Active learning ideas
Mathematics is often seen as the pinnacle of certainty, but its philosophical foundations are deeply debated. This topic asks: Is math a 'discovery' of universal truths that exist independently of us (Platonism), or is it an 'invention' of the human mind, a useful tool or language we created (Formalism/Constructivism)?
Activity 01
Students are assigned to the 'Platonist' (Discovery) or 'Formalist' (Invention) side. They must argue their case using examples like the Golden Ratio, prime numbers, or imaginary numbers.
How do historians select and interpret evidence?
Activity 02
Groups research a mathematical concept that was 'invented' for pure logic but later found to perfectly describe a physical phenomenon (e.g., non-Euclidean geometry and General Relativity). They present why this supports 'discovery.'
Can history ever be completely objective?
Activity 03
Students consider the question: 'If all sentient life vanished, would 2+2=4 still be true?' They discuss in pairs and then share how their answer reveals their stance on the nature of math.
How does the present influence our understanding of the past?
A few notes on teaching this unit
Watch Out for These Misconceptions
Mathematics is just 'counting' and 'calculating.'
Math is the study of abstract structures and relationships. Using 'Gallery Walks' of complex proofs or fractals can help students see math as a conceptual landscape rather than just a set of operations.
Mathematical truths are only true because we agree on the rules.
While the *symbols* are agreed upon, the *relationships* (like the ratio of a circle's circumference to its diameter) seem to hold regardless of our rules. Peer discussion helps students distinguish between 'notation' and 'truth.'
Methods used in this brief
Methodology in the Social Sciences
An examination of the methods used to study human behavior, including qualitative and quantitative approaches. Students will discuss the unique challenges of studying conscious, unpredictable subjects.
8 methodologies
Bias and Values in Human Sciences
This topic explores the impact of researcher bias, cultural values, and ethical constraints on social science research. Students will analyze how these factors affect the validity of findings.
8 methodologies