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.

Core Math Tools is a project from Western Michigan University that meets the urgent need of providing mathematical tools that students can use as they explore and learn mathematical concepts that are aligned with the Common Core State Standards in Mathematics (CCSSM). The developers have repurposed and modified tools originally designed for an NSF-funded curriculum project (e.g., Core-Plus Mathematics), creating a suite of tools that supports student learning of mathematics regardless of the curricula choice. Core math Tools is Java-based software that includes a computer algebra system(CAS, interactive geometry, statistics, and simulation tools together with custom apps for exploring specific mathematical and statistical topics. The designers provide exemplary lessons illustrating how the software can be used in the spirit of the new CCSSM. The goal of the project is to provide equitable and easy access to mathematical software both in school and outside of school. The tools are available to all learners and teachers through the web site of the National Council of Teachers of Mathematics (NCTM). The web site includes feedback loops for teachers to provide information about the tools. By using the NCTM website, the tools can be downloaded for use by teachers and students. The dedicated portal on the NCTM website allows supervisors to use the tools in professional development, teachers to use the tools as an integral part of instruction, and students to use the tools for exploring, conjecturing, and problem solving.

The Gateways to Algebraic Motivation, Engagement and Success (GAMES) project is designing digital games for middle school students that will help them prepare for success in Algebra. The games are intended to help students gain a deep understanding of measurement and fraction concepts that are critical as they begin to learn algebra. The design of the games is based on research on learning fractions and research on engagement. The researchers at Virginia Polytechnic Institute and State University are studying students' development of fraction concepts, their engagement in the tasks, and the use of hand-held devices as a useful platform for games. They are providing valuable information on how students develop fraction concepts and contributing to the development of a learning trajectory that will guide the teaching of measurement and fraction concepts.

The design of the games is based on engagement states that are known to facilitate learning, with specific attention to cognitive, behavioral, and affective domains. The mathematical framework driving the games is based on how students learn fraction concepts. Most grade 6 students think of fractions from a part-whole conception, but this is not an adequate base for developing algebraic concepts. The games help students develop splitting concepts by moving through activities that focus on sequencing, partitioning, and iterating. The games are designed for iOS platforms that provide ease of engagement and data collection flexibility.

The project offers a variety of products ranging from theories to games. The research is building a conceptual framework that identifies features of engagement that lead to learning, and contributing to the development of a learning trajectory related to fraction concepts. The work will produce a scalable model for developing and using digital games to increase engagement and learning of middle school students. In addition, three games and associated tasks are being developed for use with current curricula to enhance students' understanding of fractions and prepare them for learning algebra.

The researchers in the Children's Understanding of Functions project are studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers at University of Massachusetts at Dartmouth and Tufts University are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. Most research has focused on student development at the upper elementary and middle school levels, but this project will add information about early elementary learners.

The project's research methodology uses teaching experiments which allow researchers to talk directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization. Researchers have designed tasks that help students explain their thinking and solve problems where some quantities vary and others are constant. They are analyzing videos and students' written work as they build case studies about the development of algebraic thinking. External evaluation of this exploratory project is one of the responsibilities of its advisory board.

This project is connecting the algebraic thinking of younger children to what has been documented for older children. This process enables them to build an evidence-based learning trajectory about students' development of algebraic thinking. The products of this research can be used to build curricula and lessons that are aligned with what students know and can learn at various points in their development. Project findings, tasks and videos are being disseminated not only to researchers, but also to practitioners through professional publications and the DRK-12 Resource Network.

Mathematical Argumentation in the Middle School is an exploratory project that is working in collaboration with teachers to increase their knowledge of mathematics for teaching in middle school. In addition to geometry and algebra, the professional development is focusing on the role of mathematical argumentation in the middle school and strategies for increasing argumentation. The research component of the project is providing insights into how teachers use their mathematical knowledge to increase argumentation in the classroom and to help students build skills in mathematical argumentation. In addition, the project is studying student outcomes such as reasoning, communication skills, and mathematical knowledge.

