Instrument

Cluster Randomized Trial of the Efficacy of Early Childhood Science Education for Low-income Children

The research goal of this project is to evaluate whether an early childhood science education program, implemented in low-income preschool settings produces measurable impacts for children, teachers, and parents. The study is determining the efficacy of the program on Science curriculum in two models, one in which teachers participate in professional development activities (the intervention), and another in which teachers receive the curriculum and teachers' guide but no professional development (the control).

Project Email: 
vanegere@msu.edu
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1119327
Funding Period: 
Mon, 08/15/2011 - Wed, 07/31/2013
Project Evaluator: 
Brian Dates, Southwest Counseling Services
Full Description: 

The research goal of this project is to evaluate whether an early childhood science education program, Head Start on Science, implemented in low-income preschool settings (Head Start) produces measurable impacts for children, teachers, and parents. The study is being conducted in eight Head Start programs in Michigan, involving 72 classrooms, 144 teachers, and 576 students and their parents. Partners include Michigan State University, Grand Valley State University, and the 8 Head Start programs. Southwest Counseling Solutions is the external evaluator.

The study is determining the efficacy of the Head Start on Science curriculum in two models, one in which 72 teachers participate in professional development activities (the intervention), and another in which 72 teachers receive the curriculum and teachers' guide but no professional development (the control). The teacher study is a multi-site cluster randomized trial (MSCRT) with the classroom being the unit of randomization. Four time points over two years permit analysis through multilevel latent growth curve models. For teachers, measurement instruments include Attitudes Toward Science (ATS survey), the Head Start on Science Observation Protocol, the Preschool Classroom Science Materials/Equipment Checklist, the Preschool Science Classroom Activities Checklist, and the Classroom Assessment Scoring System (CLASS). For students, measures include the "mouse house problem," Knowledge of Biological Properties, the physics of falling objects, the Peabody Picture Vocabulary Test-Fourth Edition, the Expressive Vocabulary Test-2, the Test of Early Mathematics Ability-3, Social Skills Improvement System-Rating Scales, and the Emotion Regulation Checklist. Measures for parents include the Attitudes Toward Science survey, and the Community and Home Activities Related to Science and Technology for Preschool Children (CHARTS/PS). There are Spanish versions of many of these instruments which can be used as needed. The external evaluation is monitoring the project progress toward its objectives and the processes of the research study.

This project meets a critical need for early childhood science education. Research has shown that very young children can achieve significant learning in science. The curriculum Head Start on Science has been carefully designed for 3-5 year old children and is one of only a few science programs for this audience with a national reach. This study intends to provide a sound basis for early childhood science education by demonstrating the efficacy of this important curriculum in the context of a professional development model for teachers.

Cluster Randomized Trial of the Efficacy of Early Childhood Science Education for Low-income Children

LOCUS: Levels of Conceptual Understanding in Statistics

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): 
Award Number: 
1118168
Funding Period: 
Thu, 09/01/2011 - 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.

LOCUS: Levels of Conceptual Understanding in Statistics

Opportunities and Challenges for Developing and Evaluating Diagnostic Assessments in STEM Education

Day: 
Fri

Four DR K-12 projects will discuss opportunities and challenges that they have encountered when trying to harness psychometric models for diagnosis in science and mathematics education.

Date/Time: 
10:00 am - 12:00 pm
Session Type: 
Panel

What are the opportunities and challenges that arise when trying to harness psychometric models for diagnosis in STEM education?        

A growing number of projects, many funded by the National Science Foundation, have been examining how psychometric models may be harnessed to pursue STEM education research. Several of these projects are addressing the need for STEM assessments that go beyond large-scale standardized testing practice to provide beneficial information directly to professional developers, teachers, and students. These projects seek to open up new classroom assessment capabilities, new use models for classroom assessments, and new directions for STEM education research that in recent decades has relied largely on case studies and other qualitative methods to study the teaching and learning of STEM content. 

The proposed panel will bring together four currently funded DR K–12 projects that are examining how diagnostic modeling may be applied to further research in STEM education. Interest in diagnostic testing reflects recent developments in psychometric theory and modeling that are creating new possibilities for assessing STEM concepts and facets of understanding that go beyond summary or composite measures of teachers’ knowledge or students’ achievement. In particular, psychometric theory has moved from models based on test scores (e.g., classical test theory) to models based on answers to individual test items (e.g., item response theory) to models based on skills or components of reasoning required to answer particular test items (e.g., diagnostic classification). The four projects demonstrate the diversity of work in applications of diagnostic testing to STEM education research. Some of the projects are developing and implementing diagnostic tests for use in STEM classrooms or professional development of STEM teachers. Other projects are conducting retrospective diagnostic modeling of existing classroom assessments. Some projects are examining science content, others mathematics content; some are assessing teachers, others students; some are focusing on paper-and-pencil instruments, others simulation-based assessments.

