Week 4: Introducing algebra
Grandad taught me that the alien signs and symbols of algebraic equations were not just marks on paper. They were not flat. They were three-dimensional, and you could approach them from different directions, look at them from different ways, stand them on their heads. You could take them apart and put them back together in a variety of shapes, like Legos. I stopped being scared of them.
In Mal Peet’s young-adult novel,(2005), the heroine unpicks clues to her family history by investigating her grandfather’s undercover activities in World War II. In this quote, she describes algebra in a way that mirrors her quest: initially scary and flat but transformed by a teacher into a powerful and creative way of thinking about the world. This idea of algebra as a ‘habit of mind’ is largely accepted by researchers, who agree that algebraic thinking should be developed throughout primary and early secondary school, and that it involves structures, language and conjectures as much as notation.
In Weeks 4 and 5, you will consider the two main content strands of algebraic thinking: generalised arithmetic and functional thinking. In the UK, arithmetic is often seen as the concern of primary schools, while functions are only formally introduced in A-level mathematics, so being aware of this range will help you appreciate the role of algebra in making connections and progression throughout school mathematics.
In the English National Curriculum (2014), students are introduced to ‘the language of algebra’ from age 10, but many studies have shown that giving younger children experiences of informal algebraic thinking does support their later work with symbols. This week focuses on finding these algebraic opportunities within experiences of calculating with numbers and looking for generality.