1 Introduction
Learners' performance in mathematics has been worrisome for parents, teachers, and policy makers in Zimbabwe. The Nziramasanga commission (1999) cited in Mashingaidze (2012) bewailed the miserable state of mathematics instructional approaches used in Zimbabwe and asserted that the hitches of quality of mathematics teaching and learning are from various sources. With regard to the teaching and learning of mathematics, numerous researchers relate the learners' poor performance in mathematics to poor pedagogical practices employed in the classroom (D'AMBROSIO, 1985; BOALER, 2016). In Zimbabwe, the mathematics teachers have been held responsible for the learners' poor performance in mathematics (Curriculum Team Research report, 2010 cited by MASHINGAIDZE, 2012). Foster (2007) pointed out that if geometry is taught as an abstract topic without meaning, then the learners would not understand the geometry concepts such as geometry. Researchers such as Mashingaidze (2012) and Telima (2011) highlight that the problems that the learners face in geometry are due to the instructional approaches used by their teachers that do not nurture conceptual understanding. The traditional approaches that focusses mainly on providing learners with previously prescribed repetitive tasks or activities do not enhance deep-connected comprehending as well as meaningful geometry learning (BOALER, 2016).
For that reason, for countless years, researchers have been exploring diverse approaches and tactics to improve geometry teaching and learning in particular and mathematics in general. Of the numerous studies on geometry teaching, some involve making use of current technologies (JONES, 2011), applications of geometry history with appropriate historical sources including the incorporation of ethnomathematical approaches (GERDES, 2008; D'AMBROSIO, 2001). Researchers believe that ethnomathematics approaches are the most effective teaching methods (MOGARI, 2002). For instance, Kurumeh (2009) cited by Aikpitanyi and Eraikhuemen (2017), found out in her study that the ethnomathematics approach enhances understanding and efficient learning resulting in higher achievement of learners in geometry. Effective teaching of geometry consists of the processes of knowing how to come up with thought-provoking geometrical problems, appreciating the history and social context of geometry, as well as comprehending the different uses of geometry. Effective teaching of geometry to learners is important in order to ensure that they understand geometry concepts they would be learning and the processes that are involved, instead of just memorizing rules.
Zimbabwe's mathematics education has been experiencing a number of reforms. Presently, the new mathematics curriculum included as key points the need to demonstrate knowledge and appreciation of diverse Zimbabwean culture as well as relating cultural practices to the mathematics curriculum. The new curriculum also expects teachers to be knowledgeable about the teaching approaches that are receptive to the learning qualities and requirements of learners from assorted linguistic, social, religious, and socio-economic backgrounds. The resolution to develop the new mathematics curriculum was made with regards to the government's emphasis on getting Zimbabwean learners ready for the necessities of the 21st century, developing worries among key partners and policy makers in regard to the relevance of the education system and the progressions in worldwide education guidelines. Traditionally, the Zimbabwe education system, similar to others all over the world, put more emphasis on the development of strong geometry content knowledge to the detriment of critical skills and capabilities. As pointed out by Sunzuma, Ndemo, Zinyeka and Zezekwa (2012) the teaching of mathematics in Zimbabwe was teacher-centered, where the teachers were sources of geometry knowledge and information. Similar findings were reported by Telima (2011), who found out that geometry teaching was too theoretical and bookish and it lacked practical activities and real-life experiences and examples. In addition, the horrible impact experienced by learners while learning mathematics through the traditional approaches frequently keeps them from exceeding expectations, resulting in poor performance (BOALER, 2016). Such teaching approaches do not inspire learners to make logical connections as well as explaining their reasoning and geometry content knowledge mastery is inadequate as an exit trait. In Zimbabwe, there was a general outcry that school graduates were not able to apply the mathematics learned in the classroom in real-life situations (MASHINGAIDZE, 2012).
In light of the above, a new mathematics curriculum was developed in response to the poor performance and the non-utilization of the learnt mathematics concepts in real-life situations. The Zimbabwe new mathematics curriculum supports a competency-based methodology which is acknowledged through situated learning. It is perceived that the curriculum shifts from being content-based (examination bound) to a competency-based (results situated) curriculum which centers on the learners' ability to apply knowledge, skills, and attitudes in a free, hands-on, and responsive manner. Teaching approaches such as ethnomathematics enable learners to recognize the relation between various methods of representing geometry ideas as well as their connection to mathematics concepts. Such approaches are expected to help learners in retaining geometry knowledge and skills as well as enabling them to approach geometry tasks and activities confidently (JONES, 2002). Teachers are expected to help learners create capabilities to access and process geometry information freely and responsibly, as well as develop extensive life skills. The changing role of teachers was accommodated for in the new curriculum where the teachers are expected to be facilitators to the learning process. The new curriculum stresses learner-centered approaches, where learners take part in the search and discovery of new geometry knowledge. The teacher acts as a co-explorer and facilitator in the discovery of geometry knowledge in order to arrive at an objective comprehension of content and application of the skills so gained. The focal point of teaching and learning is involving the learners in dealing with real-life problems through engaging them in meaningful activities. The construction of knowledge is through social negotiation and an emphasis on problem-solving using real-life application of geometry skills.