The proposed session will highlight the opportunities and challenges that arise when harnessing psychometric models for diagnosis of STEM content. A 10-minute introduction to diagnosis from a psychometric perspective will be followed by 15-minute presentations from each of the four projects. Each presentation will provide background for the given project and identify opportunities and challenges in applying diagnostic psychometric models. Example challenges include fostering interdisciplinary collaboration among content experts, cognitive scientists, and psychometricians; coordinating psychometric models with perspectives on learning and knowledge within STEM disciplines; understanding and balancing cognitive and conceptual structures of assessments with psychometric models; and determining relationships among the number of questions needed on a test form, the number of concepts that can be diagnosed on a test form, and the number of examinees required to satisfactorily estimate diagnostic models. The presentations will be followed by 15 minutes for questions to the panel. During the final portion of the session, the panelists will be available for individual discussion with attendees at project posters. The session format will afford opportunities for attendees to consider the range of issues across projects, to learn more about particular projects, and to network with one another.

Panel presentations will allow for a broader discussion of the opportunities and challenges that the four projects have encountered when harnessing psychometric models for diagnosis in science and mathematics education. Poster presentations will allow attendees to learn more details about the projects in which they are particularly interested and afford networking. 

A Learning Progression-based System for Promoting Understanding of Carbon-transforming Processes (CCE)

This project builds on prior efforts with learning progressions, and is focused on key carbon-transforming processes in socio-ecological systems at multiple scales, including cellular and organismal metabolism, ecosystem energetics and carbon cycling, carbon sequestration, and combustion of fossil fuels. The primary project outcomes will be coordinated instructional tools that are useful to professionals at all levels in the science education system--classroom teachers, professional developers, and developers of curricula, standards and assessments

Lead Organization(s): 
Award Number: 
1020187
Funding Period: 
Wed, 09/15/2010 - Mon, 08/31/2015
Project Evaluator: 
Rose Shaw
Full Description: 

This project--led by science educators at Michigan State University, the National Geographic Society, the Natural Resource Ecology Laboratory (NREL) at Colorado State University, the Berkeley Evaluation and Assessment Research (BEAR) Center, and AAAS Project 2061, and including schools in California, Colorado, Maryland, Michigan, and Washington--builds on prior efforts with learning progressions, and is focused on key carbon-transforming processes in socio-ecological systems at multiple scales, including cellular and organismal metabolism, ecosystem energetics and carbon cycling, carbon sequestration, and combustion of fossil fuels.

The project uses an iterative design research process to develop and refine a suite of tools for reasoning and test efficacy of those tools in geographically and culturally diverse schools. The project team is:

1. Refining and validating a detailed learning progression framework covering the middle and high school years; ultimately, the framework will describe the development of students' capacity to use fundamental principles such as conservation of matter and energy to reason about carbon-transforming processes at multiple scales.

2. Refining 'Tools for Reasoning' that make hidden scientific principles - matter, energy, and scale - visible to students; the power of these tools lies in their flexible use for different processes, systems, scales, and curricular contexts.

3. Developing and refining flexible teaching strategies that engage students in cognitive apprenticeship in the practices of environmental science literacy: a) inquiry and argumentation, b) explanations and predictions, and c) decision-making about environmental issues.

4. Using and refining existing summative assessments, and developing and testing formative assessment tools; these assessment tools will provide teachers and researchers with immediate information about their students' intellectual resources and will be linked to the learning progression framework.

5. Developing, field testing, and assessing the effectiveness of six middle school and six high school units that use project tools and enact project principles; the units introduce students to fundamental principles, engage them in reasoning about carbon-transforming processes at organismal scale, and at landscape and global scales. Each unit includes a) an online formative assessment and b) activity sequences that use tools for reasoning and teaching strategies.

6. Developing, field testing, and assessing professional development materials in both face-to-face and facilitated online forms; the materials introduce teachers to learning progressions in environmental science literacy, assessment tools, tools for reasoning, teaching strategies, and teaching materials and activities, and also address difficulties that teachers encounter in using learning progressions and enacting teaching strategies.

The primary project outcomes will be coordinated instructional tools that are useful to professionals at all levels in the science education system--classroom teachers, professional developers, and developers of curricula, standards and assessments.

