Lifelong Learning: Mathematics Faculty Work to Improve Their Practice

1. Lifelong Learning:Mathematics Faculty Work to Improve Their Practice Julie Cwikla, Ph.D. Department of Mathematics University of Southern Mississippi Gulf Coast Research funded by the National Science Foundation CAREER Program #0238319

2. Universities and teachers’ colleges nationally are concerned about elementary mathematics teacher preparation. These students in general are not exceptionally strong mathematically. Ball, 1990; Post et al, 1998; Silver & Stein, 1996

3. Typical Student Population • In most cases, PST did not learn K-12 mathematics in a standards-based environment • Future teachers expected to facilitate a reform-minded mathematics classroom • How do teacher educators fight the machine?

4. Task of Teacher Educators • Help PST shift views about mathematics learning as well as extend and/or correct their understanding of the content. • Foster the development of the important knowledge and skills to better serve K-8 students’ learning Darling-Hammond, Wise, & Klein, 1999.

5. University Faculty • Views of teaching & learning range from transmission to student-centered construction (Samuelowicz & Bain, 1992). • Long-term retention for undergrad student develops from student-centered question generating exercises (King, 1992). • Interview study of university students supports faculty/student interactions – ranked as 1 of 6 most important classroom features (Clarke, 1995). • “Interactions with students” one of most stressful features of their work (Gmelch, Wilke, & Lovrich, 1996).

6. Faculty Professional Development • Reform must be driven by a faculty member’s individual “pedagogical dissatisfaction” (Gess-Newsome, Southerland, Johnston, & Woodbury, 2003, p. 763) • Faculty members in “hard sciences” less receptive to teaching improvement initiatives (Braxton, 1995) • Naturally develop as reflective practitioners through feedback from student, colleagues and consultants. (Paulsen & Feldman, 1995) • Kranier (2001) also stressed the importance of a “network of critical friends” (p. 289)

7. Wenger (1998) • A Community of Practice can be used to characterize a professional group of learners with a common goal such as educating young people, a set of norms, expectations, and standards, and a method or manner to systematically share information about their practice.

8. COP Model – 4 Dimensions • Form group identity - norms of interaction • Navigating fault lines • Negotiating the essential tension • Communal responsibility for individual growth. • Beginning, evolving, and mature. Grossman, Wineburg, and Woolworth (2001)

9. Major Research Goals • Get a clearer understanding of how mathematics faculty reflect upon and improve their practices with various types of professional experiences and support • Investigate what and how preservice teachers are learning about mathematics, mathematics pedagogy, and the national mathematics reform

10. Five Year Longitudinal Study • Funded by the NSF CAREER Program • “Investigating mathematics teacher preparation across five institutions of higher learning.” • Following PST cohort through 5 institutions into their own classroom • Coupled with faculty PD at each institution

11. Context & Participants • Greenwood University (GU) enrolls about 14,000 undergraduate students • Over 70% transfer from community colleges (CCs) • Content courses often taken at CCs • Participants: 18 Mathematics faculty from 5 IHL

12. Presentation Data Selection • College Algebra results used in COP • Classroom Video Use • Reflection • Peer Critique • “My Future Classroom” Preservice Teachers’ Classroom Vision

13. 1. College Algebra • 923 College Algebra students administered the DDA - Demographic, Disposition, and Assessment • Views of teaching and learning -“Learners benefit more if they solve a problem on their own, than if they follow someone else’s method” (score 18-72) • Assessment items multiple choice & open ended tasks, from the 8th grade TIMSS-R released items

14. Comparison Ed Majors vs. Non • Independent samples t-tests - two groups did NOT differ on their performance on • Multiple Choice t (888) = .76, p > .05 • Open Ended t (722) = -.94, p > .05 • Education majors scored higher on the 18 disposition items t (722) = -4.20, p < .001 • Endorse more student-centered attitudes than non majors

15. Student-Centered = Higher Perf • Regardless of major: • Participants who endorsed more student-centered tended to perform better on BOTH multiple choice and open-ended mathematics problems • Pattern particularly the case for education majors

16. Student-Centered = Higher Perf • Regardless of major: • Participants who endorsed more student-centered tended to perform better on BOTH multiple choice and open-ended mathematics problems • Pattern particularly the case for education majors

