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Hello, my name is Kristin Pelzel. I am a math, psych, and education major.

Summer 2010 REU Project

This year I am mainly working with Dr. Magiera again, however, the research focus within the mathematical education has slightly changed. Last year we evaluated student teacher's Habits of Mind (which you can review in the lower portion of this bio)

This year we are working on the idea of "equality" and what that means for students at different levels of learning. We have categorized 4 benchmarks of equality. These are modifications from a previous researcher (whom i will have the name up here shortly).

I should give you a little background first. The data we have collected consists of homework, tests, interviews, and reflections from students who are striving to be teachers in junior high and elementary schools. Within the homeworks and other activities the students (also known as Pre Service Teachers or PST's) demonstrated their ability and knowledge of the equal sign and also demonstrated their ability to recognize the equality benchmarks in their students. Another objective of the class was to help the PST's move their students' ability and knowledge of the = sign to the higher benchmarks and to evaluate the PST's on their ability to do this.

How is this study different from other studies? A lot of research has gone into studying the thinking strategies of elementary and middle school students. This research is focusing directly on PSTs and and their knowledge of thinking strategies. Specifically we are looking at a prospective teacher's own thinking strategies, the PSTs' knowledge of relational thinking strategies, the ability for Pre Service Teachers to analyze and interpret student thinking, and the ability of Pre Service Teachers to recognize opportunities to foster relational thinking skills in simple and complex problems.

May 24-30

May 31-June 6

June 7-13

June 14-20

June 21-27

June 28-July 4

July 5-11

July 12-18

July 19-25

July 26-August 1

August 2-8

August 9-15

Summer 2009 REU Project

I am working with Dr. Magiera, Dr. V, and Dr. Moyer on a project within the mathmatics education. We are discovering how teachers use Habits of Mind and how they evaluate their students' Habits of Mind.

Habits of Mind (HOM), in simple terms, are how one thinks. Some of the mathematical Habits of Mind we are exploring are how students "predict patterns," "justify rules," "organize data," "work backwards," "describe a rule," "describe change," "chunk information," and "different representations."

The research began with 18 Pre-Service Teachers* (PST) undergoing a mathematical elementary education class at a large Midwest school. These PST’s were involved in multiple tasks including: homework assignments, midterm and final exams, and interviews. A total of 130 activities (in written work) and 52 interviews were used in the research.

Here are some research questions that we focused on: Research Questions

▪ What links can be found between a PST’s HoM and a PST view of his/her students’ HoMs? ▪ How does PST’s algebraic thinking affect their ability to analyze (notice) middle school student’s algebraic thinking? ▪ What patterns or links can be found between each HoM? ▪ What is the relationship between PST’s algebraic thinking and their ability to analyze (notice) middle school student’s � algebraic thinking? ▪ How does PST’s reflection on their work with middle school students impact their ability to evaluate their own and middle � school students’ algebraic thinking? ▪ What effect did the specific math education class have on the PSTs’ algebraic thinking and PST evaluation of a middle � school student algebraic thinking? ▪ In what ways does the level of algebraic thinking effect whether PSTs analyze or notice HoMs in middle school student � work?

Each task was analyzed in three steps.

Step 1. Specific algebraic habits of mind elicited by the task were identified and documented.

Step 2. Pre-service teachers’ solutions to each task were qualitatively examined to identify features of algebraic � habits of mind evident in pre-service teacher work.

Step 3. Pre-service teachers’ performance on each identified feature of algebraic habits of mind was assessed � on 3 point scale (3- proficient, 2- developing, 1- no understanding).

The strengths and patterns of the PSTs’ algebraic thinking were identified by qualitatively analyzing the extent to which participants’ solutions and explanations, found in class assignments and tests (130 tasks analyzed ), exhibited various features of algebraic thinking.

Average performance scores across all tasks were used to examine patterns in pre-service teachers’ performance on different features of algebraic thinking.

Here are some results we found this summer. Take note that this research is still ongoing and the collected data are still being analyzed. Hence some of the results listed have the potential to be built upon or modified.

1. The pre-service teachers’ ability to demonstrate different features of algebraic habits of mind varied among the features examined. Among the examined features of algebraic habits of mind, the pre-service teachers’ ability to � justify was by far the weakest one and their ability to work backwards was the strongest one.

2. The overall mean performance score for demonstrating algebraic habits mind was M = 2.5, SD = 0.16.

3. Overall, pre-service teachers had difficulties eliciting and interpreting the algebraic thinking of students. Pre-service teachers were most successful in noticing and interpreting how students organize information ( M = 2.61), � chunk information (M = 2.55) and justifying a rule (M = 2.55). The weakest performance was noted for interpreting how students describe change (M= 2.27) and how they predict patterns (M = 2.27).

4. A strong relationship was found between the pre-service teachers’ ability to demonstrate features of algebraic habits of mind and their ability to interpret features of algebraic habits of mind in the work of students.

This summer was very intriguing. The experience was very worthwhile and I was honored to be picked and able to join my advisors with their research. I highly, highly recommend other undergrad students to become involved with the program next year if possible.