Mathematics Teaching 234 - May 2013
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.
Personal members can download the entire PDF of the current issue here.
John White gives a precis of the Honorary Secretary's Report for 2012
Technology can enhance the learning and understanding of mathematics by giving the teacher access to media that cannot be replicated in other ways. The power of the visual and digital media, be it through animation, audio / visual, simulation, or interactivity to engage the contemporary learner is clear when the impact of the smartphone, the smart TV, video capture, and tablet computers on children from an early age is manifest. But, in many classrooms the obvious disconnect between the media-rich world, and the world of learning is startling. The oft cited reason for this is 'funding', but as with many things in education 'it is a bit more complicated than that'. There is an informed debate that needs to be engaged with, because this 'disconnect' is real, not virtual, and it has the potential to impoverish learning for many children?
As with many articles that have their roots in the work of the Institute of Pedagogy this will not disappoint. The descriptions of how the tweaks were orchestrated, of the responses both mathematical and emotional, and of the mathematical tools considered and used are sufficient to create a sense of 'being there' for the reader. As the task unfolds, first the problem is subject to a 'tweak' then those working on the problem find they are required to 'tweak' their response appropriately. As ideas and possible scenarios unfold those working on the problem take ownership of the lines of enquiry, building models and making assumptions based on both their 'sensemaking' and their own mathematics.
ATM has given me the chance to use my current abilities and expand my managerial and administrative skills. I am happy to be ATM's new SAO. I look forward to getting to know the organisation, its members and supporting General Council as it negotiates future challenges and opportunities.
This is an account of how the process of refining a lesson to optimise student performance can work. Concept mapping is used to help students organize their knowledge and to display the interconnectedness of their understanding of facts and processes.
The notion of big ideas in mathematics is not new. The problem seems to be that a definitive set of big ideas is illusive. Maybe for mathematics teaching this is a healthy state, as long as the 'search' continues to generate discussion and the inevitable tensions. Here is a well-argued and documented contribution to contemporary thinking. More importantly this is a set of big ideas that is being used to emphasise the interconnectedness of mathematics.
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For some, the intrinsic fascination of numbers once discovered can become a lifelong passion. The author showcases her findings with an engaging and anecdotal style. Why do we remember some number facts, yet forget others? Does it make a difference if you 'discover them for yourself, or someone tells you about them? How many number facts 'out there' are likely to be 'new to you'?
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Virtual Learning Environments, VLEs, are not a new phenomenon. Learners are far from strangers to virtual environments and they regard the sophistication of the 'on screen' experience as normal. So, the task of developing a mathematical virtual environment is a significant challenge. The experiences, successful and not quite as successful, described here illustrate a journey of development. Training, familiarity, and past experience are one thing, but creating something that works 'on screen' then asking students to critique the offer might be described as bold or even folly. Developing a VLE will always be 'work in progress', but perhaps that is the both the attraction and the challenge.
This is an example of CPW with a 'slow burn', and proof that good ideas are independent of time. In mathematics teaching, how to record learning, and who is the appropriate audience for such recording is an enduring tension? If any record is to support learning and understanding then, it must have a significant 'personal' element and be free of restrictions as to format. A 'learning journal' can satisfy these challenging criteria. However, not all students can be expected to be 'wowed' by concept, but that is not to say that they ought not to be introduced to the idea. After all, they might just be going through 'the slow burn', only time will tell.
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Role play can be used to engage learners in mathematical activity, based on problem-solving, which will encourage mathematical thinking and reasoning. The scenario used here is unusual, but it does exemplify the variety of mathematics that may be 'on the agenda'.
So, GCSE is 'not fit for purpose'. Fact, fiction, or perhaps part a wider rationale for change? Call it GCSE mathematics, or O-level mathematics, or something else mathematics... does it, will it matter? Testing/assessment in mathematics will always be flawed because it requires human intervention to quantify learning in some way. However, the nature of such intervention and the drivers for such practices as coaching, have the potential to 'inflate descriptors of achievement' to render them almost meaningless. Here the case against current practice in many schools is well made. But, are league-tables the 'devil' or does the 'devil' reside elsewhere? This dilemma is a reality for many teachers of mathematics.
Education has been described as a partnership between the school, the teacher, the learner, and the 'parent'. But, all too often the partnership is less effective because the 'parent' is often 'out of the loop' when it comes to mathematics. Attitudes to mathematics are not always as positive as they might be, because of a 'history of bad experiences'. Here is an approach that sets out to 'change things'. It takes creativity and seemingly boundless energy, but the results are more than encouraging. Could community mathematics 'do it' for you?
Learning to calculate is complex. Learning how children calculate, and why they choose to complete the task using a particular strategy is possibly even more complex. This in-class project seeks to 'get behind the thinking' of the learner with the notion that such insights that can be gained have the potential to make a contribution to the 'craft' of teaching. Here real children are encouraged to say how they complete mathematical calculations, and to try to explain why they 'did it' in a particular way. According to one child in the seventh school there was a clear distinction between subtraction which involved counting backwards, and counting forwards being addition. Now, the question has to be; did his teacher know he was used to making such a distinction?
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'Designing' lessons can take many formats. Here the ideas focus on problem-solving, and lessons are trialed, reviewed, and amended with reference to the feedback from teachers, students, and observers. However, there is a significant difference in as much as these lessons include 'sample pupil work' as part of the learning resource. The 'sample pupil work' may be 'real', or it may be 'engineered' to suit the requirements of as aspect of learning. Learners bring different skills, different experiences, different likes, different dislikes, different levels of confidence, etc. to the 'problem-solving table'. It is difficult to predict the tools they will select from their mathematical kit to make-sense of a problem and then to work towards a solution of sorts. This work seeks to begin to create situations where pupils adopt similar strategies to unstructured problem solving situations. The resources are extensive and freely available, an opportunity not to be missed.
Maybe silence can be a mathematical action? The classroom is a dynamic learning environment managed by the teacher. This management is purposeful, unobtrusive, and constantly variable responding to feedback, the 'vibe', and probably the weather. But, how often in that 'management' is there a regard for the ways in which learners use, and 'manage', their own silent episodes? Here two practitioners share the benefits of working in the same classroom, where one of them assumes the role of 'observer'. In their 'research project' each was to focus on different aspects of learning mathematics, yet interesting commonalities were to emerge as time passed. Being silent is not necessarily about being disengaged, it can provide the 'space' for both thinking and, that perhaps often underrated skill of listening.
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Why is it that intelligent individuals go through life not understanding basic ideas in mathematics? Is it that primary school teachers are 'all powerful', and that they really can 'shape' leaning in mathematics in such a way as it has the potential to endure for a lifetime without question? How many adults will admit to being 'confused' about subtraction? Most just simply replicate the algorithm they were first introduced to, and 'do' the 'take-away'. Clearly there has to be a 'better way', but despite innovation, irrespective of 'new' curricula, and in the face of much improved teacher training it seems that, for some, the wait for a better way continues.
Generating tasks and activities to suit a particular learning purpose is an ever present challenge to the busy teacher. So in the spirit of 'sharing expertise and creativity' here is an idea that might have a place in many other classrooms in the not too distant future.
Another problem for the reader and students to work on. There is a link to the web-site where suggestions for use and a solution can be found alongside interactive files.