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Presented by Ozlem Korkmaz, University of Wyoming 8TH Annual Math & Science Teacher’s Conference at Casper College, 2010 Description of the Program • The virtual master’s degree program, offered jointly by the University of Northern Colorado and the University of Wyoming, started in the summer of 2009 for secondary mathematics teachers to improve mathematics achievement in secondary education in the Rocky Mountain region. Vision • Increase student understanding of mathematics by promoting a master’s degree program for 7-12 grade mathematics teachers, which aims at developing highly qualified, culturally competent, and pedagogically effective mathematics teachers in Colorado and Wyoming. Why virtual? • The Rocky Mountain region is a vast, sparsely populated, and rural region where teachers lack access to professional development programs (PD). • In-service teachers are not able to leave their positions to attend PD. • The number of faculty to provide PD in such a vast region is limited. • By means of alternative delivery formats, we make the master’s degree accessible to teachers in their home region. Why important? • Online teacher professional development programs are gaining an important place in higher education as a means to enhance students’ achievement in schools • Online professional development programs (OPD) for teachers are also increasing as the rapid development of technology allows distance education to grow. • Virtual or online degree programs provide teachers with flexibility without the constraints of geographical borders or time. Goals for Math TLC Develop a shared vision of mathematics as a culturally rich subject in which K-12 mathematics proficiency is defined by shared community standards Expand mathematical content knowledge in ways that broaden exposure to mathematical ideas and deepen understanding of topics that extend K-12 mathematics content Increase pedagogical content knowledge by examination of how students think and learn about mathematics. Empower participants as lifelong professional learners who regularly reflect on themselves, students, and community context to improve teacher practice and student learning Produce a research-based and tested model for master teacher development based on the above goals that improves mathematical achievement for all students. The goals of the master’s program Extend teachers’ content knowledge beyond the content they customarily teach to students Engage teachers in actively building their pedagogical content knowledge (Shulman, 1987), enabling them to enlarge their repertoire of pedagogical methods, skills and knowledge congruent with standards (NCTM, 2000; CDE, 2007; WDE, 2003). Support teachers to evaluate and improve their teaching practice by regularly engaging in lesson experiments and small-scale action research projects. Develop teachers’ knowledge, skills and disposition to effectively teach math in a culturally diverse classroom. Develop a shared vision of mathematics as a culturally rich subject in which K-12 mathematics proficiency is defined by shared community standards Mathematics as a culturally rich subject • Mathematics is constructed within a cultural context. • Stigler (1989) says, “Mathematics itself consists not only symbolic technologies but also of other cultural products-such as values, beliefs, and attitudes […] Educators should teach the values of mathematical culture, not because it will help children learn mathematics, but because values are part of the mathematics that children should learn.” (p. 369). Mathematics as a culturally rich subject • In ancient times, in Egypt, farmers along the Nile river needed Geometry. The Nile would flood the land and destroy the farm areas each year. When the waters receded, the boundaries had to be redefined by measuring fields. • The Egyptians (about 1800 BC) had accurately determined the volume of the frustum of a square pyramid. MCRS (Cont’…) • Babylonians’ (2000-1600 BC) geometry was empirical, and limited to those properties physically observable. Through measurements they approximated the ratio of the circumference of a circle to its diameter to be 3. • The Maya number system was a base twenty system. One of the Maya’s calendar, Tzolkin, composed of 260 days, 13 months of 20 days. Develop teachers’ knowledge, skills and disposition to effectively teach mathematics in a culturally diverse classroom What is Culturally Responsive Teaching (CRT)? Culturally Responsive Teaching (CRT) Gay (2000) defines culturally responsive teaching as using the cultural knowledge, prior experiences, and performance styles of diverse students to make learning more appropriate and effective for them; it teaches to and through the strengths of