Dynamic Geometry Project*
Professional Development Workshop
August 2-6, 2010
Stevens High School
San Antonio, Texas
Dr. Ed Dickey
78 mathematics teachers participated in 5 days of professional development activities related to the Dynamic Geometry project funded by NSF to Texas State University-San Marcos. Teachers were divided into two groups, randomly, and each group participated in a different, independent, professional development program consistent with the project’s proposal. I participated in the programs beginning at 1 pm on August 4 and until the conclusion at noon on August 6, 2010. I rotated observation between the two groups throughout my visit.
Both groups completed a pre- and then a post-test related to mathematical content knowledge about geometry. Teachers in both groups also completed a questionnaire regarding their beliefs about geometry teaching and learning. Other demographic data was also collected that included teachers gender, experience, and current teaching assignments. Later analysis will examine the degree to which the two groups are comparable and consider threats to internal validity that might arise despite the random assignments.
One group participated in extensive and in-depth training on the use of Geometers Sketchpad (GSP) software for teaching high school geometry in a manner that addresses students’ ability to make conjectures and prove theorems: the Dynamic Geometry Approach. The other group participated in similar training addressing conjecturing and proof, but using dynamic methods such as paper-folding and constructions without using dynamic geometry software.
The software group participated in structured experiences to build skills and knowledge specific to using the GSP software. These were designed to accommodate some participants who were novice users and others who were more experienced. Software group participants also worked with strategies and ideas for teaching conjecturing and proof using dynamic geometry software. This included geometry problems for the teacher participants to consider, work with, and even prove as well as discussion among participants and leader regarding the teaching of conjecturing and proof. Project PI Dr. Zhonghong Jiang, senior personnel Dr. Samuel Obara, lead teacher Janie Love, and doctoral student Alana Rossenwasser planned and led significant segments of the software group workshop.
The control group had similar experiences but structured around the teaching of conjecturing and proof using methods that do not require dynamic geometry software. This group, like the other, participated in problem solving and discussion as well as structured experiences with strategies for developing students’ ability to generate conjectures and develop proofs using methods like paper folding, straight-edge rulers, compasses, isometric dot paper, web-based applets, and applications within TI-84 calculators related to transformations with matrices and conics. Videos of students discussing conjecturing were also used with this group. A Window on Geometry booklet was provided to all participants that included print versions of the materials used during the professional development sessions. Project co-PI Dr. Gilbert Cuevas, lead teachers Lisa Villalon and Lori Robinson, and doctoral student Ewelina McBroom planned and led significant segments of the control group workshop.
All participants signed a Consent Form related to photography, videotaping, and testing and consistent with research ethics and institution review of research practices. There were a total of 78 participants with 39 in the software group and 39 in the control. Professional responsibilities prevented some participants from attending different parts of the 5 day session but group leaders and project staff provided or will provide make-up experiences to ensure that all participants completed the planned training.
My observations of the software group led me to conclude that all participants completed the training with strong baseline knowledge of the GSP software as well as a clear understanding of what the dynamic geometry approach entailed. All participants in groups of 2 or 3 prepared a lesson plan that was presented to the entire group. From the presentations, it was clear to me as well as the project leaders that teachers were capable of designing and explaining lessons that required their students to make conjectures and engage in reasoning and proof through learning within a dynamic geometry software environment. Their presentations also included actually demonstrating their ability to use the GSP software and all participants, in my estimation, were functioning at an experience level that was beyond “novice” user. Some of the participants could be characterized as “expert” users, but even those who described themselves as novices at the beginning of the training demonstrated competent and confident usage skills.
Participants in the control group demonstrated a very positive attitude to teaching geometry using a conjecturing and reasoning approach. They responded enthusiastically to activities that engage learners in inductive and deductive reasoning. I observed constructions using paper, compasses and straight-edge as well as paper folding activities. I heard participants express an eagerness to use the strategies learned during the workshop as part of their teaching.
Teachers in the software group discussed the need to address computer lab reservations and software installation issues before the beginning of school. The project director with my assistance drafted a letter to be sent to the Principal at each participating school requesting assistance with ensuring that provided GSP software was installed on school computers and that priority be given to project teachers requiring computers labs. Teachers in the software group were encouraged to have an average of 2 computer lab experiences per week. It was clearly expressed that for the curriculum units that the project developed, the 2 computer labs per week experience by students is essential. Teachers were provided with print materials developed by Key Curriculum Press on planning lessons and managing student GSP work. Resources are and will be made available to teachers using the Texas State University TRACS collaborative learning environment available to participants online. Teachers had, even during the workshop, posted their presented lessons so that others would have access during the school year.
