Exploring Zimbabwean Mathematics Teachers’ Integration Of Ethnomathematics Approaches Into The Teaching And Learning Of Geometry

This article reports on a study that explored how a group of in-service mathematics teachers integrated ethnomathematics approaches into the teaching and learning of geometry. The study used a convergent parallel mixed-methods design, which combined both quantitative and qualitative methods, to provide a deeper understanding of how the participants integrate ethnomathematics approaches into the teaching and learning of geometry. The data for the study were gathered from 40 in-service mathematics teachers through the use of questionnaires and focus group discussions. Results showed that the in-service teachers integrate ethnomathematics approaches into the teaching and learning of geometry as learning materials, resources, and the learning context. Based on the study, it is suggested that teachers should consider the incorporation of ethnomathematics approaches into the teaching and learning of geometry using technological means such as the internet, TV, and films. The findings have implications for continuous teacher professional development in the forms of workshops for the teachers involving the use of ethnomathematics approaches. Introduction and Background Currently, in Zimbabwe, geometry is one of the more difficult topics in secondary school mathematics syllabus (Mashingaidze, 2012). Many learners perform poorly in geometry (Examiner report, Zimbabwe School Examination Council (ZIMSEC), 2016, 2017 & 2018). Jones (2002) asserts that the learners’ problems with geometry are merely pedagogical, and poor performance can be attributed to the teaching approaches being used, among other factors. Scholars have argued that teaching mathematics in general and geometry, particularly as a culture-free discipline, is one of the major causes of the decline of learners’ inspiration as well as their difficulties in learning geometry in particular (Bishop, 1988; Gerdes, 2011). To bridge the gap between school mathematics and the learner’s background, the teaching of mathematics should be culturally contextual and relevant to the learner (Bishop, 1988; Rosa & Orey, 2010, Mogari, 2014). Therefore, teachers should make use of learners’ cultural background and experience as a way of augmenting their skills in teaching mathematics (Gerdes, 1998; Rosa & Orey, 2010; Mogari, 2014). Australian Journal of Teacher Education Vol 45, 7, July 2020 78 Ethnomathematics is a field of mathematics that deals with various forms of mathematics emanating from diverse cultures. Ethnomathematics comprises mathematics that is experienced, practiced, or integrated into the cultural practices or activities of diverse groups in the world (Mosimege & Ismael, 2004; D’Ambrosio & Rosa, 2017). Geometry lies at the epicenter of ethnomathematics and culture (Gerdes, 2005; Zhang & Zhang, 2010). “Geometry provides a culturally and historically rich context within which to do mathematics” (Jones 2002, p.125). Examples of ethnomathematics include geometrical motifs and cryptograms in embroidery work. These are produced by the Ikalinga tribe in India in which parallel lines, connected triangles, and zigzag patterns exemplify the mountainous surroundings of the tribe and the ridged farming on the mountain slants (Abbacan-Tuguic, 2016). Another example is fractals in African design ((Brandt & Chernoff, 2015) and shapes and designs in drawings from hip-hop culture in the United States (Eglash, 2012). Learning mathematics through the integration of cultural values instills basic concepts and expertise by linking various subject areas to mathematics concepts. Consequently, teaching geometry very well includes an appreciation and a comprehension of the history and cultural context of geometry, the ability to come up with fascinating geometrical problems and theorems, as well as geometry content knowledge, proficiency, and expertise (Jones, 2002). The Zimbabwean mathematics syllabus (ZIMSEC, 2015) suggests that geometry teaching should connect to the learners’ cultural background and environment, which is consistent with the social constructivist theory of learning. This entails using ethnomathematics approaches, which are learner-centered and activity-oriented and put emphasis on teaching mathematics using relevant, everyday cultural activities that the learners are familiar with (Mogari, 2014). Ethnomathematics approaches focus on the learners’ background, their experiences, and immediate environments incorporated with the school mathematics in a practical way as required in the teaching of geometry concepts. Learners’ construction of mathematical knowledge would be based on their general experience, which is connected to their culture and environment. As such, the objective of this study was to provide insight into how in-service mathematics teachers integrate ethnomathematics approaches into the teaching and learning of geometry at the secondary school level. Specifically, the study intends to