A Learning Progression-based System for Promoting Understanding of Carbon-transforming Processes (CCE)

Efficacy Study of Metropolitan Denver's Urban Advantage Program: A Project to Improve Scientific Literacy Among Urban Middle School Students

This is an efficacy study to determine if partnerships among formal and informal organizations demonstrate an appropriate infrastructure for improving science literacy among urban middle school science students. The study aims to answer the following questions: How does participation in the program affect students' science knowledge, skills, and attitudes toward science; teachers' science knowledge, skills, and abilities; and families engagement in and support for their children's science learning and aspirations?

Lead Organization(s): 
Award Number: 
1020386
Funding Period: 
Wed, 09/15/2010 - Wed, 08/31/2011
Project Evaluator: 
Maggie Miller
Full Description: 

This is an efficacy study through which the Denver Museum of Nature and Science, the Denver Zoo, the Denver Botanic Gardens, and three of Denver's urban school districts join efforts to determine if partnerships among formal and informal organizations demonstrate an appropriate infrastructure for improving science literacy among urban middle school science students. The Metropolitan Denver Urban Advantage (UA Denver) program is used for this purpose. This program consists of three design elements: (a) student-driven investigations, (b) STEM-related content, and (c) alignment of schools and informal science education institutions; and six major components: (a) professional development for teachers, (b) classroom materials and resources, (c) access to science-rich organizations, (d) outreach to families, (e) capacity building and sustainability, and (e) program assessment and student learning. Three research questions guide the study: (1) How does the participation in the program affect students' science knowledge, skills, and attitudes toward science relative to comparison groups of students? (2) How does the participation in the program affect teachers' science knowledge, skills, and abilities relative to comparison groups of teachers? and (3) How do families' participation in the program affect their engagement in and support for their children's science learning and aspirations relative to comparison families?

The study's guiding hypothesis is that the UA Denver program should improve science literacy in urban middle school students measured by (a) students' increased understanding of science, as reflected in their science investigations or "exit projects"; (b) teachers' increased understanding of science and their ability to support students in their exit projects, as documented by classroom observations, observations of professional development activities, and surveys; and (c) school groups' and families' increased visits to participating science-based institutions, through surveys. The study employs an experimental research design. Schools are randomly assigned to either intervention or comparison groups and classrooms will be the units of analysis. Power analysis recommended a sample of 18 intervention and 18 comparison middle schools, with approximately 72 seventh grade science teachers, over 5,000 students, and 12,000 individual parents in order to detect differences among intervention and comparison groups. To answer the three research questions, data gathering strategies include: (a) students' standardized test scores from the Colorado Student Assessment Program, (b) students' pre-post science learning assessment using the Northwest Evaluation Association's Measures for Academic Progress (science), (c) students' pre-post science aspirations and goals using the Modified Attitude Toward Science Inventory, (d) teachers' fidelity of implementation using the Teaching Science as Inquiry instrument, and (e) classroom interactions using the Science Teacher Inquiry Rubric, and the Reformed Teaching Observation protocol. To interpret the main three levels of data (students, nested in teachers, nested within schools), hierarchical linear modeling (HLM), including HLM6 application, are utilized. An advisory board, including experts in research methodologies, science, informal science education, assessment, and measurement oversees the progress of the study and provides guidance to the research team. An external evaluator assesses both formative and summative aspects of the evaluation component of the scope of work.

The key outcome of the study is a research-informed and field-tested intervention implemented under specific conditions for enhancing middle school science learning and teaching, and supported by partnerships between formal and informal organizations.

Efficacy Study of Metropolitan Denver's Urban Advantage Program: A Project to Improve Scientific Literacy Among Urban Middle School Students

Using Rule Space and Poset-based Adaptive Testing Methodologies to Identify Ability Patterns in Early Mathematics and Create a Comprehensive Mathematics Ability Test

This project will develop a new assessment for children ages 3-7 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 Ability (CREMAT) is being developed using innovative psychometric models to reveal information about children on specific attributes for each of the 10 domains.

Project Email: 
clements@buffalo.edu
Partner Organization(s): 
Award Number: 
1019925
Funding Period: 
Wed, 09/01/2010 - Sat, 08/31/2013
Project Evaluator: 
Prof. Finbar “Barry” Sloane
Full Description: 

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.

Using Rule Space and Poset-based Adaptive Testing Methodologies to Identify Ability Patterns in Early Mathematics and Create a Comprehensive Mathematics Ability Test

Language-rich Inquiry Science with English Language Learners (LISELL)

This exploratory study develops and pilot-tests a model for improving science teaching and learning with middle school ELLs. Study goals include: (1) clarifying pedagogical constructs of language-rich science inquiry and the academic language of science and their relationships across the learning contexts of middle school science classrooms, teacher professional development and family science workshops, (2) developing and refining instruments to study these constructs in context, and (3) conducting pilot tests of the model and instruments.

