Mathematics and Society, Research Paper Example

Abstract

Mathematics is extremely important to people’s lives. Inadequate mathematical knowledge keeps some cultures in poverty. When people cannot articulate concepts that prevent economic and social exploitation they remain powerless to change their socio economic circumstances. This is how knowledge becomes power.My principal aim in this study is to provide a critical review of classroom practices that menace as well as limit mathematical concepts interpretation due to diverse cultural oriented classroom environment. In doing so, Cole’s (1996) and Vygotsky’s (1978) sociocultural theories have been applied in gaining a better understanding of coping with  the constraints of a multicultural mathematics curriculum delivery.

Introduction

Mathematics emerged from one Greek word meaning three words knowledge, learning and study. With respect to study it relates to subjects exploring space, quantity (numbers), structure and change. However, the scope of Mathematics definition varies among philosophers found within the science. Essentially, mathematicians are concerned with patterns’ integration, which are utilized to create conjectures. These conjectures are either validated as truth or falsified. Culturally, over time mathematics developed from the basics of counting calculations, measurement, exploration of shapes and motions into abstract logical thinking (Jourdain, 2003). This paper seeks to place mathematical practice into a perspective of making it meaningful in a culturally diverse classrooms. Consequently, the focus will be onsome teaching and learning issues in the multicultural classroomsaffecting mathematics instructions. A review of the impact of students from different backgrounds (race, culture, language and learning) on classroom teaching and learning experience will be conducted. Finally, an exploration intoteaching mathematics in a living context that is meaningful to students with different sociocultural backgrounds will be embraced.

Teaching and learning issues in the multicultural classrooms

Witsel (2003) from the Southern Cross University advanced that teaching at tertiary or any level was rather uncomfortable even when the socioeconomic and cultural background of students are compatible with that of their tutors/professors.  Consequently, teachers have the added responsibility of motivating, assessing, negotiating, admonishing as well as teaching. The expert contends that these tasks force teachers to go beyond the call of duty placing themselves in active relationships with students and the professional responsibilities they execute on a daily basis. Therefore, the job calling becomes somewhat complicated when students appear in a classroom with various language orientations, learning styles and expectations based on their socioeconomic and cultural development (Witsel, 2003).

If teachers could understand the demands of functioning in the multicultural classroom environment the daily process involved in instruction delivery would be facilitated. Most importantly, educators must be aware that learning styles differ from one geographic location and varies from one person or group to the next. Witsel (2003) emphasized referencing data obtained from the EAIE 2000 conference, seven important differences in educational styles. They are student – lecturer relationships; class interaction models; relationships between and among students; the importance of being on time; regulation of the learning process; the aims of learning theoretical emphasis or mere understanding and use of technology in the class room (ten Dam & Hatton, 2000).

Further, other differences identified occurring at various levels encompassed learning styles in themselves. Others were metalinguistic communication meaning that every culture has it own rules regarding acceptable and unacceptable behavior. This phenomenon is evident in every multicultural classroom and greatly affects instructional outcomes. Next is the level of English-language competency of students in the classroom. While mathematics is considered a subject with a universal language embracing numbers and logic, students have to produce this ability based of a tongue in which they can articulate fluently (Windsor, 2008).

Experts have contended that a sense of self is altered when students whose second language is the one in which instruction is being communicated. Further it has been argued that the native language people use greatly influence the perspectives of their world. If this is true it explains the complexity teachers of any discipline encounter functioning in a multicultural classroom environment with speakers of differing language cultures.

In obtaining some understanding of this altered sense of self phenomenon experts question whether speakers of more than one language relinquish control of the mother tongue when communicating in the other language. They have found that while it is not clear how this psychologically influences student /educators’ teaching learning relationship, the teacher is in a power position to articulate an appropriate relinquishment strategy for that period, to a language adaptation through, which instruction can be facilitated (Gutiérrez & Rogoff, 2003).

Expressing cultural competence as an educator is another essential virtue that is necessary to function in the teaching learning multicultural classroom environment. Cultural competence allows the educator to become mindful of the cultural orientation of students by adjusting his/her own opinions of their beliefs and practices as well as limiting criticisms. These students should be embraced in a culture of safety knowing that their ethnic, socio-economic and cultural orientations are respected within the classroom environment. Essentially, the educational system under which they are instructed ought to ensure that their values are respected (John-Steiner & Mahn, 1996).

The impact of students from different backgrounds in a Mathematics classroom

Experts have confirmed that learning is a complex dynamic process.  Specific outcomes ultimately lead to the expression of one’s ability in grasping concepts, reproducing information and analyzing content by drawing inferences, but these virtues are articulated within a context of the individual’s cultural environment (Hand, 2003). It is amazing to observe how one lesson could be culturally interpreted in several ways, but carries the same message or theme. In fact this is a major example of how students from different backgrounds (race, culture, language and learning) impact classroom teaching and learning experience (Terry& Irving, 2010). This is significantly true in classrooms where students are expected to learn at the same pace.  Therefore, when learning activities in multicultural classrooms are designed, culturally appropriate ideas must be utilized in forming the classroom experience. For instance, if students from an indigenous Australian culture are in a classroom with immigrant Australian population such as Chinese or other European culture, the teaching of numbers and their relationship to the real world must coincide with artifact of the specific cultures (Nicol & Crespo, 2005). Obviously, it would necessitate more work finding appropriately relevant materials for such classroom. A major impact of this instruction model is that students in one mathematics lesson will also learn about other cultural interpretations of a lesson on numbers or abstract logical mathematical concepts (Colombo, 2005).