From the above sentiments, the new mathematics curriculum is underpinned by the social constructivist viewpoint, which proposes that the construction of knowledge and meaning is done by learners through the experiences and activities they engage in. Geometry/ mathematics is a human intervention. Geometry is a cultural product and is dynamic and socially constructed. From the social constructivist viewpoint, knowledge is constructed through numerous social interactions with the environment. Therefore, geometry teaching and learning should be contextually and culturally bound. In addition, Vygotsky (1978) suggested that construction of knowledge should be done through active participation and engagement.
D'Ambrosio (2001), regarded ethnomathematics as a teaching and learning approach, that builds on the learners prior knowledge, experience, the role played by the environment in terms of content and technique as well as their historical and current experiences of their immediate surroundings. Ethnomathematics is the association between mathematics and culture (IZMIRLI, 2011). Numerous benefits have been recognized for incorporating ethnomathematics approaches into mathematics teaching in general and geometry specifically. These include improving school mathematics learning content including geometry and promoting higher levels of intellectual skills; enabling learners to be creative; improving the learners' ability to solve geometry problems; improving the learners' tactics for obtaining information; boosting the learners' self-esteem; improving the learners' ability to work with others in the classroom; helping the learners to experience self-reliance; allowing the learners' to make their own decisions; increasing the learners' ability in making links between daily practices and school geometry; improving the learners' ability in discovering important meaning to countless complex geometry concepts taught in schools (GERDES, 1999; ADAM, 2004; ANCHOR; IMOKO; ULOKO, 2009; ROSA; OREY, 2010; IZMIRLI, 2011).
Additionally, numerous researchers (D'AMBROSIO; D'AMBROSIO, 2013; NARESH, 2015) reported that an ethnomathematics approach, in which learners use their sociocultural background to scaffold geometry concepts would assist them in seeing the applicability of mathematics to real-life situations, thus extracting the learners' creativity and critical thinking skills.
Despite the numerous benefits of integrating ethnomathematics approaches into geometry teaching, there is also some criticism labelled against such approaches. Bridge, Day and Hurrell (2012) reported that, in a classroom where geometry teaching was dominated by prescribed textbooks, and where lessons were benchmarked against mandated mathematics curriculum, teachers found it challenging to use ethnomathematics approaches in such scenarios.
However, teachers are the most important variable in the implementation of such teaching approaches in geometry teaching and learning. Teachers are responsible for creating an exciting mathematics learning environment, providing learners with positive messages they require as well as taking any mathematics tasks and provoking the learners' interest and curiosity (BOALER, 2016). The use of ethnomathematics approaches in geometry teaching and learning has significant implications for the teachers. Thus, the purpose of this study is to find out the teaching approaches being used in geometry teaching as well as the teachers' views about the integration of ethnomathematics approaches into geometry teaching.
What are the teaching approaches used in geometry teaching and learning?
How do in-service teachers view the integration of ethnomathematics approaches into geometry teaching?
2 Methodology
This section focuses on the context of the study and its participants, design, data gathering instruments, and data analyses procedures.
2.1 Context of study and Participants
The current study was conducted in the Faculty of Science Education, Department of Sciences and Mathematics Education at a conveniently located university in Zimbabwe. The mandate of the selected university is to train both in-service and pre-service Sciences and Mathematics teachers in Zimbabwe. The university offers both in-service and pre-service programs for teachers from honors degree level up to the doctoral level. For that reason, researchers assumed that the in-service teachers who participated in the current study had experience in teaching geometry and were able to provide important information concerning the teachers' geometry teaching and their views on the integration of ethnomathematics approaches.
The study population was 80 (50 men and 30 women) in-service mathematics teachers. The sample comprised of 40 in-service mathematics teachers (25 men and 15 women) who were enrolled in the Bachelor of Mathematics Honors degree at the university under study. Proportional stratified random sampling was used for the quantitative phase to ensure the in-service mathematics teachers' proportionate representation in the sample. Gender was used as the stratification variable, where the in-service mathematics teachers were divided into two groups; one for men and another one for women. Two random samples were selected independently from each group (female and male) proportionately to the gender balance in the population (CURTIS; CURTIS, 2011) by means of a simple random sampling procedure. The joined random samples of men and women in-service mathematics teachers all in all comprised the sample (40 teachers) of the current study.
