teaching

22 June 2021

Multiplication Fact Fluency survey result

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 […]
8 March 2021

Multiplication Fact Fluency

Just how important is it to know your multiplication facts? There is confusion over the aim for number fluency and the means by which is it achieved. Let me explain. Many people learned their “times tables” by rote, sometimes under threat. This led to people know the right answer, but not necessarily knowing how to apply them. For example if they were asked what is five times three they could say 15, but given \$150 to split up between five people they would not know how to proceed. (Having said that, if it’s money involved people often do better.) I […]
11 May 2020

Not all uses of equals signs are equal

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

Resources in maths and stats for a pandemic

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

Creating and critiquing good mathematical tasks with variation theory

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 […]
19 June 2019

Fluency in maths

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

Achievable challenge in teaching maths

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