Showing papers in "Educational Studies in Mathematics in 1997"

The Development of Fifth-Grade Children's Problem-Posing Abilities

Abstract: This one-year study involved designing and implementing a problem-posing program for fifth-grade children. A framework developed for the study encompassed three main components: (a) children's recognition and utilisation of problem structures, (b) their perceptions of, and preferences for, different problem types, and (c) their development of diverse mathematical thinking. One of the aims of the study was to investigate the extent to which children's number sense and novel problem-solving skills govern their problem-posing abilities in routine and nonroutine situations. To this end, children who displayed different patterns of achievement in these two domains were selected to participate in the 10-week activity program. Problem-posing interviews with each child were conducted prior to, and after the program, with the progress of individual children tracked during the course of the program. Overall, the children who participated in the program appeared to show substantial developments in each of the program components, in contrast to those who did not participate.

Students' understanding of algebraic notation: 11-15

Abstract: Research studies have found that the majority of students up to age 15 seem unable to interpret algebraic letters as generalised numbers or even as specific unknowns Instead, they ignore the letters, replace them with numerical values, or regard them as shorthand names The principal explanation given in the literature has been a general link to levels of cognitive development In this paper we present evidence for specific origins of misinterpretation that have been overlooked in the literature, and which may or may not be associated with cognitive level These origins are: intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in mathematics, and the effects of misleading teaching materials Recognition of these origins of misunderstanding is necessary for improving the teaching of algebra

The End of Innocence: A Critique of 'Ethnomathematics'

Abstract: Ethnomathematics originated in the former colonies, in response to the Eurocentrism of the history of mathematics, mathematics itself and mathematics education. It has also found expression in several other contexts. It is a part of the broader framework that elaborates the social and political dimensions of mathematics and mathematics education but especially, the dimension of culture. This focus on culture examined in the unique context of South Africa makes visible both conceptual difficulties in its formulation and also difficulties with respect to its interpretation into educational practice. This paper explores a critique of ethnomathematics using the South African situation and conceptual tools of a critical mathematrics education.

What is Normal Anyway? Therapy for Epistemological Anxiety

Abstract: This paper presents two case studies of learners attempting to make sense of the concept of normal distribution — in particular, why physical phenomena such as height fall into normal distributions. The notion of epistemological anxiety is advanced as being the source of the difficulties learners have in making sense of normal distributions. The framework of Connected Mathematics is used to analyze the learners' coming to understanding of normal distributions and as a source of therapeutic intervention for the epistemological anxiety. As both a symbolizing medium and an aid to analysis, one learner is provided with an object-based parallel modeling language (OBPML) with which the learner can formulate computational hypotheses about the local probability rules that lead to the emergence of a global distribution. Through the investigation, supported by the OBPML, the learner makes connections between the micro-rules of probability and the resultant (macro-) statistical distributions. Conclusions are then drawn about the features of a Connected Mathematics learning environment that enable confrontation with epistemological anxiety and the features of modeling languages that enable learners to conduct a successful probability investigation.

The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic

Abstract: In this paper, we explore the relationship between learners' actions, visualisations and the means by which these are articulated. We describe a microworld, Mathsticks, designed to help students construct mathematical meanings by forging links between the rhythms of their actions and the visual and corresponding symbolic representations they developed. Through a case study of two students interacting with Mathsticks, we illustrate a view of mathematics learning which places at its core the medium of expression, and the building of connections between different mathematisations rather than ascending to hierarchies of decontextualisation.

The Pseudo-Conceptual and the Pseudo-Analytical Thought Processes in Mathematics Learning

Abstract: This paper suggests a theoretical framework to deal with some well known phenomena in mathematical behavior. Assuming that the notions ‘conceptual’ and ‘analytical’ are clear enough in the domain of mathematical thinking, the notions ‘pseudo-conceptual’ and ‘pseudo-analytical’ are proposed and explained. Examples from mathematics classrooms, mathematics exams, and homework assignments are analyzed and discussed within the proposed theoretical framework.

