Dr Nic’s blog

12 March 2019

Multiplication facts or multiplicative thinking

We just want them to know their tables! It is a truth universally acknowledged by high school maths teachers that students need to be fluent in multiplication facts. (Apologies to Jane Austen) You can read more about this claim in my previous post: What Maths Teachers wish Year 9 students knew I have been thinking about why this is the case, what is so special about multiplication facts, and whether it is more an indicator of something else. Maths teachers like to teach algebra. Simplifying algebraic expression, and factorising quadratics are made much easier if one is at home with multiplication […]
26 February 2019

What Maths Teachers wish Year 9 students knew

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 […]
11 February 2019

Patterns, Mathematics and Statistics

Is mathematics really about patterns? Confession time: Just as I’ve never really thought of maths as beautiful, I’ve struggled to understand why people talk about maths being about patterns. For me maths is powerful and maths is about abstracting from reality to build models. So I thought I would explore the idea of patterns in mathematics. Number Numbers show patterns. The fact that all prime numbers over 3 occur on either side of a multiple of six, is pattern I find appealing. The digits of multiples of three sum to multiples of three. Multiples of eleven are pretty exciting with […]
16 January 2019

Learning Progression Framework – A good idea or a poor use of time?

Not all that is good needs to be done That something is a good thing to do and will improve learning outcomes for all students, is not sufficient reason for doing it. I have recently become aware of the Learning Progression Framework. As explained in a previous post, there are multiple ways of expressing the level of learning in maths for learners in New Zealand schools, including the New Zealand curriculum (broad brush), Numeracy project stages (fine uni-dimensional and embraced by Primary teachers) and National Standards (no longer current, but casting a long shadow.) To this the LPF adds steps, […]
3 December 2018

I just need to pass the course: instrumental learning and statistics

I am interested in instrumental motivation, when a learner is doing a course of study in order to get a piece of paper – a qualification, which is generally the means to an end. I suspect that many students of statistics have instrumental motivation and I am interested in what affect that has on their learning and on the teacher of the course. Personal experience of learning All my life I have been a high-achieving, engaged learner. I liked to learn and to become more knowledgeable. I still like to learn and am not interested in any more qualifications. I […]
13 November 2018

Conceptual knowledge and procedural fluency when teaching maths and stats

Conceptual vs procedural when teaching maths and stats April 2008, Salt Lake City. It was my first NCTM conference and I was awed by the number of dedicated teachers of mathematics in one place. I had soaked in a pre-conference series about teaching statistics and my head was full of revolutionary ideas. I can’t remember the workshop I was attending but I declared that I saw no point in teaching students to calculate standard deviations by hand – and that I never did. The response was awesome! There was just about a stand-up battle between teachers who agreed with me […]
26 October 2018

Evaluating Mathematics Games

Evaluating Mathematics Games A guest post by Dr Shane Dye How can you choose the right mathematics games for your classroom? Games are engaging but sometimes that engagement distracts from the learning. Can a game be both engaging and support learning? How will you know? Dr Nic and I have been pondering those questions recently. We were developing a multiplication facts card game. The game had to be a great choice for teachers. It needed a solid educational foundation and to easily engage students. That led us to think about evaluating games for the mathematics classroom. We looked at the […]
8 October 2018

Mathematics is Powerful

Mathematics is powerful The message of the moment is that Mathematics is beautiful and mathematics is playful. In my social media bubble of mathematics teachers the over-riding picture is of the joy of mathematics. I see puzzles and brainteasers aplenty on Facebook and Twitter. Mathematics educators strive to dispel the cloud of pain and drill that surrounds maths for far too many people. This site and our social enterprise are called Creative Maths, because we wish to create a world of mathematicians. The joy of maths is a wonderful message, that resonates with people like me, who already love maths. […]
18 September 2018

Understanding the Sampling Distribution

Population, Sample, Sampling distribution of the mean Among the many contenders for Dr Nic’s confusing terminology award is the term “Sampling distribution.” One problem is that it is introduced around the same time as population, distribution, sample and the normal distribution. A common confusion is between the standard error and the standard deviation. Here is how I explain it: Basic idea of inferential statistics Whenever we take a sample it will contain sampling error, which can also be described as sampling variation. No sample is a perfect representation of the population. When you calculate a sample mean, you do not […]
9 August 2018

Fun Mathematics activities for families

Mathematics is fun There are many cool, fun and exciting things you can do that are mathematical. However, parents can be a bit scared of maths because of bad experiences that left them thinking they were not mathematically inclined. Other parents may be very happy about maths, but not know what to do with their children to help them also enjoy maths. Like reading to children, doing fun maths with children can help build learning and positive feelings for life. Here is a rule: If it isn’t fun, you are doing it wrong. Do not make maths a chore or, […]