The project A Digital Resource for Developing Mathematics Teachers' TPCK is developing and conducting initial tests of a highly innovative interactive digital textbook to enhance middle grades mathematics teachers' understanding of core concepts in proportionality and their understanding of ways that technology can be used to enhance instruction. The project is led by professionals from SRI International with substantial contributions by mathematics educators at San Diego State University, San Francisco State University, the Singapore National Institute of Education, and the Center for Applied Special Technology (CAST).
The digital textbook combines elements from SimCalc, Geometer's Sketchpad, and data analysis software to teach core ideas of proportionality from algebraic, geometric, and statistical perspectives. It also includes elements designed to help teachers see the connections among those uses of proportional reasoning and the ways that such tools can be used in classroom instruction with middle school students.
The basic hypothesis of the project is that the proposed DynaBook will be a highly effective tool for mathematics teacher preparation and professional development and, ultimately, for classroom instruction of middle school students. Pilot tests in laboratory, teacher preparation, and professional development settings are providing initial empirical evidence about two core research questions:
* In what ways does the DynaBook effectively support teacher learning of pedagogical and technological content knowledge?
* Does the DynaBook foster teachers' understanding of the coherence and connectedness of middle school mathematics?
This project explores very promising new forms of instructional materials with potential to transform the ways that we think about educational texts and teaching strategies.
To improve student performance in mathematics and to meet the demands of the Common Core, the quality of teacher preparation must be improved. Our major goal has been to develop and investigate digital resources which could be used in preservice classes to improve teachers’ learning of content and pedagogy and to help teachers to learn about high value uses of technology in mathematics education. The major activities in this project included design, development, field testing, data collection, data analysis, theory-building, evaluation, engaging advisors, dissemination and reporting. The flow of the activities was highly iterative, with approximately 9 different DynaBook releases tested in our partners’ university courses or other field test situations, and extensive improvements in content, functionality, navigation and other features between releases. The improvements were based on the data collected and the interpretation of that data by partners, evaluators and advisors. Findings and outcomes of the project include empirical results, design of innovations, and broader impacts. With regard to empirical results, we found that preservice teachers could not be assumed to be "digital natives," with knowledge and confidence to use and apply technology in classroom situations. Preservice teachers lacked sufficient depth of content knowledge, had weak understanding of how to engage students in mathematical practices, and lacked knowledge of how to use technology specifically for teaching mathematics. We found preservice teachers could make rapid and measurable content knowledge gains from a well-designed digital resource, and that technology could be used to create experiences for teachers which engaged them in thinking about relationships between mathematical practices and pedagogy. We also conducted a substantial literature review and identified a key gap: in order to design effective resources for teachers, a stronger theory of how technology allows mathematical comprehension activities is needed. A further key outcome of the project was to create innovations in the use of technology in preservice teacher learning. A major design tension was between allowing teachers to read online materials in any order (nonlinear narrative) and providing a single path through the material (linear narrative). Both had advantages, and we found we could preserve both possibilities by organizing content into a matrix (of mathematics topics vs. modes of engagement) and also allowing instructors to create a linear path in the form of "an assignment" for preservice teachers to do. We also found that a "book" metaphor was not fruitful for organizing resources for teachers, and instead shifted to a "lab" metaphor. The lab metaphor emphasizes the opportunity to engage teachers in investigations of mathematical teaching and learning, grounded in real and simulated teaching scenarios. A further area of substantive innovation was in creating tools to enable teachers to better express mathematical reasoning and pedagogy. One expressive tool enabled teachers to write simulated pedagogical dialogues between a teacher and a student, also showing what each would write on a shared whiteboard. Another expressive tool enabled teachers to express a wide range of strategies and representations for solving mathematics problems, and to compare and contrast the potential advantages of each approach for student learning. Finally, this project conducted many activities with an eye to achieving broader impacts. A "teacher educator network" was initiated and used to understand requirements for more broadly sharing the tools and outcomes. Results were published and presented in print and in a variety of conferences related to teacher professional development. Graduate students were trained in design and research methods for innovation in teacher preservice education. A major partnership was developed with the California State University (CSU) system, which trains approximately 10% of all new STEM teachers in the United States, and CSU is using project results and innovations in its further innovation activities. Further, the team was invited to join 100Kin10, a network of institutions that is working towards the production of 100,000 new STEM teachers, and project results and innovations have been shared with 100Kin10 member institutions. The team is actively seeking to further scale the results and innovations for additional impacts in preservice mathematics teacher preparation both in California and nationally.
