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

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

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?

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.

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).

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)

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.

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)

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

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

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

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

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

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

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

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

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

Item 1 - Fractions & Number Sense

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 %

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

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 %

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

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.

“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).

“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).

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

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?

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

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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

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

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?

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.

Classroom Description Themes

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

Omissions for Discussion What was NOT included?

NCTM – 0 Standards – 1 Connections – 0 Thinking Tools – 0 Constructivism – 0 Drill - 4

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?

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