Saad El-ZanatiCynthia LangrallWendy O’Hanlon

Ryan BungeIllinois State University

Teacher-Scholars: Research Experiences for Pre-Service and In-

Service Secondary Mathematics Teachers

Supported by Division of Undergraduate Education Award # A0633335

Teacher-Scholars . . .

• are teacher education graduates who have experienced scholarship in mathematics

• have an understanding of what mathematics is and how it is discovered or created

• have the confidence and ability to engage students in thinking about rich mathematical ideas

Why?

• Majority of undergraduate mathematics majors at Illinois State are in secondary education.

• Talented hard-working students who want to be teachers.

Rationale

• National need for highly-qualified mathematics teachers

• Call for undergraduate experiences in which students “participate in original, supervised research”

(NRC, 1999, p. 6)

Program History

• Spring 2004: 9 students (6 Sec. Ed.) – Two research articles.

• Spring 2005: 15 students (11 Sec. Ed.) --Two research articles.

• Spring 2006: 9 students (8 Sec. Ed.) --Follow-up work has led to a successful student-faculty collaboration.

• Three Applications to NSF (El-Zanati & McCrone) --The third was funded!

Prior to Funding

• Set up an ISU Foundation Account (within Math Dept Account), with purpose of supporting undergraduate research.

• Recognized students at Departmental Awards Ceremony as “Teacher-Scholars” with a certificate & a small amount of cash!

• Solicited support from chair & colleagues

Funded-Program Overview

• Year-long

• Two junior/senior-level capstone courses: Introduction to Undergraduate Research in Mathematics (spring), Undergraduate Research in Mathematics II (fall)

• Summer component

What We’ve Done

Year 1 – Course I (Spring 2007)

• 19 participants, 15 were secondary mathematics education majors

• Course topics: proof techniques, some history of mathematics, Exercises that lead to open problems in number theory, graph theory, and combinatorial design theory

• Three groups were able to obtain original results (patterns that apply to an infinite number of cases)

Course Components:

• Open-ended assignments• Regular homework assignments• Take-home tests (including an infamous

midterm)• Group research projects• Group teaching modules• Poster presentations at ISU Undergraduate

Research Symposium

Student Research Topics

• Scheduling (e.g., Social Golfer Problem)• Graph Designs (e.g., Graph

Decompositions & Graph Factorizations)• Graph labelings (Various labelings &

their design applications)• Graph Coloring• Vector Space Partitions

Social Golfer Problem:

• Twelve friends play golf in groups of four. How many rounds must they play in order to ensure that each person plays with everyone else at least once?

• Fix the number of days and come up with a “fair” schedule.

• Vary the question. Come up with your own questions.

Vector Space Partition Problem:

• For what values of x and y can you “partition” (Z2)6 into x subspaces of dim 2 and y subspaces of dim 3 that share only the zero vector?

• For what values of x and y can you “partition” 2(Z2)5 into x subspaces of dim 2 and y subspaces of dim 3 that share only the zero vector?

• Vary the question. Come up with your own questions.

(2)4

Summer Component

• Proposed: Three two-day meetings at three week intervals. Rationale: maintaining students’ interest in program.

• Reality: Unable to give sufficient incentive for students to return. Five students returned for a one day meeting.

Year 1 – Course II (Fall 2007)

• 9 students returned, 8 secondary education majors (all had made progress on a project)

• Focus on finalizing and writing results from spring research (three research articles)

• Development of teaching modules

Research Articles from 2007 TSP:

• G. Blair, D. Bowman, S. I. El-Zanati, S. Hlad, M. Priban, K. Sebesta, On Cyclic (Cm+e)-designs, Ars Combinatoria, to appear.

• E. Butzen, S. I. El-Zanati, A. Modica, R. Schrishuhn, On rho-labeling up to ten vertex-disjoint C4x+1, J. Comb. Math. & Comb. Computing, to appear.

• S. I. El-Zanati, B. Frank, B. Renziger, On gamma-labeling the intersection graph of odd cycles, to be submitted.