A framework for assessing and nurturing young children‘s thinking in probability

Abstract: Based on a synthesis of the literature and observations of young children over two years, a framework for assessing probabilistic thinking was formulated, refined and validated. The major constructs incorporated in this framework were sample space, probability of an event, probability comparisons, and conditional probability. For each of these constructs, four levels of thinking, which reflected a continuum from subjective to numerical reasoning, were established. At each level, and across all four constructs, learning descriptors were developed and used to generate probability tasks. The framework was validated through data obtained from eight grade three children who served as case studies. The thinking of these children was assessed at three points over a school year and analyzed using the problem tasks in interview settings. The results suggest that although the framework produced a coherent picture of children‘s thinking in probability, there was ‘static’ in the system which generated inconsistencies within levels of thinking. These inconsistencies were more pronounced following instruction. The levels of thinking in the framework appear to be in agreement with levels of cognitive functioning postulated by Neo-Piagetian theorists and provide a theoretical foundation for designers of curriculum and assessment programs in elementary school probability. Further studies are needed to investigate whether the framework is appropriate for children from other cultural and linguistic backgrounds.

Uncontrollable mental imagery: graphical connections between a function and its derivative

Abstract: The view that imagery might be a disadvantage on certain tasks might surprise some mathematics educators who contend that a learner's conceptual understanding is increased whenever visual imagery is used. One of the limitations of imagery found in the literature comes to bear on a unique aspect of mathematics teaching and learning. This is the notion of an uncontrollable image, which may persist, thereby preventing the opening up of more fruitful avenues of thought, a difficulty which is particularly acute if the image is vivid. Although one calculus student's images supported high levels of mathematical functioning, occasionally his vivid images became uncontrollable, and the power of these images did more to obscure than to explain. This type of imagery can be a major hindrance in constructing meaning for mathematical concepts — contrary to the ‘panacea’ view of imagery which is sometimes expressed.

Effect of the Implicit Combinatorial Model on Combinatorial Reasoning in Secondary School Pupils.

Abstract: Elementary combinatorial problems may be classified into three different combinatorial models (selection, partition and distribution). The main goal of this research was to determine the effect of the implicit combinatorial model on pupils' combinatorial reasoning before and after instruction. When building the questionnaire, we also considered the combinatorial operation and the nature of elements as task variables. The analysis of variance of the answers from 720 14–15 year-old pupils showed the influence of the implicit combinatorial model on problem difficulty and the interaction of all the factors with instruction. Qualitative analysis also revealed the dependence of error types on task variables. Consequently, the implicit combinatorial model should be considered as a didactic variable in organising elementary combinatorics teaching.

Facilitating Learning Events Through Example Generation

Abstract: This study deals with the initial understanding that advanced undergraduate mathematics students exhibit when presented with a new concept in an environment requiring self-generation and self-validation of instances of the concept. Data were collected in spring of 1995 through interviews with 11 third and fourth year undergraduate mathematics students. We discuss the data from the perspective of the student's concept image and introduce the notion of learning event to indicate when a student communicates and applies a new understanding of a concept. We infer that the students in our study who employed an example generation learning strategy were more effective in attaining an initial understanding of the new concept than those who primarily employed other learning strategies such as definition reformulation or memorization.

From Verbal Descriptions To Graphic Representations: Stability and Change in Students' Alternative Conceptions.

Abstract: The present study investigated students' conceptions and misconceptions relating to the construction of graphs. Participants were 92 eighth-grade students randomly selected from two schools. Students were tested before and after being exposed to formal instruction on graphing. Qualitative analysis of students' responses identified three main kinds of alternative conceptions: (a) constructing an entire graph as one single point; (b) constructing a series of graphs, each representing one factor from the relevant data; and (c) conserving the form of an increasing function under all conditions. In addition, the following kinds of errors were displayed by less than 10% of the subjects: conceiving a generalized, stereotypic idea of a graph, using arrows or stairs to represent the direction of the covariation, and connecting the ticks on the axes by lines or curves. Quantitative analyses of the data indicated that overall students did not enter the learning situation as a tabula rasa. On the pretest, about a quarter of the students constructed correctly graphs representing increasing, constant, curvilinear, and decreasing functions, and many more students represented correctly at least one kind of function. Further analyses showed the stability and change in students' alternative conceptions after students were exposed to formal instruction about graphing. The theoretical and practical implications of the findings are discussed.

Defining in Classroom Activities.

