Scientific Program > Topic 8 > Session 8G >
Presentation 8G2. Understanding of Basic Probability Concepts among First Year University Students

Michael Glencross (South Africa)
Andile Mji (South Africa)


Presentation Abstract
1. Background
We live in an information society in which the need to collect, organise, display and interpret data involves almost everyone as citizens and workers. Statistical ideas are necessary in those areas of human interest that involve either measurement or quantification. Most definitions of statistics indicate that the subject is concerned with the collection, presentation, analysis and interpretation of data. It is an important area of study in its own right and is an essential tool for use in many kinds of research. The topic of probability, which is always closely linked with statistics, readily lends itself to being applied directly to the real world, while a great deal of it can be understood by using only elementary mathematics and arithmetic. At a more advanced level, most statistical theory is based on probabilistic models, so that knowledge and understanding of probability theory is necessary for any serious study of statistics. For example, knowledge of probability is indispensable to the learning and understanding of statistical inference.

2. Literature Review
In the fields of statistics and probability, it is common knowledge that many students lack understanding of basic concepts, a view that is confirmed by a number of research studies (for example, Garfield & Ahlgren, 1988; Glencross, 1998). In Australia, research suggests that in terms of the quality of students' learning of mathematics or statistics, there is a structural relationship between students' conceptions of the subject and their approaches to learning it (Crawford, Gordon, Nicholas & Prosser, 1994; Gordon, 1995, 1997; Gordon, Nicholas & Crawford, 1996). Support for this idea has been found in South Africa (Glencross, Kentane, Njisane, Nxiweni & Mji, 1997; Mji, 1995, 1998a, 1998b, 1999).

Probabilistic ideas are often concretised with such common objects as coins, dice and urns containing balls of assorted colours. Such methods enable us to model real-life random phenomena. Nevertheless, it is well known that probabilistic ideas are notoriously counter-intuitive and are easily misunderstood. Many misunderstandings may occur because the language of probability (more precise) is different from our day-to-day conversational language (less precise) (Hawkins, Jolliffe & Glickman, 1992). For example, Green (1982) has suggested that there are problems with regard to words like 'possible', 'likely', 'certain', etc., while much has been written about the ambiguities introduced into research by the wording of the questions used (Evans, 1989; Pollatsek, Well, Konold, Hardiman & Cobb, 1987; Shaughnessy, 1992). In addition to different cultural backgrounds, students for whom English is a second language often have language difficulties that may lead to misunderstanding of concepts. Of interest to the writer is the possible influence of a second language on the ability to learn and comprehend probability and statistics, because almost all students at the University of Transkei are Xhosa-speaking and communicate in English with varying degrees of competence. The 'specialist language' of probability and statistics may itself be a barrier to students' understanding and concept development. This barrier becomes even greater when the specialist language is used in complicated sentence structures (such as occurs in many mathematics and statistics textbooks), or in language patterns with which many students may be unfamiliar (such as the use of the passive voice). If the language used is not the mother tongue, then the difficulties are certain to be compounded. Thus, if students are confused by the use of statistics and probability words and phrases that are not immediately meaningful to them, their confusion may be aggravated when complex sentence structures and unfamiliar sentence patterns are also used. In this way, the development of students' understanding of probabilistic concepts is inhibited rather than aided by the specialist language.

3. Research Project: 1996-2000
The current research project is an attempt to gain insight into first year students' conceptions of basic probability concepts and their approaches to learning statistics. A pilot study was conducted in October 1996 with 25 volunteer first year students. Students were asked to complete a four-part questionnaire designed (1) to assess their understanding of basic probability concepts, (2) to find out what they think the subject Statistics is, (3) how they study and learn Statistics and (4) what feelings they have toward the subject. The results showed, inter alia, that the concepts of equally likely events and probability as relative frequency were not sufficiently well understood by many students and that the (incorrect) concept of probability as frequency only was somewhat stronger. Students' conceptions of Statistics showed that they had a fragmented view of the subject, while their approaches to learning relied mostly on learning by surface level approaches such as practicing lots of examples. Students' attitudes were predominantly positive, although there was no correlation between attitudes and performance. The questionnaire has been administered to three more groups of first year students: 62 in 1997, 67 in 1998 and 58 in 2000. The results have been consistently similar to those of the pilot study.