Year Two - Course I (Spring 2008)

• Taught by Olcay Akman (statistician)• Emphasis on mathematical & statistical

modeling• 16 students (13 in Secondary Ed.)• Data analysis from an ongoing ecology

research project• 1 research article accepted

Year 2-Course II (Fall 2008)

• One Summer Meeting • Only 3 students in Course II• Course II covered NEW topics• Another research article• No room to fit a second “elective” course in

students’ schedules

Year 3 – Course I (Spring 2009)

Course I taught by Mike PlantholtOne Week (paid) Summer session using

REU Site model.Eliminated need for 2nd course.Up to four research articles in progress.

Related Project –– REU Site:Mathematics Research Experience for Pre-service and In-service Teachers

• 8 pre-service (talented students chosen from across the country)

• 4 in-service teachers (Central Illinois)• Eight-week duration (starting 1st full week in

June). Six hours a day, five days a week• Topics similar to those in research course• Bi-weekly seminars with focus on mathematics

education issues• Last two years: Work with 3rd-5th graders—

Generalization & Representation.

REU Program Outcomes

• Worked well as a community of teacher-scholars

• Research progress in both mathematics and mathematics education

• Development of teaching modules / lessons• Follow-up reunions (or REUnions!)• Several research articles & presentations

Research on Impact of Teacher-Scholar Program & REU Programs

How does the Teacher-Scholar Program & REU enhance secondary education majors’ potential as future teachers?

More specifically, how does participation affect students …

• understanding of mathematics?• beliefs about the nature of mathematics

and the teaching & learning of mathematics?

• confidence and excitement to do mathematics?

• understanding of pedagogical content knowledge?

Data Sources

Assessment of content knowledge Beliefs surveys Interviews Reflective writings

Belief Surveys

1 - strongly agree with the statement.2 - mostly agree with the statement.3 – undecided or neutral about the

statement.4 - disagree with the statement.5 - strongly disagree with the

statement.

Beliefs about Mathematics

Q10: I can invent my own mathematics to describe patterns that I see.

Q18: Mathematics involves a great deal of creativity.

Beliefs about Learning & Teaching

Q2: The teacher should provide verification for mathematical arguments given in class rather than expecting students to do so.

Q42: Teachers should teach mathematics as an integrated whole so that students will become aware of the connections among various mathematical ideas.

Personal Learning Teaching Total

Procedural vs.

Understanding

NSB SB----

SB

DiscoveryN

NSB SB SB

Problem Solving

SB SB SB SB

Reasoning & Proof

SB NSB SB SB

ConnectionsSB NSB SB SB

PerseveranceSB SB SB SB

Communication

SB NSB SB NSB

ACESB SB SB SB

11

11 2 2

PersonalPersonal

Te

achin

gT

each

ing

ACEACE

Con

nect

ions

Con

nect

ions

Communication

Communication

Problem Solving

Problem Solving

Perse

vera

nce

Perse

vera

nce

Rea

soni

ng &

Rea

soni

ng &

Pro

ofP

roof

Dis

cove

ryD

isco

very

Student Reflection

“This program has taught me about what it is that mathematicians actually do. I’ve learned that they do not simply solve equation after equation, but that it has much more to do with finding patterns, asking questions, and persevering. If I had never had this opportunity, I would never have known for myself what mathematicians do and what it is like to truly discover mathematics, let alone show that to my students. This program has enabled me to pass this knowledge and passion to my students. I KNOW this program will make me a better teacher than I would have been otherwise.”

- Leia, pre-service teacher

Next Steps

• Impact on pedagogical content knowledge

• What is the influence of the Teacher-Scholar and REU Programs on teacher practice?

• Testing other innovative programs

Would this Model Work Elsewhere?

What is needed:Relatively large cohort of pre-service teachersMathematicians with experience with undergraduate

research.Mathematicians & Mathematics Educators that get

along well.Faculty & Administrators that value this kind of work.

Alternatives:A capstone course (or courses) co-taught by

Mathematicians & Math Educators.A mandatory Research Seminar followed by an

Undergraduate Research course.

For More Information . . .

Teacher-Scholar Program:http://www.math.ilstu.edu/Teacher_Scholar_Program/index.html

REU Site:http://www.math.ilstu.edu/reu/

It’s a pleasure to be with you!

THANK YOU!