Experimental

Pre-K Early Algebra Through Quantitative Reasoning (PreKEA)

This project is 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.

Lead Organization(s): 
Award Number: 
1212766
Funding Period: 
Wed, 09/01/2010 to Sat, 08/31/2013
Full Description: 

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.

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.

Enabling Modeling and Simulation-Based Science in the Classroom: Integrating Agent-Based Models, Real World Sensing and Collaborative Networks

This project develops and assesses the effectiveness of integrating three computation-based technologies into curricular modules: agent-based modeling (ABM), real-world sensing, and collaborative classroom networks. The STEM disciplines addressed are life sciences and physical sciences at middle and high school levels, specifically Evolution, Population Biology/Ecology, Kinetic Molecular Theory, and Electromagnetism.

Project Email: 
Lead Organization(s): 
Award Number: 
1020101
Funding Period: 
Sun, 08/01/2010 to Thu, 07/31/2014
Full Description: 

This four-year Full Research and Development project develops and assesses the effectiveness of integrating three computation-based technologies into curricular modules: agent-based modeling (ABM), real-world sensing, and collaborative classroom networks. The team brings together researchers from Northwestern, Vanderbilt and Stanford universities in collaboration with a commercial partner, Inquire Learning. The STEM disciplines addressed are life sciences and physical sciences at middle and high school levels, specifically Evolution, Population Biology/Ecology, Kinetic Molecular Theory, and Electromagnetism.

The project proceeds in two phases: The first phase is a design experiment for the iterative creation of ABM-only and enhanced-ABM modules field tested with fourteen teachers drawn from seven schools. In the second phase, an experiment is conducted that aims at providing quantitative data to help characterize the different effects of various components of the intervention and to prepare the way for future efficacy and scaling research. Between 40 and 80 teachers participate in the experiment and are assigned to immediate or lagged treatments. The four topic areas were selected because they are scientifically important; they are difficult for students, provoking significant misconceptions; they are amenable to a complex-systems and modeling approach; and prior work has prepared the PIs to develop high-quality curricular materials on these topics. The evaluation is led by a member of the advisory board which is constituted to provide guidance on the project evaluation.

The products are research findings on the achievement, engagement and attitudes of students as a result of the deep use of computational modeling technologies in science. In addition, four fully developed classroom-ready modules with teacher support materials are deployed and disseminated through a broad network of educational communities.

Embodied STEM Learning Across Technology-Based Learning Environments

This project conducts interdisciplinary research to advance understanding of embodied learning as it applies to STEM topics across a range of current technology-based learning environments (e.g., desktop simulations, interactive whiteboards, and 3D interactive environments). The project has two central research questions: How are student knowledge gains impacted by the degree of embodied learning and to what extent do the affordances of different technology-based learning environments constrain or support embodied learning for STEM topics?

Lead Organization(s): 
Award Number: 
1020367
Funding Period: 
Sun, 08/15/2010 to Sun, 07/31/2011
Project Evaluator: 
Susan Haag
Full Description: 

This project conducts interdisciplinary research to advance understanding of embodied learning as it applies to STEM topics across a range of current technology-based learning environments (e.g., desktop simulations, interactive whiteboards, and 3D interactive environments). The project builds on extensive research, including prior work of the PIs, regarding both embodied learning and statistical learning. The PIs describe embodied learning as engaging the neuromuscular systems of learners as they interact with the world around them visually, aurally, and kinesthetically in order to construct new knowledge structures. Statistical learning is described as the ability to learn, often without intent, which sequences of stimuli are consistent with a set of rules. An example of statistical learning is pattern recognition, which is central to mastery of complex topics in many STEM disciplines including physics and mathematics.

The project has two central research questions: How are student knowledge gains impacted by the degree of embodied learning and to what extent do the affordances of different technology-based learning environments constrain or support embodied learning for STEM topics? To investigate these questions, the PIs are conducting three series of experiments in five phases using two physics topics. The first four phases are developmental and the final phase implements and assesses the two modules in schools (20 plus teachers, 700 plus K-12 students) in Arizona and New York (15 total sites, 10 plus public schools, minimum one Title I school).

The aim of this project is to meld these two research trajectories to yield two key outcomes: 1) basic research regarding embodiment and statistical learning that can be applied to create powerful STEM learning experiences, and 2) the realization of exemplary models and principles to aid curriculum and technology designers in creating learning scenarios that take into account the level of embodiment that a given learning environment affords.

