This CAREER awardee at Utah State University is investigating the learning that can take place when elementary school students are directly involved in the collection, sense-making, and analysis of real, personally-meaningful data sets. The project responds to increasing attention to data collection and analysis in elementary grades and aims to make important contributions to the knowledge base on effective approaches to these topics. The hypotheses of this work are that by organizing elementary statistics instruction around the study of physical activities, students will have greater personal engagement in data analysis processes and that students will also develop more robust understandings of statistical ideas. Students and teachers from fifth grade classrooms from several elementary schools from northern Utah, are participating in the project. This work is co-funded by the EPSCoR program.

Statistics topics include measures of center and variation. Students use pedometers, heart rate monitors, other probeware, and the TinkerPlots software. The research team investigates the influence of personal ownership and relationships to data on students' understanding of learning of elementary statistics concepts and their ability to analyze data. The research involves multi-year clinical interviews and video-recorded classroom design experiments.

Research results are expected to be published in appropriate journals and are expected to be presented at professional meetings. Lesson plans and student instructional materials related to physical activity, measures of center, and data distributions are made available for use in partner elementary schools.

Developers and researchers at Ohio State University and KCP Technologies are creating, testing, refining, and studying a computer-based, individualized, interactive learning system for intermediate/middle school students that can be used by them independently (online or offline) or by teachers in classrooms. This learning system is called Individualized Dynamic Geometry Instruction (iDGi) and will contain four instructional modules in geometry and measurement that reflect the recommendations of the Common Core State Standards (CCSS). iDGi courseware fully integrates research-based Learning Progressions (LPs) for guiding students' reasoning; formative-assessment linked to LPs; instructional sequencing that interactively adapts to students' locations in LPs; built-in student monitoring, feedback, and guidance; and research-based principles of educational media into the modules. The software platform for iDGi development is an extended version of the dynamic geometry computer environment, The Geometer's Sketchpad.

The development process follows recommendations in Douglas Clements' Curriculum Research Framework and includes sequences of development, trials with students, data collection, and revision. The research and evaluation are based on random assignment of approximately 350 students to treatment and control groups. Achievement data are collected using developer-constructed instruments with items that reflect the mathematics topics in the CCSS. Researchers explore the variability at the student, teacher, and school levels using the appropriate level of hierarchical linear models.

Commercial publishers have expressed strong interest in publishing online and offline computer versions of iDGi, an iPad version of iDGi, an online management system for iDGi, and support materials for users and teachers.

A new assessment for children ages 3-7 is being developed to provide teachers with diagnostic information on a child's development of mathematics facility on ten domains such as counting, sequencing, adding/subtracting, and measurement. The Comprehensive Research-based Mathematics Assessment (CREMA) is being developed using innovative psychometric models to reveal information about children on specific attributes for each of the 10 domains. The CREMA will produce information based on carefully developed learning trajectories in a relative short period of time by using computer adaptive testing. The project is guided by two goals: 1) to produce a cognitively diagnostic adaptive assessment that will yield more useful and detailed information about students' knowledge of mathematics than previously possible, and 2) subject the developmental progressions to close cognitive diagnosis using cutting-edge psychometric approaches. An item pool of about 350 items is being developed that can be used to identify the level of understanding children ages 3-7 have on the 10 domains that have been identified as foundational to further learning in mathematics. A research team headed by Dr. Douglas Clements at the University of Buffalo is conducting the development work while being assisted by Dr. Curtis Tatsuoka, a statistician at Case Western Reserve University.

The CREMA is being developed using leading-edge psychometric models based on Q-Matrix theory, rule-state models, and posets. The initial item pool includes items from the REMA, a previously developed instrument based on unidemensional IRT models. New items are being piloted with at least 200 students from a group of a total of 800 students evenly distributed among pre-K to grade 2. The successful items then are used to create the new CREMA. The new assessment is being field tested with 300 children, pre-K to grade 2. A random sample of 50 students (at least 10 from each grade) is being video taped as they work the items. Specific criteria of convergence are being used for feedback on how specific items are performing to meet the required specifications. An external evaluator is auditing the process and is doing spot checks of item codings and other analyses performed.

The main product will be the CREMA that will be made widely available. This instrument using computer adaptive testing will provide teachers with ready information on young children's understanding of critical mathematical ideas. The new psychometric models that will be used and developed to process multiple attributes from individual items will make large strives to move forward the field of mathematics assessment of young children. A publisher has expressed interest to make the assessment widely available that increases the likelihood the assessment will have large impact on early childhood mathematics learning.

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STORE is developing and piloting classroom uses of GIS-based interactive data files displaying climatological, topographical, and biological data about an especially ecologically and topographically diverse section of mid-California and a section of western New York State, plus projected climate change outcomes in 2050 and 2099 from an IPCC climate change model. Both areas contain weather stations. The participating students and teachers live in those areas, hence the place-based focus of the project.

To help teachers make curricular decisions about how to use these data with their students, the project has, with input from six design partner teachers, produced a curriculum module exemplar consisting of six lessons. The lessons start with basic meteorological concepts about the relationship between weather systems and topography, then focus on recent climatological and land cover data. The last two lessons focus on IPCC-sanctioned climate change projections in relation to possible fates of different regional species. Technology light versions of these lessons send students directly to map layers displaying the data for scientific analysis. Technology-heavy versions address the additional goal of building students' capacities to manipulate features of geographic information systems (GIS). Hence, the technology-heavy versions require use of the ARC GIS Explorer Desktop software, whereas the technology light versions are available in both the ARC software and in Google Earth. Google Earth makes possible some student interactivity such as drawing transects and studying elevation profiles, but does not support more advanced use of geographic information system technology such as queries of data-containing shape files or customization of basemaps and data representational symbology.

