IS PROBABILITY DIFFICULT?

By Beniel Seka

The Mathematical Association of Tanzania (‘Chama cha Hisabati Tanzania’) or MAT/CHAHITA as it is usually abbreviated, conducts a mathematics seminar during its annual general meeting (AGM). The meeting which takes six days includes the AGM, lecture of the year, mathematics teaching aids exhibition, academic and general topics. This year’s (2012) AGM will took place at  Tumaini University, Makumira in Arusha from 17^th September to 22^tnd September, 2012.

At the end of each seminar, the organizers conduct an evaluation to assess the success of the conference. During the evaluation session, participants are given the opportunity to suggest academic topics to be included in the next AGM. It is interesting to note that probability is always mentioned among the ten topics. It was also presented this year. Unfortunately, no opportunity is provided in the evaluation form for participants to substantiate their suggestions. It has always been taken for granted that it is a difficult topic.

MAT/CHAHITA National committee always looks for experts to present the so –called difficult topics. About two decades ago, the presentations used to be monopolistic. Presenters used to spend a lot of time lecturing and leaving very little time at the end for participants to interact. It was soon realized that most of the participants were not benefitting from the lectures because their problem was not the academic part but the pedagogy.

This was learnt when one of the National committee members was invited to attend a zonal MAT/CHAHITA meeting/conference in Tanga conducted at Usagara Secondary School. The zonal leadership had invited Mr Mrema, then Headmaster of Tanga Technical Secondary School to close the meeting. Mr Mrema said, “I wonder why a topic such as ‘probability’ is said to be difficult. You are conducting the seminar to the teachers. If teachers are finding it difficult, what about the pupils? Teachers must find it easy so that they can help the pupils who find it difficult”

In view of the challenge raised, the organizers decided to change the modality of the paper presentation. It was decided to split the paper presentation into three sessions. The first session is for the presenter to highlight a few facts and difficulties encountered in the teaching of the topic. The second session is for participants to sit in groups to discuss pertinent issues raised by the presenters including guided exercises. The third session is devoted to summary where the presenter ties together pieces raised during the discussion and make recommendations.

MAT/CHAHITA organizers usually respect recommendations made by the participants. What puts them in a difficult situation is why the topic on probability keeps coming up when difficult topics are listed. When presenters are assessed, they are praised for good presentations with no exceptions. It means that probability is also well presented. So what is the problem?

One might say that those recommending the topic were satisfied with the presentation and wish a repetition for those who have not had an opportunity to attend the meeting. But what about those who will attend again? Will it not be monotonous? One needs to do a down to earth research to find out the cause of the difficulty.

The following reasons can be investigated.

• Some people mystify it. They put the cart before the horse. If you scare people about probability, they may not study it, leave alone hearing it.
• Some teachers go straight to theoretical probability. Because of the assumptions made in theoretical probability such as equally likely events, fair coins and dice, some practical cases fail to click.
• The word ‘probable’ which leads to the word ‘probability’ sometimes give wrong predictions. One might use data to predict the probability of the event happening. For example one may say that the probability that it will rain in the afternoon is 0.8. When it does not rain, one questions of the prediction.

In spite of these allegations, probability is very useful in life. Predictions are necessary for planning. In demography it is very useful especially in census. In surveys it is very useful because samples are used to represent population. Statistics based on the sample are used to make decisions. Knowledge of probability is also needed in the study of economics.

Researches need probability when they want to test hypothesis. In order to do that they study inferential statistics which employ probability.

Recently a female MBA student was heard telling her friend, “Today we started quantitative methods. The first topic was probability. I left mathematics a few years ago and one of the topics I did not even look at was probability. They told me it was very difficult.”

Her friend consoled her and said, “I have realized that probability is not as difficult as some people put it. I have learned to be friend with it. You can do the same. I will assist you in case you have a problem. I applied it in my data analysis for my Phd.

Probability is taught in secondary schools and in post secondary education. In the late 70’s it was included in the primary school modern mathematics trial programme with the name “yamkini”. This topic was removed from the primary school syllabus following an evaluation conducted by the Institute of Education in 1979. Teachers teaching the subject at that level had complained that pupils were unable to learn the topic because it was difficult. Do you agree?

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