Enhancing Mathematics Pedagogy through Cooperation between Mathematics and Mathematics Education Faculty Roozbeh Vakil and Bishnu Naraine Saint Cloud State

Enhancing Mathematics Pedagogy through Cooperation between Mathematics and

Mathematics Education Faculty

Roozbeh Vakil and

Bishnu NaraineSaint Cloud State University, MN

TEAM-Math Partnership Conference Pre-Session

September 11, 2009Tuskegee University, Alabama

Enhancing Mathematics Pedagogy through Cooperation between Mathematics and Mathematics Education Faculty

Although there is good evidence that team teaching in higher education would improve teacher preparation programs, there is not enough collaboration between college faculty for this purpose in general and between mathematics faculty in particular. In this report, a mathematics and a mathematics education faculty collaborated to team teach a methods course in mathematics. Team teaching evinced positive effects on student learning and cooperation between faculty.


“The mathematical education of teachers should be seen as a partnership between mathematics faculty and mathematics education faculty.”-- The Conference Board of the Mathematical Sciences (CBMS, 2001)


• There is good evidence that team teaching in higher education would improve teacher preparation programs (see for example, J. York-Barr et al., 2004)

• There is some collaboration between college faculty

for this purpose.

• Very difficult to find any collaboration between mathematics and mathematics education faculty.


• We will share our experiences in team teaching a methods course in mathematics.

• We hope this will help to open a constructive dialogue that will lead to increased collaboration between mathematics and mathematics education faculty.


• We will start by describing our team teaching experience.

• We will then discuss the benefits of team teaching for our students, faculty, and department.

• We will also address some of the practical challenges inherent in the team teaching model.


• TQE (Teacher Quality Enhancement) grant to team teach a methods course for secondary school pre-service teachers in mathematics during spring semester 2006.

• Funding from the grant provided released time for one of us.

• Team teaching without released time would have resulted in us teaching a total of eight classes (four each) instead of seven.


• As a public comprehensive university enrolling approximately 16, 000 students, SCSU produces roughly half of the teachers in the state. The mathematics department has 25 full-time faculty offering B.A. (non-teaching) and B.S. (teaching certified) undergraduate programs, an elementary education mathematics minor, and an M.S. (teaching) graduate program.


Co-teaching is defined as two teachers working together with groups of students and sharing

the planning, organization, delivery and assessment of instruction and physical space.


Approaches to Co-Teaching:

A. One teach, One Observe • In this model, one teacher has primary instructional responsibility while

the other gathers observational information on students in the class. It is important to remember that either teacher could take on either role.

B. One teach, One Drift • This approach is an extension of teach/observe. One teacher has primary

instructional responsibility while the other assists students with their work, monitors behavior, corrects assignments, and the like.

C. Parallel Teaching • In this model, each teacher instructs half the student group. The two

teachers are addressing the same instructional material.



D. Supplemental or Alternative Teaching • In this model, one teacher presents the lesson in standard format. The

other works with students who cannot master the material, simplifying it and otherwise adapting it to meet their needs.

E. Station Teaching • In this model, teachers divide instructional content into two parts (e.g.

vocabulary and content; new concepts and review). Each teacher instructs half the class in one of the areas; they then switch student groups so all students receive the same instruction.

F. Developmental/Extended • In this model, one teacher instructs students who have mastered the

material to be learned while the other takes students who have not mastered the material and re teaches it.



G. Team Teaching • In this model, two teachers serve as one. Both teachers are

actively involved in classroom management and instruction.

(Friend, M. & Cook, L. (l996a). Interactions: Collaboration skills

for school professionals. White Plains: Longman Publishers)

A Typical Day’s HandoutsMath 432: Professional Subject Matter for Secondary school Mathematics

Instructors: Dr. Bishnu Naraine and Dr. Roozbeh Vakil

Day N1. Today’s Activities: (a) Playing the game I have . . . Who has . . .? (b) Problem of the Day:Square corners are cut from a rectangular sheet of paper. The sides are then folded up to make a box open at the top. Find the length of one side of the square for which the box has maximum volume.