these students. A learning experience drawn from a legend of Maori people in New Zealand In the South Island [of New Zealand] there is a lake whose waters, by day and by night, rise and fall. The Maori people know that the pulsing of the water comes from the beating of a giant’s heart, the heart of Matau who was burnt by the brave Matakauri. The waters of Lake Wakatipu rise and fall about every five minutes. If the lake was formed about 1000 years ago, how many times has Matau’s heart beat since then? If Matau’s heart beat once every three minutes, how many times would Lake Wakapitu have risen and fallen over the last 100 years? (Heays, Copson, & Mahon, 1994, p.8 as cited by Averill, Anderson, Easton, Te Maro, Smith, and Hynds (2009).) Literature suggests • Developing a knowledge base about cultural diversity • Learning mathematical content from ethnically and culturally diverse origins • Participating in and building a caring community of learners-this includes developing ways to calibrate teacher intentions with student perceptions. Literature suggests (Cont’…) • Seeing personal communication patterns and using that awareness to learn to communicate effectively with diverse students. • Responding supportively to socio-economic, cultural, and ethnic diversity in the delivery of instruction. Characteristics described by Gay (2000) • It acknowledges the legitimacy of the cultural heritages of different ethnic groups, both as legacies that affect students' dispositions, attitudes, and approaches to learning and as worthy content to be taught in the formal curriculum. • It builds bridges of meaningfulness between home and school experiences as well as between academic abstractions and lived sociocultural realities. • It uses a wide variety of instructional strategies that are connected to different learning styles. • It teaches students to know and praise their own and each others' cultural heritages. • It incorporates multicultural information, resources, and materials in all the subjects and skills routinely taught in schools Some of the Principals of CRT • Communication of High Expectations There are consistent messages, both There are from consistent the teacherfrom andboth the the messages, whole teacherschool, and thethat whole school, that students will students will succeed,based basedupon upon succeed, genuine respect for for students genuine respect and belief in student students and belief capability. in student capability. Principals of CRT • Active Teaching Methods Instruction is designed promote There are to consistent student engagement messages, from both the by requiring that teacher and the whole school, thatplay students students an will succeed, based active role in upon genuine respect for students crafting curriculum and belief in student and developing capability. learning activities. Principals of CRT • Teacher as facilitator Within an active teaching There are consistent environment, messages, fromthe both the teacher's rolethe is one teacher and whole school, that students will of guide, mediator, succeed, based upon and knowledgeable genuine respect students consultant, as for well as and belief in student instructor. capability. Principals of CRT • Inclusion of Culturally and Linguistically Diverse Students There is an ongoing participation in dialogue with students, parents, There are consistent and community messages, from both the teacher and on theissues whole school, members that students succeed, important to will them, based respect alongupon withgenuine the for students and belief in inclusion of these student capability. individuals and issues in classroom curriculum and activities. Principals of CRT • Cultural Sensitivity To maximize learning opportunities, teachers gainconsistent There are knowledge of theboth the messages, from teacher andrepresented the whole school, cultures that students will succeed, in their classrooms based upon genuine and translate this respect for students and belief in knowledge into student capability. instructional practice. Extend teachers’ content knowledge beyond the content they customarily teach to students Polygons on earth Regular Hexagon in chemistry Snow flakes- Regular Hexagon Honey comb-Regular Hexagon The name of polygon N= 3 N=4 N=5 N=6 The number of diagonals passing by one vertex The number of diagonals The number of triangles formed by drawing all diagonals passing through one vertex What is the total sum of the measure of the interior angles? What is the total sum of the measure of the exterior angles? For n-sided polygon • Find the number of diagonals passing by one vertex • Find the formula that determines the number of diagonals. • Determine the number of triangles formed by drawing all diagonals passing through one vertex • What is the total sum of the measure of the interior angles? • What is the total sum of the measure of the exterior angles? Definition • Let v 0 , v1, v 2 ,...,v n where n 3 be a set of points in the plane such that v0 vn . • The union of the line segments v0 v1, v1v2 ,...,vn1vn is an n-sided polygon whose vertices are v 0 , v1 , v2 ,...,vn and whose edges are the line segments v0 v 2 ,...,vn1vn . 