A Virtual Master’s Degree Program for Secondary Mathematics Teachers

1. A Virtual Master’s Degree Program for Secondary Mathematics Teachers Presented by Ozlem Korkmaz, University of Wyoming 8TH Annual Math & Science Teacher’s Conference at Casper College, 2010

2. Distance Education around the world

3. United States of America

4. 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.

5. 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.

6. 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.

7. 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.

8. Goals for Math TLC

9. The goals of the master’s program

10. Develop a shared vision of mathematics as a culturally rich subject in which K-12 mathematics proficiency is defined by shared community standards

11. 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).

12. 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.

13. 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.

14. Develop teachers’ knowledge, skills and disposition to effectively teach mathematics in a culturally diverse classroom

15. What is Culturally Responsive Teaching (CRT)?

16. 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. 

17. 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).)

18. 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.

19. 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.

20. 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

21. Some of the Principals of CRT There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability. There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability. Communication of High Expectations

22. Principals of CRT There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability. Instruction is designed to promote student engagement by requiring that students play an active role in crafting curriculum and developing learning activities. Active Teaching Methods

23. Principals of CRT There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability. Within an active teaching environment, the teacher's role is one of guide, mediator, and knowledgeable consultant, as well as instructor. Teacher as facilitator

24. Principals of CRT There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability. There is an ongoing participation in dialogue with students, parents, and community members on issues important to them, along with the inclusion of these individuals and issues in classroom curriculum and activities. Inclusion of Culturally and Linguistically Diverse Students

25. Principals of CRT There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability. To maximize learning opportunities, teachers gain knowledge of the cultures represented in their classrooms and translate this knowledge into instructional practice. Cultural Sensitivity

26. Extend teachers’ content knowledge beyond the content they customarily teach to students

27. Polygons on earth

28. Regular Hexagon in chemistry

29. Snow flakes- Regular Hexagon

30. Honey comb-Regular Hexagon

32. 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?

33. Definition • Let where be a set of points in the plane such that . • The union of the line segments is an n-sided polygon whose vertices are and whose edges are the line segments .

34. A student might ask… • Although the definition admit , what if n=1, n=2? How can it be called and represented?

35. Response… In spherical geometry, it is possible to have a two sided polygon, namely digon

36. Spherical triangle

37. Euclid’s Postulates on the Sphere • Postulate 1: Two points determine a unique line • Is this postulate valid in spherical geometry?

38. 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.

39. 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.

40. 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.

41. 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).

42. 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.

43. Empower participants as lifelong professional learners who regularly reflect on themselves, students, and community context to improve teacher practice and student learning

44. Action Research Project (ARP) Reflection Planning Action Data Collection Data Interpretation

45. ARP Example

46. Courses & Curricula • The Math TLC provides 30- credit hour, 2-year master’s program, which involves face-to-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 K-12 students.

47. Mathematics Courses

48. Mathematics Education Courses

49. 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

50. 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.