Teacher Content Knowledge

Expanding and Sustaining Understanding Evolution

This project will (1) identify the characteristics and needs of college-level target learners and their instructors with respect to evolution, (2) articulate the components for expanding the Understanding Evolution (UE) site to include an Undergraduate Lounge in which students and instructors will be able to access a variety of evolution resources, (3) develop a strategic plan for increasing awareness of UE, and (4) develop a strategic plan for maintenance and continued growth of the site.

Award Number: 
0841757
Funding Period: 
Wed, 10/15/2008 to Thu, 09/30/2010
Full Description: 

The University of California Museum of Paleontology (UCMP) will bring together an experienced group of evolution educators in order to inform the development and maintenance of an effective resource for improving evolution education at the college level. This effort falls under the umbrella of UCMP's highly successful Understanding Evolution (UE) project (http://evolution.berkeley.edu), which currently receives over one million page requests per month during the school year. UE was originally designed around the needs of the K-12 education community; however, increasingly, the site is being used by the undergraduate education community. UCMP intends to embark on an effort to enhance the utility of the UE site for that population, increase awareness of the site at the college level, and secure the project's future so that it can continue to serve K-16 teachers and students. To inform and guide these efforts, UCMP proposes to establish and convene a UE Advisory Board, which will be charged with helping to: (1) identify the characteristics and needs of college-level target learners and their instructors with respect to evolution, (2) articulate the recommended components for expanding the UE site to include an Undergraduate Lounge in which students and their instructors will be able to access a variety of resources for increasing understanding of evolution, (3) develop a strategic plan for increasing awareness of UE within the undergraduate education community, and (4) develop a strategic plan for maintenance and continued growth of the UE site.

Changing Curriculum, Changing Practice

This project 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.

Award Number: 
1019945
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2012
Full Description: 

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.

Expanding PhET Interactive Science Simulations to Grades 4-8: A Research-Based Approach

Colorado’s PhET project and Stanford’s AAALab will develop and study learning from interactive simulations designed for middle school science classrooms. Products will include 35 interactive sims with related support materials freely available from the PhET website; new technologies to collect real-time data on student use of sims; and guidelines for the development and use of sims for this age population. The team will also publish research on how students learn from sims.

Project Email: 
Lead Organization(s): 
Award Number: 
1020362
Funding Period: 
Wed, 09/01/2010 to Sat, 08/31/2013
Project Evaluator: 
Stephanie Chasteen
Full Description: 

In this DRK12 project, the PhET Interactive Simulations group at the University of Colorado and the AAALab at Stanford University are working together to produce and study learning from interactive simulations designed for middle school science classrooms. We are developing a suite of 35 high-quality, interactive simulations covering physical science topics. These simulations include innovative technologies that provide teachers with real-time, formative feedback on how their students are using the simulations.  The research investigates how various characteristics of the simulation design influence student engagement and learning, and how this response varies across grade-level and diverse populations. The research also includes an investigation of different ways of using simulations in class, and how these approaches affect student preparation for future learning when they are no longer using a given simulation.

      The original PhET simulations were designed for college use, but overtime, they have migrated to lower grades.  The current suite of free research-based, interactive PhET science simulations are used over 10 million times per year.  To optimize their utility for middle school science, we are conducting interviews with diverse 4-8th graders using 25 existing PhET simulations to help identify successful design alternatives where needed, and to formulate generalized design guidelines. In parallel, pull-out and classroom-based studies are investigating a variety of lesson plans to identify the most promising approach. These studies include controlled comparisons that collect both qualitative and quantitative data.

      On the basis of our emerging design principles, we are developing 10 new simulations in consultation with teachers, who are helping to identify high need areas for simulations. These new simulations also include a back-end data collection capability that can collect, aggregate, and display student patterns of simulation use for teachers and researchers. The design of the data collection and presentation formats depends on an iterative process done in collaboration with teachers to identify the most useful information and display formats. A final evaluation compares student learning with and without this back-end formative assessment technology.   

This project is working to transform the way science is taught and learned in Grades 4-8 so that it is more effective at promoting scientific thinking and content learning, while also being engaging to diverse populations. The project is expected to impact many, many thousands of teachers and students through its production of a suite of 35 free, interactive science simulations optimized for Grades 4-8 along with “activity templates”, guidance, and real time feedback to teachers to support pedagogically effective integration into classrooms. Finally, the intellectual merit of the project is its significant contributions to understanding when, how, and why interactive simulations can be effective learning and research tools.

