Mathematics Teaching 227 - March 2012
Mathematics Teaching is the journal of the Association of Teachers of Mathematics. It is a professional journal sent to all members of the Association. It is not a refereed journal. Submissions are reviewed by the editorial team. Many articles have additional information or associated files placed on the journal website.
Conference is particularly enjoyable for me because it is a time to meet members, both those I have known for a long time but also to make new acquaintances who I hope I will be able to persuade to do some writing for Mathematics Teaching. At this next conference the editorial team are going to run an extra session for those delegates who have often thought they might like to write an article.
The notion of ‘understanding’, and its place in the learning process, is often placed in sharper focus when considered in the context of learning and teaching algebra. There are tensions between ‘doing’ algebra, following algorithms, using ‘rules’, or ‘tricks’, and understanding ‘what you are doing’. How does this impact the ‘way’ that algebra is ‘taught’? Without doubt, there is a debate to be had. The ideas, questions and challenges highlighted here pose an imperative to such a debate.
There are, it seems, few instances when ‘unintended consequences’ are regarded as having a positive and beneficial effect. Here a well-used activity takes on a ‘life of its own’ as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the ‘teacher’. Maybe it is possible to become ‘too comfortable’ with a familiar, and well received, task or activity?
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The potential, for the learner, of a maths trail was documented in MT219. Here, the focus is on the planning element of such an event from the perspective of a group of student teachers. Personal reactions, and insights are used to demonstrate that ‘real, and authentic, learning’ takes place for all those involved in the activity.
The supposed pre-eminence of an external examination can exert a disproportionate influence on a curriculum and the associated learning and teaching. Teaching can easily subordinate learning and understanding to curriculum coverage if the society develops a culture that appears to make such demands. This study focuses on Tanzania and provides the detail to support the notion that ‘it really doesn’t have to be that way’.
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This is an account of events in a real classroom when the notion that there is a distinction between calculation by counting, and calculation by structuring is a focus for learning. Pupils have ‘hands-on’ experiences that support their understanding of ‘number’. The teaching ‘aid’ might be unfashionable in contemporary classrooms, but the learning was far from unfashionable. At www.atm.org.uk/mt227 you can find a video clip of Geoff introducing the Japanese Soroban. This is likely to be a pre-requisite for all those unfamiliar with this device.
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‘Probability is a difficult concept to teach, because children and adults find it counterintuitive.’ This is impetus to consider the detailed planning of a set of lessons with a ‘mixed’, in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is more intuitive? The outcomes reported here would suggest that is the case, in all probability!
To be part of small scale classroom research for many practitioners is nothing more than a dream. This account describes how student teachers use such an approach to consider the rationale that underpins the teaching and learning of primary mathematics, and to enable them to question current debates, policies, and practices. The accounts from those involved demonstrate how such a venture has the potential to increase not only teacher knowledge, skills and understanding, but also confidence in, and enthusiasm for, mathematics.
How often does reading through an approach to a problem in mathematics trigger thoughts of past experiences? These experiences then enable a new ‘take’ on the problem that moves the collective thinking to a new resolution. Here, such an event is documented and the results display an elegance that it is difficult to deny. Maybe other ‘takes’ will be triggered by this account, only time will tell.
Last years’ conference was very successful with over 200 keen mathematics teachers from various areas of teaching who experienced interesting and thought provoking sessions, had a great time and came away exhilarated and revitalised.
The ‘smartphone’ is an everyday phenomenon, it can support the teaching and learning of mathematics through ‘apps’. This review of ‘apps’, currently available from ‘The Market’, or ‘App Store’, does much of the background work necessary to make the reader aware of what is available free, or for a small fee. As smartphones become powerful data handling tools their development is fast moving and dynamic, so to be ‘current’ is difficult. The ‘apps’ listed here give the reader ‘somewhere to stand’ when seeking to use this technology in the context of teaching and learning mathematics.
The use, and misuse, of statistics is commonplace, yet in the printed format data representations can be either over simplified, supposedly for impact, or so complex as to lead to boredom, supposedly for completeness and accuracy. In this article the link to the video clip shows how dynamic visual representations can enliven and enhance the appreciation of it. Suddenly data is interesting and informative, leaving the ‘end user’ wanting more. Try the video clip, it might transform well-entrenched reactions to all that we simply label as statistics.
High School Students’ Conceptions of the Minus Sign - Lisa L. Lamb, Jessica Pierson Bishop, Randolph A. Philipp
The minus sign is a mathematical symbol that is multi-functional. Yet, how often is its use explicit to the non-mathematician, or more importantly the learner, who is expected to interpret the symbolism appropriately, when often the ‘meaning’ stems from context of its use. From the perspective of the learner, such nuances of use simply lead to confusion which has the potential for lifelong misconceptions within their personal mathematics. This commentary is based on working with children on their journey through mathematics, it provides insights into the complexity of mathematical communication for those ‘learning the language’.
Ofsted was asked to provide evidence of effective practice in the teaching of early arithmetic, its report entitled; Good practice in primary mathematics: evidence from 20 successful schools, was published in November 2011. Did this report pass you by? Unfortunately, as with many other reports not blessed with a ‘high profile’ the findings have little impact on those teaching primary mathematics day-by-day. The Ofsted evidence is reviewed here with some insightful comment and opinion. The policy makers are supposedly signed up to ‘evidence based practice’, well, put quite simply, here it is.
Designing quality CPD for those teaching mathematics in primary schools is a challenge. If the CPD is to be built on the scaffold of five big ideas in mathematics, what might be these five big ideas? Might it just be a case of, if you tell me your five big ideas, then I’ll tell you mine? Here, there is well-argued agreement on the big five, and the subsequent nature, and impact, of the CPD is described in detail.