Researchers, at the University of Houston, are designing, implementing and studying a curriculum that prepares preservice, elementary teachers for equitable teaching of mathematics. The program increases the mathematical knowledge of preservice teachers and helps them recognize and implement equitable instruction. The preservice teachers are learning to recognize equitable practices by using the Mathematical Quality and Equity Observation Protocol (MQE) to assess teaching as viewed in video cases. The program includes mini courses of one hour that are spread throughout the program, ending just prior to student teaching.

Building on prior NSF-funded research, the researchers are investigating ways to help preservice teachers of mathematics at the elementary level to learn the mathematics needed for teaching and how to provide equitable instruction that encourages all students to share their mathematical thinking. Based on data collected in this exploratory study, researchers will revise the MQE and improve the validity and reliability of the instrument. They are also developing ways to use the MQE for both assessment and for instruction.

The materials, curriculum, and model produced by this project are helping elementary teachers learn important mathematics and learn to teach that mathematics in an equitable way. Although the model includes mini courses that are taught throughout the program, the materials can easily be adapted to a longer, traditional course for preservice teachers. The revisions of the MQE are producing an observational protocol that has the potential to vastly improve the way researchers study teachers' instructional practices.

The goal of Spatial Mathematics, Engineering, and Science: Toward an Integrated STEM Education is to develop a provisional learning progression spanning grades K-5 that articulates and tests the potential of experiencing, describing, and representing space as the core of an integrated STEM education. The science of space has an extensive scope within and across disciplinary boundaries of science, mathematics and engineering, the project will create a coherent approach to elementary instruction in which mathematical reasoning about space is systematically cultivated. Simultaneously, researchers are exploring the potential of spatial mathematics as a resource for engineering design of kinematic machines and for the development of mechanistic reasoning about the behavior of these machines. Work across these disciplines situates and motivates the mathematical work and also provides opportunities to investigate the intersections and contrasts among signature disciplinary practices, such as definition and proof in mathematics, design in engineering, and modeling in science. The research and development is being conducted in a middle school which is a full partner in the project.

In partnership, researchers and participating teachers are designing and implementing curricular approaches intended to support spatial knowledge and reasoning. Professional development will enhance and capitalize on teachers' roles as specialists in student thinking. The research consists of design studies conducted in 12 participating classrooms, K-5, and small-scale teaching experiments conducted with children across the same grade span. The research will establish provisional pathways and landmarks in learning about space, as well as the curricular activities and teacher practices necessary to support integrated STEM learning.

The project is novel in three ways. First, it provides children with early and systematic access to multiple geometries (e.g., plane, cylinder, sphere) to develop sophisticated understandings of powerful, yet experientally accessible concepts, such as straight, and STEM-related practices, such as model, definition and proof. Second, both the National Research Council Science/Engineering and the Common Core State Standards Mathematics highlight the role of practices in the development of disciplinary knowledge, and this project is providing a practical avenue for coordinating the co-development of disciplinary practices and knowledge. Third, the unifying theme of space is threaded through problems and contexts in mathematics, science and engineering, which provide a sound basis for generative STEM integration-integration that does not lose sight of the distinctive practices in different disciplines, but, instead, leverages these distinctions to produce multiple ways of knowing about space. Research and development is being conducted with underrepresented populations of students who are typically underserved in STEM education. Although the numbers of students reached in this phase of the work are relatively modest, the longer-term potential is great, because instruction anchored in space may be more accessible to students who struggle with traditional forms of mathematics education. The increased attention to integrated STEM education at the national level also ensures that this effort is likely to contribute to the knowledge base required to advance interdisciplinary forms of schooling.

Concord Consortium is exploring K-2 students' understanding of heat and temperature in two Massachusetts school districts using sensors that display temperatures as colors. The project is investigating the following research questions:

- How can visualizations, data collection linked to everyday experiences, and student reflection integrated into creative exploration address student preconceptions and promote K-2 student understanding of temperature and heat?

- How can the use of replay of video and reflection aid in addressing K-2 student preconceptions and improve student understanding of heat and temperature?

