Number Sense

Learning Mathematics of the City in the City

This project is developing teaching modules that engage high school students in learning and using mathematics. Using geo-spatial technologies, students explore their city with the purpose of collecting data they bring back to the formal classroom and use as part of their mathematics lessons. This place-based orientation helps students connect their everyday and school mathematical thinking. Researchers are investigating the impact of place-based learning on students' attitudes, beliefs, and self-concepts about mathematics in urban schools.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1222430
Funding Period: 
Sat, 09/01/2012 to Mon, 08/31/2015
Full Description: 

Learning Mathematics of the City in The City is an exploratory project that is developing teaching modules that engage high school students in learning mathematics and using the mathematics they learn. Using geo-spatial technologies, students explore their city with the purpose of collecting data they bring back to the formal classroom and use as part of their mathematics lessons. This place-based orientation is helping students connect their everyday and school mathematical thinking.

Researchers are investigating the impact of place-based learning on students' attitudes, beliefs, and self-concepts about mathematics in urban schools. Specifically, researchers want to understand how place-based learning helps students apply mathematics to address questions about their local environment. Researchers are also learning about the opportunities for teaching mathematics using carefully planned lessons enhanced by geo-spatial technologies. Data are being collected through student interviews, classroom observations, student questionnaires, and student work.

As the authors explain, "The use of familiar or engaging contexts is widely accepted as productive in the teaching and learning of mathematics." By working in urban neighborhoods with large populations of low-income families, this exploratory project is illustrating what can be done to engage students in mathematics and mathematical thinking. The products from the project include student materials, software adaptations, lesson plans, and findings from their research. These products enable further experimentation with place-based mathematics learning and lead the way for connecting mathematical activities in school and outside of school.

Developing Teaching Expertise in K-5 Mathematics

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

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

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

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

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

Teachers Empowered to Advance Change in Mathematics (TEACH MATH): Preparing Pre K-8 Teachers to Connect Children's Mathematical Thinking and Community-Based Funds of Knowledge

This project will modify the teacher preparation program for preK-8 teachers. The program is designed to help pre-service teachers learn mathematics well, learn to access students' cultural funds of knowledge, and learn to encourage students' mathematical thinking. The developers are designing (a) modules that can be used in teacher preparation courses, (b) a mentoring program for new teachers, and (c) on-line networks to facilitate collaboration among participating teachers and institutions.

Lead Organization(s): 
Award Number: 
1228034
Funding Period: 
Thu, 09/01/2011 to Thu, 08/31/2017
Project Evaluator: 
Research Institute for Studies in Education
Full Description: 

This research and development project will modify the teacher preparation program for preK-8 teachers at six universities located in different regions of the U.S. The new program is designed to help pre-service teachers learn mathematics well, learn to access students' cultural funds of knowledge in ways that will help them teach mathematics, and learn to encourage students' mathematical thinking. By integrating these important bodies of knowledge, pre-service teachers should be better prepared to teach mathematics to the variety of students in their classes. The developers are designing (a) modules that can be used in teacher preparation courses, (b) a mentoring program for new teachers, and (c) on-line networks to facilitate collaboration among participating teachers and institutions.

The project includes a study of how pre-service teachers learn to apply the knowledge they have gained in the program. The research team has planned a longitudinal collection of data that will track the pre-service teachers into their careers. Their goal is to document teachers' understandings of children's mathematical thinking and children's cultural funds of knowledge and to understand the relationship between teachers' understandings and the learning and disposition of preK-8 students. The study will be implemented at all six universities with staggered start dates allowing for analysis and revisions between cohorts.

These research and development efforts have the potential to impact preK-8 teacher preparation through (1) the development of modules that integrate several relevant proficiencies in mathematics teaching, and (2) the research that studies the impact of such a program on the mathematical learning and disposition of preK-8 students.

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.

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.

Introducing Dynamic Number as a Transformative Technology for Number and Early Algebra

This project operationalizes research in number, operation, and early algebra. It builds on the paradigm of Dynamic Geometry (the interactive and continuous manipulation of geometric shapes and constructions) with a new technological paradigm, Dynamic Number, centered on the direct manipulation of numerical representations and constructions. Using The Geometer’s Sketchpad as a starting point, KCP Technologies is developing new software tools to deepen students’ conceptions of number and early algebra in grades 2–8.

