Developers and researchers at the University of Michigan and the State University of New York, Buffalo 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 Buffalo, State University of New York. 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.

Mathematical Argumentation in the Middle School is an exploratory project that is working in collaboration with teachers to increase their knowledge of mathematics for teaching in middle school. In addition to geometry and algebra, the professional development is focusing on the role of mathematical argumentation in the middle school and strategies for increasing argumentation. The research component of the project is providing insights into how teachers use their mathematical knowledge to increase argumentation in the classroom and to help students build skills in mathematical argumentation. In addition, the project is studying student outcomes such as reasoning, communication skills, and mathematical knowledge.

The project researchers are using both qualitative and quantitative methodologies to ensure that they have high quality data and analysis that will provide insights into the following research questions: 1) How do teachers use what they learn from the professional development (PD) experiences when they teach in the classroom? 2) To what extent does teachers? use of the project materials and what they learn in the PD result in mathematical argumentation in their classroom discourse? 3) Do students gain conceptual understanding of the mathematics as a result of their participation in argumentation in the classroom? Based on previous research, there is adequate evidence to believe that argumentation in the classroom does increase for participants in the workshop, but the researchers are seeking a better understanding of how teachers use their knowledge and the project materials to enact such an important change in mathematics lessons and in student learning. The professional development uses the dynamic software Geometers' Sketchpad, a carefully-designed, geometry curricular unit, and student materials to help teachers see how to set up a classroom environment that supports mathematical conjectures, arguments, and discussion. The research is done in the classroom and assesses the various components of the professional development in promoting argumentation.

The project is providing insights into how teachers use their mathematical knowledge to implement changes in the classroom. The project is creating effective professional development strategies, a middle school curriculum unit on geometry that emphasizes argumentation, and associated materials. The research is explaining how teachers use their knowledge and the materials and providing information on how students' conceptual knowledge develops through argumentation.

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.

This project involves a longitudinal, ethnographic study of children's mathematical performances from preschool to first grade in both formal classroom settings and informal settings at school and home. The proposed site for the study is a small, predominately African-American pk-12 school. The study seeks to identify opportunities for mathematical learning by young children across multiple contexts, to map varied performances of mathematical competence by young children, to chart changes in young children's mathematical performance over time, and to design and assess the impact of case studies for teacher education that explore young children's mathematical competencies. Research questions focus on mathematical opportunities for learning in various contexts, children's development of knowledge, skills, and dispositions over time, the characteristics of competent mathematical performances, and the role of case studies in helping beginning teachers to understand young minority children's mathematical thinking. Data collected will include video tapes of classroom activities, written fieldnotes of formal and informal settings, student work, parent focus group transcripts, and children's interview performances. Analysis will involve both thematic coding and construction of case studies. The overarching goal of this project is to transform the ways that researchers think about and study the mathematical learning of young minority children as well as the quality of schooling these children experience.

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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The project is conducting repeated randomized control trials of an approach to high school geometry that utilizes dynamic geometry (DG) software and supporting instructional materials to supplement ordinary instructional practices.  It compares effects of that intervention with standard instruction that does not make use of computer drawing/exploraction tools. The basic hypothesis of the study is that use of DG software to engage students in constructing mathematical ideas through experimentation, observation, data recording, conjecturing, conjecture testing, and proof results in better geometry learning for most students. The study tests that hypothesis by assessing student learning in 76 classrooms randomly assigned to treatment and control groups. Student learning is assessed by a geometry standardized test, a conjecturing-proving test, and a measure of student beliefs about the nature of geometry and mathematics in general. Teachers in both treatment and control groups receive relevant professional development, and they are provided with supplementary resource materials for teaching geometry. Fidelity of implementation for the experimental treatment is monitored carefully. Data for answering the several research questions of the study are analyzed by appropriate HLM methods. Results will provide evidence about the effectiveness of DG approach in high school teaching, evidence that can inform school decisions about innovation in that core high school mathematics course. The main research question of the project is: Is the dynamic geometry approach better than the business-as-usual approach in facilitating the geometric learning of our students (and more specifically our economically disadvantaged students) over the course of a full school year?

The main resources/products include geometry teachers’ professional development training materials, suggested dynamic geometry instructional activities to supplement current high school geometry curriculum, instruments such as Conjecturing-Proving Test, Geometry Belief Instrument, Classroom Observation Protocols, DG Implementation Questionnaire and Student Interview Protocols. 

The general plan for the four-year project is as follows:

Year 1: Preparation (All research instruments, professional development training and resource materials, recruitment and training of participants, etc.); 

Year 2: The first implementation of the dynamic geometry treatment, and related data collection and initial data analysis; 

Year 3: The second implementation of the DG treatment, and related data collection and data analysis; 

Year 4: Careful and detailed data analysis and reporting.

We are now in project year 3. Data are collected for the second implementation of the DG treatment. For data collected during project year 2, some initial analysis (the analysis on the geometry pretest and posttest data and the psychometric analysis on the project developed instruments) has been conducted. More thorough analysis of the collected data is still on going. The analysis on the geometry test shows that the experimental group significantly outperformed the control group on geometry performance.

The evaluation will be implemented throughout the project’s four-year duration, with an evolving balance of formative and summative evaluation activities.  In the project’s first three years, the evaluation will emphasize formative functions, designed to inform the project research team of the relative strengths and weaknesses of the research design and execution, and target corrections and improvements of the research components. Summative evaluation activities will also take place in these years with the collection of data on student achievement and teacher change. Evaluation activities for year 4 will focus on the summative evaluation of the project’s accomplishment and especially its impact on participating teachers and students. Evaluation reports will be issued annually with a final summative report presented at the end of year 4.

The research results will be disseminated via the following efforts: 1) Creating and constantly updating the project web site; 2) Publishing the related research articles in research journals such as Journal for Research in Mathematics Education; 3) Presenting at state, regional, national, and international research and professional meetings; 4) Meeting with state and local education agencies, schools, and mathematics teacher educators at other universities for presenting the research findings and using the DG approach in more schools and more mathematics teacher education programs; and 5) Contacting more school districts, with a view to developing relationships and ties that would smooth the way to disseminate the research results.  

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 The Children's Measurement Project examines children's developing knowledge from PreKindergarten through Grade 5 as they develop the capacity and strategies they need to measure geometric space (length, area and volume), investigating number concepts, early algebra, or variability. We investigate ways children learn to use measures as evidence for scientific or mathematical claims. We began by examining the literature on learning trajectories and progressions to interpret existing research on children's understanding of length, area and volume. Our work engages both Rasch modeling and learning/teaching experiments within clinical and classroom contexts to collect data for longitudinal accounts of children's development of measurement concepts and strategies. The work is being conducted as a collaboration of Illinois State University and the University at Buffalo (State University of New York). We are beginning the fourth year of our project (2010).