- Can the use of visualizations and data collection via digital sensing technology advance K-2 students past the goals of the K-2 science frameworks?

The project is being implemented in 10 classrooms for about 250 children representing diverse populations. Exploration activities are being created, and students are being videotaped carrying out the activities. Students complete a short assessment for each activity. Project staff will revisit the videos with the students to explore student concepts at a deeper level. David Reider of Education Design Inc. is conducting the evaluation which will focus on 1) program efficacy and design and 2) alignment with research design. It is formative in design with annual summative reports. From their data, the project is constructing a progressive hierarchy of student theories of heat and temperature. The project is also producing a protocol that teachers can use to have better dialogues with children that support children's reconstruction of their initial conceptions. The exploration activities, assessments, and project data are available via open source through a website at Concord Consortium and are being presented to multiple professional audiences.

This exploratory project examines how teachers of second grade students scaffold the development of student conceptual models and their understanding of the nature of scientific models and modeling processes in physical science conceptual areas associated with the particulate nature of matter. Teachers receive professional development around ways in which they can facilitate productive disciplinary discussions with young children that result in students coming to understand core ideas in the Next Generation Science Standards. The project focuses on the topics of matter and sound based on the FOSS units "Solids and Liquids" and "Water," and the STC unit "Sound". It builds on an earlier project on life science for kindergarten teachers and students to expand the research communities understanding of how young children learn in science. Researchers from Purdue University are working with public schools in Lafayette that have high Hispanic populations and low SES, as well as a private school system with a more affluent population.

This project employs a mixed methodological research design that incorporates rich qualitative data collection and analysis combined with a quasi-experimental design that examines student learning across a treatment and comparison group with the same curricular materials but with differing support for teachers to engage students in disciplinary productive discussions about the science phenomena that they are studying. Research questions are designed to elicit descriptions of the differing aspects of learning that are evidenced by students together with rich descriptions of the teaching strategies that are associated with the classroom environments. Because this is an exploratory study, no causal comparisons between teacher practices and student outcomes are drawn, but the project provides the underpinnings that will support future research that would take a more rigorous approach. The project further develops the methodology of examining disciplinary rich description of student models to advance the understanding of how content and reasoning interact with young children.

Recent research in cognition has demonstrated that young children reason in a more sophisticated manner than previously understood. The Next Generation Science Standards has a strong focus on student reasoning practices, and the development of student explanations of science phenomenon requires that students have the opportunity to experience classrooms in which discussions of scientific ideas are scaffolded. Teachers need examples of how to interact with young children and of how to interpret what students say in ways that move the understanding of scientific concepts forward. This foundational research provides descriptive exemplars that can be shared in both the research literature and in practitioner publications as examples of what cognitively rich pedagogy can achieve.

The Impact of Early Algebra on Students' Algebra-Readiness is a collaborative project at the University of Wisconsin and TERC, Inc. They are implementing and studying a research-based curriculum that was designed to help children in grades 3-5 prepare for learning algebra at the middle school level. Researchers are investigating the impact of a long-term, comprehensive early algebra experience on students as they proceed from third grade to sixth grade. Researchers are working to build a learning progression that describes how algebraic concepts develop and mature from early grades through high school. This study helps to build our knowledge about the piece of the progression that is just prior to entering middle school where many students begin formal instruction in algebra.

Building on previous research about early algebra learning, researchers will teach a curriculum that was carefully designed to reflect what we know about learning algebraic concepts. Previous research has shown that young children from very diverse backgrounds have the ability to construct algebraic ideas such as equality, representation, generalization, and functions. Researchers are collecting data about students' algebraic knowledge as well as arithmetical knowledge.

We know that the majority of students in the United States struggle with learning formal algebra. By studying the implementation of the research-based curriculum for an extended period of time, researcher's are learning about how algebraic ideas are connected and whether or not early instruction on algebraic ideas will help students learn more formal ideas in middle school.

