Mathematics

Examining Teacher Discourse and Whole-class Interaction: A Social Semiotics Model for Mathematics Lesson Study Groups

The project is an exploratory, qualitative case study of a mathematics Lesson Study group for 12 beginning mathematics teachers working in high-poverty middle schools in Brooklyn. The project's Lesson Study model employs social semiotics to examine the intersection between language and learning in mathematics classrooms. Additionally, on-site Lesson Study groups will also be launched in some participating schools.

Partner Organization(s): 
Award Number: 
0822223
Funding Period: 
Mon, 09/01/2008 to Wed, 08/31/2011

Physical Science Comes Alive: Exploring Things that Go

This project creates eight half-year units in two subject areas—Force and Motion, and Energy Systems— for three grade bands, pre-K–1, 2-3 and 4–6. These projects integrate engineering, science, math literacy and art in the context of design, construction and testing of toys using inexpensive or recycled materials.

Lead Organization(s): 
Award Number: 
0733209
Funding Period: 
Sat, 09/01/2007 to Sat, 09/01/2012
Project Evaluator: 
Dr. Marie Hoepfl
Full Description: 

 The goals of the project are to develop and support the use of materials that promote integration of engineering with science, math, literacy and art in the elementary grades. Children engage in designing, making and testing their own devices. These include cardboard mechanisms that animate stories; paper pop-ups; gravity-, elastic- and electric-powered cars, and gadgets with hidden switches that produce light, sound and/or motion when opened or closed. Through these activities, students develop facility with materials, plus an understanding of systems, models, design, constraints, redesign and troubleshooting, which are core concepts in engineering education. Physics concepts include motion, force and energy. Writing is an essential component of the project, and of science education generally.

There are eight curriculum units in two sets of four each, under the headings of Force & Motion and Energy Systems. Each set consists of one unit each for grades K-1 and 2-3, and two units for 4-5. Classroom sets for the units cost between $100 and $300 apiece, and many of the materials can be acquired by recycling instead of purchase. As part of the Energy Systems Curriculum, students create gravity-powered cars in the K-1 unit Invent-a-Wheel, wind-up vehicles in the 2nd-3rd grade unit Fantastic Elastic, and electric cars in 4th and 5th grades in the EnerJeeps unit. In the course of this work students write their own equipment lists, instruction manuals, trouble-shooting guides and analyses of how their devices work. The analysis leads directly to basic concepts of physical science. When students operate their wind-ups, for example, they experience the use of their own power to store energy in a rubber band, and witness its release as kinetic energy when they let it go.

Project Delta: Digital Environments for the Learning and Teaching of Algebra

The purpose of Project Delta is two-fold: (1) to extend an existing library of 17 interacting CD-ROM digital learning environments on numbers and operations by adding an algebra strand, and (2) to evaluate the impact of the new algebra materials on teacher development. Each of the digital environments features classroom sessions that allow for exploration of a mathematics topic, children learning over time, and teachers? instructional techniques.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0822034
Funding Period: 
Fri, 08/15/2008 to Sat, 07/31/2010

Inquiry-based Laboratories for Engaging Students of Creative and Performing Arts in STEM

This project develops, implements, and evaluates new multimedia laboratory activities designed to engage students in science, technology, engineering, and mathematics (STEM). The project specifically targets artistically gifted students who are often steered towards more traditionally creative areas (e.g., arts and humanities) and away from STEM. The goals to help students understand that scientific principles permeate the creative and performing arts and that creativity and expression are also embraced by STEM.

Lead Organization(s): 
Award Number: 
0733284
Funding Period: 
Wed, 08/15/2007 to Sat, 07/31/2010

Coherent Implementation of Mathematics Instructional Materials: A Study of the Variations and Effects of District Supports for Implementation

This project is a four-year, longitudinal, mixed-methods study of 12 school districts’ implementation of elementary mathematics instructional materials. It investigates the relationships among the district level of coherence of implementation, the school level of support for implementation, the school level of use of materials, and the effects on student outcomes.

Award Number: 
0918109
Funding Period: 
Thu, 10/01/2009 to Mon, 09/30/2013
Project Evaluator: 
Cynthia Char

Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students

This project is developing a two-year, intensive professional development model to build middle-grades mathematics teachers’ knowledge and implementation of formative assessment. Using a combination of institutes, classroom practice, and ongoing support through professional learning communities and web-based resources, this model helps teachers internalize and integrate a comprehensive understanding of formative assessment into daily practice.

Project Email: 
Award Number: 
0918438
Funding Period: 
Tue, 09/15/2009 to Tue, 08/31/2010
Project Evaluator: 
Cynthia Char
Full Description: 

Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students (FACETS) 

This project is submitted as a full research and development project that addresses challenge #3, how can the ability of teachers to provide STEM education be enhanced?

The FACETS project will develop a 2-year, intensive professional development model to build middle grades mathematics teachers’ knowledge and implementation of formative assessment. Using a combination of institutes, classroom practice, and ongoing support through professional learning communities and web-based resources, this model will help teachers internalize and integrate a comprehensive understanding of formative assessment into daily practice. As part of the professional development model, we will create a variety of products:

  • a facilitator’s guide describing the components of the professional development model and suggestions for using the model to provide a professional development program,
  • cyberlearning products such as interactive forums and a vetted resource library, and
  • video and other materials for the professional development activities and resource library.

FACETS includes a formative research component centered on the following questions:

1. How do mathematics teachers’ knowledge and practice of formative assessment change as a result of participation in the proposed professional development?

2. What learning trajectory describes teachers’ learning about formative assessment, and what are common barriers to successful implementation?

Reports of research findings will include journal articles on teachers’ learning trajectory for formative assessment and common barriers to successful implementation faced by teachers.

