Q) I am a student teacher and am looking for information on primary pupils' misconceptions about probability. I have searched the university library and have drawn a blank. Is this because there aren't any misconceptions?
A) I saw a thread about this topic on the TES maths staffroom forum. There were some interesting replies, which you might like to check out (www.tes.co.uksectionstaffroom). Before I address the question, I wonder if you have searched the internet on this topic. I have purposely not provided a full answer in this column, but have given ideas of how you might find the information, as I guess this is a piece of coursework which you should be researching.
One of the ways to find answers to these pedagogic questions is to include the word "research" in the search box. This should lead you to the names of researchers or groups of researchers in the area you are investigating.
There might be pdfs of their published papers with further references. My research bought up several interesting references, the most useful of which was at www.ex.ac.ukcimthelph10prob2.pdf. This pdf is of Primary Demonstration Project: 10B Probability, which was developed for the Mathematics Enhancement Project by the CIMT School of Education at the University of Exeter. On page five they list of some of the misconceptions about probability.
* All events are equally likely.
* Later events may be affected by, or compensate for, earlier ones.
* When determining probability from statistical data, sample size is irrelevant.
* Results of games of skill are unaffected by the nature of the participants.
* "Luckyunlucky" numbers and so on, can influence random events.
* In random events involving selection, results are dependent on numbers rather than ratios.
* If events are random then the results of a series of independent events are equally likely, eg HH is as likely as HT.
* When considering spinners, probability is determined by number of sections, rather than size of angles.
This is followed by loads of useful and engaging activities that can be used in the classroom with pupils. The activities are transferable to the secondary maths classroom as well.
The website for the Mathematics Enhancement Project, led by Professor David Burghes, began in secondary mathematics and is available at www.intermep.org. Here you will find lots of really useful materials and ideas.
Sometimes it is helpful to do a little research yourself. Perhaps with some primary-aged children. Set a series of experiments and questions of the "what if" category and see what their responses are. For example, try tossing a coin: if you get a head as an outcome, what would they expect to happen when you toss the coin again?
Q) I am a senior lecturer in the sports science department at London Metropolitan University. I'm currently completing the final year of an MA in learning and teaching. As part of my final year dissertation, I have developed (in conjunction with a learning technologist) a series of five interactive Flash simulations, known as Learning Objects (LOs), aimed at introductory level maths. There is one learning object each for the teaching of fractions, decimals, percentages, pie charts and probability, most of which appear in the syllabus for key stage 2 maths.
I would like to gain some feedback as to the suitability and effectiveness of the LOs for use with primary and secondary school students. This information would form a valuable part of the evaluation of my dissertation. The information I wish to collect would be in the form of observations, notes and conversationsinterviews with a small group of the children.
Any feedback from teaching staff would also be much appreciated. All LOs are available via the university website at http:homepages.unl.ac.ukhaynesrsports_science2005
A) I had a look at the activities you created. I liked the ideas and thought that I could take some of them further with my classes. I liked the fact that they would be suitable not just for primary-aged learners, but could also be easily used with an adult class.
I would be interested to hear from readers on how they use them with their classes. I have included your email address so readers can contact you if they would like to help you with your work.