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Closing the gap between rhetoric and behaviour – John Hibbs – OU mathematics tutor, OFSTED ITT Inspector, ex HMI.

John started by setting the rules for his presentation by saying there would be no PowerPoint, no interruptions, no questions and no note taking! He gave an entertaining and interesting resume of his career and proceeded to give some ‘top tips’ from his own experience of many classrooms both as teacher and observer.

Karen has been a member of ACME since January 2004. She is a mathematics teacher and currently Director of Quality Assurance and Curriculum Audit at Kingston College. Karen introduced us to the Advisory Committee on Mathematics Education (ACME) and its mission statement. ACME is an independent committee that acts as a single voice for the mathematical community, seeking to improve the quality of mathematics education. ACME was established by the Royal Society and the Joint Mathematical Council of the UK (JMC) , is supported by the Gatsby Charitable Foundation and deals solely with England.

Karen outlined ACME’s membership and how it works. Key events in 2004 included ACME’s report on 14-19 assessment in mathematics (due out in the autumn), the Post 14 Mathematics Inquiry and the Government’s response to this. Karen outlined the future work of ACME in the follow up to the Smith Report, its responses to the Working Group on 14-19 Reform and Tomlinson’s final report and its continued work with Government, QCA and others. Possible future projects for ACME include “ICT in the mathematics curriculum”, “Primary Mathematics – a vision for the future” and “The Core within the Diploma Framework” (as outlined in the Tomlinson Report). Karen indicated her strong desire to continue working with NANAMIC and welcomes our views. She can be contacted at acme@royalsoc.ac.uk (DM)

Satisfying the professor of hard sums: The professional development programme for adult numeracy - Graham Griffiths, LLU+, London South Bank University

All new adult numeracy teachers are now required to satisfy FENTO Subject Specifications for Adult Numeracy. The London Adult Numeracy Centre (LLU+), which is a part of London South Bank University (LSBU), has been running a number of courses tailored to the needs of numeracy teachers.

Existing courses accredited by City and Guilds have ranged from the intensive 2 week/50 hour course for experienced teachers with A level mathematics or equivalent, to the 20 week/120 hours course for trainees who have just completed C&G 7406 Stage 2. The LSBU accredited course ran for 30 weeks/90 hours.

Numeracy Learning and Development in Context

Personal Numeracy Skills

Graham provided brief details of the content and assignment tasks for each area. Participants then had an opportunity to try out examples of some of the learning activities that are being used at LLU+.

[LLU+ have set up a JISCMAIL discussion list to allow numeracy practitioners to exchange news and ideas. If you are involved in Adult Numeracy join the JISCMAIL UK Adult Numeracy List by visiting the LSBU website at www.lsbu.ac.uk/numeracy/ and clicking on subscribe to add your name to the discussion list.] (DP)

Generating discussion in the mathematics classroom – John Hibbs – OU mathematics tutor, OFSTED ITT Inspector, ex HMI.

John introduced a collection of activities where students and others have to talk to one another to solve a mathematical problem. One example is to get students to sit back to back and for one student to make a drawing or model from the other student’s description. In another activity a set of cards is dealt to members of a group. On each card is written a piece of information. Information must be shared verbally if a solution is to be found. The activities are suitable for a wide age range and were enjoyed by all participants in the workshop.

The Zin Obelisk reproduced from M.Woodcock, D.Francis & D.Young, ‘Team Problem solving: The Zin Obelisk,’ in D.Francis & D.Young, Improving work Groups: A practical Manual for Team Building, San Diego, CA: University Associates, 1979.

Making a Cake taken from Mathematics Teaching December 1990 (MT 133) “Using Mathematical Discussion in the Classroom”; Jan Winter & students from 2P2, Monk’s Park School.

Mathematics Teaching September 1990 (MT 132) “A Conference Tale”; Chris Hopkins.

Activities for Learning - Anne Haworth, University of Manchester

To demonstrate the non-passive teaching of mathematics Anne led the group through five distinct sets of activities.

In the first one, each member of the group had to solve a simple mathematical problem that gave a numerical solution. This number became the individual’s position in a human number line that formed the x-axis. The human axis made a line in the corridor, and at this point I made a mental note to include “the corridor” in my list of resources needed to deliver future mathematics lessons.

While in the corridor the group followed a series of instructions to form itself into a straight line, which was reflected in the y-axis and the x-axis. The final instruction put the human co-ordinates into a “circle”. This was quite an achievement for a large group in a narrow corridor but the point was well made by this time, namely, that we can use people as co-ordinate points and show how the relationship between the co-ordinate points produce different graphs. Personally, I found it quite challenging to be a thinking co-ordinate but also found the fun element high on the list of motivational factors for using this technique. An Ofsted Inspector might have pointed out the need for colleges to have wider corridors to accommodate larger numbers of students and facilitate the cost effective use of this method of learning!

Our second activity was less energetic. We now tried, as a group, to say whether a series of statements were “always”, “sometimes” or “never” true. We discussed the use of this technique to show the difference between

which is sometimes true, in particular, when the function is sin(x) and the trigonometric identities like

which are always true. If we use graphical means to prove the last equivalence, Anne pointed out that research suggests that such a graphical approach has positive effects on the way students perform in science subjects like Physics.

Our third task was a more verbal activity where the group had to find a “particular example”, a “peculiar example” and a “general example” to illustrate specific mathematical statements. For example, by looking for peculiar examples such as the statement that “There are an infinite number of quadratics that pass through any point in two dimensions.” This led to the group discussing the peculiar example of fitting a quadratic into three points in the plane when the three distinct points are co-linear. By following this approach we packed a lot of mathematical discussion into a short space of time.

