controversy
8 March 2021
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 […]
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 […]
16 January 2019
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(broad brush), Numeracy project stages (fine uni-dimensional and embraced by Primary teachers) and National Standards (no longer current, but casting a long shadow.)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, […]
13 November 2018
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 […]
16 June 2018
Numeracy levels are reaching crisis point An article in Stuff on 16 June 2018, We are barely functioning, literally, highlighted the problem of literacy and numeracy in New Zealand. The article focusses on literacy, but numeracy levels are possibly worse. This comes as no surprise to me. The problem according to Doctor Nic The lack of numeracy skills is not new. Generations of people have struggled with maths and many suffer maths trauma, where even the thought of working with numbers can cause symptoms such as panic, the brain shutting down, tears, avoidance. Maths evokes your classic fight, flight or […]
2 May 2018
Why decimals are difficult Recently a couple of primary teachers admitted a little furtively to me that they “never got decimals”. It got me wondering about what was difficult about decimals. For people who “get” decimals, they are just another number, with the decimal point showing. Clearly this was not the case for all. So in true 21st century style I Googled it: “Why are decimals difficult” I got some wonderfully interesting results, one of which is a review paper by Hugues Lortie-Forgues, Jing Tian and Robert S. Siegler, entitled “Why is learning fraction and decimal arithmetic so difficult?”, which I draw […]
5 April 2018
Statistical software for worried students: Appearances matter Let’s be honest. Most students of statistics are taking statistics because they have to. I asked my class of 100 business students who choose to take the quantitative methods course if they did not have to. Two hands went up. Face it – statistics is necessary but not often embraced. But actually it is worse than that. For many people statistics is the most dreaded course they are required to take. It can be the barrier to achieving their career goals as a psychologist, marketer or physician. (And it should be required for many other […]
15 February 2018
The message of many popular mathematics and statistics videos is harming people’s perceptions of the nature of these disciplines. I acknowledge the potential for conflict of interest in this post – critically examining the role of video in learning and teaching mathematics and statistics – when StatsLC has a YouTube channel, and also provides videos through teaching and learning systems. But I do wonder what message it sends when people like Sal Khan of Khan Academy and Mister Woo are applauded for their well-intentioned, and successful attempts to take a procedural view of mathematics to the masses. Video by its […]
10 January 2018
This hour long conversation gives insights into how three high achieving women feel about mathematics. Nicola, the host, is the author of this blog, and has always had strong affection for mathematics, though this has changed in nature lately. Gina and Suzy are both strongly negative in their feelings about maths. As the discussion progresses, listen for the shift in attitude. Listen here to the podcast. And here is a picture of the three of us. Here are some of the questions we discuss over the hour: Tell me about your relationship with maths. How do you think your feelings […]
13 July 2017
Study elections in mathematics because it is important Too often mathematics is seen as pure and apolitical. Maths teachers may keep away from concepts that seem messy and without right and wrong answers. However, teachers of mathematics and statistics have much to offer to increase democratic power in the upcoming NZ general elections (and all future elections really). The bizarre outcomes for elections around the world recently (2016/2017 Brexit, Trump) are evidence that we need a compassionate, rational, informed populace, who is engaged in the political process, to choose who will lead our country. Knowledge is power, and when people […]