Published on International Journal of Biology, Physics & Mathematics
Publication Date: April 17, 2019
Robert Mugabe School of Education and Culture, Great Zimbabwe University
Journal Full Text PDF: Culturally Responsive Teaching in Mathematics: Insights from A Preliminary Study.
The qualitative case-study from which this paper is premised linked the mathematical knowledge being taught in a school close to a cultural village to the knowledge and activities of the cultural village itself – interrogating connections between mathematics and indigenous knowledge systems. Three Grade 9 mathematics teachers from one school participated in a collaborative school–based professional development intervention facilitated by an external subject specialist (mathematics teacher educator). Through mathematizing culturally-based activities, the research team indigenised (i.e. adapted to local culture) two Grade 9 mathematics topics. A teaching and learning unit was designed and implemented in five Grade 9 classes at the same school. Contrary to arguments that ethnomathematics may not be a viable route into ‘solid’ mathematics, the analysis from this study is used to counter such arguments, and propose that culturally-based activities are highly-useful yet underutilized vehicles as an entry point into academically proven mathematics. The paper demonstrates that the experience of designing, implementing, and reflecting on the intervention study had some positive contribution to participating teachers’ pedagogical repertoire. However, it is noted that although involving teachers in an activity like this might be worthwhile, some teachers expressed apprehension of working outside their comfort zones. Participation in this study led to teachers’ awareness of a mismatch between the materials developed in the intervention and those recommended by their Department of Education.
Keywords: Professional development; comfort zone; indigenisation; mathematisation; culturally responsive teaching.
Educational reform is now creating challenges to the teaching and learning strategies. Some education reform policies indicate that learners should be getting education which is relevant to their cultures. The cultural placement of an educational system is probably the most relevant fact in modern development of education (D’Ambrosio, 1979). Many researchers have agreed that teaching must be related to its cultural and geographical context (Bishop, 1988; Kroma, 1996; Ascher, 1994; Gerdes, 1999; Mosimege, 2000, 2003; Madusise, 2010, 2013). The common consensus amongst these researchers is that mathematics is being perceived as dry, uninteresting and irrelevant because familiar subject matter and experiences that could be used to lay the foundations of the discipline, arouse learners’ interests and challenge their intellect early in life have been largely neglected.
South Africa has embarked upon a curriculum that strives to enable all learners to achieve to their maximum potential (Revised National Curriculum Policy, 2002). Curriculum outcomes encourage learner-centred and activity-based approaches. Policy statements for Grades R-9 Mathematics envisage learners who will “be culturally and aesthetically sensitive across a range of social contexts” (DoE, 2002: 2). Interestingly, some assessment standards require learners to be able to describe and illustrate the historical developments of some mathematical concepts in a variety of historical and cultural contexts. Learners are also expected to be able to solve problems in contexts that may be used to build awareness of social, cultural and environmental issues. From a curriculum perspective, the inclusion of the local, historical and cultural contexts in the teaching and learning of mathematics suggests mathematisation of cultural activities. Part of the teacher’s work involves coming to an argument for ethnomathematics as a cultural way of doing mathematics. This calls for a radical change on the part of the teacher in order to see mathematics incorporated in the real world as a starting point for mathematical activities in the classroom. For there to be a real possibility of implementing such kind of classroom activity, there is need to investigate the mathematical ideas and practices of the cultural, ethnic, linguistic communities of the learners. There has been a growing attempt to relate mathematics and science to some of the cultural background of the learners. Khisty, (1995) argues that learners of all background would benefit from the opportunity to learn about and identify with their rich mathematics heritage and on-going cultural practices. Mathematics correlates closely with human life.
Although these new understandings of mathematics teaching and learning may sound very good, the implementation and impact of explicit instructional strategy may not be widespread. This stagnancy in classroom pedagogy maybe in part related to the failure of educational research to adequately investigate and promote the relationship between teacher professional development and enhanced understanding of the required pedagogical shifts. There is widespread agreement that improving teaching and learning requires that teachers participate in high-quality professional development (Elliot, & Kazemi, 2007). Such professional learning communities are largely linked to teacher learning in and from practice. Effective teacher professional development has been characterised as being long-term, collaborative, school-based and focused on student learning (Hiebert, Gallimore, & Stigler, 2002). Little (1987) describes professional development as an activity that is intended partly or primarily to prepare teachers for improved performance in present or future roles in their schools (Desimone, 2009:182).
The major aim of the professional development was to base the teaching of mathematics on the cultural background of the learners, using out-of-school, culturally-based activities. Thus extracting mathematical ideas from the environment and embedding them within mathematical instruction. Embedded instruction suggests building scaffold for the learners to construct their knowledge in the process of learning, instead of providing students with prepared knowledge.
This paper traces the journey of extracting mathematical ideas from cultural activities at the cultural village, designing and implementing an intervention teaching and learning unit at Grade 9 based on the extracted mathematical ideas, and discusses the impact of this intervention study on the participating teachers. It addresses the following central research question: What is the potential of mathematical ideas associated with activities at a cultural village for informing the teaching and learning of Grade 9 mathematics?