1 , v1v A student might ask… • Although the definition admit n 3 , what if n=1, n=2? How can it be called and represented? Response… In spherical geometry, it is possible to have a two sided polygon, namely digon Spherical triangle Euclid’s Postulates on the Sphere • Postulate 1: Two points determine a unique line • Is this postulate valid in spherical geometry? Spherical Geometry Terms • Polar points are the end points of the sphere’s diameter (called as antipodal) • Straight lines are great circles; that is circles that contain any pair of polar points. • A segment (arc segment) on a sphere is the shortest distance between two points. • A segment is always part of a great circle, and is also called geodesic. Response to the question • If two points are antipodal, then there are an infinite number of straight lines containing these two points, such as all the lines of longitude. Euclid’s first postulate is therefore not valid in spherical geometry. Euclid’s parallel postulate • Given a line L and a point P not on L, there exists a unique line though P parallel to L. • How would you re-word this postulate so that it is true for spherical geometry? • Given a line G and a point P not on G, every line through P intersects G; that is, no line through P is parallel to G. Engage teachers in actively building their pedagogical content knowledge (Shulman, 1987), enabling them to enlarge their repertoire of pedagogical methods, skills and knowledge congruent with standards (NCTM, 2000; CDE, 2007; WDE, 2003). Cone Project • Teacher participants explored geometry on the cone in groups of three. • Teacher participants explored what interested them, wrote a report, and presented their findings to their classmates. • Engaging in such a project will enable them to apply the same pedagogy in their practice. Empower participants as lifelong professional learners who regularly reflect on themselves, students, and community context to improve teacher practice and student learning Action Research Project (ARP) ARP Example Courses & Curricula • The Math TLC provides 30- credit hour, 2year master’s program, which involves faceto-face and online courses. • Of 30 credits, 18 hours mathematics and 12 hours are mathematics education courses. • All courses address NCTM principals and standards: teachers experience as learners the kinds of instruction recommended for K12 students. Mathematics Courses Mathematics Education Courses Research-based course design characteristics • Employ a research-based instructional design, modeling learning strategies that promote effective classroom learning and teaching, and that teachers can also use with their students. (Bybee, 2006) • Build new knowledge upon teachers’ prior knowledge. • Support learning through interaction among teachers about mathematical ideas Research-based course design characteristics (Cont’…) • Convey clear purpose and outcomes. (NRC, 1999, 2005). • Incorporate a variety of learning activities to engage teachers, appeal to different learning styles, and explore the cultural capital of teachers and the students they teach (Bourdieu, 1986; Civil, 2002; Kuhn, 2005; NRC, 2000). • Assess teacher understanding frequently. Research-based course design characteristics (Cont’…) • Situate learning within meaningful, relevant contexts (e.g., action research; Nentwig & Waddington, 2005). • Cultivate a safe, non-threatening, low-risk environment for teachers to express new ideas and try out new approaches, such as incorporating collaborative learning strategies within course designs. Questions?? References • Averill, Anderson, Easton, Maro, Smith, & Hynds (2009). Culturally responsive teaching of mathematics: Three models from linked studies. Journal for Research in Mathematics Education, 40(2), 157186. • Bishop, A. J. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19(2), 179-191. Retrieved from http://www.jstor.org/stable/3482573?seq=2 • Bishop, A. (1991). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht: Kluwer • Ross, S. W., (2000). Non-Euclidean Geometry. Retrieved from http://library.umaine.edu/theses/pdf/RossSW2000.pdf • Stigler, J. W. (1989). Review: Mathematics meets culture. Journal for Research in Mathematics Education. 20(4), 367-370. Retrieved from http://www.jstor.org/stable/pdfplus/749442.pdf • http://www.intime.uni.edu/multiculture/curriculum/culture/Teaching.htm • THANK YOU