Curriculum

The Challenge of Interdisciplinary Education: Math-Bio

This project continues research and development work on high school instructional materials that integrate biology, computing, and mathematics. The project goal is to develop and test a one-semester high school course. The course consists of some modules developed under a previous NSF grant as well as some new material. Intended deliverables include up to five new instructional modules and a coherent one-semester course suitable for the increasing state requirements for a fourth year of mathematics.

Project Email: 
Award Number: 
1020166
Funding Period: 
Wed, 09/15/2010 to Sun, 08/31/2014
Project Evaluator: 
Len Albright at CSU
Full Description: 

Developers and researchers at Rutgers University, Boston University, Colorado State University, and the Consortium for Mathematics and Its Applications (COMAP) are continuing research and development work on high school instructional materials that integrate biology, computing, and mathematics. The project goal is to develop and test a one-semester high school course. The course consists of some modules developed under a previous NSF grant as well as some new material.

COMAP leads the effort to develop the instructional materials and the process involves mathematicians, biologists, computer scientists, teachers, and writers. The materials are pilot- and field-tested in a number of schools and revised after each test. Subject matter experts review the materials for accuracy and teachers and education professionals review them for their usability. Researchers at Colorado State University collect and analyze data on student learning and interest at all stages of the pilot- and field-testing.

The intended deliverables include up to five new instructional modules and a coherent one-semester course suitable for the increasing state requirements for a fourth year of mathematics. The course is supported by a book in print and electronic format and includes teacher training support tools and activities to prepare teachers to present interdisciplinary bio-mathematics material.

Pre-K Early Algebra Through Quantitative Reasoning (PreKEA)

This project is 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.

Lead Organization(s): 
Award Number: 
1212766
Funding Period: 
Wed, 09/01/2010 to Sat, 08/31/2013
Full Description: 

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 (PreK Early Algebra through Quantitative Reasoning) 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.

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 to 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.

Integrating Engineering and Literacy

This project is developing and testing curriculum materials and a professional development model designed to explore the potential for introducing engineering concepts in grades 3 - 5 through design challenges based on stories in popular children's literature. The research team hypothesizes that professional development for elementary teachers using an interdisciplinary method for combining literature with engineering design challenges will increase the implementation of engineering in 3-5 classrooms and have positive impacts on students.

Lead Organization(s): 
Award Number: 
1020243
Funding Period: 
Wed, 09/01/2010 to Wed, 05/31/2017
Full Description: 

The Integrating Engineering and Literacy (IEL) project is developing and testing curriculum materials and a professional development model designed to explore the potential for introducing engineering concepts in grades 3 - 5 through design challenges based on stories in popular children's literature. The project research and development team at Tufts University is working with pre-service teachers to design and test the curriculum modules for students and the teacher professional development model. Then the program is tested and refined in work with 100 in-service teachers and their students in a diverse set of Massachusetts schools. The research team hypothesizes that professional development for elementary teachers using an interdisciplinary method for combining literature with engineering design challenges will increase the implementation of engineering in 3-5 classrooms and have positive impacts on students. The driving questions behind this proposed research are: (1) How do teachers' engineering (and STEM) content knowledge, pedagogical content knowledge, and perceptions or attitudes toward engineering influence their classroom teaching of engineering through literacy? (2) Do teachers create their own personal conceptions of the engineering design process, and what do these conceptions look like? (3) What engineering/reading thinking skills are students developing by participating in engineering activities integrated into their reading and writing work? The curriculum materials and teacher professional development model are being produced by a design research strategy that uses cycles of develop/test/refine work. The effects of the program are being evaluated by a variety of measures of student and teacher learning and practice. The project will contribute materials and research findings to the ultimate goal of understanding how to provide elementary school students with meaningful opportunities to learn engineering and develop valuable problem solving and thinking skills.

DRK12-Biograph: Graphical Programming for Constructing Complex Systems Understanding in Biology

This project will investigate how complex systems concepts supported by innovative curricular resources, technology applications and a comprehensive research and development structure can assist student learning in the domain of biology by providing a unifying theme across scales of time and space. The project seeks to address four areas of critical need in STEM education: biological sciences, complex systems, computational modeling, and equal access for all.

