This CAREER awardee at Michigan Technological University is investigating the outcomes of a teacher education model designed to foster prospective mathematics teachers' abilities to notice and capitalize on important mathematical moments in instruction. The researcher engages prospective teachers in research-like analysis of unedited teacher-perspective classroom video early in their teacher education coursework in order to help them learn to identify, assess the mathematical potential of, and respond to important student ideas and insights that arise during instruction.

The research is based on a quasi-experimental design and involves three cohorts of prospective teachers. Practicing teachers from local schools collaborate with the research team. The data collected consists of classroom video. The video is coded and analyzed using Studiocode, which allows for real-time coding and for multiple users to code and annotate video segments.

The research findings are integrated into the institution's teacher education program and are also disseminated more broadly through publication and presentations at professional meetings.

The Lynch School of Education and the Urban Ecology Institute at Boston College are partnering with the Center for Applied Special Technology (CAST) to develop, test, evaluate and disseminate a year-long set of urban ecology course materials for use in high school-level capstone science courses. The standards-based materials emphasize locally-relevant field studies and incorporate principles of Universal Design for Learning and Educative Curriculum. Other features include (1) an on-line resource center that links to professional development resources, (2) a student-written urban environment newspaper called "Green Times," and (3) a writing support toolkit. Evaluation and research studies focus on measuring effectiveness of the materials in promoting content understanding, self-efficacy in science and inquiry abilities of students in urban high schools, particularly those from underrepresented groups.

Developers and researchers at Rutgers University, Boston University, Colorado State University, and the Consortium for Mathematics and Its Applications (COMAP) are continuing research and development work on high school instructional materials that integrate biology, computing, and mathematics. The project goal is to develop and test a one-semester high school course. The course consists of some modules developed under a previous NSF grant as well as some new material.

COMAP leads the effort to develop the instructional materials and the process involves mathematicians, biologists, computer scientists, teachers, and writers. The materials are pilot- and field-tested in a number of schools and revised after each test. Subject matter experts review the materials for accuracy and teachers and education professionals review them for their usability. Researchers at Colorado State University collect and analyze data on student learning and interest at all stages of the pilot- and field-testing.

The intended deliverables include up to five new instructional modules and a coherent one-semester course suitable for the increasing state requirements for a fourth year of mathematics. The course is supported by a book in print and electronic format and includes teacher training support tools and activities to prepare teachers to present interdisciplinary bio-mathematics material.

Developers and researchers at North Carolina State University and Horizon Research, Inc. are adapting and studying successful discourse strategies used during language arts instruction to help teachers promote mathematically-rich classroom discourse. Of special interest to the project is the use of models to promote mathematics communication that includes English language learners (ELL) in mathematics discourse.

The project is conceived as a design experiment that includes successive instructional engineering cycles in which the R&D team designs professional learning tasks, implements the tasks with teachers, and revises the tasks and their sequencing to better support the desired learning outcomes. The members of the project team then examine the effects of the PD on teachers' instruction and the possibilities for scaling up the materials across PD facilitators, grade levels, and curriculum materials. The overarching research questions guiding the research and development effort proposed in this project are: How do generalist elementary teachers learn to promote high quality mathematics discourse that includes all students in their classrooms and engages those students in meaningful mathematics learning opportunities? How do we scale up an intervention designed to support elementary teacher learning of ways to promote high quality mathematics discourse in their classrooms?

The project will result in a full 40-hour professional development module to support mathematics discourse for Grade 2 teachers, with an emphasis on place value, multidigit addition and subtraction, and linear measurement. The main professional learning tasks of the program will have been piloted and studied in a series of sessions with mathematics coaches and teachers.

The Value of Computational Thinking (VCT) project combines the talents and resources of STEM professionals at the Rutgers University DIMACS Center, the Consortium for Mathematics and Its Applications (COMAP), Colorado State University, Hobart and William Smith College, the Computer Science Teachers Association, and five partner school districts to develop and test a set of 12 curriculum modules designed to engage high school students and their teachers in the process of applying computational concepts and methods to problem solving in a variety of scientific contexts. The project perspective is that computational thinking can be usefully thought of as a specialized form of mathematical modeling. The product of computational thinking in a particular domain is a model of a situation, a structuring and representation of the situation, that enables computations to be performed to answer questions, solve problems, control processes, predict consequences, or enhance understanding.

Since computational thinking is a relatively new construct in STEM and STEM education, there are few available curriculum materials to support instruction intended to develop the understanding, habits of mind, and specific techniques that are involved. The fundamental goal of the VCT project is to answer an engineering research question: "What kinds of instructional materials and learning experiences will develop effective computational thinking skills and attitudes?" The VCT project is applying a design research process involving iterative phases of development, pilot testing, and revision to produce prototype instructional materials that will be useful as stand-alone curriculum modules or when collected into different packages to support full high school courses. Project field test evaluation will provide preliminary evidence about the efficacy of the materials in developing desired student learning.

Proponents of computational thinking in STEM and STEM education have argued that it offers a powerful general approach to problem solving in discipline-specific and inter-disciplinary settings. They also argue that, when properly taught, it can provide an effective introduction and attraction to careers in computer science and other computing-intensive fields. Thus the VCT project has a long-term goal of broadening participation in computer science and related technology fields. Materials are being designed with special features to enhance their effectiveness in reaching this objective.