Abstract: This paper discusses some aspects concerning the defining process in geometrical context, in the reference frame of the theory of ‘figural concepts’ The discussion will consider two different, but not antithetical, points of view On the one hand, the problem of definitions will be considered in the general context of geometrical reasoning; on the other hand, the problem of definition will be considered an educational problem and consequently, analysed in the context of school activities An introductory discussion focuses on definitions from the point of view of both Mathematics and education The core of the paper concerns the analysis of some examples taken from a teaching experiment at the 6th grade level The interaction between figural and conceptual aspects of geometrical reasoning emerges from the dynamic of collective discussions: the contributions of different voices in the discussion allows conflicts to appear and draw toward a harmony between figural and conceptual components A basic role is played by the intervention of the teacher in guiding the discussion and mediating the defining process

An alternate route to the reification of function

Abstract: This paper presents an alternate perspective for utilizing the action/process/object framework when discussing student development of conceptions of function After a review of related theories, a property-oriented view of function is described which is based on visual aspects of functional growth The theory is supported with data on student learning The property-oriented view of function incorporates and extends previously described frameworks used in analyzing functional understandings, including the covariance and correspondence views (Confrey & Smith, 1991; Thompson, 1994) The property-oriented view differs from the covariance view in that less emphasis is placed on the manner in which the variables are changing and more emphasis is placed on the properties that result from these changes The property-oriented view differs from a correspondence view in that functional properties such as invertibility and domain give rise to a different kind of thinking about functions than do properties such as symmetry, linearity, continuity, etc Implications for further research and curriculum development are also provided

Preparing teachers for realistic mathematics education

Abstract: A shift in mathematics education in the Netherlands towards the so-called realistic approach made it necessary to prepare prospective teachers for a type of curriculum different from what they experienced as pupils. This article describes the characteristics of a preservice programme aiming at this goal and presents an analysis of the development of the student teachers' views of mathematics and mathematics education during the programme as well as their classroom behaviour. This analysis is based on two research studies. The first was a longitudinal study in which the student teachers were followed during $${2}$$ years by means of questionnaires and interviews. The second was a study in which graduates from this programme were compared with graduates from a more traditional preparation programme by means of two teacher questionnaires and a pupil questionnaire, the latter measuring the pupils' perceptions of the actual teaching behaviour of the graduates. The teacher education programme appeared to be successful in changing the student teachers' views of mathematics education, especially in the direction of a more inquiry oriented approach, and in promoting effective teacher behaviour in the classroom. As far as their facilitating role as a teacher is concerned, the student teachers seemed to go through a two-stage learning process. Most of them reached the first stage, in which they realize that pupils have different preferences for learning and that a variety of possible explanations for problems should be offered. However, only a small number of student teachers seem to reach the second stage, in which they recognize the principle of building on pupils' own constructions, an important feature of realistic mathematics education. Possible explanations for the low impact of the programme, as well as solutions are discussed.

Metaphors in the Teaching of Mathematical Problem Solving

Abstract: This article reports on a study1 that investigated the teaching of mathematical problem solving from a teacher's perspective The study focused on three teachers and their way of making sense of teaching problem solving Data collected through interviews and classroom observations were analyzed in the context of an interpretive qualitative study to understand the meanings of the participants' classroom processes The findings indicated that the participants unconsciously constructed personal metaphors that became the basis of their conceptualization of problems and making sense of their teaching “Community”, “adventure” and “game” were determined to be the key metaphors of the three participants, respectively These metaphors embodied their personal experiences and personal practical beliefs that provided the unique meanings associated with their classroom processes The outcome suggested that the study of such metaphors could be a promising avenue in enhancing mathematics teacher education and in problem solving research in the quest to make the teaching of problem solving more meaningful and effective in a classroom context

The Equation, the Whole Equation and Nothing But the Equation! One Approach to the Teaching of Linear Equations

Abstract: There exists an extensive range of research looking at the teaching and learning of linear equations, resulting in many papers highlighting a range of teaching approaches and illustrating a variety of significant cognitive problems and stumbling blocks to the learning of linear equations with understanding. Building on this literature, this paper presents some of the results of a case study which looked at the mathematics classroom of one particular teacher, Alwyn, trying to teach mathematics with meaning to less able pupils at secondary school level. Our interest here is those lessons which dealt specifically with the learning of linear equations, in which firstly a different approach was utilised and secondly many of the problems referred to in the literature were not present. We contrast this method with the teaching of linear equations to a variety of ability levels in several other classrooms that we have studied and we attempt through use of the Pirie-Kieren model, to analyse and account for the successful growth of understanding of the lower ability, year eight pupils in one particular classroom.

