Disciplinary Content Knowledge

Developing Teaching Expertise in K-5 Mathematics

This project designs materials and an accompanying support system to enable the development of expertise in the teaching of mathematics at the elementary level. The project has four main components: online professional development modules; practice-based assessments; resources for facilitators; and web-based technologies to deliver module content to diverse settings. Three modules are being developed and focus on fractions, reasoning and explanation, and geometry. Each module is organized into ten 1.5 hour sessions.

Project Email: 
Award Number: 
1118745
Funding Period: 
Thu, 09/01/2011 to Fri, 08/31/2018
Project Evaluator: 
American Institutes for Research
Full Description: 

Developers and researchers at the University of Michigan and the University of Denver are engaged in a project to design materials and an accompanying support system to enable the development of expertise in the teaching of mathematics at the elementary level. The project has four main components: a set of online professional development modules; practice-based assessments; a set of resources for facilitators; and web-based technologies to deliver module content to diverse settings. Three modules are planned: one focused on fractions and one focused on reasoning and explanation designed by Deborah Ball, Hyman Bass and the University of Michigan development team; and one on geometry developed by Douglas Clements and Julie Sarama at the University of Denver. Each module is organized into ten 1.5 hour sessions. 

Each module goes through a two-year design and development process that includes initial design, piloting, revision, and dissemination. Modules are piloted in a variety of settings, including university based courses for practicing teachers and district based in-service activities. These contexts include face-to-face professional development, real-time distance learning, and combinations of the two. Data are collected on participant engagement with the modules, on teacher classroom practice, and on mathematical knowledge for teaching.

The modules and associated materials will be widely available and will be free to schools. The materials can be imported into any learning management system, such as Blackboard, Moodle, and others.

Levels of Conceptual Understanding in Statistics (LOCUS)

LOCUS (Levels of Conceptual Understanding in Statistics) is an NSF Funded DRK12 project (NSF#118618) focused on developing assessments of statistical understanding. These assessments will measure students’ understanding across levels of development as identified in the Guidelines for Assessment and Instruction in Statistics Education (GAISE). The intent of these assessments is to provide teachers and researchers with a valid and reliable assessment of conceptual understanding in statistics consistent with the Common Core State Standards (CCSS).

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1118168
Funding Period: 
Thu, 09/01/2011 to Fri, 08/31/2012
Project Evaluator: 
TERC, Jim Hammerman
Full Description: 

The goal of this project is to develop two tests (instruments) to assess conceptual understanding of statistics. The instruments are based on the levels A/B and on level C of statistical understanding development as described in the American Statistical Association Guidelines for Assessment and Instruction of Statistics Education (GAISE) framework. These instruments will be used to assess knowledge of statistics by grades 6-12 students. The instruments will have multiple-choice and constructed response (CR) items. The CR items will have scoring rubrics. The assessments will be pilot tested in school districts in six states. The instruments will be used by teachers to analyze students' growth in understanding of statistics and will be useable for both formative and summative purposes. An assessment blueprint will be developed based on the GAISE framework for selecting and constructing both fixed-choice and open-ended items. An evidenced-based designed process will be used to develop the assessments. The blueprint will be used by the test development committee to develop items. These items will be reviewed by the advisory board considering the main statistics topics to be included on the assessments. Through a layering process, the assessments will be piloted, revised, and field tested with students in grades 6-12 in six states. A three-parameter IRT model will be used in analyzing the items. The work will be done by researchers at the University of Florida with the support of those at the University of Minnesota, the Educational Testing Service, and Kenyon College. Researchers from TERC will conduct a process evaluation with several feedback and redesign cycles.

The assessments will be aligned with the Common Core State Standards for mathematics (CCSSM) and made available as open-source to teachers through a website. The research team will interact with the state consortia developing assessments to measure students' attainment of the CCSSM. As such, the assessments have the potential of being used by a large proportion of students in the country. The more conceptually-based items will provide teachers with concrete examples of what statistics students in grades 6-12 should know.

Continuous Learning and Automated Scoring in Science (CLASS)

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.

