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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
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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
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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?
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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.
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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).
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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)
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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.
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COP Model – 4 Dimensions
(1) Form group identity - norms of interaction(2) Navigating fault lines(3) Negotiating the essential tension(4) Communal responsibility for individual
growth.
Beginning, evolving, and mature. Grossman, Wineburg, and Woolworth
(2001)
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Major Research Goals1. Get a clearer understanding of how mathematics
faculty reflect upon and improve their practices with various types of professional experiences and support
2. Investigate what and how preservice teachers are learning about mathematics, mathematics pedagogy, and the national mathematics reform
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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
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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
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Presentation Data Selection
1. College Algebra results used in COP
2. Classroom Video Use Reflection Peer Critique
3. “My Future Classroom” Preservice Teachers’ Classroom Vision
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1. College Algebra1. 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
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Comparison Ed Majors vs. NonComparison 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
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Student-Centered = Higher PerfStudent-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
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Student-Centered = Higher PerfStudent-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
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Education Majors More ConsistentEducation 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
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Item 1 - Fractions & Number Sense
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Item 1 - Fractions & Number Sense
Percentage of Students with Correct Response
Education Majors All College Algebra (N=730) U.S. 8th Graders on TIMSS-R
51%
51 %
49 %
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Item 2 - Spatial RelationsHow many of the shaded right triangles are needed to exactly cover the surface of the rectangle?
2 cm 4 cm
3 cm 6cm
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Item 2 - Spatial RelationsHow many of the shaded right triangles are needed to exactly cover the surface of the rectangle?
2 cm 4 cm
3 cm 6cm
Percentage of Students with Correct Response
Education Majors All College Algebra (N=730) U.S. 8th Graders on TIMSS-R
30%
41 %
36 %
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2. Classroom Video Use2. 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
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2a. Reflection on Own Practice2a. 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.
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“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).
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“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).
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b. Making Practice Publicb. Making Practice Public Clips from 9 classes shared with the COP Coded 3 groups G1, G2, and G3 All provided non-anonymous feedback
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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?
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Classroom Being Observed G1 – Standards Based Methods with
Minimal Lecture G2 – Lecture with Some Standards Based
Methods G3 – Traditional Lecture Format
G1
Students had ample opportunity to be engaged in lesson through individual class work and open discussion.
Students were totally engaged After group work is completed, have some
or all groups share results using overhead calculator.
Continue using her questioning techniques – this allows her to provide immediate feedback
Have students work in groups and interact with individual groups.
Maybe students could work in “pairs” then some could share for a change of pace
Ask them “Why?” Ask your students to explain and tell you
what to do next Call on the students by name when
asking questions- Then wait for them to answer.
Talk more directly to them - not so much to the board.
Be sure to ask probing questions about the details of the problem presented. Relate algebraic steps to similar steps in an arithmetic problem. Make connections.
Hopefully students are “thinking” as they take notes but they could be rotely copying what is presented.
Ask students to share answers after question is presented
Ask your students questions. Let them tell you how to solve or have them come to the board and solve.
Have the students tell you what to do next. . . . Use manipulatives, relate to real world
G2
Wonderful job! You have inspired me to give group work a concentrated effort!
The students were very engaged. Even when she wasn’t helping one, they were helping each other!
She did a great job. She even noticed one student who was not at the right place and helped him get back on track.
Allow more time for student questions. Make it a point to ask them leading questions if they say they have none.
Ask leading questions that force students to answer. This way the teacher will know if students are really learning.
Create opportunity for interaction
Tea
cher
Gro
up P
rovi
ding
Fee
dbac
k
G3
No comments were made by any of the G3 participants about the G1 classes and what they could do to improve.
She asked questions. She made them think about what points of a graph really meant.
I think a student here has a very positive experience
It seemed to be a formula driven assignment. I heard “b over a”, etc.
I think for a class of that size, the students were extremely involved in the lesson
Look at the students more- but this was a very short clip
Ask more questions of the class She continued to involve her students-
good job
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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
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3. “My Future Classroom” N=5093. “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?
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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.
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Classroom Description Themes
050
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calc
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ent
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Highest Frequency Codes Student groups, group working Fun Centers Manipulatives Hands on Order Bulletin Board Worksheet
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Omissions for Discussion What was NOT included?
NCTM – 0 Standards – 1 Connections – 0 Thinking Tools – 0 Constructivism – 0 Drill - 4
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Conclusions and DiscussionConclusions and Discussion 1) Student assessment data – Accreditation
What are they learning? Current/changing beliefs? Content knowledge? Pedagogical content knowledge?
2) Classroom video data What is actually going on? What does good teaching look like? How are my peers teaching this course?
3) Students’ future classroom vision “What will I do when I grow up? What impact is your program having on the answer?
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Thank you.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