This article discusses the importance of mathematical intuition in education and outlines the tasks that improve this. Intuition gained credibility in the 19th Century when academics began to identify the need to deepen students’ understanding of difficult mathematical questions. Bruner (1960) identified the importance of intuition in mathematics and science education, which was broadly missing in the schooling system.[1] However, as mathematical intuition is a theoretical concept, there is a significant lack of research involving its application to teaching and learning (see Fischbein 1987 for further info).

Mathematical intuition enables students to attempt and understand reasoning and problem-solving questions.[2] This skill supports students as they move to KS4 learning and has become increasingly important since the new GCSE specification was introduced in 2015. The introduction of questions, such as ‘Hannah’s sweets’, that do not lend themselves to following logical thought processes require mathematical intuition to succeed (Tall 1980, 1).[3]

However, mathematical intuition is not only a skill that should be used during KS4 years to support their GCSEs. Including tasks and questions that aid students’ mathematical intuition at KS3 will ensure they have more time to improve their skills. Therefore, sooner is better.

How do we improve students’ mathematical intuition? 

Integrating mathematical intuition into a streamlined task that could be taught to students is, unfortunately, impossible. However, academics have identified a range of specific tasks that give students the best possible chance to stimulate their mathematical intuition, and these are as follows:

1. Investigations

These can be whole lesson tasks or take no longer than 5 minutes. When a teacher introduces addition into their lesson with their year 7s, instead of modelling a basic question to the class and cold calling, they should ask the students what the sum of the numbers from 1 to 100 is [?]. This creates the shift where students are in control of their learning, leading to multiple answers.

2. Group Oracy tasks

Working with others is a great way to develop students’ mathematical intuition.  This is because it allows the students to draw on the understanding of one or two of their peers without directly relying on their teacher. The example is a great way to bring Oracy and reasoning tasks together.

3. Reasoning 

Reasoning is a skill that students need to be encouraged to do all the time. With an “explain the mistake task”, students deepen their understanding of topics and improve their intuition through application.

4. Problem-solving, having a guide

Often, with questions such as ‘Hannah’s sweets’, it is about getting the students to understand that there is no quick answer. It will take time to do the method, drawing from many topics along the way. The example is an excellent way of bringing oracy and problem-solving tasks together.