Award Number: 
1119670
Funding Period: 
Thu, 09/01/2011 to Mon, 08/31/2015
Full Description: 

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 (i.e., short essays, science narratives, concept mapping, graphing problems, and virtual experiments) into the "Web-based Inquiry Science Environment" (WISE) program. WISE is an online science-inquiry curricula that supports deep understanding through visualization of processes not directly observable, virtual experiments, graphing results, collaboration, and response to prompts for explanations. In partnership with Educational Testing Services (ETS), project goals are: (1) to develop five automated inquiry assessment activities that capture students' abilities to integrate their ideas and form coherent scientific arguments; (2) to customize WISE by incorporating automated scores; (3) to investigate how students' systematic feedback based on these scores improve their learning outcomes; and (4) to design professional development resources to help teachers use scores to improve classroom instruction, and administrators to make better informed decisions about teacher professional development and inquiry instruction. The project targets general science (life, physical, and earth) in three northern California school districts, five middle schools serving over 4,000 6th-8th grade students with diverse cultural and linguistic backgrounds, and 29 science teachers. It contributes to increase opportunities for students to improve their science achievement, and for teachers and administrators to make efficient, evidence-based decisions about high-quality teaching and learning.

A key research question guides this effort: How automated scoring of inquiry assessments can increase success for diverse students, improve teachers' instructional practices, and inform administrators' decisions about professional development, inquiry instruction, and assessment? To develop science inquiry assessment activities, scoring written responses include semantic, syntax, and structure of meaning analyses, as well as calibration of human-scored items with a computer-scoring system through the c-rater--an ETS-developed cyber learning technology. Validity studies are conducted to compare automated scores with human-scored items, teacher, district, and state scores, including sensitivity to the diverse student population. To customize the WISE curriculum, the project modifies 12 existing units and develops nine new modules. To design adaptive feedback to students, comparative studies explore options for adaptive guidance and test alternatives based on automated scores employing linear models to compare student performance across randomly assigned guidance conditions; controlling for covariates, such as prior science scores, gender, and language; and grouping comparison studies. To design teacher professional development, synthesis reports on auto-scored data are created to enable them to use evidence to guide curricular decisions, and comments' analysis to improve feedback quality. Workshops, classroom observations, and interviews are conducted to measure longitudinal teachers' change over time. To empower administrators' decision making, special data reports, using-evidence activities, individual interviews, and observation of administrators' meetings are conducted. An advisory board charged with project evaluation addresses both formative and summative aspects.

A research-informed model to improve science teaching and learning at the middle school level through cyber-enabled assessment is the main outcome of this effort. A total of 21 new, one- to three-week duration standards-based science units, each with four or more automatically scored items, serve as prototypes to improve students' performance, teachers' instructional approaches, and administrators' school policies and practices.

Enhancing Games with Assessment and Metacognitive Emphases (EGAME)

This development and research project designs, develops, and tests a digital game-based learning environment for supporting, assessing and analyzing middle school students' conceptual knowledge in learning physics, specifically Newtonian mechanics. This research integrates work from prior findings to develop a new methodology to engage students in deep learning while diagnosing and scaffolding the learning of Newtonian mechanics.

Lead Organization(s): 
Award Number: 
1119290
Funding Period: 
Thu, 09/01/2011 to Mon, 08/31/2015
Full Description: 

This development and research project from Vanderbilt University, Facet Innovations, and Filament Games, designs, develops, and tests a digital game-based learning environment for supporting, assessing and analyzing middle school students' conceptual knowledge in learning physics, specifically Newtonian mechanics. This research integrates work from prior findings and refines computer assisted testing and Hidden Markov Modeling to develop a new methodology to engage students in deep learning while diagnosing and scaffolding the learning of Newtonian mechanics.

The project uses a randomized experimental 2 x 1 design comparing a single control condition to a single experimental condition with multiple iterations to test the impact of the game on the learning of Newtonian physics. Using designed based research with teachers and students, the researchers are iteratively developing and testing the interactions and knowledge acquisition of students through interviews, pre and post tests and stealth assessment. Student learner action logs are recorded during game-play along with randomized student interviews. Students' explanations and game-play data are collected and analyzed for changes in domain understanding using pre-post tests assessment.