Answer keys are provided for each lesson. Teachers have in addition access to geospatial data files that display some storm systems that moved over California in the winter of 2010-2001 so that students can study relationships between actual data about storm behavior and relationship to topography and the climatological data which displays those relationships in a summary manner. This provides the student the opportunity to explore differences between weather and climate.

To increase the likelihood of successful classroom implementation and impact on student learning, the professional development process provides the conditions for teachers to make good adaptability decisions for successful follow-through. Teachers can implement the six lessons or adapt them or design their own from scratch. The project requires that they choose from these options, explain on content representation forms their rationales for those decisions, and provide assessment information about student learning outcomes from their implementations. The project provides the teachers with assessment items that are aligned to each of the six lessons, plus some items that test how well the students can interpret the STORE GIS data layers.

All of this work is driven by the hypothesis that science teachers are more likely to use geospatial information technology in their classrooms when provided with the types of resources that they are provided in this project. In summary, these resources include:

1.     tutorials about how to use the two GIS applications

2.     sufficiently adaptive geospatial data available in free easily transportable software applications

3.     lessons that they can implement as is, adapt, or discard if they want to make up their own (as long as they use the data)

4.     supportive resources to build their content knowledge (such as overview documents about their states' climates and information about the characteristics of each data layer and each data set available to them).

The growth and evolution of the teachers' technological pedagogical content knowledge is being tracked through interviews, face-to-face group meetings, and classroom observations. Also being tracked is the extent to which the teachers and students can master the technology applications quickly and on their own without workshops, and how well teachers provide feedback to the students and assess their learning outcomes when implementing STORE lessons. As the project moves into its third and final year, we will be studying outcomes from the first classroom implementation year (i.e. year two of the project) and determining to what extent the professional development strategies need to be revised in relation to how the teachers are responding to the project resources and forms of professional support. In the end, the project will contribute to the knowledge base about what professional development strategies are appropriate for getting teachers to use these types of resources, what decisions teachers make about how to use the resources for different courses and student groups they teach, and what are the outcomes of those uses in terms of curricular material, instructional strategies, and student learning.

NSF DR K-12: PreK Early Algebra through Quantitative Reasoning (PreKEA)

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 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.

This project is a collaborative effort involving scientists, science educators, and teachers from TERC, Clark University, Tufts University,and urban Massachusetts schools that aims to develop a grade 3-5 Learning Progression that will provide a coherent approach to teaching energy in elementary school and lay a strong foundation for further learning in middle school. The work draws on and complements the learning progression and curriculum for matter developed and tested in the Inquiry Project (NSF award 0628245). The project will identify a network of core concepts and principles about energy that are fundamental and general enough to be compatible with scientific ideas about energy, yet within reach of 5th graders.

This project explores the hypothesis that, while the scientific concept of energy is too abstract and difficult to understand in early grades, useful foundations can be established early on by elaborating a learning progression for energy. Clinical interviews will be administered to 24 pairs of 3rd, 4th, and 5th graders recruited from urban after-school programs, to identify precursors to the core ideas as well obstacles to learning them. This research will help the investigators design key learning experiences that could allow students to progress from initial ideas toward a scientific understanding of energy. Those learning designs will then be tested in teaching interviews with 3 small groups of students in the same settings.

The result of the project will be an outline for a grade 3-5 learning progression for energy taking into account the project research findings as well as relevant standards, curricula, and science education literature.

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.

 The project began as a collaborative research effort among six organizations—a non-profit research company (SRI International), a university (University of Maryland), a commercial test publishing company (Pearson), Minnesota’s (MN) state department of education, a software engineering firm (Codeguild, Inc.), and an educational evaluation firm (Haynie Research and Evaluation). Due to changes in the affiliation of key personnel, the project transitioned to a collaboration among five organizations--SRI International, ETS, University of Maryland, Pearson and Haynie Research and Evaluation. Together these groups designed and implemented several studies to document the influence of evidence-centered design when applied to Pearson's science assessment design and development processes.

The goals of the project are: (1) to determine leverage points by which ECD can enhance the quality of large-scale technology-based assessments and the efficiency of their design, (2) to implement resulting procedures in operational test development cycles, (3) to evaluate efficiency, effectiveness and generalizability of these procedures, (4) to develop two software wizards to support design of task-based scenarios and assessment items, and (5) to disseminate findings to the assessment community.

This project will develop an exemplar set of design patterns based on the critical benchmarks identified in the Minnesota Academic Standards for science and on the GED science practice indicators and content targets. It is of particular interest in this project that elements of ECD will be applied to an existing large-scale accountability and credentialing assessments, in the context of existing test development and delivery processes.  The project is constrained to maintain adherence to existing test specifications, “look and feel” of tasks, timelines, and delivery and scoring procedures.  Rather than designing new assessment systems or re-engineering existing ones, the present project seeks to identify and implement ideas from ECD in existing large-scale, high-stakes testing programs. Principles of ECD have been implemented in several training workshops for assessment designers and item writers to support the development of scenario-based science tasks. The project's technical report series is available at http: //ecd.sri.com.