Mathematics Teaching 189 - Dec 2004
Available FREE to ATM Members. Non-members can buy them using the link.
But why not join ATM and get them all free.
These items available to all website visitors.
Special Issue
Engagement and excitement in mathematics – teachers are learners too...
Introduction
This issue of MT is almost entirely devoted to the research day that was held on Saturday 8th of November 2003 to celebrate Kath Cross's contribution to mathematical education over the last 40 years. Over 50 friends and colleagues from all over the country converged on a hotel near to where Kath has always lived in Lancashire.
Engagement and excitement in mathematics - Kath CrossBuy MT1890406 for £3
Inevitably, as I retire after more than 37 years as teacher and an HMI, this is going to be a very personal note. As someone who has not written much under my own name - because HMI's could not do that - it looks pretty poor if, when I do write, I only say the things I have said before. But then does it matter? I decided not to look back over previous articles, booklets or talks, but to rely on my memory for key statements that have been significant for me. Not surprisingly, it turns out that all the things that were important when I started to teach and really began to think about how pupils learn are still important now.
More about and by Kath Cross at ATM People
Powers of three - John Mason and Anne WatsonBuy MT1890809 for £3
The first power of three we introduced is a task structure, which encourages learners to explore beyond obvious answers. Open questions such as this do not stop at mindless sharing, but support learners in constructing unusual examples and using the full extent of possibilities. Write down a time when the hands of a clock are at right-angles; write down another such time; and another… When we use this structure, we pause to let people work on each one in turn, as it is a completely different experience to being asked for three straight away. In this case, while the first two can be found by thinking about clocks, the third turns out to be rather challenging.
Happy 21st birthday Cockcroft - Geoff Faux
Planning for Kath Cross' research day forced me to get out my Cockcroft Report. Cockcroft is remembered for paragraph 243. 243 = 35. The numeracy strategy uses the three-part lesson as one of its cornerstones. Is it likely that the numeracy strategy's 'three' will be remembered with the same affection as Cockcroft's 243 twenty-one years from now? If 243 is so important, what about paragraphs 3, 9, 27, 81...?
Read some responses to this article
Early years' hooks for mathematical fishing - Sue GiffordBuy MT1891415 for £3
I wanted to run some research findings past colleagues in an informal setting and also, to see whether those findings could be used to devise mathematical activities for young children. The ATM workshop seemed an ideal opportunity, especially as I have recently been struck by the relevance of Cockcroft's paragraph 243 to the foundation stage. The 'cognitive and emotional hooks' had originated from work with nursery children and number. One of the most interesting aspects of this was the discovery of nursery children's number jokes, which arose from an incident outdoors one morning.
Mathematics post-16 - Anne Haworth and Geoff WakeBuy MT1891619 for £3
Freestanding mathematics qualifications have been designed for post - 16 students with the aim of ensuring that students become more actively involved in their learning of mathematics (and therefore following the recommendations of Cockcroft 243). Although the specifications define qualifications, they also attempt to put in place a curriculum and promote teaching and learning that allows students to; develop mathematics within different contexts; apply mathematics to solve problems that are meaningful to them...
Wax on, wax off - Aidan HarringtonBuy MT1892627 for £3
A while ago I became interested in Alexander Technique who works on posture. My first lesson began with being asked to stand up and take a few steps forward. I was immediately interested in some form of feedback from my teacher. That's what teachers do isn't it? Give you feedback and technical advice. A moment of frustration - none was forthcoming. I was then asked in the following week to notice how others perform the same action. The exercises I was asked to do all had the aim to help me become aware of my habits without directly working at changing them. The idea was that this would happen intuitively. How challenging a notion is this? How can I achieve my goals without working on them directly?
Cockcroft 243 today - Barbara Ball and George Knights
Soon after the Cockcroft report was published in 1982 ATM organised two writing weekends about the report, to which it invited a wide range of members involved in different aspects of mathematical education. The members divided into groups and our group found ourselves working on paragraph 243. Our brief was to make this paragraph accessible to teachers, using it as a means of understanding better the variety of activity in the mathematics classroom. The group consisted of ourselves, together with Kath Cross, Gill Close, Dave Kirby, Noel Fowler and Mike Jarvis.
Engaging with isometries - Dave Wilson and Letitia SchenkBuy MT1893235 for £3
The activity which Letitia and I based our joint session came from a lesson on length preserving transformations (the isometries) aimed at secondary school pupils. It was based around working with a dynamic geometry file (created using Cabri Geometre on one of the isometries projected onto an electric whiteboard. The particular transformation used at the ATM day was a glide reflection (product of a reflection and a translation) which, given the nature of the group, we conjectured would provide a suitable challenge.
The Cabri file can be downloaded or used within the CabriJava applet
Problem solving and me . . . - James RobinsonBuy MT1893638 for £3
'Direct teaching and good interaction are as important in group work and paired work as they are in whole class work. Organising pupils as a whole class... helps to maximise their contact with you…' The KS 3 strategy encourages us to use an open investigative approach with the provision for work on consolidation etc., and it also shows that the Cockcroft report and the KS 3 strategy are not opposites, but complementary in terms of advice.
Epilogue - John Hibbs
Old ideas are not necessarily bad ideas. For example the idea of a mathematics lesson having a start, a middle and an end (the three part lesson) seems to me like a good, old idea. The idea that we might share with pupils some idea about what they may expect to learn is not only an old idea but, it seems to me, an extremely sensible one as does the idea of explaining to a class what shape a lesson will take and why it is planned that way.
Feature
A tribute to Phil Boorman: Honorary member of ATM
More about Phil Boorman at ATM People
Centre feature
A day to remember - Lyndon Baker and Ian Harris
Miscellaneous
The future of ATM journals
Corrections to David Fielker's article in MT188
Global Collaboration - Peter Stephenson
Regular features
Reflections - Laurie Jacques
Professional Officer's Update - Barbara Ball
Letter
See also
- MT Home Page
- MT Archive
- Coming Up in MT
- Letters to the Editor
- Webwatch
- Contributing to MT
- Advertising
- Micromath
- Primary Subjects
Subscribe to MT...
Editors