2. Theoretical framework
The study is framed and guided by two interrelated learning theories: Ladson-Billings’ culturally relevant pedagogy and Wenger’s (1998) theory of learning as social practice. Ladson-Billings (1994, p .17-18) defines culturally relevant instruction as a pedagogy that can empower learners intellectually, socially, emotionally and politically by using cultural referents to impart knowledge skills and attitude. On the other hand, situated learning regards learning, thinking and knowing as “relations among people engaged in, with and arising from the socially and culturally structured world” (Lave, 1993, p.67). Learning occurs with the practices of communities as social and cultural contexts. In this sense, knowledge is shaped by the contexts in which it is acquired and used (Eraut, 2000). Social component is a critical component of situated learning; learners become involved in a “community of practice” where they are working together (Lave, & Wenger, 1991). Ultimately, “cooperation, community and connectedness are also central features of culturally responsive teaching. Learners are expected to work together and are held accountable for one another’s success” (Gay, 2000, p.36).
Wenger (1998) came up with a model showing meaning, practice, community, and identity as components of a social theory of learning. In this model identity is a way of talking about how learning changes who we are and creates personal histories of becoming in the context of our communities. Consequently, “culturally responsive teaching can be considered transformative, as it recognises the existing strengths and accomplishments of the students and then enhances them further in the instructional process” (Gay, 2000, p. 33). Also, besides addressing learners’ achievement, the underpinnings of culturally relevant pedagogy help learners accept and affirm their cultural identity.
Wenger (1998) further argues that learning needs to be presented in authentic contexts, settings and situations that would normally involve that knowledge. Finally, by connecting mathematics learning to the authentic problems\ activities that have directed its development, educators can help learners situate the learning of mathematics concepts in the context from which the ideas developed.
The two theories were found to be relevant to the study as they can both provide a complex and powerful methodology which involves participation in a learning community which may possibly leads to some identity transformation. Three mathematics teachers from one middle school in the North West Province of South Africa constituted as a community of practice. These teachers and the researcher collaboratively used mathematical ideas extracted from culturally-based activities to enact culturally responsive teaching in their Grade 9 mathematics classes. In this paper I explore how mathematics teachers’ participation in a professional learning community influenced their classroom teaching practices.
3.1 Samples and sampling procedures
The sample in this study comprised of three mathematics teachers from one middle rural government school in the North West Province of South Africa and their Grade 9 learners. Purposive and convenience sampling was used to select the research sites (Patton, 1990). Merriam (2009) identifies purposive sampling as one appropriate sampling strategy in case-study design. Merriam (2009) further adds that purposeful sampling is based on the assumption that one wants to discover, understand, gain sight; therefore one needs to select a sample from which one can learn the most. In this case, a cultural village was identified as the research site and mathematics teachers who teach at a school very close to the selected cultural village were focused on. A cultural village was selected with the belief that it is where the community’s indigenous knowledge is preserved. The intention was to make the cultural village a mathematics teaching resource centre. A school close to the cultural village was chosen with an assumption that its members (including the school children) are quite familiar with the activities taking place at the cultural village.
Grade 9 was chosen basing on the argument that it is the transitional grade from general education training (GET) to further education training (FET) where students after Grade 9 are to choose between Mathematics and Mathematical Literacy. At Grade 9 learners are learning mathematics which combines aspects of both Mathematics and Mathematical Literacy. At Grade 9 learners (14 to 15 year olds) have more experience with mathematics than learners at earlier grades. Doing the study at FET level would have limited the number of participating learners as some learners might have perceived it as being linked to Mathematical Literacy and would therefore withdraw.
3.2 Data collection instruments and procedures
Data sources included video clips of cultural activities, video-based lesson observations (the lessons were taught by both the researcher and the teachers), two learner questionnaires, teacher and learner interviews, artefacts, such as learners’ lesson journals, teachers’ lesson reflective forms, transcripts from reflective meetings and learners’ work which served as corroborating evidence to enrich the picture of teaching practices presented in the study. The multiple sources of data provided converging lines of evidence to enhance credibility of assertions (Yin, 2003). All video and voice recordings were transcribed and inductively analysed using narration to report the results.
Participating teachers were interviewed at the beginning and end of the study and they also completed lesson reflection forms at the end of each and every lesson taught. Learners completed two questionnaires, one at the beginning and the other one towards the end. Learners were also interviewed to probe further on what they had written on the questionnaires and lesson journals. However, for the purpose of this paper only data from participating teachers is going to be used. Group discussions were carried with teachers when viewing video-clips from cultural village activities, when planning lessons and when reflecting on lessons taught.
3.3 Data presentation and discussion
Table 1 shows the participating teachers coded TR A, TR B, and TR C for confidentiality reasons. All the teachers had a minimum of seventeen years teaching middle grades (Grade 7 to 9) mathematics, which means they had gained some experience of teaching mathematics up to Grade 9.