Executive Summary of Results

We used a teaching approach that integrates dynamic geometry software Geometer’s Sketchpad (GS) into a classroom environment structured with a Problem-Based Learning (PBL) approach, incorporating an Academic Service Learning component. The approach was used in three classes, one for future high school teachers and two for future elementary school teachers. One-day workshop with GS-PBL activities was offered for 31 in-service teachers in Northwest Indiana.

We shared our experience, including the quantitative evaluation of our project, in several presentations at national and regional meetings. The paper that we are writing analyses the teaching approach that we used and will be submitted to a refereed journal.

Need for the Project

The traditional approach in teaching geometry at all levels has produced generations of students who identify geometry as a closed branch of mathematics having its own peculiar language in which every question has a unique answer attainable through a compulsory series of steps, which are supposed to be passively absorbed from the all-knowing teacher and memorized for later assessment. Unfortunately, until recently, the college experience of future teachers reinforced sterile attitudes by reinforcing passive learning. New teachers were sent into classrooms ready to offer the same to younger generations. This cycle can and should be broken. A better approach is to integrate dynamic geometry software into a classroom environment structured with a Problem-Based Learning approach, incorporating an Academic Service Learning component.

Use of Technology

We chose to use the dynamic geometry software package Geometer’s Sketchpad (GS). GS enriches the range and quality of active investigations by providing a view of geometric ideas from multiple perspectives and in a dynamic form.

Instructional Design Plan

Describe how the use of technology used supported your teaching approach:

• What student learning outcomes were expected?
• How did your teaching plan encourage active learning, provide feedback, address respective learning styles, and build collaboration?
• What resources were used? (campus technology support services, etc.)
• Would your project be easily understood and executed by other faculty?

We expect students to:

1. Discover geometric patterns and formulate conjectures by exploration and investigation,
2. Employ critical thinking skills in comprehension and application of geometry,
3. Analyze and construct logical arguments,
4. Identify areas of geometry that are most useful in solving practical problems, and
5. Use information technology in the learning and teaching environment.

The PBL approach eliminates lecturing in the classroom/lab and replaces it with sessions of collaborative learning, guided by carefully constructed problems. The problems are challenging, open ended, exploratory in nature, and require the use of GS. The ability to adapt to different learning styles is woven into the very fabric of the approach, as students set their own pace through discovery activities. Most of the work in class and in the Academic Service Learning component are done in collaborative group setting. We used early student feedback, mid- and end-of-course surveys, course evaluations, and interviews with teachers and students to constantly modify and improve our approach.

We taught courses in computer classrooms, GS was installed on all machines in open labs, and the student version of GS was available in the bookstore. Java sketches and Workshop for Teachers materials were published on the Web.

Our project is easily understood and could be executed by other faculty. GS is easy to learn and our students become proficient users after one semester.

Potential to Impact Student Learning

Clearly define how your project improved student learning - include specific examples of how your project:

• Fostered depth of learning
• Supported efforts to improve retention
• Fostered the learning of large numbers of students
• Has broader applications that will affect learning K-12 or community environments?

Our students’ comments testify to fostered depth of learning:

1. The most evident ability I have developed is to question. I have learned that there are a lot of mathematical things that I have simply memorized without actually understanding.
2. Geometer's Sketchpad is very helpful, it's hands on-I think that helps solidify concepts.
3. I think I am more able to sit, think and reason out a problem than just jolting down the first answer that comes to mind.
4. I enjoyed the teaching style. It is one I hope to employ in my own classroom someday.

On May 19 2001, we offered a one-day workshop with GS-PBL activities for 31 in-service teachers in Northwest Indiana. It was a great success and most of the teachers wanted a follow-up sessions.

Assessment Plan

Briefly explain the effectiveness of your assessment plan:

• What measure of assessment was used?
• How did your approach obtain measures of performance?
• Did you feel your measurement was accurate and effective?

We used early student feedback, mid- and end-of-course questionnaires, course evaluations, and interviews with teachers and students to modify and improve our approach. We would like to change several questions asked on the questionnaires when we use the approach next time. We are in a process of writing a paper that analyzes quantitative data from questionnaires that were given to our students.

The first box plot illustrates students’ - future elementary teachers’ opinions on several issues. On a scale from 1-7 they expressed:

1. how enjoyable their previous college courses were
2. how enjoyable their previous mathematics college courses were
3. how much did they retain from previous college courses
4. how much did they retain from previous mathematics college courses
5. how relevant were their previous college courses
6. how relevant were their previous mathematics college courses.

The next box plot shows the improvement from pre- to mid- semester in students’ opinions about the problem based learning approach experience.

Plan for Colleague Development

Describe your role and activities as a mentor:

• What mentoring activities were implemented to assist colleagues?
• How did you help to develop colleague's instructional technology skills?
• How do you think your contributions to the Knowledge Base will help colleagues planning similar projects?
• Is your project approach potentially applicable to other contexts or disciplines?
• What tips would you offer?

We offered a Saturday workshop on the use of Sketchpad for our colleagues and tutors in the Math Lab. Our ultimate goal is to positively impact not only IUN students enrolled in the courses that are part of this project but also the local K-12 schools. We are confident that experiencing an active learning environment with intense use of information technology will have a positive lasting effect on the pedagogical practices of our students in their future classrooms. Certainly our project had a concrete influence on the local school system through the Academic Service Learning component, additional pilot activities at IUN's annual Calculator Tournament and the Indiana State Mathematics Competition, and a workshop for in-service teachers in May 2001. Easy access to Web-published GS-PBL activities makes collaborations with local schools very effective and potentially long lasting. PBL and ASL components of our project are applicable to other contexts and disciplines. We would like to make the May workshop for teachers and our Web sites with java sketches available through the Knowledge Base.

Final Comments on Project Results

• Do you think you met the goals of your project?
• What, if anything,would you do differently?
• Did you have any unexpected outcomes? (positive or negative)
• Would you recommend this teaching approach to colleagues?
• What other comments or suggestions would you offer to complete this report?

We believe we met the goals of our project. As mentioned earlier we would like to change several questions asked on the questionnaires when we use the approach next time. We were not able to use all the data from the anonymous questionnaires because students forgot their codes. We would set up this part differently next time. The approach we used was more successful with future high school teachers than with future elementary school teachers. We believe that modified approach will better suit future elementary school teachers. We shared our experience, including the quantitative evaluation of our project, in several presentations at national and regional mathematics meetings. The paper that we are writing analyses the teaching approach that we used and will be submitted to a refereed mathematics education journal.

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