The project will afford the validation of EGAME as an enabler of new knowledge in the fields of cognition, conceptual change, computer adaptive testing and Hidden Markov Modeling as 90 to 300 middle school students learn Newtonian mechanics, and other science content in game-based learning and design. The design of this digital game platform encompasses a very flexible environment that will be accessible to a diverse group of audiences, and have a transformational affect that will advance theory, design and practice in game-based learning environments.

Investigating and Supporting the Development of Ambitious and Equitable Mathematics Instruction at Scale

This project is supporting and investigating the implementation of reformed mathematics instruction at the middle school level in two large school districts. The primary goal of the project is to develop an empirically grounded theory of action for implementing reform at school and district levels. The researchers are investigating reform within a coherent system that focuses on leadership and school-based professional development.

 

Lead Organization(s): 
Award Number: 
1119122
Funding Period: 
Mon, 08/15/2011 to Tue, 07/31/2012
Full Description: 

The Development of Ambitious and Equitable Mathematics Instruction project is supporting and investigating the implementation of reformed mathematics instruction at the middle school level in two large school districts. Project researchers are asking: What does it take to support mathematics teachers' development of ambitious and equitable instructional practices on a large scale? The project has built on what was learned in a previous, successful project studying the implementation of a middle school mathematics curriculum. The primary goal of the new project is to develop an empirically grounded theory of action for implementing reform at school and district levels. The researchers are investigating reform within a coherent system that focuses on leadership and school-based professional development. In addition, they are facilitating a longitudinal study of the curriculum implementation by continuing the data collection from the original study.

In order to build a theory of action, the project team is synthesizing data from a variety of domains including instructional systems (e.g., curriculum, materials, professional development, support for struggling students, and learning communities), mathematics coaching, networks of teachers, school leadership, and district leadership. Investigators are using a variety of analytic techniques to successfully integrate both quantitative and qualitative data as they seek to understand how school district strategies are playing out in schools and classrooms and how those strategies can be revised in order to improve student learning of mathematics.

An empirically grounded theory of action for implementing reform will help the mathematics education community to implement and to understand the process of reforming mathematics instruction at the middle school level. Many advances in mathematics instruction have been documented within a limited context, but researchers and practitioners need to understand the full range of action necessary to achieve similar successes at a district-wide level. The model developed from this project, in conjunction with longitudinal data, has the potential to guide future reform efforts that seek to provide ambitious and equitable mathematics instruction.

Supports for Learning to Manage Classroom Discussions: Exploring the Role of Practical Rationality and Mathematical Knowledge for Teaching

This project focuses on practicing and preservice secondary mathematics teachers and mathematics teacher educators. The project is researching, designing, and developing materials for preservice secondary mathematics teachers that enable them to acquire the mathematical knowledge and situated rationality central to teaching, in particular as it regards the leading of mathematical discussions in classrooms.

Award Number: 
0918425
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2018
Project Evaluator: 
Miriam Gamoran Sherin
Full Description: 

Researchers at the Universities of Michigan and Maryland are developing materials to survey the rationality behind secondary mathematics teaching practice and to support the development by secondary mathematics preservice teachers of specialized knowledge and skills for teaching. The project focuses on the leading of classroom discussions for the learning of algebra and geometry.

Using animations of instructional scenarios, the project is developing online, multimedia questionnaires and using them to assess practicing teachers' mathematical knowledge for teaching and their evaluations of teacher decision making. Reports and forum entries from the questionnaires are integrated into a learning environment for prospective teachers and their instructors built around these animated scenarios. This environment allows pre-service teachers to navigate, annotate, and communicate about the scenarios; and it allows their instructors to plan using those scenarios and share experiences with their counterparts.

The research on teachers' rationality uses an experimental design with embedded one-way ANOVA, while the development of the learning environment uses a process of iterative design, implementation, and evaluation. The project evaluation by researchers at Northwestern University uses qualitative methods to examine the content provided in the environment as well as the usefulness perceived by teacher educators of a state network and their students.

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