Schemata and Intuitions in Combinatorial Reasoning.

Abstract: The problem that inspired the present research refers to the relationships between schemata and intuitions. These two mental categories share a number of common properties: ontogenetic stability, adaptive flexibility, internal consistency, coerciveness and generality. Schemata are defined following the Piagetian line of thought, either as programs for processing and interpreting information or as programs for designing and performing adaptive reactions. Intuitions are defined in the present article as global, immediate cognitions. On the basis of previous findings (Fischbein et al., 1996; Siegler, 1979; Wilkening, 1980; Wilkening & Anderson, 1982), our main hypothesis was that intuitions are always based on certain structural schemata. In the present research this hypothesis was checked with regard to combinatorial problems (permutations, arrangements with and without replacement, combinations). It was found that intuitions, even when expressed as instantaneous guesses, are; in fact, manipulated'behind the scenes' (correctly or incorrectly) by schemata. This implies that, in order to influence, didactically, students' intuitions, those schemata on which these intuitions are based should be identified and acted upon.

On Mathematical Visualization and the Place Where We Live

Abstract: This paper is a case study of how a high school student, whom we call Karen, used a computer-based tool, the Contour Analyzer, to create graphs of height vs. distance and slope vs. distance for a flat board that she positioned with different slants and orientations. With the Contour Analyzer one can generate, on a computer screen, graphs representing functions of height and slope vs. distance corresponding to a line traced along the surface of a real object. Karen was interviewed for three one-hour sessions in an individual teaching experiment. In this paper, our focus is on how Karen came to recognize by visual inspection the mathematical behavior of the slope vs. distance function corresponding to contours traced on a flat board. Karen strove to organize her visual experience by distinguishing which aspects of the board are to be noticed and which ones are to be ignored, as well as by determining the point of view that one should adopt in order to ‘see’ the variation of slope along an object. We have found it inspiring to use Winnicott's (1971) ideas about transitional objects to examine the role of the graphing instrument for Karen. This theoretical background helped us to articulate a perspective on mathematical visualization that goes beyond the dualism between internal and external representations frequently assumed in the literature, and focuses on the lived-in space that Karen experienced which encompassed at once physical attributes of the tool and human possibilities of action.

Epistemological Investigation of Classroom Interaction in Elementary Mathematics Teaching.

Abstract: In everyday teaching, the mathematical meaning of new knowledge is frequently devalued during the course of ritualized formats of communication, such as the “funnel pattern”, and is replaced by social conventions. Problems of understanding occurring during the interactively organized elaboration of the new knowledge require an analysis of the interplay between the social constraints of the communicative process and the epistemological structure of the mathematical knowledge. Specific aspects of the problem of meaning development are investigated in the course of two exemplary second-grade teaching episodes. These are then used to develop and discuss decisive requirements for the maintenance of an interactive constitution of meaning for mathematical knowledge.

A Participatory-Inquiry Approach And The Mediation Of Mathematical Knowledge In A Multilingual Classroom

Abstract: This article describes and analyses a short teaching episode in a multilingual secondary mathematics classroom in South Africa where the teacher is using a participatory-inquiry approach. The episode is used to illuminate the general claim that such an approach, because of the particular communicative demands it places on teachers and learners, can create specific dilemmas of mediation. Teachers are often aware of dilemmas they face. However, what can be obscured is how a participatory-inquiry approach can inadvertently constrain mediation of mathematical activity and access to mathematical knowledge.

THE WORLD ACCORDING TO JOHNNY: A Coping Perspective in Mathematics Education

Abstract: Students in mathematical problem-solving situations often experience confusion and loss of meaning. In these situations, affective and social factors are as much part of the student's thinking and behavior as are cognitive factors. These additional factors might include, for example, the need to make sense and the need to meet expectations of the authority figure involved (e.g., teacher or researcher). In this paper we attempt to analyze students' productions, taking into account such additional affective and social factors. To this end, we have tried to reproduce the student's voice in what we call virtual monologue. It consists of a monologue in the student's voice given in first person language, in which we try to describe as vividly and as faithfully as we can our picture of what might be going on in the student's mind during such situations.