As a result of my observations during the workshop, I confidently conclude that the professional development experiences by both groups during the week of August 2-6 were entirely consistent with the Dynamic Geometry in Classrooms proposal. The project team was especially successful in building enthusiasm and support by teachers in both groups related to the project goals. Careful planning of meaningful mathematics experiences, demonstrated respect for teachers’ time and needs, and care to ensure the comfort and convenience of all participants helped to secure the cooperation and commitment critical to a project of this type. As proposed, professional development will continue during the school year, but at this time, participating teachers are well prepared to implement strategies that promote conjecturing and proof as part of high school geometry learning. Discerning whether the dynamic geometry approach has a significantly stronger effect on students’ ability to generate conjectures and proofs will be possible based on the parallel professional development offered to both participant groups.
* Dynamic Geometry in Classrooms is a four-year, more than $2 million research project funded on July 7, 2009 by the National Science Foundation (Award# 0918744) to Texas State University, San Marcos. The project is conducting repeated randomized control trials of an approach to high school geometry that utilizes Dynamic Geometry (DG) software and supporting instructional materials to supplement ordinary instructional practices. The key personnel of this project are Dr. Zhonghong Jiang (Principal Investigator), Dr. Gilbert Cuevas (Co-Principal Investigator), Dr. Selina Vasquez, Dr. Alexander White, Dr. Samuel Obara, and Dr. Alejandra Sorto. Doctoral research assistants are Alana Rosenwasser and Ewelina McBroom. Project coordinator is Jean Pena.
The general plan for the project is as follows: Year 1: Preparation (All research instruments, professional development training and resource materials, recruitment and training of participants, etc.); Year 2: The first implementation of the dynamic geometry (DG) treatment, and related data collection and initial data analysis; Year 3: The second implementation of the DG treatment, and related data collection and initial data analysis; Year 4: Careful and detailed data analysis and reporting.
White House Science Fair
Dr. Jian Shen's team Siemens team was invited to attend the White House Science Fair on Oct. 18, 2010.
The is the first time for the White House to hold such an event for high school students. So 35 or so national winners from various competitions in math, science and technology were invited to the White House. Dr. Shen was greatly inspired by projects done by all teams. The students stayed in the White House for about 3 hours. President Obama made a 15-minute speech and Dr. Shen's team got to shake hands with the President. Only students were allowed in the White House conference room during the President's speech. Dr. Shen, as well as the other mentors, parents, and sponsors were put in a different room in the Eisenhower Building for simulcast viewing.
April is Mathematics Awareness Month
ESSENTIAL SKILLS: Mayor Susan Narvaiz presents a proclamation for Mathematics Awareness Month in April to the award-winning Texas State University MathWorks Program, an internationally recognized center for excellence in mathematics education. L-R, front are Mayor Narvaiz, Dr. Max Warshauer, Dr. Stan Wayment, Chair; Hiroko Warshauer and Jean Davis of the Texas State Mathematics faculty; back row: City Council Members Kim Porterfield, Gaylord Bose and John Thomaides.
(Photo by Don Anders)
Dr. Nathaniel Dean Lectures at the 2010 MAA MathFest
Dr. Nathaniel Dean presented the J. Sutherland Frame Lecture at the 2010 MAA MathFest in Pittsburgh, PA. This was the first time the MAA has recorded the invited lectures and posted them on the web. Dr. Dean was also inducted into Pi Mu Epsilon as part of the banquet preceeding the lecture.
Holding their $100,000 check, left to right, are Sean Karson, Kevin Chen and Dan Liu, who won the prestigious Siemens math and science competition for a project they developed at Texas State’s Honors Summer Math Camp under the direction of Texas State mathematics professor Jian Shen.
Siemens (NYSE-listed SI) visits the NYSE to salute the winners of the Siemens Competition in Math, Science and Technology, a signature program of the Siemens Foundation. The annual awards were presented on December 7, 2009 at New York University.
In honor of the occasion, Tom McCausland, Chairman of the Board, Siemens Foundation; Jim Whaley, President, Siemens Foundation; Jeniffer Harper-Taylor, Vice President, Siemens Foundation; Diane Tsukamaki, Director, National Recognition & Scholarship Programs, The College Board; and Siemens Competition Grand Prize winners Ruoyi Jiang and the team of Sean Karson, Dan Liu and Kevin Chen will ring The Closing BellSM.