provide answers to the following question: How are in-service teachers integrating ethnomathematics approaches into the teaching of geometry? Ethnomathematics and Social Constructivism Social constructivism theory is connected to the ethnomathematics approaches, which put more emphasis on the importance of culture in the teaching and learning process and the significance of the learners’ interaction with social values and essentials for the purpose of acquiring the essential geometry knowledge. From the social constructivist theory perspective, learners initially attain societal mathematics ideas from their surroundings, which act as a mediator between the learners and the social values and ideas, and continue to acquire and consolidate them in school, which logically processes and manages knowledge. Ethnomathematics approaches and social constructivism share similar views on two major enlightening assumptions that influence how mathematics should be taught in schools (Matang, Australian Journal of Teacher Education Vol 45, 7, July 2020 79 2009). Firstly, learners socially construct knowledge through their social interactions with the immediate environment. Secondly, learning occurs through realistic and contextualised activities that provide the appropriate contextual meaning to what is being learned or taught in the classroom. Although ethnomathematics and social constructivism share similar views, ethnomathematics specifically deals with mathematics teaching and learning. In contrast, social constructivism is a lens to view teaching and learning of various areas, including mathematics. According to Vygotsky (1978) and Woolfolk (2010), learning cannot occur in vacuity. This has some implications for geometry teaching in the sense that teachers should connect their teaching to the learners’ experiences and environments. Both ethnomathematicians and social constructivists support this view. These implications may have beneficial effects if suitable instructional approaches are utilised in tapping into the ethnomathematical knowledge that might be used as a starting point in the teaching and learning of geometry/mathematics (Matang, 2009). Possibilities of Integrating Ethnomathematics Approaches in the Mathematics Curriculum Researchers have suggested more cultural activities, practices, and ideas to be integrated into the formal mathematics curriculum (D’Ambrosio, 1985; Adam, 2004; Mogari, 2014; Fouze & Amit, 2018). The integration is essential in the approach to mathematics learning, the mathematics content, its epistemology, and the classroom culture (Adam, Alangui & Barton, 2003). For pedagogical reasons, there has been increasing interest in how ethnomathematics approaches can be integrated into the school mathematics curricula (Adam, 2004; Gerdes, 2005; Paraide, 2015). Adam (2004) identified five options for an ethnomathematical curriculum. All the options are grounded in an understanding that an ethnomathematical curriculum is one in which the social facets of the learners’ backgrounds are holistically integrated into the teaching and learning environment (Adam, Alangui & Barton 2003). The first option for an ethnomathematical curriculum is regarded as “mathematics in a meaningful context” (Adam, 2004; Fouze & Amit, 2018). Such a curriculum presents mathematics as a social reaction to human desires (Fouze & Amit, 2018). This kind of an ethnomathematical curriculum draws examples from the learners’ own experiences or practices that are common in the social surroundings of the learners (Adam, 2004). It is postulated that a curriculum of this kind would influence the learners’ thinking about mathematics instead of what or how they learn (Bishop, 1988; Mogari, 2014). The second option is the one that views ethnomathematics as a specific social content that is distinctive from the universal mathematics theories/concepts taught in the classroom, such as distinct designs or ornamental arrangements, for example, those displayed in weaving (Adam, 2004). Such ethnomathematical content could include mathematical concepts, activities, and practices drawn from a specific cultural or social group. It could also include the historical development of mathematics in diverse ethnic groups as well as incorporating culturally diverse mathematics resources into the teaching and learning process. It is acknowledged that such a curriculum would have motivational learning benefits for the learners (Gerdes, 2011, Hunter 2013). The third option is based on the notion that ethnomathematics consists of developmental stages in mathematics related to the contextual thinking that learners go through in their mathematics education (Adam, 2004). Such an ethnomathematical curriculum is psychological, Australian Journal of Teacher Education Vol 45, 7, July 2020 80 in the sense that mathematical thinking develops concretely from practical situations. Vygotsky, cited by Fouze & Amit (2018), reported that language determines the development of thought. Hence the learning atmosphere consists of the learne