The origin of the degrees in a circle dates back circa 3,000 years to the Babylonians, who used 360 days for a year. It’s a useful illustration that some ideas stick while others get lost along the way.
It is easy to overlook that we used to live without fridges – the majority of Britons only had a fridge from around the mid – 1970s. As technology advances so other competencies wane – preserving, fermenting, and curing fruit, vegetables and meat widely used for thousands of years is largely forgotten.
These tendencies apply to maths education too. Perhaps there’s value in hunting out the maths educators of the past. Caleb Gattagno (Gattegno Geoboards, 1954) explored manipulatives to aid the learning of geometry, and suggested that learning through memorisation, or when a subject is not engaging, is expensive cognitively. Kasner (Mathematics and the Imagination, 1949) explored the why of maths, whilst Gelfand (1960s) explored the depths of high school maths. T. Sundara Row (Geometric Exercises in Paper Folding, 1893) authored a helpfully self – explanatory title.
More recently there was a push in the late 1980s by the National Council of Teachers of Mathematics (NCTM) in the USA to help children engage with maths through a more integrated mathematics program (IMP) which focussed on collaborative problem-solving across multiple inter-related topics over 5 – 8 week periods – see Dan Fendel (Integrated Maths Program, 1989). The Common Core Standards (2010) evolved from this work and 36 US states have adopted them.
A special mention should go to Dan Cohen (Calculus By and For Young People (ages 7, yes 7, and up), 1989) who explored how to teach higher-level concepts to young children, in particular the ideas around calculus.
It would feel remiss not to mention Mark Driscoll (Reaching All Students with Mathematics, 1993) and Steven Chinn (How to Teach Maths: Understanding Learners’ Needs, 2020) who strive to help maths teachers find and fill knowledge gaps, and therefore enable a broader range of people to participate in maths successfully.
Cultures tend to defend their status quo and resist change; mathematics seems to be no different. Gently testing, questioning and challenging is important. John Mighton (The Myth of Ability: Nurturing Mathematical Talent in Every Child, 2003) and his JUMP project has been doing that for a couple of decades, an advocate of slow maths at a time when speed is increasingly prioritised (at least up to age 16).
As with everything, fads in maths come and go, and while a number are dropped for good reason, one ought to entertain the idea that some great approaches get lost along the way. As maths educators we want students to be curious, explore, be patient and play – it is important for students to see teachers living these traits, trying ideas, testing methods, playing with new habits.
Great educators continue to unearth the best from the past. Enjoy the treasure hunting.
By David Carlin
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