The project researchers are using both qualitative and quantitative methodologies to ensure that they have high quality data and analysis that will provide insights into the following research questions: 1) How do teachers use what they learn from the professional development (PD) experiences when they teach in the classroom? 2) To what extent does teachers? use of the project materials and what they learn in the PD result in mathematical argumentation in their classroom discourse? 3) Do students gain conceptual understanding of the mathematics as a result of their participation in argumentation in the classroom? Based on previous research, there is adequate evidence to believe that argumentation in the classroom does increase for participants in the workshop, but the researchers are seeking a better understanding of how teachers use their knowledge and the project materials to enact such an important change in mathematics lessons and in student learning. The professional development uses the dynamic software Geometers' Sketchpad, a carefully-designed, geometry curricular unit, and student materials to help teachers see how to set up a classroom environment that supports mathematical conjectures, arguments, and discussion. The research is done in the classroom and assesses the various components of the professional development in promoting argumentation.

The project is providing insights into how teachers use their mathematical knowledge to implement changes in the classroom. The project is creating effective professional development strategies, a middle school curriculum unit on geometry that emphasizes argumentation, and associated materials. The research is explaining how teachers use their knowledge and the materials and providing information on how students' conceptual knowledge develops through argumentation.

Research in biology has become increasingly mathematical, but high school courses in biology use little mathematics. To address this concern, this project will develop three replacement units for biology and refine them through classroom testing. The units will be models of STEM integration by using the important concepts of proportional reasoning and algebraic thinking and engineering re-design to address big ideas in science while also promoting the learning of 21st century skills. The materials build on existing work on the use of model eliciting activities and focus science and technology instruction on high-stakes weaknesses in mathematics and science. They address the scaling issue as part of the core design work by developing small units of curriculum that can be applied by early adopters in each context. The materials will undergo many rounds of testing and revision in the early design process with at least ten teachers each time. The materials will be educative for teachers, and the teacher materials and professional development methods will work at scale and distance.

Learning of science content will be measured through the use of existing instruments in wide use. Existing scales of task values, achievement goals and interest are used to measure student motivation. The work performed is guided by a content team; a scaling materials team; a scaling research team; the PI team of a cognitive scientist, a robotics educator, and a mathematics educator specializing in educational reform at scale; and the summative evaluation team lead by an external evaluator.

There is great interest in understanding whether integrated STEM education can interest more students in STEM disciplines. The focus on mathematics integrated with engineering in the context of a science topic is interesting and novel and could contribute to our understanding of integrating mathematics, engineering and science. The development team includes a cognitive scientist, a mathematics educator, teachers and scientists. The issues and challenges of interdisciplinary instruction will be investigated.

The CME Project Mathematical Practices Implementation Study project (formerly called "Changing Curriculum, Changing Practice"), led by mathematics educators at the Education Development Center, is studying the impact of implementing a NSF-funded, high school mathematics curriculum that emphasizes mathematical habits of mind. This curriculum focuses on ways of thinking and doing mathematics in contrast with curricula that focus on mathematical topics. The project is studying the development of teachers' mathematical knowledge for teaching and their capacity to align their instruction with the new curriculum. The project includes a moderate level of professional development and the development of valid and reliable instruments to assess teachers' mathematical knowledge for teaching and their instructional practices.

This four-year, mixed-methods study is investigating the conjecture that high school teachers' implementation of a curriculum emphasizing mathematical habits of mind will lead to measurable changes in teachers' mathematical knowledge and their instruction. The investigators are also interested in the relationships among (1) teachers' prior knowledge, (2) their use of the curriculum and (3) the school-level support for implementation. The investigators are studying the implementation of the curriculum by 70 teachers in 12 schools that vary in socio-economic status of the students and geographic location. The research design includes observations of the instruction of a sub-sample of nine teachers to obtain a finer-grained measure of instructional practice. They are developing or adapting existing instruments that measure teachers' knowledge and alignment of instruction with the goals of teaching mathematical habits of mind. Using the Instructional Quality Assessment rubric during visits to the classroom, they are assessing students' opportunities to develop mathematical thinking skills. The use of mixed-methods approaches will allow the researchers to analyze the data from multiple perspectives.

