Exploring the meaning of letters by Martin Jones
Algebraic notation has been bedazzling learners for generations, yet despite research, learned papers, comparative studies, and a great deal of hard work on the part of classroom practitioners the situation remains a stubborn constant. In this article some small-scale research has highlighted some issues that might find a resonance in many classrooms. This is not an exhaustive approach but it does provide insights that might just begin to clarify notation for some learners.
Educational Issues by Matthew McMillan
Two disruptive Year 8 students were the starting point for the chain of events described in this piece. Just knowing that students will be disruptive, because that's what they do, is just the start. Why are they disruptive? Is it them, or is it me? Who must be the driving force to resolve this unhelpful classroom situation? The author, a student teacher, concludes that he must change, if he is to begin to deal with the disruptive learners. So, what changes, and did they work? ... the story unfolds here.
Working alongside teachers in their classrooms by Sukhjit Dhillon Mike Ollerton Sarah Jayne Plant
Playing games in the mathematics classroom has seemingly become unfashionable. Is it that games suddenly are regarded as ‘lacking in purpose’? Maybe games are seen as incompatible with the ‘lesson plan and objectives’? Or is it that games and learning are not two words that are expected to appear in the same sentence? Prepare for the mythology surrounding games as a trivial learning experience to be well and truly ‘busted’. There are no losers, it seems, in the classrooms described here. Mathematics educators, teachers, classroom assistants, and pupils all learn from their experiences. Taking turns, talking, explaining, checking, captivation, engagement, ...and so much more make playing games an effective teaching and learning strategy.
Gravity in a Galaxy by Robert Dixon
The clarity of the argument, and the detail in the mathematics, make this a real piece of ‘mathematics in context’. However, while this might be not described as ‘mathematics for the faint hearted’, there are classroom implications for application, interest, and motivation. ‘All things solar’ have seen a rise in popularity through the serious media and here the author tells an intriguing story. The ‘storyline’ is supported by insights into the work of eminent players in the field such as Newton. This is far from fiction, but nevertheless it is certainly a story told with conviction and passion.
A Recipe for Ratio by Pam Moffett
Many learners still struggled to appreciate, and understand the difference between, the concepts of fractions and ratio. This is not just a UK phenomenon, which is demonstrated here by the use of a resource developed by the Wisconsin Centre for Education, in association with the Freudenthal Institute of the University of Utrecht, with a group of Year 7 learners in Northern Ireland. The author chronicles student experiences, over a sequence of threelessons, where the teacher uses a strategy inspired by the principles of Realistic Mathematics Education — RME. The outcomes, observed in both the classroom and in student work, are used to signpost a case for a more considered approach to the conceptual development of fractions and ratio.
The ‘Concrete—Pictorial—Abstract’ heuristic by Ruth Merttens
A report entitled ‘What we can learn from the English, mathematics and science curricula of high-performing jurisdictions’ seems taken to suggest... ‘that imitating the content, pace and pedagogy of Singapore and Hong Kong in particular, would enable us to improve the mathematical performance of English children’. This is surely ‘a gift’ to the headline writers eager to undermine the work of educators, of classroom teachers and, in no small part, to belittle the performance of learners. But, learning in mathematics is a complex dynamic and any simplistic means to improve the status quo by policy makers should be subject to professional scrutiny. Here, the author scrutinises the facts and presents a forensic report on the reality of the situation. ‘Face value’ can be seductive but, as ever, the demons can be slain by expert detailed analysis.
On Solving the Equation f(x) = f-1(x) by Ng Wee Leng Ho Foo Him
Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed at improving the experience for the learner by making links for the teacher. If you have seen it ‘all before’, then take comfort in the fact that you ‘got there first’, but it might just give you a sense of satisfaction that others have also ‘arrived’.
The entry-level system by Mark Pepper
Assessment of performance, when national standards are required, has to be sustained by confidence. Confidence in the learner that they are engaged in learning that will provide them with a qualification that is worthwhile, and the confidence of the end user that the assessment is rigorous, equitable institution to institution, and accurate. Without consistency of approach and application any qualification can be devalued. So, is ‘entry-level’ fit for purpose? Evidence is all too often anecdotal, yet even this is sufficient to raise questions and require all those involved to reflect on the status quo. Here, some of that reflection is well documented, together with some suggestions that might shape things for the better as instruments of assessment are revised and developed.
On the trail of multiplicative thinking by Michael Drake
Sequel to ‘The lure of algorithms’ — see MT 221. Here the author tells the story of an exploration he undertook, what he learned, and the questions he was able to answer as a result. Thinking, on the part of the learner, is complex, far from explicit, and some might say intangible. But, by recognising certain ‘clues’ it might be possible to begin to understand how different types of thinking influence how students react when faced with a problem, or calculation. You might not recognise the term multiplicative thinking, but you will certainly know when you see it demonstrated by a learner in a mathematics classroom.
Equations with technology different tools different views by Paul Drijvers Bärbel Barzel
News from ATM by John White
A summary of the report that John White presented to the AGM at the 2012 annual conference in Swansea.
Dandelion Clocks by Paul Stephenson
A small item to intrigue and amuse you!
Creativity and mathematics using learning journals by Alf Coles Gemma Banfield