mathematics
22 June 2021
I recently asked over 300 teachers about their multiplication fluency thoughts. This is a brief post summarising the results. Background 83% of the respondents were primary or middle school teachers, 12% were secondary school teachers and the rest were parents and other roles. Some people were teachers as well as parents and other roles. Which tables I asked which tables their learners should be fluent in. 61% said 0 to 12 and 36% said 0 to 10. This is interesting as the New Zealand curriculum requires up to ten, not twelve. You can see in the graph that nearly twice […]
11 May 2020
The problem with equals signs The sign “=” was invented in 1557 by Robert Recorde a Welsh mathematician. He was tired of having to write out the phrase “is equal to” too often. Now we cannot imagine maths without an = sign. Using an equals sign correctly can be a challenge. Whenever an equals sign is used, it signifies that the expressions on either side are equal. A sequence of expressions separated by equals signs should all be equal to each other. For example: 4 + 5 = 3 × 3 = 21 – 12 However, the equals sign often […]
18 March 2020
We live in interesting times. It warms my heart to see my discipline of mathematical modelling used to predict and manage the outbreak behaviour. How much easier it will be to explain Operations Research after this! In New Zealand we have yet to feel the full force of the Covid-19 pandemic, but anxiety hangs in the air. Around the world schools and colleges are closing their doors to slow the spread of the virus and students and teachers are forced to enter the world of distance learning. Nine years ago the Christchurch earthquakes meant that the University where I worked […]
26 November 2019
Variation Theory applied to teaching mathematics and statistics Highlights Careful selection of exercises can turn purposeful practice in maths into a task that also develops conceptual understanding. Poor, off-the-cuff or random selection of exercises can create barriers, feed misconceptions and at best miss out on opportunities for better learning. Using a framework of variation theory can help teachers examine and improve their practices and tasks, preferably collaboratively Spurious rules If students can learn a spurious rule for answering questions rather than the desired concept, they will grab it with both hands. In my class a student worked out that if […]
12 September 2019
Three types of people There are three types of people in the world: those who can count and those who cannot. Just kidding. But the ways people respond to mathematics can be put roughly into three groups – the maths-likers, the perplexed and the traumatised. See “Writing about Maths for the Perplexed and Traumatized” by Steven Strogatz. Maths-likers Strogatz uses the term “naturals” for this group. The maths-likers are people who liked maths at school and find it interesting. Some maths-likers go on to become maths teachers or accountants or statisticians or work in some other area that uses mathematics. […]
12 August 2019
Multiplication facts matter Fluency with multiplication facts makes learning later skills easier. When simplifying fractions, it is helpful to know multiples of numbers. When learning division algorithms, fluency in the basic facts means that the brain is free to learn the new procedure. In algebra, it is extremely helpful to be able to recognise common factors of two numbers, such as 36 and 24. Being fluent with multiplication facts is invaluable for estimating in many areas of life. A recent survey of high school teachers reported that they value knowledge of tables highly. Parents helping The advantage a parent has […]
19 June 2019
Fluency in language I can recite Latin verbs: the present tense of love is amo, amas, amat, amamus, amatis, amant. I recited them as I swam up and down the pool forty years ago: Amabo, amabis, amabit (breathe) amabimus, amabitis, amabunt (breathe). But if I were suddenly faced with an ancient Roman and had to express my affection, it would take a bit of thinking. I lack fluency in speaking Latin. When we are fluent in a language, we can respond and converse without having to think too hard. The language comes naturally, and we do not use up space […]
5 June 2019
I like a good challenge I always choose the most difficult Sudoku puzzles. I like it best if I get really stumped and have to leave the puzzle and come back later. If I do manage to crack it, I feel a sense of achievement, and completion. From time to time I have tried “The most difficult sudoku” but have never managed to place more than one number. There isn’t a lot of fun in that. Fun exists in what is sometimes called “The Goldilocks zone” – not too easy, not too difficult, but just right. I have also seen […]
1 May 2019
Fractions are a big deal When you ask people what topics in maths they like and dislike, fractions tend to appear in the dislike column – often vehemently. Recent polling found that maths teachers think fractions are important for students entering High School. I teach in a career course in maths for people who have missed out on maths on the way through school, and a large component of that is fractions. I love fractions. I prefer them to decimals because they are more exact. One seventh is so much neater than its decimal equivalent. I like adding fractions and […]
26 February 2019
What do high school teachers want from their students when they arrive in Year 9? This is an important question. One of the biggest jumps in education in New Zealand is from primary/intermediate (years 1 to 8) to secondary (Years 9 to 13). In most cases children are taught by generalist teachers in primary/intermediate (which I will call primary from now on) and by specialist maths teachers at secondary school. Please be clear that this is NOT a criticism of Primary teachers. Primary teachers do an amazing job teaching such a wide range of subjects in a crowded curriculum to […]