The Impact of Early Algebra on Students' Algebra-Readiness is a collaborative project at the University of Wisconsin and TERC, Inc. They are implementing and studying a research-based curriculum that was designed to help children in grades 3-5 prepare for learning algebra at the middle school level. Researchers are investigating the impact of a long-term, comprehensive early algebra experience on students as they proceed from third grade to sixth grade. Researchers are working to build a learning progression that describes how algebraic concepts develop and mature from early grades through high school. This study helps to build our knowledge about the piece of the progression that is just prior to entering middle school where many students begin formal instruction in algebra.

Building on previous research about early algebra learning, researchers will teach a curriculum that was carefully designed to reflect what we know about learning algebraic concepts. Previous research has shown that young children from very diverse backgrounds have the ability to construct algebraic ideas such as equality, representation, generalization, and functions. Researchers are collecting data about students' algebraic knowledge as well as arithmetical knowledge.

We know that the majority of students in the United States struggle with learning formal algebra. By studying the implementation of the research-based curriculum for an extended period of time, researcher's are learning about how algebraic ideas are connected and whether or not early instruction on algebraic ideas will help students learn more formal ideas in middle school.

The Enhancing Mathematics Teaching and Learning in Urban Elementary Schools project is working with all teachers in grades three through five in the Portland, OR Public Schools in order to test the feasibility and efficacy of the Mathematics Studio Model of professional development. The model requires professional development to occur at the school level involving both teachers and principals. The professional development is conducted at the school and is integrated with instruction. The goal of the project is to improve students' engagement and learning in mathematics by fostering effective instruction. Partners in the project include Teachers Development Group, Portland State University, Portland Public Schools and Horizon Research.

The researchers are identifying the key ingredients that make the professional development successful. They are using a cluster-randomized research design to examine the efficacy of their model. They are using observational measures to identify successful teaching practices as well as student discourse patterns. They are studying the fidelity of implementation of the model and are looking for specific variables that may be particularly helpful for students who have not been successful in learning mathematics.

It is difficult to implement professional development at a large enough scale to make a significant difference in student achievement within a district. This research is important because it tests the use of a practice-based, professional development model within a large, public school system, and documents the challenges of implementation as well as the variables that contribute to student learning of mathematics.

This award is doing a research study of three models of professional development (PD) to test the efficacy of a practicum for grade 3-5 in-service teachers organized in three cohorts of 25. Model 1 is a one-week institute based on classroom discourse practices and a 2-week practicum (cohort 1). Model 2 is the one-week institute (cohort 2). Model 3 is a "business as usual" model (cohort 3) based on normal professional development provided by the school district. Cohorts 1 and 2 experience the interventions in year 1 with four follow-up sessions in each of years 2 and 3. In year 4 they receive no PD, but are being observed to see if they sustain the practices learned. Cohort 3 receives no treatment in years 1 and 2, but participates in a revised version of the institute plus practicum in year 3 with four follow up sessions in year 4. The Lawrence Hall of Science provides the professional development, and Stanford University personnel are conducting the research. The teachers come from the Oakland Unified School District. Science content is the GEMS Ocean Sciences Sequence.

There are 3 research questions;

1. In what ways do practicum-based professional development models influence science instructional practice?

2. What differences in student outcomes are associated with teachers' participation in the different PD programs?

3. Is the impact of the revised PD model different from the impact of the original model?

This is a designed-based research model. Teacher data is based on interviews on beliefs about teaching and the analysis of video tapes of their practicum and classroom performance using the Discourse in Inquiry Science Classrooms instrument. Student data is based on the GEMS unit pre- and post-tests and the California Science Test for 5th graders. Multiple analyses are being conducted using different combinations of the data from 8 scales across 4 years.

There will be 75 teachers and their students directly impacted by the project. Additional impacts of the project are research results and professional development materials, including a PD implementation guide and instructional videos. These will be presented in publications and conference presentations and be posted on linked websites at the Lawrence Hall of Science and the Center to Support Excellence in Teaching at Stanford University.

