A Teacher‐Researcher Perspective on Designing Multicultural Mathematics Experiences for Preservice Teachers

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<ul><li><p>This article was downloaded by: [Stony Brook University]On: 19 October 2014, At: 07:35Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK</p><p>Equity &amp; Excellence in EducationPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/ueee20</p><p>A TeacherResearcher Perspective on DesigningMulticultural Mathematics Experiences for PreserviceTeachersJanet M. SharpPublished online: 09 Jul 2006.</p><p>To cite this article: Janet M. Sharp (1999) A TeacherResearcher Perspective on Designing Multicultural MathematicsExperiences for Preservice Teachers, Equity &amp; Excellence in Education, 32:1, 31-42, DOI: 10.1080/1066568990320104</p><p>To link to this article: http://dx.doi.org/10.1080/1066568990320104</p><p>PLEASE SCROLL DOWN FOR ARTICLE</p><p>Taylor &amp; Francis makes every effort to ensure the accuracy of all the information (the Content) containedin the publications on our platform. However, Taylor &amp; Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor &amp; Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. 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Terms &amp; Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions</p><p>http://www.tandfonline.com/loi/ueee20http://www.tandfonline.com/action/showCitFormats?doi=10.1080/1066568990320104http://dx.doi.org/10.1080/1066568990320104http://www.tandfonline.com/page/terms-and-conditionshttp://www.tandfonline.com/page/terms-and-conditions</p></li><li><p>A Teacher-Researcher Perspective on DesigningMulticultural Mathematics Experiences for PreserviceTeachers</p><p>JANET M. SHARP</p><p>Many cultures come together to shape the learn-ing environment of an elementary classroom.A teacher has personal connections to one ormore cultures, the teacher's style of and skill at communi-cation is cultural, and, of course, the students bring theirown unique cultures to the classroom environment.Moreover, the various subject matters studied withinthose classroom walls also have cultural connections.Teachers who are knowledgeable about the culture-relatedactivity in their classrooms can use this knowledge to pro-vide effective instruction. Boyer's (1990) stage theory ofethnic growth can provide guidance to teachers who rec-ognize the need to develop culturally rich experiences fortheir classrooms. However, part of a teacher's multicul-tural awareness also must be in relation to the historicaland cultural aspects of the subject matter itself.</p><p>For instance, in mathematics, it is a fact that two plus twois four. Unless some nontraditional algebraic structures aredefined, such as an alternative base system, two plus two isalways four. Mathematics, in this skeletal sense, is a disci-pline free from cultural biases. However, the Indian nu-meral 2 (Menninger, 1969) and the German notation +(Smith, 1919) provide evidence of cultural artifacts inmathematics. In ancient Greece, a learner would have usedspatial thinking to mentally arrange two items and twoitems in order to imagine the sum of four as shown in Figure1. The Greek learner might also have additionally notedthat four is a square number, resulting from 2x2.</p><p>In addition, examples and contexts selected by teachersmay affect the cultural communication of the classroomenvironment. Consider a young boy who grew up on afarm being taught about "2+2" within the context of count-ing floors in a skyscraper. Next, visualize a young girl who</p><p>Figure 1A Mental Image of "2 Plus 2"</p><p>grew up in an urban neighborhood being taught about"2+2" within the context of counting cattle in a pasture. Therespective cultures of the students (and teachers) have cre-ated two different cultural experiences for the learning of2+2. Effective mathematics teachers know about the cul-ture of their subject area and about the cultures of their stu-dents and then adjust instruction accordingly.</p><p>Mathematics is a dynamic collection of mental ideasresulting from beliefs and values from a myriad of cul-tures. In fact, van Oers characterized mathematics as be-ing defined through "a long series of lively debatesamong mathematicians about what is to be accepted asvalid mathematics" (1996, p. 95). So, the cultures of thosemathematicians will impact the debate, and mathemat-ics cannot truly be considered a culture-free discipline.Moreover, the mental nature of mathematics precludesseparation from the learning and teaching of mathemat-ics, which are not culturally neutral activities (see Ander-son, 1990; Bishop, 1988; D'Ambrosio, 1990; Rauff, 1996;and Sleeter, 1989). Anderson (1990) outlines six "peda-gogical disasters" in mathematics teaching which arebased on the belief that there exist certain hidden realitiesa learner must experience before being able to learnmathematics. Acceptance of "the myth that mathematicsis pure abstraction and, therefore, antithetical to one'scultural and working environment" (p. 350) is amongthose pedagogical disasters because it reinforces the no-tion that mathematics is separate from culture. The pur-pose of this article is to discuss the appropriateness andimpact of some multicultural mathematics education as-signments for future elementary teachers, assignmentsthat were designed to counter the above myth. Thisstudy will discuss a teacher-researcher's efforts to useBoyer's stage theory to guide her students' developmentof cultural awareness with respect to mathematics andthe teaching of mathematics.