4. Research Project: 2001
For 2001, a modified version of the questionnaire will be administered to first year students and semi-structured focused interviews will be conducted with a number of students. The interviews, which will be video-recorded, will be used for several purposes. First, to explore more deeply students understanding of probability concepts using questions selected from the questionnaire. These will be supplemented with suitable apparatus (e.g., spinners). Students will also be interviewed about how they study and learn Statistics. Almost all our students are Xhosa-speaking for whom English is a second language. The interviews will also be used to explore some cultural beliefs (related to random events and probability) that, on the basis of my interactions in workshop situations with students and local junior secondary teachers, may play a role in the learning of probability.
The video-recorded interviews will be conducted in both English and Xhosa. This will permit a careful exploration of students' understanding of probability concepts and related cultural beliefs. Written transcripts will be made of the interviews, together with translations from Xhosa into English. It is anticipated that this approach will allow for in-depth probing of students' ideas in a non-threatening way.

5. References
Crawford, K., Gordon, S., Nicholas, J. & Prosser, M. (1994) Conceptions of mathematics and how it is learned: the perspectives of students entering university. Learning and Instruction, 4, 331-345.
Evans, J. St B. T. (1989) Bias in Human Reasoning, Causes and Consequences. Essays in Cognitive Psychology, Lawrence Erlbaum Associates Inc.
Garfield, J. & Ahlgren, A. (1988) Difficulties in learning basic concepts in probability and statistics: implications for research. Journal for Research in Mathematics Education, 19, 44-63.
Glencross, M. J. (1998) Understanding of chance and probability concepts among first year university students. In L. Pereira-Mendoza, L. S. Kea, T. W. Kee & W-K. Wong (Eds.) (1998) Proceedings of the Fifth International Conference on Teaching Statistics. Voorburg: ISI Permanent Office, Vol. 3, 1091-1095.
Glencross, M. J., Kentane, L. H., Njisane, R. M., Nxiweni, J. G. & Mji, A. (1997) Conceptions of science subjects and how they are learned: views of first year students. In M. Sanders (Ed.) (1997) Proceedings of the Fifth Annual Meeting of the Southern African Association for Research in Mathematics and Science Education. Johannesburg: University of the Witwatersrand, 114-118.
Gordon, S. (1995) A theoretical approach to understanding learners of statistics. Journal of Statistics Education (Online), 3(3).
Gordon, S. (1997) Students' orientations to learning statistics. In F. Biddulph & K. Carr (Eds.) Proceedings of the Twentieth Annual Conference of the Mathematics Education Research Group of Australasia Inc., University of Waikato, New Zealand: MERGA, 192-199.
Gordon, S. Nicholas, J. & Crawford, K. (1996) Psychology students' conceptions of a statistics course. In Puig & Gutierrez (Eds.) Proceedings of the Twentieth Conference of the International Group for the Psychology of Mathematics Education. Valencia: University of Valencia, Vol. 3, 11-18.
Green, D. R. (1982) Probability Concepts in 11-16 year old Pupils. (2nd ed.) Loughborough: Centre for Advancement of Mathematical Education in Technology, University of Technology.
Hawkins, A. Jolliffe, F. & Glickman, L. (1992) Teaching Statistical Concepts. London: Longman.
Mji, A. (1995) First year university students' conceptions of mathematics and approaches to learning the subject: a phenomenographic study. Unpublished MEd dissertation, University of Transkei, Umtata.
Mji, A. (1998a) Conceptions of learning: the view of undergraduate mathematics students. Psychological Reports, 83. 982.
Mji, A. (1998b) Prospective teachers' conceptions about, and approaches to learning mathematics. Journal of the Southern African Association for Research in Mathematics and Science Education, 2, 72-76.
Mji, A (1999) Understanding learning: a survey of undergraduate mathematics students' perceptions. South African Journal of Higher Education, 13, 155-163.
Pollatsek, A., Well, A. D., Konold, C., Hardiman, P. & Cobb, G. (1987) Understanding conditional probabilities. Organisational Behavior and Human Decision Processes, 40, 255-269.
Shaughnessy, J. M. (1992) Research in probability and statistics: reflections and directions. In D. A. Grouws (Ed.) (1992) Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan, 465-494.


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