Algebraic procedures used by 13-to-15-year-olds

Abstract: Students of Grade 7 were given a test followed by individual interviews; at the end of Grade 8 the same students were subject to an analogous test and interviews. Each student had to simplify certain algebraic expressions. This article is focussed on what types of procedures were used by the students performing the task and how they were explained during the interviews. The author identifies seven types of procedures used by students, labelled: (A) Automatization, (F) Formulas, (GS) Guessing-Substituting, (PM) Preparatory Modification of the expression (this includes a subtype: Atomization), (C) Concretization, (R) Rules, (QR) Quasi-rules. Part of the students' procedures led to correct results, others were wrong. Most of the procedures appeared spontaneous in the sense that they had not been taught in the classroom. Prior to the tests, the teachers (in accordance with the curriculum) had done their best to explain the validity of algebraic transformations by referring to the commutativity of addition and multiplication, distributivity, and to geometric interpretation; however, the interviewees (even explicitly asked) seldom used such arguments.

When negotiation of meaning is also negotiation of task

Abstract: Much recent research in mathematics education has been concerned with the negotiation of meaning between students or between students and teacher. But meaning is always meaning in particular context. Therefore, the negotiation of meaning presupposes a taken-to-be-shared understanding of the situation. In familiar situations, this is relatively unproblematic, but it becomes less so in instances where more than one interpretation of the task at hand is possible. This is perhaps the core of the apparent problems many students seem to have when working with applied mathematics. When more students are working together in such situation, a negotiation of the perspective from which the content should be adderessed must be undertaken.

Gender Differences on the Math Subtest of the Scholastic Aptitude Test May Be Culture-Specific.

Abstract: Cross-cultural studies can shed new light on theories of gender differences in cognition. In the present study, Chinese students were given items from the math subtest of the Scholastic Aptitude Test (SAT) that have been found to produce the largest gender differences in American students. The authors describe how four different explanations of gender differences make different predictions regarding the possible size of the gender difference in Chinese students. Consistent with the Differential Coursework view but contrary to the predictions of several other views, the results revealed no difference in performance on the SAT items between Chinese males and females.

Le Logiciel ‘Derive’ comme revelateur de phenomenes didactiques lies a l'utilisation d'environnements informatiques pour l'apprentissage

Abstract: In this article, we address the issue of integration of computer environments in the mathematics secondary curriculum, by referring to the results of a research project carried out with the software DERIVE. Firstly, we present the research project and its theoretical framework, secondly, we evidence some didactical phenomenas linked to the DERIVE transposition of mathematical knowledge and learning processes in this environment which, in our opinion, play a crucial role in integration issues.

The Role of the History of Mathematics in the Teaching and Learning of Mathematics : Discussion Document for an ICMI Study (1997-2000)

Abstract: In recent years there has been growing interest in the role of history of mathematics in improving the teaching and learning of mathematics. ICMI, the International Commission on Mathematics Instruction, has set up a Study on this topic, to report back at the next International Congress on Mathematical Education (ICME) in Japan in the year 2000. The present document sketches out some of the concerns to be addressed in the ICMI Study, in the hope that many people across the world will wish to contribute to the international discussions and the growing understandings reached in and about this area. This discussion document will be followed by an invited conference (to be held in France in April 1998), from which a publication will be prepared to appear by 2000. The next section of the present document surveys the questions to be addressed. Your views are solicited both on the questions and on how to take the issues forward as implied in the commentary.

Raisonnements arithmétiques et algébriques dans un contexte de résolution de problèmes: difficultés rencontrées par les futurs enseignants

Abstract: Le probleme de l'articulation entre les raisonnements arithmetiques et raisonnements algebriques nous renvoie entre autres au rapport que l'enseignant – ou le futur enseignant – entretient lui-meme a priori avec ces modes de traitement, une telle relation ayant une incidence sur les choix didactiques qui seront eventuellement poses par cet intervenant en regard d'une introduction a l'algebre dans un contexte de resolution de problemes. Une experimentation, visant a mettre en evidence si les futurs enseignants peuvent etablir ou non une dialectique entre ces deux modes de raisonnements dans le contexte particulier de la resolution de problemes, a ete conduite aupres de trois groupes de futurs enseignants (164 sujets); des entrevues individuelles et dyadiques realisees aupres de quelques sujets pointent leurs difficultes dans le passage d'un mode de traitement a l'autre. Dans le present article, sont relatees les resistances rencontrees specifiquement dans le passage a l'algebre. ABSTRACT. The problem of articulation between arithmetic teaching and algebra teaching concerns among other things the relationship the teacher or pre-service teacher has with the knowledge to be taught (relation au savoir), which produces an impact on the choices that he makes concerning the approaches they are to favour in an introductory algebra context. Three groups of future teachers (164 students) were questioned with a view to analyzing to what extent these students were able to shift back and forth between these two methods within the particular context of problem solving. Interviews on either an individual basis or in a dyad format were conducted with a number of subjects, and have served to bring out their difficulties in articulation between these two fields. Only the difficulties observed in the transition from arithmetic to algebra are presented in this article.