17. Education Majors More Consistent • Consistency across similar belief items • Education majors appeared to be developing a more consistent philosophy on pedagogic processes than their Non-Ed peers

18. Item 1 - Fractions & Number Sense

19. Item 1 - Fractions & Number Sense

20. Item 2 - Spatial Relations How many of the shaded right triangles are needed to exactly cover the surface of the rectangle? 2 cm 4 cm 3 cm 6cm

21. Item 2 - Spatial Relations How many of the shaded right triangles are needed to exactly cover the surface of the rectangle? 2 cm 4 cm 3 cm 6cm

22. 2. Classroom Video Use • Faculty member provided with CD copy of their classroom video • 15 Reflection questions about practice • What surprised you about your practice? • What might another mathematics educator learn from watching your classroom? • 6 Peer evaluation questions • Clips shared, peers offer feedback, suggestions

23. 2a. Reflection on Own Practice • University faculty members’ views of teaching and learning scores were indicative of level of reflection on own teaching. • Sample responses from least to most reflective.

24. “What surprised you about your practice?” • I didn’t realize how much I talk with my hands! (Olivia,47,G2) • My lesson was too cut and dry. I also made some stupid mistakes that confused the students (Fran, 63, G3-O). • I did not learn this but I do know that in the ideal situation there should be more student participation (Betty, 39, G3). • I am really quick to ask “Are there any questions?” and quickly say “OK” and progress with the lesson (Lisa, 60, G1).

25. “What immediate changes might you make to your teaching practice?” • I didn’t notice anything I would improve (Allison, 38, G3). • I always hope to do a better job next semester. Any changes that I make are usually minor (Betty, 39, G3). • I am going to begin incorporating problems that students must work together in small groups to solve at some point during my lecture (Anita, 46, G2). • I plan to spend more time prior to the class planning ways of providing students opportunities for small group interaction (Elaine, 60, G1).

26. b. Making Practice Public • Clips from 9 classes shared with the COP • Coded 3 groups G1, G2, and G3 • All provided non-anonymous feedback

27. Video Feedback – 6 Prompts • Briefly describe the learning environment in this classroom. • What are these students learning, how do you know? • What have you learned from watching this video that you might try in your own class? • How and in what ways does this lesson challenge the students’ thinking? Be specific. • As a peer what advice would you give this teacher about gauging students’ understanding of the lesson? • What could this teacher have done differently to further engage her students in the content/lesson?

29. Environment Analysis • More diverse comments from Groups 1 and 2 • Agreement about what is traditional lecture format • Group 3 – noticed little difference between G1 & G2 • Groups 1, 2 used “cooperative,” “students interacting,” and “individual attention” to describe Group 1 • Group 3 respondents’ comments were vague, no vivid description of what was occurring

30. 3. “My Future Classroom” N=509 • In what ways do future teachers envision their mathematics classroom and teaching time? • How does this vision change over time and throughout the progress in their teacher education programs?

31. Classroom Description Task • As a future elementary teacher please imagine what your future classroom will be like and specifically what the mathematics learning time will look like. Describe the setting, what the students will be doing, what you will be doing, what kinds of materials you might have in the classroom, what kinds of mathematical tasks or activities the students will be working on, and anything else you think is important as you visualize your future role as an elementary teacher.

33. Highest Frequency Codes • Student groups, group working • Fun • Centers • Manipulatives • Hands on • Order • Bulletin Board • Worksheet

34. Omissions for Discussion • What was NOT included? • NCTM – 0 • Standards – 1 • Connections – 0 • Thinking Tools – 0 • Constructivism – 0 • Drill - 4

35. Conclusions and Discussion • Student assessment data – Accreditation • What are they learning? Current/changing beliefs? • Content knowledge? Pedagogical content knowledge? • Classroom video data • What is actually going on? • What does good teaching look like? • How are my peers teaching this course? • Students’ future classroom vision • “What will I do when I grow up? • What impact is your program having on the answer?

36. Thank you.http://ocean.otr.usm.edu/~w362384/http://www.mathematicseducation.org/ Julie Cwikla, Ph.D. Associate Professor Associate Director of the Center for Creative Opportunities in Science and Technology Department of Mathematics University of Southern Mississippi Gulf Coast Long Beach, MS