A reflective project for pre-service teachers in university mathematics courses

Dr. Angie Hodge

North Dakota State University

My role in teacher prep Joint appointment

Mathematics (55%) Teacher education (45%)

Teach mathematics courses

Teach secondary methods courses

Serve as a liaison between departments

Background Pre-service secondary mathematics

teachers (PSMTs) complete a significant portion of their coursework in mathematics departments.

Background The Committee on Undergraduate Program in

Mathematics (CUPM, 2004) recommends that 9-12 teachers:

Learn to make appropriate connections between the advanced mathematics they are learning and the secondary mathematics they will be teaching. They should be helped to reach this understanding in courses throughout the curriculum and through a senior-level experience that makes these connections explicit. (p. 52)

Background Pre-service secondary mathematics teachers

(PSMTs) do not always see these connections (Staples & Hodge).

There is a need to help PSMTs make connections between their coursework and their future teaching.

Role of university geometry

What are some ways you believe university geometry courses can/could contribute to PSMTs’ future classroom teaching?

Purpose To understand how the structure and

content of a university geometry course can help PSMTs in connection to their future classroom teaching.

Axiomatic Geometry 3 credit, upper-division course

PSMT requirement

Math/Stat elective

Mixture of non-Euclidean and Euclidean geometry

Axiomatic Geometry 14 students enrolled in the course

14 students participated in the study

9 of these were PSMTs

At least 1 PSMT in each group

Class structure Limited lecture

Focus on group work

Group and individual assessments

Final project I included a final project to help

understand how the students thought the structure and content of the course was benefical for them in their future careers.

Focus here is on PSMTs.

Final Project (PSMTs) Presentations and summaries of how the class

would help PSMTs in future careers.

How does the structure of the course help pre-service teachers?

How could the topics in this course help someone teach geometry at the middle or high school level?

Why is this course required of pre-service teachers as part of their undergraduate degree?

Final project Duration: 45 minute presentations.

Form: Students’ choice.

Requirement: Handout for others.

Final project Specific topics as well as structure of

the class were to be included to make points.

Encouraged to examine NCTM standards and/or high school textbooks to justify claims.

Results related to structure Group work

Teaching opportunities Obtaining a sense of what it “feels like” to partake

in group work Saw a balance of independent/group learning in

action

Non-traditional format Provided a model for PSMTs to use in their

classrooms

Results related to structure Learning from mistakes.

Ability to re-do homework problems.

Repetition of homework/proof concepts. Proving exactly one.

Results related to material Deeper Understanding

Enabled them to provide a better explanation of material.

Brought to light concepts that are taken for granted in Euclidean Geometry Parallel lines

General skills (proof construction) practiced throughout course

Relevance to teaching degree Provided a good foundation of geometry

Provided the why’s and how’s

Provided bridge between math and education

Implications We should consider ways to provide

PSMTs opportunities to reflect on how their coursework relates to their future teaching.

Future directions Follow up with PSMTs in the

classrooms.

Compare/contrast with other schools.

Compare/contrast with other courses.

Questions? Angela.Hodge@ndsu.edu