Intellectual merit: Our field work, supported by existing research, has shown that math teachers have difficulty fully implementing formative assessment in their classroom. Existing professional development programs either present a comprehensive understanding without a focus on mathematics, or focus on mathematics but only emphasize some of the critical aspects needed to bring out the full potential of formative assessment. This project will develop a professional development model that a) presents a comprehensive understanding of formative assessment and b) focuses specifically on mathematics. Furthermore, this project proposes to contribute to the field of mathematics teacher education through a deeper insight into mathematics teachers’ learning and practice of formative assessment. This insight can be used by professional developers and teacher educators in mathematics to make decisions that help teachers progress more effectively in their learning. This project brings together a multi-disciplinary team with expertise in formative assessment, professional development, mathematics, mathematics education, and teacher education research.

Broader impacts: We anticipate that the professional development will have an immediate impact on participating teachers, and on their students, as they learn about and implement formative assessment in their classrooms. Individual districts and schools have expressed an interest in the FACETS professional development program. The New Hampshire State Department of Education also indicates support for statewide implementation. In addition, research results regarding teachers’ learning trajectories for formative assessment will be crucial to inform future professional development and teacher education programs, and to help teachers reflect on, and guide, their own learning. Data regarding the major barriers to teachers’ learning of formative assessment will also impact future professional development by identifying issues needing additional focus, as will data regarding the effect on those barriers of factors such as teaching experience and mathematical knowledge for teaching. Finally, as there is a paucity of video and other examples of formative assessment in mathematics classrooms, the resource library will make widely available a sorely needed resource to teachers grappling with understanding and implementing formative assessment in mathematics classrooms in a practical way.

Transition to Algebra: A Habits of Mind Approach

This research and development project provides resources for ninth-grade mathematics students and teachers by developing, piloting, and field-testing intervention modules designed as supplementary materials for Algebra 1 classes (e.g., double-period algebra). Rather than developing isolated skills and reviewing particular topics, these materials aim to foster the development of mathematical habits of mind—in particular, the algebraic habit of abstracting from calculations, a key unifying idea in the transition from arithmetic to algebra.

Project Email: 
Award Number: 
0917958
Funding Period: 
Tue, 09/01/2009 to Sat, 08/31/2013
Project Evaluator: 
Jim Hammerman, TERC
Full Description: 

Transition to Algebra, A Habits of Mind Approach, is aimed at very quickly giving students the mathematical knowledge, skill, and confidence to succeed in algebra, and showing them that they can be good at things they believed they couldn't do. The students were all smart and intrepid when they were six. Even now, they are better and more persevering than we are about figuring out their smartphones and video games. Transition to Algebra aims to tap that smart, intrepid, persevering spirit of puzzling things out and making sense of them by presenting mathematics based in common sense, not arbitrary rules.

This project is developing a collection of modules introducing key ideas of algebra in ways that complement the core curriculum when a school is offering double period algebra. The key habit of mind being developed is abstracting from calculation. Modules deal with the transition from arithmetic to algebra, rational numbers, expressions/equations/word problems, graphs and equations, geometry of algebra, and proportional reasoning. The target population is students in urban high poverty schools with a significant ELL sector.

Our hypothesis is that instructional materials focused on developing conceptual understanding and mathematical habits of mind can complement traditional skill-focused algebra instruction in ways that are engaging to students. Furthermore, they argue that using materials with such meta-cognitive aims will actually strengthen the learning of core algebraic concepts and skills.

The supplementary algebra modules are being developed by a form of design research. Concurrent with development and field test of the student and teacher materials, the investigators are addressing four research questions. The first two questions are focused on the effects of the intervention in developing student habits of mind and in improving their competence and confidence in algebra. The other two address the feasibility of implementing the new approach to double-period algebra in a variety of school settings. A small-scale quasi-experimental field test is being used to give preliminary estimates of the effectiveness of the instructional materials and the implementation guidelines. The core purpose of these research activities is to inform development and refinement of the student and teacher instructional materials.

Products of this development effort will be a valuable resource to schools as they devise strategies for helping all students master the essentials of elementary algebra.

Effective Use of Mathematical Instructional Materials

This project aims to identify and organize research that is most useful to K-12 mathematics curriculum decision makers and to develop improved mechanisms for them to make good use of such research. Products will include research reports and an annual seminar. The goal is to create an infrastructure designed to support K-12 mathematics leaders in their efforts to better use research to inform curricular decision-making processes.

Award Number: 
0454022
Funding Period: 
Tue, 03/01/2005 to Tue, 08/31/2010

Linear Algebra and Geometry: Advanced Mathematics for More Students

EDC is developing a high school capstone course in linear algebra. Student resources contain a core semester that develops two- and three-dimensional geometry using vectors and that treats matrix algebra and its applications to geometry; a semester of material that completes a typical undergraduate course (exploring bases, determinants and eigentheory); and 5 stand-alone modules that develop applications of this core to mathematics, engineering, science, and other STEM fields.

Project Email: 
Award Number: 
0733015
Funding Period: 
Mon, 10/01/2007 to Mon, 09/30/2013
Project Evaluator: 
University of New Hampshire

Resources for Supporting Lesson Study in Mathematics

This project creates professional development materials that support secondary mathematics teachers in improving teaching and learning through lesson study. Project resources support school districts in launching a lesson study program with a strong mathematical focus, an emphasis on teacher learning within the lesson study model and support for building the local lesson study leadership needed to implement and expand a lesson study program.

Award Number: 
0554527
Funding Period: 
Mon, 05/01/2006 to Fri, 04/30/2010

Pages

Subscribe to Mathematics