Award Number: 
1019236
Funding Period: 
Sun, 08/15/2010 - Wed, 07/31/2013
Full Description: 

This exploratory study develops, pilot-tests, and refines a model for improving middle school English Language Learners' (ELLs) science learning. The model incorporates two pedagogical constructs (language-rich science inquiry and academic language development); and three learning settings (teacher professional development workshops, middle school science classrooms, and parent-student-teacher science workshops). The specific objectives of the study are: (1) to clarify the two pedagogical constructs and their relationships across the three learning contexts, (2) to develop and refine instruments that will be useful for the study of these constructs in these learning contexts, and (3) to conduct pilot tests of the model and instruments.

The study's development phase consists of the production, adaptation, and pilot testing of instructional strategies for teachers and learning materials for students. Instructional strategies for teachers are centered on three key inquiry practices: (a) coordinating theory and evidence, (b) controlling variables, and (c) cause and effect reasoning across 6th grade earth science, 7th grade life science, and 8th grade physical science. Learning materials for students consist of lessons in a workbook with units highlighting the study of academic language. Also, this phase of the study includes the development of resources to support parents' participation and measurement instruments to gather data during the research phase of the study.

The research phase of the study consists of pilot testing of the model. Two research questions guide the study: (1 What is the value for ELL students, their teachers and their parents of an instructional model that highlights language-rich science inquiry practices and academic language development strategies?; and (2)What is the value for ELL students, their teachers and their parents of an instructional model that is enacted in the contexts of middle school science classrooms, student-parent-teacher science workshops, and teacher professional development workshops? Assuming a quasi-experimental, pretest-posttest design, a power analysis defined a sample size of 1,000 middle school students (800 for the treatment group, and 200 for the control group) in 40 classrooms of three middle schools in the state of Georgia. A total of 12 teachers (8 science teachers and 2 English for Students of Other Languages teachers) were selected using a targeted strategy; and 40 randomly selected parents constitute the remaining population sample. The intervention consists of the use of teacher instructional strategies focused on exploring and elaborating cause-effect relationships, differentiating between evidence and theory, and identifying and controlling variables; students' use of instructional materials on academic language; and exploration of parents' science funds of knowledge. Data gathering strategies employ five instruments: (a) a teacher-focus-group interview protocol, (b) a teacher observation protocol, (c) a parent-student interview protocol, (d) a student academic language writing test, and (e) a student-constructed-response science inquiry test. Data interpretation strategies include qualitative analysis using narrative and semantic structure analysis and statistical analyses. An advisory board and an evaluator conduct the evaluation component of the study, inclusive of formative and summative aspects.

The outcome of this study is a research-informed and field-tested science instructional model focused on the improved learning of ELLs and a set of valid and reliable measuring instruments.

Language-rich Inquiry Science with English Language Learners (LISELL)

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: 
evaluatingdmi@terc.edu
Lead Organization(s): 
Award Number: 
1019769
Funding Period: 
Wed, 09/01/2010 - 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.

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

Using Routines as an Instructional Tool for Developing Students' Conceptions of Proof

This project will develop and systematically investigate a teaching model to assist teachers in developing ideas about proof in grades 2-5. The teaching model provides both a tool for learning on the part of elementary teachers and a model of practice from which they can learn as they implement it.

Lead Organization(s): 
Award Number: 
1019482
Funding Period: 
Wed, 09/01/2010 - Fri, 08/31/2012
Project Evaluator: 
Megan Franke
Full Description: 

Developers and researchers at TERC, the Education Development Center, and Mount Holyoke College are participating in the development and systematic investigation of a teaching model to assist teachers in developing ideas about proof in grades 2-5. The teaching model provides both a tool for learning on the part of elementary teachers and a model of practice from which they can learn as they implement it.

The project is a teaching experiment in which the model is iteratively implemented and refined, first with teachers experienced in incorporating ideas about proof into their classroom instruction (Phase 1), then with teachers who are relatively inexperienced, both in their own understanding of proof and in their knowledge of how their students can learn about proof (Phase 2). Research questions focus on developing the components of the model, the learning of teachers as they implement the model, and the learning of students as they engage in the instruction that is guided by the model, with particular attention to students with varied histories of achievement in grade-level work on number and operations.

The expected outcome is a teaching model that can be tested on a larger scale as well as instruments for assessing student learning and teacher understanding of proof. The model includes printed material with descriptions of the routines and instructional sequences, guidelines for implementing each component, and a teaching framework as well as written and video case examples.

Using Routines as an Instructional Tool for Developing Students' Conceptions of Proof

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.

Lead Organization(s): 
Award Number: 
0952415
Funding Period: 
Mon, 03/15/2010 - 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.

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