</p><p>BACKGROUND</p><p>Multicultural education is first of all a complete edu-cational program with curriculum, pedagogy, and ac-</p><p>April 1999 Equity &amp; Excellence in Education 31</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [</p><p>Ston</p><p>y B</p><p>rook</p><p> Uni</p><p>vers</p><p>ity] </p><p>at 0</p><p>7:35</p><p> 19 </p><p>Oct</p><p>ober</p><p> 201</p><p>4 </p></li><li><p>tion in which students acquire academic content.Secondly, multicultural education guides students to-ward the development of an understanding of theirown backgrounds, backgrounds of others (Bennett,1990), and the ability to make decisions and engage insocial actions reflective of that knowledge (Nieto, 1996).In a multicultural education experience, students areencouraged to respect, appreciate, and celebrate diver-sity and to overcome ethnocentric and prejudicial atti-tudes and discriminatory behaviors.</p><p>The mathematics typically nurtured in the culture ofthe school classroom consists of a Western view ofmathematics, which is characterized by structure, de-duction, operations, and applicability (Nelson, Joseph,&amp; Williams, 1993; Powell &amp; Frankenstein, 1997; Rauff,1996). Many mathematics classroom environments donot recognize the multicultural nature of mathematicsand tend to initiate students into the Eurocentric viewof mathematics (Bishop, 1988; Frankenstein, 1997; Pinx-ten, 1994). However, one aspect of social constructivistlearning theory has provided an avenue to challengethis approach to teaching. Proponents of this theory de-scribe teaching as the creation of social classroom situa-tions to give students shared experiences to construct"shared" mathematical knowledge (Wood, Cobb, &amp;Yackel, 1995). By definition, those social, albeitknowledge-gaining, experiences are inseparable fromstudents' cultures and histories (Bauersfeld, 1995), andthe teacher must learn to find appropriate mathemati-cal situations that match those students' cultures(Sleeter, 1989).</p><p>On the one hand, "teaching becomes a matter ofcreating situations in which children actively partici-pate in scientific, mathematical, or literary activitiesthat enable them to make their own individual con-structions" (Wood, 1995, p. 337). On the other hand,to consciously engage in such instruction, "it is nolonger sufficient to just look at cultural influences,with adjustment of teaching style and class atmos-phere to perceived student preference; rather there isa need for an understanding of the importance of aca-demic competence combined with an understandingof academia as culture" (Garaway, 1994, p. 109). Ifteachers are able to avoid narrow views that inadver-tently promote single-culture learning of mathemat-ics and instead are able to know their students,complete with history and culture, teachers will beable to provide better mathematical learning experi-ences for their students.</p><p>Mathematics learned from such a consciously multi-cultural perspective results in students' more completeunderstanding of the subject (Frankenstein, 1997; Katz,1994), as well as an understanding that mathematics isdeveloping from beliefs and values from many cultures(Joseph, 1993). This rich multicultural perspective in-cludes use of culturally relevant mathematics class-</p><p>room activities that celebrate the diversity that character-izes American society.</p><p>Such a view of the teaching and learning of mathemat-ics leads students toward an understanding of ethno-mathematics. Ethnomathematics is a global view ofmathematics as a field of study which developed througha unique interplay of cultural activity. Multiculturalmathematics is about the celebration of the many culturalaspects of the school curriculum and pedagogy associ-ated with the teaching and learning of mathematics.D'Ambrosio defines ethnomathematics as "a programmewhich looks into the generation, transmission, institu-tionalization and diffusion of knowledge with emphasison the socio-cultural environment" (1990, p. 369). It is themathematics born and nurtured within a cultural system.Therefore, ethnomathematics is shaped by the history,mores, and morals of that culture and the people's indi-vidual experiences while serving their society. Successfulteaching is the quest to enable students to value, access,and utilize their ethnomathematical understandings,without narrow constraints associated with singular cul-tural viewpoints.