Teaching Styles in the Teaching of Mathematics Thematically

CHARACTERISTICS OF TEACHING AND LEARNING MATHEMATICS 
THEMATICALLY 
Thematic units typically consist of three main elements: (a) facts and information, (b) 
topics and (c) themes. According to Freeman and Sokoloff (1995, p. 1): 
Facts focus on basic information and narrowly defined ideas understood in 
discrete items. Topics provide a context for facts and information, and 
present a way of organizing discrete bits of information into classes of 
experience recognizable by scholars within traditional disciplines. Themes 
defined as broad existential questions, transcend disciplines, allowing 
learners to integrate the information and the topic within the full range of 
human experience. 
A typical relationship among facts, topics and themes, as visualised by Freeman and 
Sokoloff (1995), is shown in Figure 1. The representation indicates that within a thematic 
unit, facts and topics are taught within the context of an overarching theme.
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Figure 1. Structure of a Thematic Unit as visualised by Freeman and Sokoloff 
 
Thematic instruction in mathematics is an umbrella term for a wide range of educational 
experiences that relate mathematics to real life situations (Handal, 2000). In those 
experiences, the real world serves as a representation of a mathematical concept or 
technique. This representation constitutes a movement from the concrete, "the every day 
world of things, problems, and applications of mathematics", to the abstract world, 
"mathematics symbols, operations and techniques", and/or vice versa (Schroeder & 
Lester, 1989, p. 33). In general, thematic instruction could best be characterised by (a) 
conceptual mathematization from the concrete to the abstract, (b) free production mainly 
in the form of projects and investigations, (c) interactive learning, (d) interdisciplinary 
learning, and (e) assessment based on constructivist principles and not on rote learning 
(Freundenthal, 1991, cited by De Lange, 1993). 
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Thematic instruction in mathematics might take different general orientations and 
emphases. For example, a topic is taught and subsequently is reinforced through 
applications of mathematics, although these applications are not very often integrated 
under a single central theme but beneath multiple small themes. This is the simplest form 
of teaching mathematics thematically. Another approach consists of discussing the 
mathematical implications of a theme, such as sports, followed by the teaching of 
mathematical concepts in examples related uniquely to the theme. For example, if the 
concept concerned is "rates", students would be asked to compare run and strike rates in 
cricket. A more sophisticated approach consists of introducing the thematic situation 
first, that is, a real-life problem, followed by a lesson structure that leads to the discovery 
of the mathematical concept concerned or to the building of a mathematical model. 
In brief, guidelines are vague and only reveal general principles on how to proceed with 
teaching mathematics thematically. These guidelines suggest more use of co-operative 
learning, use of concrete materials, discussion, guided discovery (Henderson & 
Landesman, 1995), formulating and solving a problem, data gathering, practical work, 
alternative interactional patterns in the classroom, fieldwork and use of technology 
(Abrantes, 1993). As Seely (1995) and Freeman and Sokoloff (1995) have argued, a 
broad range of constructivist practices like those mentioned above are necessary to 
effectively implement the teaching of mathematics thematically.