A Typical Day’s HandoutsMath 432: Professional Subject Matter for Secondary school Mathematics

Instructors: Dr. Bishnu Naraine and Dr. Roozbeh Vakil

Day N2. Reading DiscussionDr. Naraine and Dr. Vakil will jointly discuss with students the previous day’s reading assignments. 3. Writing Discussion—Problems From the ClassroomDr. Naraine and Dr. Vakil will jointly discuss with students the previous day’s writing assignments.

Problem of the Day:Finding the maximum volume of a box given a fixed area of material.

(i) We will introduce the problem and brainstorm with students about possible ways of solving it.


Approaches to the Box Problem: The Cubical Box: Removing equal-sized squares from the corners of a

rectangular sheet and folding to make an open-top box.1. Model the problem via paper cutting and folding.2. Discuss one possible solution using spreadsheets3. Discuss one possible solution using graphing calculators.4. Discuss solving the problem using Geometer’s Sketchpad.5. Discuss solving the problem using calculus.6. Generalize the problem to any cubical box.


(ii) Dr. Vakil will then lead discussion on modeling the problem via paper cutting and folding.


(iii) Dr. Naraine will discuss one possible solution using spreadsheets.


(iv) Dr. Vakil will discuss one possible solution using graphing calculators.


(v) Dr. Naraine will discuss one possible solution using the Geometer’s Sketchpad software.


Both instructors will engage the class in reflecting on the activity and how we went about solving the problem. We’ll discuss with students how we planned the activity and how we planned the sequencing of the presentation.At every stage of the activity, we will try to model effective teaching techniques.Students will be challenged to make suggestions on how to improve on the presentationWhat would they have done differently and why?

Benefits of Team Teaching

Benefits to StudentsOne of the principal advantages of team teaching a topic . . . is that hearing the

discussion between the two professors gives permission and encouragement to the rest of

the class to engage in discussion. (AD)


Benefits to StudentsSometimes I find it too easy to adopt the view of one speaker, rather than thinking

critically about what the speaker is hearing and posing questions about the topic. Having two professors provided alternate views and

explanations, along with the questioning necessary to understand the activity.(BS)


Benefits to StudentsAs usual, Roozbeh presented the more

formal, mathematical side while Bishnu presented the more practical and pragmatic. It was a nice balance. The two perspectives

helped me to better understand the methods and the concepts. (MR)


Benefits to StudentsAs both instructors took time to talk

individually to each group, we were provided with alternate ideas, methods, and

approaches. (AD)


Benefits to StudentsWhen one teacher was presenting a solution the other would add little things here and there that he felt was important, again adding to the depth of our understanding.

(NS)

ChallengesPlanning: We came up with two levels of planning, long-term and short-term planning.

In addition, we negotiated content, sequencing, roles, instructional design,

teaching style.

Short-term planning comprised our weekly preparation for class. Each week we

met for two hours to prepare the materials, and for each class session we met for

one hour to discuss the class meeting, final touch of the materials, deal with

technical issues, and negotiate the role each of us would play in that day. Long-

term planning addressed our overall strategy to design and implement our lesson

plans to reflect our objectives.

Challenges

Assessment was dealt with upfront. If the two gradings were reasonably close, the reporting grade was the average. Otherwise, we negotiated our differences.

Negative Aspects of Co-Teaching

• Confusion about whom to go to• Grading/Homework concerns• Inequitable division of instructional time• Seemed disorganized• Too many interruptions• Just prefer having one instructor• Overwhelming—too much information

Positive Aspects of Co-Teaching

• Two perspectives/two opinions• Two styles of instruction• Accessibility of instructors• Teachers build off each other/Get more information• Modeling collaboration• Smaller groups• Time seems to go faster• Better discussions• Developed community/positive learning environment

Documents

Enhancing Mathematics Pedagogy through Cooperation between Mathematics and Mathematics Education Faculty Roozbeh Vakil and Bishnu Naraine Saint Cloud State