Effective Programs for Elementary Science: A Best-evidence Synthesis

This synthesis project is a systematic review of experimental research evaluating programs and practices in elementary science. The systematic review addresses all areas of science in the elementary grades. The review uses an adaptation of best-evidence synthesis previously applied to elementary and secondary mathematics and reading, and includes experimental and quasi-experimental research on the outcomes of alternative approaches to elementary science.

Lead Organization(s): 
Award Number: 
1019306
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2012
Full Description: 

This synthesis project is a systematic review of experimental research evaluating programs and practices in elementary science. The systematic review addresses all areas of science in the elementary grades. Different versions of the synthesis are written for audiences of researchers, policy makers, principals, and teachers. The review uses an adaptation of best-evidence synthesis previously applied to elementary and secondary mathematics and reading, and includes experimental and quasi-experimental research on the outcomes of alternative approaches to elementary science. The review is a part of a series of reviews that are part of the Best Evidence Encyclopedia (BEE), an on-line resource that disseminates systematic reviews of research on achievement outcomes of programs at all subject areas and grade levels (see www.bestevidence.org), and is led by Robert Slavin of Johns Hopkins University.

The review is carried out by a US-UK partnership of science educators and experts on systematic reviews of research. An advisory group of scientists, science educators, and experts on research review oversees the design of the review, monitors review procedures, and comments on drafts. This review takes a broad approach to searching the literature in order to locate every study that meets inclusion requirements for valid research. It includes electronic searches of educational databases (JSTOR, ERIC, EBSCO, Psych INFO, Dissertation Abstracts) using different combinations of key words (for example, "elementary students" and "science achievement"), covering the years 1970-2010. Results are narrowed by subject area (for example, "educational software", "science achievement", "instructional strategies"). Web-based repositories and education publishers' websites are included. The review also discusses each study that meets the inclusion requirements for a valid research design.

A strength of this work is that it takes on the synthesis of what is known about best practice for elementary science education, relying only on studies that meet the criteria for inclusion as having credible research designs. This is a review that is sorely needed in the field of science education. The lengthy and detailed review will be available on the BEE network, along with educator-friendly summaries. The work is also vetted via publication in a top, peer-reviewed journal. The study will include a set of tables showing ratings of programs according to consistent criteria in terms of the strength of the evidence base for each, with brief descriptions of the methods and findings. This educators' summary, patterned on Consumer Reports, is intended primarily for superintendents, principals, and teachers who are making choices among programs for implementation with their children.

INK-12: Teaching and Learning Using Interactive Ink Inscriptions in K-12 (Collaborative Research: Koile)

This is a continuing research project that supports (1) creation of what are termed "ink inscriptions"--handwritten sketches, graphs, maps, notes, etc. made on a computer using a pen-based interface, and (2) in-class communication of ink inscriptions via a set of connected wireless tablet computers. The primary products are substantiated research findings on the use of tablet computers and inscriptions in 4th and 5th grade math and science, as well as models for teacher education and use.
Award Number: 
1020152
Funding Period: 
Wed, 09/01/2010 to Sun, 08/31/2014
Project Evaluator: 
David Reider, Education Design Inc.
Full Description: 

The research project continues a collaboration between MIT's Center for Educational Computing Initiatives and TERC focusing on the enhancement of K-12 STEM math and science education by means of technology that supports (1) creation of what are termed "ink inscriptions"--handwritten sketches, graphs, maps, notes, etc. made on a computer using a pen-based interface, and (2) in-class communication of ink inscriptions via a set of connected wireless tablet computers. The project builds on the PIs' prior work, which demonstrated that both teachers and students benefit from such technology because they can easily draw and write on a tablet screens, thus using representations not possible with only a typical keyboard and mouse; and they can easily send such ink inscriptions to one another via wireless connectivity. This communication provides teachers the opportunity to view all the students' work and make decisions about which to share anonymously on a public classroom screen or on every student's screen in order to support discussion in a "conversation-based" classroom. Artificial intelligence methods are used to analyze ink inscriptions in order to facilitate selection and discussion of student work.

The project is a series of design experiments beginning with the software that emerged from earlier exploratory work. The PIs conduct two cycles of experiments to examine how tablets affect students learning in 4th and 5th grade mathematics and science. The project research questions and methods focus on systematic monitoring of teachers' and students' responses to the innovation in order to inform the development process. The PIs collect data on teachers' and students' use of the technology and on student learning outcomes and use those data as empirical evidence about the promise of the technology for improving STEM education in K-12 schools. An external evaluator uses parallel data collection, conducting many of the same research activities as the core team and independently providing analysis to be correlated with other data. His involvement is continuous and provides formative evaluation reports to the project through conferences, site visits, and conference calls.