This study is part of a long-term effort to help high school students develop specific mathematical habits of mind. The current study is building on previous curriculum development and also developing insights for future studies investigating students' adoption of mathematical habits of mind. The current project is an important effort to understand the roles teachers play in implementing curricular changes that have the potential for improving student achievement in mathematics. Teachers are the critical bridging agents who connect curriculum and learners. This study will help to explain how teachers' knowledge, teachers' instruction, and teachers' contexts within schools contribute to or detract from the faithful implementation of the goals intended by a curriculum. It will lay a foundation for understanding future efforts to assess what students learn and how they learn it.

This is an exploratory project that endeavors to initiate an innovative approach to preK students’ development of quantitative reasoning through measurement. This quantitative approach builds on measurement concepts and algebraic design of the pre-numeric stage of instruction found in the successful Elkonin-Davydov (E-D) elementary mathematics curriculum from Russia. The PreKEA project will adapt and refocus the conceptual framework of the E-D pre-numeric stage with respect to early algebra in the context of teaching experiments with preK and kindergarten students. A primary goal of the project is to obtain a proof-of-concept and lay down a conceptual and empirical foundation for a subsequent full research and development DR K-12 proposal.

The importance of early algebra (EA) in mathematics education has been acknowledged by the publication of a separate chapter solely devoted to early algebra and algebraic reasoning in the second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007). Given that “much prior research highlights the difficulties that middle and high school students have with algebra,” the proponents of EA argue that “the weaving of algebra throughout the K-12 curriculum could lend coherence, depth, and power to school mathematics, and replace late, abrupt, isolated, and superficial high school algebra courses” (Carraher & Schliemann, 2007, pp. 670-671). At the same time, “quantitative thinking is unavoidable in EA” as it “does not seem realistic to first introduce youngsters to the algebra of number and then proceed to problems steeped in quantities as ‘applications’ of algebra” (ibid., p. 671). While the E-D curriculum with its proven track record focuses on the development of quantitative and measurement reasoning among elementary-aged children in grades 1–6, it is feasible that much younger children, even four-year-olds, can access the pre-numeric ideas. This is supported by research by Baillargeon (2001) and Wynn (1997) who showed that infants as young as two-months old demonstrate the development of number and measurement concepts. The PreKEA project will identify key concepts of the E-D pre-numeric stage relevant to four-year-olds and develop and explore lesson units which can be integrated into US preK settings. The project team combines the international expertise of PI Berkaliev who served as project coordinator and international liaison for an NSF-funded international project US-Russian Working Forum on Elementary Mathematics: Is the Elkonin-Davydov Curriculum a Model for the US? and who also brings the perspective of a mathematician, with the theoretical, methodological, and empirical expertise of co-PI Dougherty who has been one of the leading figures in working with, adapting, and studying the implementations of the E-D curriculum in the US, as well as a group of five leading Russian experts who developed, implemented, and studied the original E-D curriculum. The project resources include the E-D curriculum materials and articles only available in Russian.

The PreKEA (PreK Early Algebra through Quantitative Reasoning) project has the potential to make contributions beyond the preK early algebra curriculum that it will develop and implement. The PreKEA project can benefit disadvantaged students by using an innovative approach to EA instruction that has the potential to broaden access and at an early stage change the situation when disproportionately many disadvantaged students are not prepared adequately for learning quantitative reasoning and algebra. With research in preK narrowly focused on particular topics, the results of this project have the potential to inform a broader field including mathematics education and early childhood education with evidence that young children can access and interact with more complex mathematics, extending beyond counting.

Developers and researchers at the Illinois Institute of Technology and Iowa State University are initiating an innovative approach to pre-K students' development of quantitative reasoning through measurement. This quantitative approach builds on measurement concepts and algebraic design of the pre-numeric stage of instruction found in the Elkonin-Davydov (E-D) elementary mathematics curriculum from Russia. The project team is adapting and refocusing the conceptual framework and learning tasks of the E-D pre-numeric stage for use with four-year-olds. The adaptation is being done in collaboration with experts in Russia who were involved in the original E-D development. A primary goal of the project is to obtain a proof-of-concept and lay down a conceptual and empirical foundation for a subsequent research and development.

The research progresses using teaching experiments involving six students. Each student is engaged in 15 minute one-on-one sessions twice each week. Sessions are videotaped and transcribed for further analysis. The analysis of the data is conducted by the project team in collaboration with Russian consultants.