A reaction to burn's "what are the fundemental concepts of group theory?"

Abstract: In his abstract, Burn calls his paper is a \\: : :critical analysis of Dubinsky et al (1994): : :\" and we are profoundly puzzled over what appears to be an interesting discussion, but which certainly does not seem to be about our paper. Consider for example, the following two quotes, rst from the rst paragraph in Burn and then from the rst page of Dubinsky et al (op cit). Burn: \\It (Dubinsky et al) is a report of a novel teaching procedure using the computer software ISETL in the teaching of group theory.\" Dubinsky et al: \\In this paper we hope to open a discussion concerning the nature of knowledge about abstract algebra, in particular group theory, and how an individual may develop an understanding of various topics in this domain: : : We include, at the end, a brief discussion of some pedagogical suggestions arising out of our observations, but a full consideration of instructional strategies and their eeect on learning this subject must await future investigations yet to be conducted.\" The paper is not about teaching abstract algebra, with ISETL or otherwise. ISETL itself is not mentioned at all in the body of the paper, nor are there any examples of computer activities, or indeed any speciics of the pedagogy. The teaching method used in the course under discussion was mentioned only incidentally (in a single paragraph), as part of the background for the research. In fact we make no claims whatever in this paper on the teaching of abstract algebra. Rather, this paper presents research that attempts to contribute to knowledge of how stu-dents' understanding of certain group concepts (group, subgroup, coset, normality, quotient group) may develop. As such, it has a clearly stated research methodology and a theoretical framework within which it analyzes the data. Most of the discussion is devoted to excerpts from in-depth interviews of students and interpretations that try to relate students' responses 1

Concept formation of triangles and quadrilaterals in the second grade

Abstract: In order to understand the concept of an n-gon it can be characterized by a commutative diagram which is composed of four ways of judging a given figure as an n-gon, and it is examined through some cases on the introductory instruction on the concept of triangles and quadrilaterals In each of these cases, it was observed that some children gave persuading arguments containing a critical idea and the concept formation corresponded to a structure-preserved transformation in the diagram Following the diagram, four stages on the concept formation and its development are introduced According to two operations in the diagram, essentially two kinds of teaching tools can be distinguished Putting these issues together, an experimental instruction is designed and implemented

A developmental approach to mathematics testing for university admissions and course placement

Abstract: Decisions on admissions to university and placement into university courses are usually based on the results of achievement (as in secondary school exams) and/or aptitude (in intelligence-type tests and SAT). This paper argues that in a situation where educational provision at secondary school level is highly unequal, a third approach to testing offers an alternative which is preferable both on grounds of theory of cognitive psychology and because it yields much better discrimination. The Alternative Admissions Research Project at University of Cape Town has developed a mathematics test according to the dynamic testing approach as advocated by Miller (1990) for admission of African students from grossly under-resourced schools, as well as for placing these and other students into a diversifying first year curriculum. This approach aims to assess the ability of a candidate to learn from authentic academic material within the test. This paper focuses on the reasons for the development of the mathematics test and the process by which the test questions were developed and piloted. The reliability of the test and correlations of this test with subsequent mathematical performance data are discussed. Following the encouraging data for the test as an admission mechanism, the value of the dynamic testing approach for furnishing additional information for placement into an increasingly varied curriculum at first year level was investigated. This enabled the piloting of more topics and more comprehensive validation of this type of testing. The paper concerns itself with the reliability and predictive value of each of the topics in this placement test for a range of core courses in various faculties and the extent to which these tests can identify potentially at risk students who should be placed onto an appropriate curriculum.