Project Email: 
Lead Organization(s): 
Award Number: 
0918733
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
John Olive

Diagnostic E-learning Trajectories Approach (DELTA) Applied to Rational Number Reasoning for Grades 3-8

This project aims to develop a software diagnostic tool for integrating diagnostic interviews, group administered assessments, and student data in real-time so that teachers can enter and view student status information. This project would concentrate on rational number learning in grades 3-8. The design is based on a model of learning trajectories developed from existing research studies.

Project Email: 
Award Number: 
0733272
Funding Period: 
Sat, 09/01/2007 to Tue, 08/31/2010
Project Evaluator: 
William Penuel (SRI)
Full Description: 

This project aims to develop a software diagnostic tool for integrating diagnostic interviews, group administered assessments, and student data in real-time so that teachers can enter and view student status information. This project would concentrate on rational number learning in grades 3-8. The design is based on a model of learning trajectories developed from existing research studies.

The diagnostic system to be developed for teachers would be used in assessing their students' knowledge and would identify difficulties in understanding five key clusters of concepts and skills in rational number reasoning. It would also investigate the diagnostic system's effects on student and teacher learning in relation to state standards, assessments, and curricular programs. The five areas include understanding: (1) multiplicative and division space; (2) fractions, ratio, proportion and rates; (3) rectangular area and volume; (4) decimals and percents; and (5) similarity and scaling.

The diagnostic measures will include diagnostic interviews collecting data using a handheld computer, two types of group-administered assessments of student progress, one set along learning trajectories for each of the five sub-constructs and one composite measurement per grade. The diagnostic system will produce computer-based progress maps, summarizing individual student and class performance and linking to state assessments.

Nurturing Multiplicative Reasoning in Students with Learning Disabilities in a Computerized Conceptual-modeling Environment (NMRSD-CCME)

The purpose of this project is to create a research-based model of how students with learning disabilities (LDs) develop multiplicative reasoning via reform-oriented pedagogy; convert the model into a computer system that dynamically models every students’ evolving conceptions and recommends tasks to promote their advancement to higher level, standard-based multiplicative structures and operations; and study how this tool impacts student outcomes.

Project Email: 
Lead Organization(s): 
Award Number: 
0822296
Funding Period: 
Fri, 08/01/2008 to Wed, 07/31/2013
Project Evaluator: 
Dr. C. Brown
Full Description: 

Math Pathways and Pitfalls: Capturing What Works for Anytime Anyplace Professional Development

Math Pathways & Pitfalls lessons for students boost mathematics achievement for diverse students, including English Learners, English Proficient students, and Latino students. This project develops modules that increase teachers’ capacity to employ the effective and equitable principles of practice embodied by Math Pathways & Pitfalls and apply these practices to any mathematics lesson. This four-year project develops, field tests, and evaluates 10 online professional development modules.

Lead Organization(s): 
Award Number: 
0918834
Funding Period: 
Tue, 09/15/2009 to Fri, 08/31/2012
Full Description: 

Researchers and developers at WestEd are developing, field-testing, and evaluating ten online professional development modules anchored in research-based teaching principles and achievement-boosting mathematics materials. The modules provide interactive learning opportunities featuring real classroom video demonstrations, simulations, and scaffolded implementation. The professional development module development builds on the Math Pathways and Pitfalls instructional modules for elementary and middle school students developed with NSF support. The professional development provided through the use of these modules is web-based (rather than face-to-face), is provided in chunks during the school year and immediately applied in the classroom (rather than summer professional development and school year application), and explicitly models ways to apply key teaching principles to regular mathematics lessons (rather than expecting teachers to extract and apply principles spontaneously).

The project studies the impact of the modules on teaching practice with an experimental design that involves 20 treatment teachers and 20 control teachers. Data are gathered from teacher questionnaires, classroom observations, and post-observation interviews.

A Study of the Struggling Learner's Knowledge and Development for Number and Operation

This project targets first- and second-grade children who struggle to develop a deeper understanding of the mathematical strand of number and operation. The research team will (a) identify the various specific cognitive obstacles of first- and second-grade students who are struggling in number and operation, and (b) explore how instructional tasks designed to address specific cognitive obstacles affect the learning trajectory of struggling learners in number and operation.

Lead Organization(s): 
Award Number: 
0918060
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
Dr. Jeff Barrett

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