The primary products are substantiated research findings on the use of tablet computers, inscriptions, and networks in 4th and 5 grade classrooms. In addition the PIs develop models for teacher education and use, and demonstrate the utility of artificial intelligence techniques in facilitating use of the technology. With the addition of Malden Public Schools to the list of participating districts, which includes Cambridge Public Schools and Waltham Public Schools from earlier work, the project expands the field test sites to up 20 schools' classrooms.

CAREER: Learning to Make Mathematical Connections

The main goal of this mathematics education research project is to determine through experimentation specific teaching strategies that can be used to support middle school students in drawing connections between mathematical representations (fractions and ratios). The potential instructional strategies were identified from the Third International Mathematics and Science Study (TIMSS) video analyses study as the ones that best distinguished high performing countries from low performing countries.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1313531
Funding Period: 
Fri, 03/01/2013 to Fri, 07/31/2015
Full Description: 

The main goal of this mathematics education research project is to determine through experimentation specific teaching strategies that can be used to support middle school students drawing connections between mathematical representations (fractions and ratios). The potential instructional strategies were identified from the Third International Mathematics and Science Study (TIMSS) video analyses study as the ones that best distinguished high performing countries from low performing countries. Prior studies were used to pilot the research approach and potential results. The problem, expected solution responses, and instructional sequences are drawn from a model of a Japanese lesson. This CAREER award will be operated through the University of California-Irvine by Assistant Professor Lindsey Richland.

Six experiments will be conducted, each on one strategy and designed to help develop optimal instructional routines. The six conditions are: 1) making student responses or key ideas visible, 2) making compared student responses or key ideas visible simultaneously, 3) visually organizing the student responses or key ideas to highlight key connections, 4) using at least one well-known student response or key idea to compare with something new, 5) using gestures between connected student responses, and 6) using visual imagery. Fifth and sixth grade students from three classrooms will be randomly selected to participate in one of two conditions (high support and low support) for the six experiments. For each experiment, each condition will be studied with 30 students. Data for all six experiments will be collected from a total of 360 students. All students will be given the same word problem requiring proportional reasoning. Then students will be shown an instructional video of a teacher presenting a lesson related to the problem. Students will be given pre- and post-tests and a new problem to solve as measures of effects. An ANOVA (pretest/posttest) with conditions as a between-subjects variable (high support/low support) will be used in the analysis. Two additional case studies will investigate the training of two teachers to use the most effective of the strategies in the first six experiments. Videotapes of these two teachers using the optimal strategies in their classrooms will be analyzed using the same protocol used in TIMSS. A highly qualified advisory board will serve as the external evaluation. An education plan includes mentoring graduate students and undergraduate researchers; educating pre-service teachers; collaborating through in-service teacher professional development with teachers from regional schools; and disseminating results in academic venues.

Positive results of this application of cognitive science to the teaching and learning of mathematics will inform the field of mathematics education on routine of practices that distinguish high performing countries in mathematics achievement. The work may be of greatest benefit to English language learners and other under-represented groups. If the instructional strategies are viable, then teachers will have specific ways they can reduce the cognitive load on students who may be processing two languages while trying to learn mathematics.

This project was previously funded under awarde # 0954222.

CAREER: Exploring the Role of Variability as an Organizing Concept for the Teaching and Learning of Statistical Reasoning in Middle School

This CAREER project explores interrelated research questions: (1) What understandings of variability can provide conceptual support for the scheme of ideas that underlie statistical inference--making claims about a population on the basis of samples? (2) What conceptions about variability do students bring to study of data analysis and statistical reasoning in middle grades? (3) How can instruction support students in coming to develop understanding and skill in reasoning about variability?

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0953987
Funding Period: 
Thu, 04/01/2010 to Thu, 03/31/2011
Full Description: 

This CAREER project explores the role of variability as a central concept for organizing the teaching of statistical thinking to middle school students. The work addresses three interrelated research questions that frame and guide the project:

(1) What understandings of variability can provide conceptual support for the scheme of ideas that underlie statistical inference--making claims about a population on the basis of samples?

(2) What conceptions about variability do students bring to study of data analysis and statistical reasoning in middle grades?

(3) How can instruction support students in coming to develop understanding and skill in reasoning about variability?

The project is addressing these questions through content analysis of the variability concept as it is used in statistical reasoning, surveys of student thinking about the concept, and a series of design experiments aimed at enhancing student and teacher understanding of the concept. The project is producing guidance for design of curricula, instructional materials, and teaching strategies related to statistics in the middle grades.

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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