This award is doing a research study of three models of professional development (PD) to test the efficacy of a practicum for grade 3-5 in-service teachers organized in three cohorts of 25. Model 1 is a one-week institute based on classroom discourse practices and a 2-week practicum (cohort 1). Model 2 is the one-week institute (cohort 2). Model 3 is a "business as usual" model (cohort 3) based on normal professional development provided by the school district. Cohorts 1 and 2 experience the interventions in year 1 with four follow-up sessions in each of years 2 and 3. In year 4 they receive no PD, but are being observed to see if they sustain the practices learned. Cohort 3 receives no treatment in years 1 and 2, but participates in a revised version of the institute plus practicum in year 3 with four follow up sessions in year 4. The Lawrence Hall of Science provides the professional development, and Stanford University personnel are conducting the research. The teachers come from the Oakland Unified School District. Science content is the GEMS Ocean Sciences Sequence.

There are 3 research questions;

1. In what ways do practicum-based professional development models influence science instructional practice?

2. What differences in student outcomes are associated with teachers' participation in the different PD programs?

3. Is the impact of the revised PD model different from the impact of the original model?

This is a designed-based research model. Teacher data is based on interviews on beliefs about teaching and the analysis of video tapes of their practicum and classroom performance using the Discourse in Inquiry Science Classrooms instrument. Student data is based on the GEMS unit pre- and post-tests and the California Science Test for 5th graders. Multiple analyses are being conducted using different combinations of the data from 8 scales across 4 years.

There will be 75 teachers and their students directly impacted by the project. Additional impacts of the project are research results and professional development materials, including a PD implementation guide and instructional videos. These will be presented in publications and conference presentations and be posted on linked websites at the Lawrence Hall of Science and the Center to Support Excellence in Teaching at Stanford University.

This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This four-year, mixed methods research project tests, revises and extends learning trajectories (LTs) for children's knowledge of geometric measurement across a ten-year span of human development. Specifically, research teams from Illinois State University and the University at Denver are working with children in urban and suburban schools to (1) validate and extend prior findings from previous NSF-funded research developing measurement learning trajectories with children in pre-K to Grade 5, and (2) generate and extend portions of trajectories for geometric measurement for Grades 6-8.

The project employs a form of microgenetic studies with 24-50 children per grade from pre-K through Grade 5 representing a stratified random sample from a specific set of suburban schools. These studies will test the validity, replicability and generalizability of the LTs for length, area, and volume. The goal will be to validate all components of each learning trajectory, goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments. Analysis of variance measures with pre/post assessments in an experimental/control design will complement the repeated sessions method of microgenetic analysis.

To explore and extend LTs for children in Grade 6-8, the project employs teaching experiments. This design is used to generate and extend portions of trajectories for geometric measurement, and to explore critical aspects of measurement in clinical and classroom contexts. This work is coordinated with the teaching and learning standards issued by the Council of Chief State School Officials/National Governors Association, the National Council of Teachers of Mathematics, the National Science Teachers Association, the American Association of the Advancement of Science, and the National Research Council with cognitive and mathematics/science education literature. Emerging constructs for the hypothetical LT levels in relation to relevant frameworks generated by other researchers and those implied by standards documents to establish ongoing sequences of the experimental interventions for grades 6-8 are being compared, critiqued and evaluated.

This project provides a longitudinal account of pre-K to Grade 8 children's ways of thinking and understanding mathematical and scientific concepts of measurement based upon empirical analysis. The resulting learning trajectory will represent state of the art integrated, interdisciplinary, theoretically- and empirically-based descriptions of increasingly sophisticated and complex levels of thinking in the domain of measurement (albeit, more tentative for Grades 6-8). This account will be used to verify and/or modify existing accounts of children's development of reasoning from short-term analyses of learning or cross-sectional studies. There are not yet integrative longitudinal studies describing this cognitive domain for area or volume measurement. This trajectory-based analysis of development and instruction supports the design and testing of integrative, formative assessment of individuals and groups of children. Such learning trajectories will be useful in implementing the standard-focused curriculum described in the Common Core State Standards Mathematics and in supporting the multiple large assessment projects currently underway