We used a research-based recruitment, whereby the same in-service mathematics teachers (40 teachers) who completed the questionnaires also took part in focus-group discussions, in keeping with the view of Hennink (2014). The 40 in-service mathematics teachers who completed the questionnaires after being selected through proportional stratified random sampling techniques were also randomly chosen to take part in the focus-group discussions. The focus group discussions involved five groups, each comprising of three female and five male in-service mathematics teachers. Despite the fact that proportional stratified random sampling and research-based recruitment were used to select the in-service mathematics teachers, their involvement in this study was voluntary.
The 40 in-service mathematics teachers were Degree holders who were teaching mathematics at the secondary school level in Zimbabwe. With regarding to the teaching profession, (37.5%, n = 15), had 2-5 years of teaching experience, (50%, n = 20) had 6-10 years of teaching experience, and 12.5% (n = 5) had between 11-15 years of teaching experience. In-service mathematics teachers are only enrolled for the program if they have two years of teaching experience in secondary schools.
2.2 Design
We used a convergent mixed methodological approach combining both quantitative and qualitative data gathering and analysis. The rationale for combining qualitative and quantitative data was to triangulate the data (GRAY, 2011). The convergent mixed method approach involved gathering both qualitative and quantitative data simultaneously and then merging the data in the analysis and interpretation stages (CRESWELL; PLANO CLARK, 2011).
2.3 Instruments
Focus group discussions were used to generate qualitative data as well as questionnaires that generated both quantitative and qualitative data (MCMILLAN; SCHUMACHER, 2010), which is an important element of convergent parallel mixed-methods design that allows for data triangulation. The questionnaire comprised of closed items and open-ended questions to enable the teachers to express their views on the integration of ethnomathematics approaches into geometry teaching and learning and how they teach geometry. The closed questions provided the quantitative data in form of frequencies and percentages while open-ended questions gathered qualitative data. Questionnaires were employed as they were capable of providing information about views on the integration of ethnomathematics approaches into the teaching geometry as well as on how they teach geometry (GRAY, 2011). Nonetheless, the use of questionnaires only hampers their aptitude to provide in-depth and thick descriptions, hence, the use of focus group discussions. Data from the focus group discussions provided supplementary ample information on teachers' views on integration of ethnomathematics approaches into the teaching and learning of geometry.
The validity and reliability were accomplished predominantly through methodological triangulation which made use of two data gathering methods on the same research question. In addition, both focus-group discussion items and questionnaire items were content-validated by three specialists in mathematics education. Their comments and suggestions were used to improve the items.
2.4 Procedure
In order to conduct the study, the university gatekeeper granted us permission in accordance with research policy. The participants signed an informed consent letter before they took part in the study. To enable a high response rate and a shorter period of gathering data, the questionnaires were self-administered to the teachers in a lecture room. A box was placed near the room exit for dropping in the questionnaires, which helped in ensuring confidentiality as well as maximizing the response rate (GRAY, 2011). Focus-group discussions were conducted immediately after the teachers completed the questionnaires.
2.5 Data Analysis
The researchers transcribed the audio-recorded focus group discussions. An ‘inductive’ (CRESWELL, 2015) data analysis process, which involved code creation by the authors through direct interaction with the data, was used for qualitative data from both the open-ended questionnaire questions and focus-group discussions. Inductive data analysis is a process that entails the identification of patterns and themes in the data (CURTIS; CURTIS, 2011). Interpretive data analysis which provide meanings that go beyond direct description of the statistical data was employed for the quantitative data. For the quantitative component, descriptive statistical visual strategies were employed to analyze as well as to interpret the data (COHEN; MANION; MORRISON, 2015). In the current study, the quantitative data was presented as frequencies and percentages (COHEN et al., 2015).
4 Conclusion
The findings showed that both teacher-centered and learner-centered approaches were being used by the teachers in geometry teaching and learning. These findings also showed that most of the participating teachers thought that cultural examples and activities should be incorporated into geometry teaching. Furthermore, as highlighted by the findings, the benefits of integrating ethnomathematics approaches into geometry teaching were relevance of geometry, motivation and interest, facilitating the understanding of geometry concepts and application of geometry concepts. Findings on such benefits are in line with those of other researchers (ADAM, 2004; KANG, 2004; ANCHOR et al., 2009; ROSA; OREY, 2010) in terms of enabling learners to comprehend, understand, and appreciate as well as apply geometry concepts, ideas, processes, and practices in solving practical problems in their societies. Furthermore, the findings showed that this approach to geometry teaching would motivate learners to learn geometry and to recognize geometry as part of their daily lives, enhance their ability to make meaningful geometrical links and deepen their understanding of all forms of geometry, which concurs with Boaler (1993), Ernest (1998) and Adam, Alangui and Barton (2003).
Furthermore, very few teachers (2.5%) from the closed end questionnaire data thought that the quality of geometry education would deteriorate if ethnomathematics were integrated into geometry teaching.