In teaching and learning mathematics thematically, instruction is organised around thematic units or projects. Generally speaking, a thematic unit is a collection of learning experiences that assist students to relate their learning to an important question (Freeman & Sokoloff, 1996). Themes are the organisers of the mathematical curriculum, and concepts, skills and strategies are taught around a central theme that is intended to give meaning and direction to the learning process (Freeman & Sokoloff, 1995; Perfetti & Goldman, 1975).
The rationale for teaching mathematics thematically addresses situated–learning and constructivist concerns that the teaching of mathematics occurs within a context that is more meaningful to students than traditional mathematical instruction. It can be considered as a response to the need to humanise school mathematics (Clements, 1987). Its origins can be traced to Dewey’s (1938) progressive ideas on curriculum integration and to Bruner’s (1960) thoughts on the centrality and repetition of knowledge through the enactment of a spiral curriculum. The teaching of mathematics thematically is considered as belonging to the realm of situated learning because the content is embedded in themes that in turn serve as learning contexts (Henderson & Landesman, 1995). Situated learning is primarily concerned with the need to contextualise instruction since, by definition, all learning is situated. Learning is seen not as a matter of ingesting pre-existent knowledge but as a way of developing knowledge in meaningful and practice-bounded contexts (Putnam & Borko, 2000; Streibel, 1995). In turn, this situated perspective is associated with constructivist ideas of teaching and learning mathematics due to their shared interest for building mathematical knowledge within those contexts (Anderson Reder & Simon, 1996; Murphy, 1997). The thematic approach is also directly associated with constructivist ideas since it provides an environment where knowledge can be individually and socially constructed (Freeman & Sokoloff, 1995; Good & Brophy, 1994; Seely, 1995).
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). The representation indicates that within a thematic unit, facts and topics are taught within the context of an overarching theme. 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).
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.
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