The impact of thinking fast and slow on teaching and learning strategies in mathematics
Professors Layal Hakim and Peter Ashwin recently ran an insightful session exploring how the two different thinking systems proposed by psychologist Daniel Kahneman affect learning maths. Their talk, based on Kahneman’s acclaimed book ‘Thinking, Fast and Slow’, provided some great takeaways for engaging students in deeper thinking.
The Two Systems of Thinking
According to Kahneman, there are two main ways our minds process information:
- System 1: Fast, intuitive, and emotional. It relies on mental shortcuts and heuristics which can sometimes lead to biases.
- System 2: Slow, deliberate, and logical. It requires effort and concentration but enables complex reasoning and deeper learning.
In learning maths, over-relying on System 1 thinking can prevent students from fully grasping underlying concepts. But prolonged System 2 thinking can be mentally taxing and frustrating. The ideal approach combines both systems effectively.
Implications for Problem Solving
Several System 1 biases can hamper effective maths problem solving:
- Loss aversion – An unwillingness to abandon a faulty approach already invested time and effort into.
- Sunk cost fallacy – Persisting with an unproductive method simply because of the effort already expended on it.
To counter such biases, students need to engage more System 2 thinking through practices like:
- Comprehensively reflecting on why a particular method is incorrect or ill-suited to the problem.
- Constructing their own detailed proofs and explanations for concepts from first principles.
- Using techniques like the ‘Know, Want, Challenges’ framework to methodically break down multi-step problems.
Educators can further prompt System 2 engagement through problem and assignment design elements including:
- Incorporating worked examples with intentionally faulty logic that require deeper analysis to spot the flaws.
- Requiring students to come up with counter-examples disproving statements.
- Adding open-ended problems with no obvious ‘textbook’ solution method.
Implications for Student Engagement
Overusing System 2 thinking without success on difficult problems can quickly lead to frustration and disillusionment. It’s important for educators to provide enough detailed, personalised explanations and support to guide students in applying slow, deliberate thinking effectively.
The design of assessments and assignments also matters – they should require deep conceptual understanding over mere pattern recognition and other System 1 heuristics. This develops students’ minds and primes them for tackling more advanced mathematical topics further down the line.
Implications for Teaching
Maths educators can promote deeper System 2 engagement through techniques like:
- Using analogies, examples, and intuitive explanations to introduce new concepts before presenting formal definitions.
- Framing novel problem-solving approaches in a compelling way that convinces students of their applicability.
- Designing term papers and projects that demand thorough literature review and analysis rather than regurgitation.
- Explicitly teaching and rewarding metacognitive practices like reflecting on the problem-solving process itself.
The insights from ‘Thinking, Fast and Slow’ provide a useful framework for tackling the inherent challenges of teaching and learning maths. Understanding the thought patterns behind how students learn enables educators to better motivate engagement with deeper, System 2 thinking critical for mastering mathematical concepts.
- Students need to move beyond over-reliance on System 1 thinking to grasp math concepts.
- Prolonged System 2 thinking can be draining without enough support.
- Teachers should design assessments and instruction to nudge System 2.
- A balance of both thinking systems is ideal for math learning.
This blog post was developed by Jo Sutherst, following an interview with Professors Layal Hakim and Peter Ashwin.