Thoughts about maths thinking /mathslearning/ en Complex lines with i-arrows again /mathslearning/news/list/2024/10/03/complex-lines-with-i-arrows-again <p><span><span><span>Once upon a time (<a data-entity-substitution="canonical" data-entity-type="node" data-entity-uuid="172e6829-8771-4b78-bf5a-112396bbe1c6" href="/mathslearning/news/list/2016/08/05/where-the-complex-points-are" title="Where the complex points are">in 2016</a>), I created a way to visualise where the complex points are in relation to the real plane, and then more recently (<a data-entity-substitution="canonical" data-entity-type="node" data-entity-uuid="8db829ce-5a4b-4d8a-921d-787948a725d8" href="/mathslearning/news/list/2022/07/26/where-the-complex-points-are-i-arrows" title="Where the complex points are: i-arrows">in 2022</a>), I modified it to become the concept of <em>i-arrows</em>. I reread those blog posts recently while updating the blog to the new website, and I got all interested in them again. Here is what I’ve been working on over the last few weeks.</span></span></span></p> October 03 2024 David Butler /mathslearning/news/list/2024/10/03/complex-lines-with-i-arrows-again Why mathematical induction is hard /mathslearning/news/list/2023/06/06/why-mathematical-induction-is-hard <p>Students find mathematical induction hard, and there is a complex interplay of reasons why. Some years ago I wrote an answer on the Maths Education Stack Exchange describing these and it's still something I come back to regularly. I've decided to post it here too.</p> June 06 2023 David Butler /mathslearning/news/list/2023/06/06/why-mathematical-induction-is-hard Where the complex points are: i-arrows /mathslearning/news/list/2022/07/26/where-the-complex-points-are-i-arrows <p>Once upon a time in 2016, I created <a data-entity-substitution="canonical" data-entity-type="node" data-entity-uuid="172e6829-8771-4b78-bf5a-112396bbe1c6" href="/mathslearning/news/list/2016/08/05/where-the-complex-points-are" title="Where the complex points are">the idea of iplanes</a>, which I consider to be one of my biggest maths ideas of all time. It was a way of me visualising where the complex points are on the graph of a real function while still being able to see the original graph. But there was a problem with it: the thing I want, which is to <em>see</em> where the complex points are (or at least look like they are) is several steps away from locating them.</p> July 26 2022 David Butler /mathslearning/news/list/2022/07/26/where-the-complex-points-are-i-arrows The Solving Problems Poster /mathslearning/news/list/2020/11/19/the-solving-problems-poster <p>This blog post is about the Solving Problems poster that has been on the MLC wall for more than ten years in one form or another.</p> November 19 2020 David Butler /mathslearning/news/list/2020/11/19/the-solving-problems-poster Sticky operations /mathslearning/news/list/2020/11/02/sticky-operations <p>This blog post is about a metaphor I use when I think about the order of operations: the idea that the various operations are stickier than the others, holding the numbers around them together more or less strongly.</p> November 02 2020 David Butler /mathslearning/news/list/2020/11/02/sticky-operations Replacing /mathslearning/news/list/2020/09/16/replacing <p>I have had many people say to me over the years, "But algebra is easy: just tell them to do the same thing to both sides!" This is wrong in several ways, not least of which is the word "easy". The particular way it's wrong that I want to talk about today is the idea that doing the same thing to both sides is somehow the only move in algebra, because it's not even the most important or the most common move.</p> September 16 2020 David Butler /mathslearning/news/list/2020/09/16/replacing Changing the goal of the Numbers game /mathslearning/news/list/2020/09/06/changing-the-goal-of-the-numbers-game <p>I conscripted the game Numbers and Letters seven years ago to help promote the Maths Learning Centre and the Writing Centre at university events like O'Week and Open Day. Ever since then, it has always bothered me how free and easy participation in the Letters game is, while the Numbers game is much less so. This Open Day I had a remarkable idea: instead of stating in the rules that the goal is to achieve the target, and trying to encourage people to take a different approach, what if I just <em>changed the stated goal! </em>I don't know why I didn't think of it before, to be honest!</p> September 06 2020 David Butler /mathslearning/news/list/2020/09/06/changing-the-goal-of-the-numbers-game Number Neighbourhoods /mathslearning/news/list/2020/09/05/number-neighbourhoods <p>This blog post is about a game I invented in February 2020, the third in a suite of Battleships-style games. (The previous two are <a data-entity-substitution="canonical" data-entity-type="node" data-entity-uuid="625d6909-e3ea-4ea7-827a-f8f739fd4486" href="/mathslearning/news/list/2020/08/18/which-number-where" title="Which Number Where">Which Number Where</a> and <a data-entity-substitution="canonical" data-entity-type="node" data-entity-uuid="40c35305-0bf7-4e3f-9250-bb602c672fec" href="/mathslearning/news/list/2019/09/21/digit-disguises" title="Digit Disguises">Digit Disguises</a>.)</p> September 05 2020 David Butler /mathslearning/news/list/2020/09/05/number-neighbourhoods Roosters don't lay p-values /mathslearning/news/list/2020/08/24/roosters-dont-lay-p-values <p>I've just started teaching an online course, and one module is a very very introductory statistics module. There are a couple of moments when we ask the students to describe how they interpret some hypothesis tests and p-values, and a couple of the students have written very lengthy responses describing all the factors that weren't controlled in the experiments outlined in the problem, and why that means that the confidence intervals/p-values are meaningless. When all we wanted was "we are 95% confident that the mean outcome in this situation is between here and here".</p> August 24 2020 David Butler /mathslearning/news/list/2020/08/24/roosters-dont-lay-p-values Which Number Where /mathslearning/news/list/2020/08/18/which-number-where <p>Last year I invented a game called <a data-entity-substitution="canonical" data-entity-type="node" data-entity-uuid="40c35305-0bf7-4e3f-9250-bb602c672fec" href="/mathslearning/news/list/2019/09/21/digit-disguises" title="Digit Disguises">Digit Disguises</a> and it has become a regular feature at One Hundred Factorial and other events. But before Digit Disguises came along, there was another game with a similar style of interaction that we played regularly, and this blog post is about that game. The game is called "Which Number Where?"</p> August 18 2020 David Butler /mathslearning/news/list/2020/08/18/which-number-where