Evaluating the Developing Mathematical Ideas Professional Development Program: Researching its Impact on Teaching and Student Learning

This is a 3.5-year efficacy study of the Developing Mathematical Ideas (DMI) elementary math teacher professional development (PD) program. DMI is a well-known, commercially available PD program with substantial prior evidence showing its impact on elementary teachers' mathematical and pedagogical knowledge. However, no studies have yet linked DMI directly with changes in teachers' classroom practice, or with improved student outcomes in math. This study aims to remedy this gap.

Project Email: 
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1019769
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2012
Project Evaluator: 
Bill Nave
Full Description: 

This is a 3.5-year efficacy study of the Developing Mathematical Ideas (DMI) elementary math teacher professional development (PD) program. DMI was developed by staff from Education Development Center (EDC), SummerMath for Teachers, and TERC, the STEM research and development institution responsible for this research. DMI is a well-known, commercially available PD program with substantial prior evidence showing its impact on elementary teachers' mathematical and pedagogical knowledge. However, no studies have yet linked DMI directly with changes in teachers' classroom practice, or with improved student outcomes in math. This study aims to remedy this gap.

The research questions for the study are:

1) Does participation in the Developing Mathematical Ideas (DMI) professional development program lead to increases in reform-oriented teaching?

2) Does participation in DMI lead to increases in students' mathematics learning and achievement, especially in their ability to explain their thinking and justify their answers?

3) What is the process by which a reform-oriented professional development program can influence teaching practice and, thus, student learning? Through what mechanisms does DMI have impact, and with what kinds of support do we see the desired changes on our outcome measures when the larger professional development context is examined?

The dependent variables for this study include a) teachers' pedagogical and mathematics knowledge for teaching; b) the nature of their classroom practice; and c) student learning/ achievement in mathematics.

The study uses experimental and quasi-experimental methods, working with about 195 elementary grades teachers and their students in Boston, Springfield, Leominster, Fitchburg, and other Massachusetts public schools. Volunteer teachers are randomly assigned either to PD with DMI in the first year of the efficacy study, or to a control group that will wait until the second year of the study to receive DMI PD. Both groups of teachers will be followed through two academic years. Analyses use OLS regression, hierarchical modeling, and structural equation modeling, as appropriate, to compare the two groups and to track changes over time. In this way, the project explores several aspects of a conceptual framework hypothesizing relationships among PD, teacher mathematical and pedagogical knowledge, classroom teaching practice, and student outcomes. There are multiple measures of each construct, including video-analysis of teacher practice, and a new video-based measure of teacher knowledge.

The study tests the impact of DMI in a range of districts (large urban, small urban, suburban) serving an ethnically and economically diverse mix of students. It provides much needed, rigorous evidence testing the efficacy of this reform-oriented professional development program. It also directly explores the commonplace theory that teachers' understanding of content and student thinking and their encouragement of rich mathematical discourse for student sense-making lead to improvement on measures of mathematics achievement. Findings from the study are disseminated to both research and practitioner communities. The project provides professional development in mathematics to about 195 teachers to improve their ability to teach important concepts. If the evidence for efficacy is positive, then even larger-scale use of this PD program is likely.

Differentiated Professional Development: Building Mathematics Knowledge for Teaching Struggling Learners

This project is creating and studying a blended professional development model (face-to-face and online) for mathematics teachers and special educators (grades 4-7) with an emphasis on teaching struggling math students in the areas of fractions, decimals, and positive/negative numbers (Common Core State Standards). The model's innovative design differentiates professional learning to address teachers' wide range of prior knowledge, experiences, and interests.