The research findings and methodology will provide grounds for supporting more complex and sophisticated mathematical ideas that will inform curriculum development for pre-K students and teachers. Results will be published and reported widely.

The UPDATE project seeks to enable significant advances in K-12 teacher and student learning of mathematics by using of items and data from the Program for International Student Assessment (PISA) in ways that enhance the work of mathematics teachers and teacher educators. We hypothesize that PISA can be useful to the field in much the same way as the National Assessment of Educational Progress (NAEP), which has long served as a key source of information for the mathematics education community. In contrast to NAEP and TIMSS, the Program for International Student Assessment (PISA) in the area of mathematics has received little or no attention within the U.S. mathematics education community, beyond noting that the performance of U.S. students is mediocre compared to that of students in many other countries in Asia and Europe. A consequence of the lack of attention to PISA in the U.S. is that we have underutilized a potentially valuable source of information for improvement of mathematics education.

In this project we use PISA as a base to develop resources for mathematics educators to use in teacher education settings. One type of resource comes in the form of prototype professional learning materials that provide opportunities for teachers and students to analyze complex mathematical tasks and student responses to those tasks, focusing on both the mathematics entailed in the task and the understandings of mathematics reflected in students’ responses. The materials will be designed to engage teachers in individual and collaborative inquiry aimed at developing their specialized content knowledge and their pedagogical content knowledge. Materials will be field tested in preservice and inservice teacher professional education settings and also shared at regional and national meetings. A second type of resource comes in the form of PISA-based, research-grounded articles written specifically for mathematics teachers and teacher educators and published in journals that reach these audiences. The articles will be informed not only by our experiences in developing and using the prototype materials, but also by the findings of selected secondary analyses of data collected in the 2003 PISA assessment.

Our work is organized around three distinct focus areas: (1) Algebra – a traditional content topic familiar to mathematics teachers that can be approached in a novel way through PISA tasks; (2) Quantitative Literacy – a nontraditional content topic less familiar to mathematics teachers that can be accessed directly through PISA tasks, and (3) Equity – an issue of import to mathematics educators that can be examined carefully using PISA data. In each component our work blends research inquiry and development, integrating the analysis of tasks and data from the PISA mathematics assessment with the creation of prototype teacher education materials and the preparation of PISA-based, research-grounded articles for teachers and teacher educators.

The results of this exploratory study will be disseminated broadly, and they are likely to generate new activity in research and development related to PISA. Mirroring the tradition of the interpretive reports of NAEP results, we will produce PISA-based resources that can have a significant impact on the mathematics education community as teachers, teacher educators, and graduate students examine the materials and reports we produce and use them to improve the quality of teacher and student learning of mathematics.

This exploratory project led by faculty from the University of Michigan uses items and data from the Program for International Student Assessment (PISA) to develop two kinds of resources for preparation and professional development of secondary mathematics teachers. One type of resource comes in the form of prototype professional learning materials that provide opportunities for teachers and students to analyze complex mathematical tasks and student responses to those tasks, focusing on both the mathematics entailed in the task and the understandings of mathematics reflected in students' responses. A second type of resource comes in the form of PISA-based, research-grounded articles written specifically for mathematics teachers and teacher educators. Work on both resources will focus on the critical content areas of algebra and quantitative literacy and on factors influencing educational equity.

The project is driven by the hypothesis that PISA assessment instruments and findings can be useful to teachers in much the way that prior analyses of NAEP frameworks, items, and data have been. To address the first project objective, the research team will use selected PISA items and student responses to those items to design, develop, and test a collection of professional learning tasks that engage mathematics teachers in individual and collaborative inquiry aimed at enhancing their specialized content knowledge and their pedagogical content knowledge. To address the second project objective, the research team will prepare articles for practitioner journals that will be informed by experiences in developing and using the prototype materials, but also by the findings of selected secondary analyses of data collected in the 2003 PISA assessment.

The results of this work will be a collection of resources for use in various teacher preparation and professional development settings to stimulate thinking of secondary mathematics teachers about issues of curriculum content, student learning, teaching, and assessment.