This exploratory research study will bring together two promising innovations that have the potential to help more students meet high standards and prepare for college and 21st century careers. One innovation is a new high school course entitled Energizing Physics, designed to help students with a wide range of capabilities by applying best practices and presenting a relatively small number of key concepts in depth. Another is the BEAR assessment system, designed to provide frequent formative assessment data to students and teachers. The goal is to develop and test a formative assessment system for Energizing Physics that has the potential to enable all students to learn how to learn physics, so they can succeed in their first physics course in college. Partners include course authors Aaron Osowiecki and Jesse Southworth from Boston Latin School in Boston, Massachusetts, Cary Sneider and graduate students at Portland State University in Portland, Oregon, and assessment specialists Mark Wilson and Karen Draney at the Graduate School of Education, University of California at Berkeley.

The project will proceed in five phases. Phase I: During the summer of 2010 project teams from Massachusetts and Oregon will meet with assessment experts in California for training in the BEAR assessment system. Phase II: During the subsequent year the team will collaborate remotely to embed the BEAR system into the course materials, and recruit eight teachers (four in Massachusetts and four in Oregon) who will test the new materials in a variety of high school settings. Phase III: Weeklong workshops will be held in Oregon and Massachusetts during the summer of 2011 to familiarize teachers with the course and assessment system. Phase IV: Teachers will present the course to their students, collect pre-post test data on students' conceptual understanding and problem solving abilities, as well as work samples, and report on successes and challenges. Teams will conduct classroom visits and interview teachers at school sites. Phase V: During the summer of 2012 the teams will analyze the results, modify the course materials as appropriate, and report on findings.

Given the substantial body of research on the value of formative evaluation for supporting learning, this exploratory study has the potential to develop a physics course that could help teachers support learning among students with a wide diversity of capabilities. Further, since this research builds on a similar study of the high school course Living by Chemistry, which also uses the BEAR formative evaluation system, it may be possible to generalize ways that high school science courses can be designed to help more students succeed in college science.

The aim of this CAREER project led by Amy Ellis at the University of Wisconsin is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Work of the project will produce: (a) insights into ways of unifying two previously disconnected lines of research on quantitative reasoning and proof; (b) models describing realistic ways to support development of students' proof competencies through quantitative reasoning; (c) improvement in students' understanding of algebra through engagement in proof practices based on quantitative reasoning; (d) insights into middle-school students' thinking as they negotiate the transition from elementary to more advanced mathematics; and (e) increased understanding of teachers' knowledge about proof and their classroom practices aimed at helping students progress towards understanding and skill in proof.

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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.  It compares effects of that intervention with standard instruction that does not make use of computer drawing/exploraction tools. The basic hypothesis of the study is that use of DG software to engage students in constructing mathematical ideas through experimentation, observation, data recording, conjecturing, conjecture testing, and proof results in better geometry learning for most students. The study tests that hypothesis by assessing student learning in 76 classrooms randomly assigned to treatment and control groups. Student learning is assessed by a geometry standardized test, a conjecturing-proving test, and a measure of student beliefs about the nature of geometry and mathematics in general. Teachers in both treatment and control groups receive relevant professional development, and they are provided with supplementary resource materials for teaching geometry. Fidelity of implementation for the experimental treatment is monitored carefully. Data for answering the several research questions of the study are analyzed by appropriate HLM methods. Results will provide evidence about the effectiveness of DG approach in high school teaching, evidence that can inform school decisions about innovation in that core high school mathematics course. The main research question of the project is: Is the dynamic geometry approach better than the business-as-usual approach in facilitating the geometric learning of our students (and more specifically our economically disadvantaged students) over the course of a full school year?

The main resources/products include geometry teachers’ professional development training materials, suggested dynamic geometry instructional activities to supplement current high school geometry curriculum, instruments such as Conjecturing-Proving Test, Geometry Belief Instrument, Classroom Observation Protocols, DG Implementation Questionnaire and Student Interview Protocols. 

The general plan for the four-year 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 treatment, and related data collection and initial data analysis; 

Year 3: The second implementation of the DG treatment, and related data collection and data analysis; 

Year 4: Careful and detailed data analysis and reporting.

We are now in project year 3. Data are collected for the second implementation of the DG treatment. For data collected during project year 2, some initial analysis (the analysis on the geometry pretest and posttest data and the psychometric analysis on the project developed instruments) has been conducted. More thorough analysis of the collected data is still on going. The analysis on the geometry test shows that the experimental group significantly outperformed the control group on geometry performance.

The evaluation will be implemented throughout the project’s four-year duration, with an evolving balance of formative and summative evaluation activities.  In the project’s first three years, the evaluation will emphasize formative functions, designed to inform the project research team of the relative strengths and weaknesses of the research design and execution, and target corrections and improvements of the research components. Summative evaluation activities will also take place in these years with the collection of data on student achievement and teacher change. Evaluation activities for year 4 will focus on the summative evaluation of the project’s accomplishment and especially its impact on participating teachers and students. Evaluation reports will be issued annually with a final summative report presented at the end of year 4.

The research results will be disseminated via the following efforts: 1) Creating and constantly updating the project web site; 2) Publishing the related research articles in research journals such as Journal for Research in Mathematics Education; 3) Presenting at state, regional, national, and international research and professional meetings; 4) Meeting with state and local education agencies, schools, and mathematics teacher educators at other universities for presenting the research findings and using the DG approach in more schools and more mathematics teacher education programs; and 5) Contacting more school districts, with a view to developing relationships and ties that would smooth the way to disseminate the research results.  

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