This project will provide an empirically-supported learning progression for a key scientific practice, scientific modeling. The specific instructional materials created as part of the project can serve as a model other developers can use to design materials supporting scientific modeling and other practices. The model for educative curriculum materials as a form of teacher support can be adapted to support teacher learning about modeling or other scientific practices in other curriculum materials.

# Projects

This project targets first- and second-grade children who struggle to develop a deeper understanding of the mathematical strand of number and operation. The research team will (a) identify the various specific cognitive obstacles of first- and second-grade students who are struggling in number and operation, and (b) explore how instructional tasks designed to address specific cognitive obstacles affect the learning trajectory of struggling learners in number and operation.

This project will study the activities of a Networked Improvement Community (NIC) as a vehicle to bridge gaps across four identified steps along the science teacher training and development pathways within local contexts of 8 participating universities. The overarching goal of the project is to strengthen the capacity of universities and school districts to reliably produce teachers of science who are knowledgeable about and can effectively enact the Next Generation Science Standards (NGSS), although prepared in varied organizational contexts.

This project is carrying out a research and development initiative to increase the success rates of our most at-risk high school students—ninth-grade students enrolled in algebra classes but significantly underprepared for high school mathematics. It will also result in new understandings about effective approaches for teaching mathematics to struggling students and about effective ways for implementing these approaches at scale, particularly in urban school districts.

The goal of this project is to develop learning progressions and assessment items targeting computational thinking. The items will be used for a test of college-ready critical reasoning skills and will be integrated into an existing online assessment system, the Berkeley Assessment System Software.

This project will build on prior funding to design a next generation diagnostic assessment using learning progressions and other learning sciences research to support middle grades mathematics teaching and learning. The project will contribute to the nationally supported move to create, use, and apply research based open educational resources at scale.

*Understanding Science *provides an accurate portrayal of the nature of science and tools for teaching associated concepts. This project has at its heart a public re-engagement with science that begins with teacher preparation. To this end, its immediate goals are (1) improve teacher understanding of the nature of the scientific enterprise and (2) provide resources and strategies that encourage and enable K-16 teachers to incorporate and reinforce the nature of science throughout their science teaching.

Advancing Reasoning addresses the lack of materials for teacher education by investigating pre-service secondary mathematics teachers' quantitative reasoning in the context of secondary mathematics concepts including function and algebra. The project extends prior research in quantitative reasoning to develop differentiated instructional experiences and curriculum that support prospective teachers' quantitative reasoning and produce shifts in their knowledge.

This study seeks to describe trajectories that describe the ways in which Black learners develop as particular kinds of mathematical learners. The study takes place in the context of an established, multi-year college bridge program that has as its goals to increase the representation of historically marginalized groups in the university community.

This project will design and develop specialized instructional materials and guidelines for teaching secondary algebra in linguistically diverse classrooms. These materials will incorporate current research on student learning in mathematics and research on the role of language in students' mathematical thinking and learning. The work will connect research on mathematics learning generally with research on the mathematics learning of ELLs, and will contribute practical resources and guidance for mathematics teachers who teach ELLs.

This project is documenting how students with learning disabilities (LD) access and advance their conceptual understanding of fractions. Rather than focusing on the knowledge students do not have, this work is focused on uncovering students' informal knowledge that can bridge to fractions and how instruction can be used to promote conceptual change.

The proposed project initiates new research and an integrated education plan to address specific problems in middle school mathematics classrooms by investigating (1) how to effectively differentiate instruction for middle school students at different reasoning levels; and (2) how to foster middle school students' algebraic reasoning and rational number knowledge in mutually supportive ways.

This program of research will examine how middle school pre-service teachers' knowledge of mathematical argumentation and proving develops in teacher preparation programs. The project explores the research question: What conceptions of mathematical reasoning and proving do middle school preservice teachers hold in situations that foster reasoning about change, proportionality, and proportional relationships, as they enter their mathematics course sequence in their teacher preparation program, and how do these conceptions evolve throughout the program?

Most students learn about negative numbers long after they have learned about positive numbers, and they have little time or opportunity to build on their prior understanding by contrasting the two concepts. The purpose of this CAREER project is to identify language factors and instructional sequences that contribute to improving elementary students' understanding of addition and subtraction problems involving negative integers.

The purpose of this project is to examine the process by which math language instruction improves learning of mathematics skills in order to design and translate the most effective interventions into practical classroom instruction.

The aim of this project 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.

This project addresses a gap between vision and implementation of state science standards by designing a coordinated suite of instructional, assessment and teacher professional learning materials that attempt to enact the vision behind the Next Generation Science Standards. The study focuses on using state-of-the-art technology to create an 8-week long, immersive, life science field experience organized around three investigations.

Computational and algorithmic thinking are new basic skills for the 21st century. Unfortunately few K-12 schools in the United States offer significant courses that address learning these skills. However many schools do offer robotics courses. These courses can incorporate computational thinking instruction but frequently do not. This research project aims to address this problem by developing a comprehensive set of resources designed to address teacher preparation, course content, and access to resources.

This project will adapt and study a promising and replicable teacher professional development (PD) intervention, called Collaborative Math (CM), for use in early childhood programs. Prepared as generalists, preschool teachers typically acquire less math knowledge in pre-service training than their colleagues in upper grades, which reduces their effectiveness in teaching math. To address teacher PD needs, the project will simultaneously develop teacher content knowledge, confidence, and classroom practice by using a whole teacher approach.

The project continues and completes the development and refinement of an electronic Test of Early Numeracy (e-TEN) in English and Spanish, focused on number and operations for young learners. The assessment incorporates a learning trajectory approach that describes students' development of the understanding of numbers. The electronic assessment allows for the test to adapt to students' responses and incorporate games increasing children's engagement with the tasks.

This project will design, develop, and examine the learning outcomes of a new curriculum unit for biology that embodies the conceptual framework of the Next Generation Science Standards (NGSS). The curriculum materials to be developed by this project will focus on two areas of study that are central to the life sciences: genetics and the processes of evolution by natural selection.

This five-year project investigates how to provide continuous assessment and feedback to guide students' understanding during science inquiry-learning experiences, as well as detailed guidance to teachers and administrators through a technology-enhanced system. The assessment system integrates validated automated scorings for students' written responses to open-ended assessment items into the "Web-based Inquiry Science Environment" (WISE) program.

This project is working to create a cyber infrastructure that supports development and documentation of additional interventions for teacher professional development using the video collection, as well as other videos that might be added in the future by teacher educators or researchers, including those working in other STEM domains.

This project is developing a model for integrating best practices in technology-supported instructional design and formative assessment for genetics instruction in upper elementary, middle and high school. Using the Web-based Inquiry Science Environment platform, the project is developing school curriculum that scaffold and model scientific practices, enable students to interface with real-world problems, provide opportunities for students to make connections between visible phenomena and underlying genetic processes, and promote student monitoring and reflection on learning.

This project is developing and testing a curricular learning progression of early algebra objectives and activities for students in grades 3 - 5. The goal of the work is to provide teachers with curricular guidance and instructional resources that are useful in preparing students for success in study of algebra at the middle grade level. The project is also developing and validating assessment tools for evaluating student progress toward essential pre-algebra mathematical understandings.