</p><p>This perspective also includes teacher/student discoursein which a diversity of children's culturally determined,problem-solving strategies are valued (Nelson, 1993). Whenthe learning environment enhances all students' understand-ings of mathematics, and as classroom activities come to re-flect all students' cultures, the cultural nature of mathematicsbecomes a natural part of the curriculum. There are multicul-tural resources providing examples of such lessons (e.g.,Grant &amp; Sleeter, 1989; Joseph, 1990; Nelson, Joseph, &amp; Wil-liams, 1993; and Zaslavsky, 1973), but, in the end, it is theteacher who knows the students and must learn to connectthe learning situation to individual students. Belief in learn-ing as a construction process built upon previous knowledgerequires teachers to know the ethnomathematics of each stu-dent, as well as the world in general, and to provide corre-sponding learning experiences.</p><p>Teachers who base teaching episodes on this multicul-tural constructivist belief consistently expose their viewsof teaching and learning of mathematics within lessonscelebrating diversity. These teachers view the mathemat-ics curriculum as a multicultural entity complete with arich history inclusive of all cultures (Nelson, 1993).Moreover, they know that mathematicians are a group ofpeople whose diversity is so complex that no culture,gender, economic level, or ethnic group is viewed as hav-ing superior innate capabilities. Their rich learning expe-riences are demonstrative of the belief that all childrencan learn mathematics (NCTM, 1989). From such class-rooms come the sounds of children's voices whosemathematical curiosity has been deliberately triggeredby a carefully created mathematical situation. Theseteachers act on the belief that all children do learn mathe-matics through a multicultural mathematics educationprogram.</p><p>32 Equity &amp; Excellence in Education Vol. 32, No. 1</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [</p><p>Ston</p><p>y B</p><p>rook</p><p> Uni</p><p>vers</p><p>ity] </p><p>at 0</p><p>7:35</p><p> 19 </p><p>Oct</p><p>ober</p><p> 201</p><p>4 </p></li><li><p>For instance, Moore (1988) taught iteration (a repetitiveprocess), tessellations (covering of a plane with repeatedtracings of a fundamental figure), and symmetry (both ax-ial and central) through views of petroglyphs (drawings"created and carved on surfaces of caves, cliffs, and stonesby the ancestors of the American Indians" (p. 30)). Taylor,Stevens, Peregoy, and Bath (1991) taught middle-gradestudents how Native American mathematicians used tes-sellations in creative work ranging from sand paintings torugs and jewelry. When one of the students at that NativeAmerican school created a tessellation of an eagle, it wasan obvious example of the student's real-world cominginto the mathematics classroom. "The tessellated eagle...is culturally relevant, as eagles hold a special place ofhonor in Indian cultures" (p. 17).</p><p>Unfortunately, such examples are not standard fare formathematics classrooms. Typically, teachers claim that in-clusion of diverse people in the mathematics curriculum isinapplicable (Sleeter, 1989) or is achieved by inserting cul-tural names into typical word problems (Trent &amp; Gilman,1985). These teachers do not view mathematics as a multi-cultural discipline, and they do not think of mathemati-cians as being representatives from culturally diversepeople. In fact, many historical works have obscured theheritage of many mathematicians or implied that mathe-maticians of importance hailed only from Greece orEurope (Powell &amp; Frankenstein, 1.997). For example, thereexists no evidence to suggest that Euclid was not a BlackEgyptian or African mathematician (Lumpkin, 1997), yethe continues to be portrayed as Greek in many works. Togain understanding of multicultural mathematics educa-tion and apply it in terms of curriculum, pedagogy, and ac-tion, future mathematics teachers must experience aprocess of personal and professional development.</p><p>STAGE THEORY</p><p>Boyer (1990) developed an eight-stage theory about in-dividual ethnic growth, in which he outlines a person'sprogressively sophisticated multicultural view of self andsociety. These stages can be generalized to the classroomenvironment:</p><p>Celebration all learners experience a festive freedom for ac-tive participation in the larger society at a levelvoid of apprehension or negative responses</p><p>Appreciation all learners feel a positive visualization of theirprofiles because they are clearly a legitimate partof all phases of the school experience</p><p>Respect all learners...</p></li></ul>