The next activity involved the group having a piece of information that referred to a particular quadratic equation. The group, with the assistance of two very able helpers, had to sort themselves into sets of quadratics, or their solutions, that were alike. Of course the challenge lay in the fact that the same quadratic had quite a few representations. Our biggest problem seemed to be to place the “completed square” representation in the correct group without the aid of alcohol!

Our final challenge divided us into groups of five. Each member of the group had cards that contained two facts about a given situation. The members of the group could not show the cards to the remainder of the group but had to describe the contents of their cards. The challenge here was to describe accurately the information on the cards without reading the contents verbatim, whilst also listening to the facts presented and jointly trying to sequence the information so that the group could identify the problem and suggest a solution.

The activities each illustrated a different aspect of being “active” and activating parts of the brain that traditional teaching has failed to reach. (AC)

Footnote: Anne has kindly made her resources available to us. They can be found on the NANAMIC website at www.nanamic.org.uk under Resources.

Census4Learning – Integrating Real Data and ICT – Claire Turner, Centre for Statistical Education

At some time or other, I’m sure we have all asked that question when faced by a class starting their GCSE coursework or Application of Number portfolios.

Claire Turner from Census4Learning was able to answer the question and direct us to useful sites:

Claire also told us of future developments such as the IssuesAtSchool project and SurveyAtSchool which will provide a simple means of designing a questionnaire and collecting data on a college website. A National Lottery Simulation is also being developed ^¹.

This was an interesting and informative session from which the participants went away with a wealth of useful websites and ideas to use in their classrooms. (FMA)

Bernard described a new initiative from MEI which aims to increase the supply of teachers competent to teach advanced maths. Based at Warwick University, the one-year TAM course is aimed at those non-maths graduates with experience of teaching maths to GCSE who want to develop into A level teachers. The course is supported by web-based material and involves some intensive residential schools and some teaching practise which must be organised by the students themselves. The debate after Bernard's talk was interesting mainly the current arrangements for the course apparently make it inaccessible to FE college staff, and therefore, so far, recruits are only from state schools and independent schools. The course is fully recruited for 2004-5 but the organisers will be looking to extend its reach for the following year. Further information is available though the MEI's website www.mei.org.uk (SC)

Joan has been teaching mathematics at Exeter College for three years. She brings to mathematics a richmess of experience developed through a degree in philosophy, a career in nursing, bringing up four children, the study of mathematics with the Open University and a PGCE in secondary mathematics amongst other things. Joan outlined and illustrated the use of PowerPoint in teaching mathematics and numeracy. She drew on a wide range of Level 2 materials to draw out and illustrate ideas that were also equally relevant at many different levels. She outlined the strong visual impact that using PowerPoint can offer and the particular benefits this method offers for ‘visual learners’. Joan reminded us of how PowerPoint presentations can be used and reused through sharing with colleagues, by students who have missed lessons and for students for revision and self study. A wide range of examples from ‘Area and Perimeter’, ‘Negative Numbers’, ‘Algebra’, ‘Simultaneous Linear Equations’, ‘Misleading Graphs’, ‘Scatter Diagrams’, ‘Cumulative Frequency Graphs and Box and Whisker Diagrams’, ‘Adding and Subtracting Fractions’, ‘Geometry’ and ‘Sequences’ illustrated well these points and how in using PowerPoint her focus had moved to covering concepts rather than on the mechanics of getting diagrams right. (DM)

During this session Robin told us of a successful project he has been running where students teach each other. It is an enrichment session, held for an hour on a Friday afternoon (!). Each GCSE student is assigned a tutor who is now studying AS level Mathematics and students work in pairs on a topic of their choice with Robin in a supervisory role. Tutors receive four hours of formal training initially and then about an hour every three weeks when they are encouraged to reflect on how the learning partnership is working. Tutors are encouraged to take their role seriously and receive a payment of £200 if they complete the year successfully. It is clear that both partners benefit enormously. One receives individual tuition while the other deepens their knowledge and understanding of mathematics, often discovering that they didn’t fully understand topics themselves when they try to explain them to others. Robin made it clear that a great deal of time was put into getting the scheme up and running because a lot of discussion with individuals was needed. However, the benefits have been great and several of the tutors are now considering becoming mathematics teachers.

Further information is available from Robin Samson at Tower Hamlets College (JA)

Fiona’s session in the computer suite was definitely ‘hands on’. She began by demonstrating how text boxes can be used to make a more interactive worksheet. Students can ‘drag and drop’ from a given list and then print off the result. Another idea is to get students to log on to an ‘interactive word document’ with a web site address to ‘click on.’ Hot Potatoes can be downloaded to make multiple choice questionnaires from http://web.uvic.ca/hrd/halfbaked/

Promoting active learning in mathematics – Jane Imrie, DfES Standards Unit

Inspection reports on post 16 mathematics provision paint a gloomy picture of dull and undemanding teaching with little learner involvement. Jane described how the DFES Standards Unit is attempting to address this by developing a "toolkit" of activities that promote active learning. Bearing in mind research shows that we remember 5% of what we hear, 75% of what we do and 90% of what we do and discuss with others, the materials are designed to get students totally immersed in developing and consolidating concepts by talking about them.

In small groups, we were given a set of cards to organise, which included things like:

As we laid out our piles, we were given similar further challenges with decimals or fractions that provoked discussion on the common misconceptions that students have.

The similar materials for GCSE algebra produced by Malcolm Swann have proved to be stimulating for students and I look forward to trying out more in the same genre. (AB)

1 In the meantime you can find a useful simulation of the National Lottery at www.mis.coventry.ac.uk/research/discus/prob.xls FMA

Conference report June 2004

Numeracy Learning and Development in Context

Personal Numeracy Skills

Activities for Learning - Anne Haworth, University of Manchester