Award Number: 
1020163
Funding Period: 
Wed, 09/01/2010 to Wed, 08/31/2011
Project Evaluator: 
Teresa Duncan
Full Description: 

This project under the direction of the Education Development Center is creating and studying a  professional development model for middle school mathematics teachers with an emphasis on teaching struggling math students in the areas of fractions and rational numbers. There are three components to the PD for teachers: online modules, professional learning communities, and face-to-face workshops. There are four online modules 1) Fraction sense: concepts, addition, and subtraction, 2) Fraction multiplication and division; 3) Decimal and percent operations; and 4) Positive/Negative including concepts and operations. Each module is one week long. There are common sessions and special emphasis ones depending on the needs of the teacher. The project addresses three research questions: 1) To what extent do participating teachers show changes in their knowledge of rational numbers and integers, pedagogical knowledge of and beliefs about instructional practices for struggling students and abilities to use diagnostic approaches to identify and address student difficulties?; 2) To what extent do students of participating teachers increase their mathematical understanding and skill?; and 3) To what extent do students of participating teachers show positive changes in their attitudes toward learning mathematics?

In the first year of work on the professional development program, fifty-five teachers will test the initial components of the differentiated modules. In years two and three an additional 160 teachers will participate in the professional development and research to test efficacy of the professional development model. In addition to this testing, twelve teachers will be selected for intensive case studies. Teacher content knowledge, pedagogical content knowledge, and attitudes will be assessed by various well-validated instruments, and changes in their classroom practice will be assessed by classroom observations. Effects of the teacher professional development on student learning will be evaluated by analysis of data from state assessments and by performance on selected items from NAEP and other standardized tests.

This project will result in a tested innovative model for professional development of mathematics teachers to help them with the critical challenge of assisting students who struggle in learning the core concepts and skills of rational numbers and integers. Deliverables will include the on-line modules, materials for workshop and professional learning community work, new research instruments, and research reports.

Virtual Learning Communities: An Online Professional Development Resource for STEM Teachers

This project will design, develop, and test a virtual learning community (VLC) to enhance the ability of first- and fourth-grade teachers to provide mathematics education. The goal is to produce a prototype of a VLC for first- and fourth-grade Everyday Mathematics teachers that integrates three primary elements: (a) learning objects rooted in practice, such as lesson video, (b) community-building tools offered by the internet, and (c) focused content that drives teachers' professional learning in mathematics.

Project Email: 
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1020083
Funding Period: 
Thu, 07/15/2010 to Sun, 06/30/2013
Project Evaluator: 
none
Full Description: 

Researchers and developers at the University of Chicago are conducting an exploratory project to design, develop, and test a virtual learning community (VLC) to enhance the ability of first- and fourth-grade teachers to provide mathematics education. The project deploys cyberlearning technologies to allow teachers to interact with one another and with experts across the U.S. The goal is to produce a prototype of a VLC for first- and fourth-grade Everyday Mathematics teachers that integrates three primary elements: (a) learning objects rooted in practice, such as lesson video, (b) community-building tools offered by the internet, and (c) focused content that drives teachers' professional learning in mathematics.

This VLC is developed during two engineering cycles in which the project team engages teachers as central partners. The quality and utility of the resultant VLC is tested against the anticipated outcomes of (a) sustained participation by teachers in the VLC and (b) changes in teachers' "professional vision" in mathematics education. Sustained participation is tracked using web analytics and user logs. Changes in professional vision are measured by on-line assessment tools used by approximately 150 teachers.

The VLC develops learning objects; community-building tools; and focused content. The VLC will be launched during the third year of the project by way of the Everyday Mathematics website, which has over 6000 visitors per day, and the University of Chicago School Mathematics Project newsletter, which has a circulation of 40,000. The potential audience is quite large since Everyday Mathematics is used in 185,000 classrooms.

CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

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.

Award Number: 
0952415
Funding Period: 
Mon, 03/15/2010 to Mon, 02/28/2011
Full Description: 

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.

Across the Sciences: Multidisciplinary Learning for Teachers through Multimedia

This project will conduct a professional development series to improve the content knowledge of science teachers. "Across the Sciences," a ten-unit series requiring approximately 145 hours to complete, will better qualify 9th and 10th grade science teachers to teach multidisciplinary science courses. Teachers prepared in one science discipline will benefit from opportunities to increase and deepen their interdisciplinary science content knowledge and their understanding of student needs associated with learning science.

