual-headed arrow, ↔)
- On each arrow, the teacher writes a short explanation about how the key ideas are linked. The teacher explains that the text clarifies what the relationship is.
- The teacher leads a summary discussion about the key ideas and the links between them.
As students become more familiar with concept mapping, they can be scaffolded to independently construct their own maps. The below example shows how this can be done in a Year 9 class.
Example of concept maps
Consider the example below for teaching the topic 'Trigonometry' in a Year 9 class (VCMMG319).
- Ask students to list all of the key ideas for trigonometry on a blank sheet of paper. Students list key ideas such as: similar triangles, sine, cosine, tangent, hypotenuse, adjacent, opposite, use of similarity to find values for trigonometric ratios, etc.
- Ask students to share key ideas in a class discussion. Different ways of expressing key ideas could be discussed.
- Ask students to draw arrows between related key ideas.
- Ask students to add text and/or examples on each arrow to show what they have learned about the connections between the key ideas.
- Ask pairs of students to discuss their concept maps and to compare the key ideas and explanation of links.
HITS 10: Differentiated teaching: For students who are seeing concept maps for the first time, the activity can be further scaffolded by preparing a sheet with useful terms and examples that can be cut out and arranged to form a concept map.
The task is then modified so that what is required is an arrangement of text to show how the various ideas are connected. Students can then add the links between these ideas.