Michael Cole(1996) in Cultural psychology: A once and future discipline advances that students bring cultural artifacts into their classrooms because when they attend school it is placing them in an environment to confirm what is already known from the mind’s exposure to ideas previously. The information found in mind is culturally imposed. Social psychologists in the caliber of Lev Vygotsky’s‘(1978) supporting contend that humans are a product of their environment. The production is their cultural heritage. Consequently, no effective learning process can occur without educators becoming sensitive to the cultural environment in which they and their student function (Blake &Tambra, 2008).

Consequently, a constructivist approach to cultural diversity can be adapted whereby the instructor promotes learning of mathematics within a framework to be grasped from a culturally related perspective.  For example, Lev Vygotsky’s (1978) zone of proximal development  (ZPD) indicates that children learn from adults in their environment. These values they take with them to their respective environments including the classroom. Ultimately, they develop the ability to conduct tasks without the help of adults. The zone of proximal development paradigm enables the teacher to collaboratively devise cultural meanings to concepts being clarified and interpreted personally. These concepts are consistent with their personal ability to produce outcomes without help from teachers. They are also aligned to racial orientations, belief paradigms, language and learning differences developed from imitations of adults..  Multicultural classroom education  utilizing the zone of proximal development technique in mathematics can, therefore, produce both confidences in their abilities as well as awareness of the cultural backgrounds that have been brought to the learning environment (Barta, 1995).

Teaching mathematics in a living context

According to Ukpokodu (2011) teaching mathematics in a living context which is meaning full to students of various sociocultural orientations require specific strategic theoretical interventions. The expert advances from research a theoretical premise indicative of students of a minority culture being mostly affected by difficulties interpreting mathematical concepts. In fact he contends that there is a teaching learning mathematics crisis across the globe, which is gaining momentum.  As such, a culturally responsive pedagogy is a favorable theoretical application to the crisis as it pertains to teaching mathematics in a living context which becomes meaningful to all students irrespective of their cultural backgrounds (Ukpokodu, 2011).

In a supporting response Michael Cole’s (1996) theory emphasizes the consideration of cultural compatibility of mathematics instruction in the modern classroom environment. The assumptions are embedded in “Cultural Psychology: A Once and Future Discipline” framework drawing upon the social psychology of learning.  The contention here is that culture provides an environment whereby young minds could appropriate learning within a particular context. The context relates to inherited beliefs, customs and values as practiced in ethnomathematics classrooms in Africa, advancing the rectangular base theory (Abraham & Bibby, 1988).

Specific recommendations advanced by this model included oral story telling in teaching of mathematics. The stereotype instructions of chalkboards relation of concepts are grossly inadequate and obsolete in producing a culturally responsive living mathematics classroom environment. Stories involving numbers and reasoning applications described in a culturally compatible design are very effective in bringing life to a culturally diverse mathematical classroom environment (Banks, 2001).

Essentially, Lev Vygotsky’s (1978) “Mind in society: The development of higher psychological processes”, emphasizes that a child’s learning begins long before he/she attends school (Vygotsky, 1978).  As such, the social setting and symbols with which the child interacts develop paradigms of learning, which are insidious to his/her social atmosphere. For instance, children exposed to the media hear and grasp concepts without being taught. Some children learn numbers through repetition just hearing words, seeing symbols and replicating them even though mathematical concepts are not known (Ball, 2005).

Besides, in this age of such technological development children from a very early age, as young as one year old have access tablets. These are created with mathematical programs for their specific age and grade levels. This technology could be introduced in a mathematics classroom. As  students with different sociocultural backgrounds view these programs if they are at an age whereby meaningful discussion could be conducted questions can be encouraged pertaining to the differences in their world view of the signs and diagrams communicated in the tablet. Even cell phones once the student has a Netflix account mathematics learning programs can be accessed which are culturally compatible designed. These devices can be used in a mathematics classroom, whereby mathematics is brought alive amidst cultures (Berry, 2008).

Ethnomathematics and the mathematics curriculum, is an intervention wherebymethods of “rectangle bases” construction are often utilized among Mozambican peasantry in Africa. These people do not have access to tablets, IPads and cell phones or sophisticated devices as persons in developed nations. However, the capability of teaching mathematics in a living context that is meaningful to students with different sociocultural backgrounds does exist among them. This methodology of utilizing the rectangular mathematical concept as architectural measurements is being introduced in African high schools as a culturally relevant living mathematical adaptation (Zhang & Zhang, 2010).

Conclusion

Cole (1996) argues that there are culturally relevant objects and ideas that influence students’ adaptation to academic learning. Symbolic interactions have been created with these objects/ideas that can either create the global mathematics crisis to which Ukpokodu (2011) alludes, or resolve it (Bishop, 1988). Therefore, it would be desirable to ask the question how do educators incorporate symbolic interactions as a culturally applicable concept in mathematics classroom environment. Cole’s (1996) paradigm inclusive of mediated artifacts is assuming a symbolic interactionist approach to instruction in the mathematics classroom environment (Cole, 1996).  There is a global mathematics teaching learning crisis. Children find it difficult grasping advanced mathematical concepts even when the basics have been mastered. The few who excel are considered prodigies evolving into scientists. Importantly, they excel in physics and chemistry too. Could it be that the world’s educational system pertaining to the teaching and learning of mathematics is not culturally competent to professionally address the distinct differences of students in a diverse and multicultural environment?

References

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