Lead Organization(s): 
Award Number: 
0554217
Funding Period: 
Sat, 07/01/2006 to Thu, 06/30/2011
Full Description: 

Biological Sciences Curriculum Study (BSCS) and Oregon Public Broadcasting (OPB) will conduct a professional development series to improve the content knowledge of science teachers. "Across the Sciences," a ten-unit series requiring approximately 145 hours to complete, will better qualify 9th and 10th grade science teachers to teach multicisciplinary science courses. The number of these courses is increasing. Teachers prepared in one science discipline will benefit from opportunities to increase and deepen their interdiciplinary science content knowledge and their understanding of student needs associated with learning science. The target audience is in-service and pre-service teachers who anticipate teaching courses that use a multidisciplinary approach, or teachers who over the past 3-5 years have begun to teach multidisciplinary science. Special care is given to materials developed for teachers in resource-poor schools and for those who need additional knowledge to deliver science in a culturally competent framework. Teachers participating in this project have the option to register for college credit through Montana State University and thus move toward recertification and/or earning an advanced degree.

Mapping Developmental Trajectories of Students' Conceptions of Integers

This project is using data from interviews with 160 K-12 students and 20 adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers.

Project Email: 
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0918780
Funding Period: 
Sat, 08/15/2009 to Sun, 07/31/2011
Project Evaluator: 
West Ed (Juan Carlos Bojorquez)
Full Description: 

The project Mapping Developmental Trajectories of Students' Conceptions of Integers, led by faculty from San Diego State University, is using data from 160 interviews with K-12 students and 20 adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers.

Two questions frame and guide the proposed research:

* What are students' conceptions of integers and operations on integers?

* What are possible developmental trajectories of students' understandings?

The investigators are seeking answers to those questions through structured interviews with students in elementary grades prior to instruction about negative numbers (Grades 2 and 4), students in middle grades whose formal learning experiences have already included explicit instruction about integers (Grade 7), high school students who are expected to use prior knowledge about integers in more advanced mathematics (Grade 11 PreCalculus and Calculus students), and adults who use integers in their work.

In addition to providing an empirically-based picture of ways that students reason about negative numbers, the project is producing useful interview protocols and a reliable and valid assessment instrument for describing the understanding and skill of students at various stages on such a progression.

Both the characterization of common learning progressions and the assessment instruments will be broadly useful to curriculum and test developers and teachers in K-12 mathematics classrooms.

Math Snacks: Addressing Gaps in Conceptual Mathematics Understanding with Innovative Media

This project is developing and evaluating effectiveness of 15 - 20 short computer mediated animations and games that are designed to: (1) increase students' conceptual understanding in especially problematic topics of middle grades mathematics; and (2) increase students' mathematics process skills with a focus on capabilities to think and talk mathematically.

Lead Organization(s): 
Award Number: 
0918794
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
Sheila Cassidy WEXFORD INC.
Full Description: 

View a project spotlight on Math Snacks.

This project Math Snacks: Addressing Gaps in Conceptual Mathematics Understanding with Innovative Media, led by mathematics and education faculty at New Mexico State University, is developing and evaluating effectiveness of 15 - 20 short computer mediated animations and games that are designed to: (1) increase students' conceptual understanding in especially problematic topics of middle grades mathematics; and (2) increase students' mathematics process skills with a focus on problem-solviing and communicating mathematically. The basic research question for this project is whether the planned collection of computer-mediated animations and games can provide an effective strategy for helping students learn core middle grades mathematics concepts in conceptual areas that research suggests are difficult for these students.  A second question relates to types of delivery that are effective for mathematics learning using these tools including in classrooms during extended learning time at home or in informal educational settings. The project is developing and testing the effectiveness of a set of such learning tools and companion print materials, including student and teacher guides, and short video clips documenting best practices by  teachers using the developed materials with students. A pilot study in year 3 and a substantial randomized control trial in year 4 will test the effects of using the Math Snacks web-based and mobile technologies on student learning and retention of identified core middle school mathematics concepts, as measured by performance on disaggregated strands of the New Mexico state standardized mathematics assessments. Thus the project will produce animations and games using the web and new mobile technologies, and useful empirical evidence about the efficacy of their use. One of the key features of the Math Snacks project is development of the mediated games and simulations in a form that can be used by students outside of normal classroom settings on media and game players that are ubiquitous and popular among today's young people. Thus the project holds the promise of exploiting learning in informal settings to enhance traditional school experiences.

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