Mathematics Teaching 237 - November 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.
If as an association we are to have an impact on the way teachers work with learners, both because of and in spite of changes imposed through policy, we need practitioners who are committed to mathematics education to be involved as members of ATM and of GC.
The conference is a time when delegates can come together, refresh themselves after a busy term, and return to teach in the summer term with renewed energies. Because we are all teachers of mathematics the conference is built around an open mathematics workshop; equipment in plenty, activities in plenty and people to engage with, or space to think.
Presenting the opening plenary session at Conference is both a challenge and something of an honour. The planning involved needs a rigour that might not come easy to the best of presenters. Here is the result of a rigorous planning process that seeks to set a mathematical scene, within a theme that both engaged delegates, and provided much food for thought.
Not a member? Join or click to buy ‘Pythagoras believed: What was his evidence?’ for £3
The plenary session at conference is a big 'event'. If you were there it is likely that you are still reflecting on what was said. If you were unable to attend this account will provide a sense of drawing the strands, which emerge from the conference theme, to something of a conclusion. Contemporary mathematics teaching is set within a context of the pressures and tensions created by policy makers together with the inexorable changes within our society, and within our culture.
Conference success is far from being a given. Rigorous planning over an extended period of time can ensure that things run smoothly, but a great deal of confidence is invested in those who present sessions. The time and energy devoted to preparing for the opening and closing plenary sessions is significant by any yardstick.
Conference themes, events, and sessions are about mathematics and mathematics teaching. But, Conference in many ways is about people, people who share a passion for mathematics and a mission to enable learners to understand, and use mathematics at every age, and every level. Delegates can be inspired, enthused, challenged, and even on occasions confused, whatever, a total melange of emotional responses to a variety of stimuli.
Working with fellow delegates at conference can prove both inspirational and insightful. The opportunity to discuss a problem, at your own level, can enable insights as to how the same task, or problem, might be used in your own classroom. In this account the problem was used with a Year 9 set, all of whom appeared confident in their mathematics. As it happens students were somewhat less confident with their mathematics in a new situation.
Not a member? Join or click to buy ‘Napkins and Pythogorean triples’ for £3
Magic squares, far from being a new classroom phenomenon still retain an element of surprise for learners. In addition, it seems that many teachers, and trainee teachers of mathematics, have never been introduced to such numerical structures as part of their personal mathematical development. The idea of an algebraic template that can be used to explore magic squares will undoubtedly add 'legs' to the classroom appeal.
This might be described as a result of unintended consequences. Allowing oneself to be side-tracked is something time often will not 'allow', but on occasions curiosity overcomes the 'time' demon. Here is a well-documented account of following a mathematics byway because it was interesting. Post Conference 2013 the intrigue continued through an inset session, and beyond.
What is it to be a mathematician? Is it a job title open only to a privileged few? This question was a response, by the author, to being told that she was not a mathematician. Is being a mathematician something that is more aspirational than achievable? Is being a mathematician age-related? However, wanting pupils to think like real mathematicians by developing chronicles of their own mathematical adventures, inspired by the maths journal concept, is undoubtedly a worthy aim.
Listening to Geoff Faux's opening plenary on Pythagoras' claim that the gods used the whole numbers to design the universe at Conference 2013, Tandi was startled by the number of proofs of Pythagoras's Theorem that were mentioned. Then, wandering around the Publishers' Exhibition some beautiful models of a variety of proofs by dissection were found. This is the story of what happened when she returned to Uganda.
Not a member? Join or click to buy ‘Proving Pythagoras in Uganda’ for £3
This piece describes an attempt to make algebra more accessible to learners in Year 7. The context is a school prepared to pilot new resources and blend these with existing support materials. The outcomes are certainly encouraging, even with students still at the 'early algebra' stage. The notion that there is a clear progression through forming and transforming expressions that can make applying a set of 'rules' a thing of the past for learners.
Not a member? Join or click to buy ‘Can all pupils engage in algebraic reasoning?’ for £3
The importance of problem solving, and the associated ways of working, for both learner and teacher, are well documented. Translating this notion to the classroom setting is something that, in the busy and often 'functional' classroom, proves a significant challenge to practitioners – even when there is a desire to create a problem solving approach to learning. Here is a model, with exemplars, that has proved to be both inspirational, and effective. Students are offered choices, and given the opportunity to take responsibility for their learning.
Reflecting on what has happened, what we think, what we decide to do next, are all essential parts of developing a problem solving strategy. This 'reflecting' is in the moment, and some might say just happens naturally. Here is a description of how to gain a sense of the process of 'reflecting'.
Not a member? Join or click to buy ‘Starting with Pythagoras' Theorem’ for £3
The devil is in the detail, but for those unaware of the detail the devil has the potential to become 'supersized'. HMI are entreated to resort to plain English as opposed to 'inspector speak', but, it seems, their training where issues that relate to the teaching of mathematics remains, to all intents and purposes, within the HMI 'closed loop'.
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.