Award Number: 
1019228
Funding Period: 
Wed, 09/01/2010 to Sun, 08/31/2014
Project Evaluator: 
David Reider
Full Description: 

This proposal outlines a research and development project that investigates how complex systems concepts supported by innovative curricular resources, technology applications and a comprehensive research and development structure can assist student learning in the domain of biology by providing a unifying theme across scales of time and space. The project seeks to address four areas of critical need in STEM education: biological sciences, complex systems, computational modeling, and equal access for all. This proposal explores how these needs are addressed through a curricular and technological intervention that structures biology learning through the framework of complex systems and computational modeling. The primary partners are the Massachusetts Institute of Technology and the University of Pennsylvania, working with eight teachers in four schools in the Boston area.

The project integrates graphical programming and simulation software, StarLogo TNG, into the standard high school biology curriculum to improve learning of biology concepts through the introduction and understanding of core complex systems processes. Instead of learning biology in discrete chunks, the chosen biological topics are connected through the framework of complex systems, and successively build in complexity from the basic building blocks of life to the interdependence and sustainability of life forms. This approach is designed to help students understand how processes at one level are connected to those at another level. The research is designed to answer the following questions: 1. Does a learning progression based on the complex systems ideas of scale and emergence enable students to make connections across biological topics, remediate known misconceptions, and apply core complex systems principles better than traditional instructional sequences? 2. What are the on-going affordances and constraints of implementation taking into consideration structural, functional and behavioral variables and what changes to project activities yield increased implementation and learning capacities? 3. Does programming of simulations increase understanding of complex systems and biology concepts compared to use of previously constructed simulations? The evaluation is designed to collect data and provide feedback on the adherence to the plan, the implementation challenged, and how research informs development.

The project anticipates a number of deliverables towards the end of the project and beyond. These include the creation of a unified high school biology curricular sequence that builds in increasing spatial and temporal scales to deepen student understanding of four core biology topics; the production, implementation and testing of curricular activities that acknowledge and ameliorate known implementation challenges; and the development of curricular strategies and tools to help teachers and students improve knowledge and skills in computational modeling, computer programming and participation in the cyberinfrastructure. In order to increase ease of integration into schools, and enhance scalability, the simulation activities are facilitated by a new web-based version of StarLogo TNG that integrates the curricular materials all of which will be distributed freely. Additional dissemination strategies include a website, conferences, a newsletter, community activities, active dissemination, and academic presentations.

The Value of Computational Thinking Across Grade Levels

This project is developing and testing a set of 12 curriculum modules designed to engage high school students and their teachers in the process of applying computational concepts and methods to problem solving in a variety of scientific contexts. The project perspective is that computational thinking can be usefully thought of as a specialized form of mathematical modeling.

Project Email: 
Award Number: 
1020201
Funding Period: 
Thu, 07/01/2010 to Mon, 06/30/2014
Project Evaluator: 
Len Albright and Andrea Weinberg at CSU
Full Description: 

The Value of Computational Thinking (VCT) project combines the talents and resources of STEM professionals at the Rutgers University DIMACS Center, the Consortium for Mathematics and Its Applications (COMAP), Colorado State University, Hobart and William Smith College, the Computer Science Teachers Association, and five partner school districts to develop and test a set of 12 curriculum modules designed to engage high school students and their teachers in the process of applying computational concepts and methods to problem solving in a variety of scientific contexts. The project perspective is that computational thinking can be usefully thought of as a specialized form of mathematical modeling. The product of computational thinking in a particular domain is a model of a situation, a structuring and representation of the situation, that enables computations to be performed to answer questions, solve problems, control processes, predict consequences, or enhance understanding.

Since computational thinking is a relatively new construct in STEM and STEM education, there are few available curriculum materials to support instruction intended to develop the understanding, habits of mind, and specific techniques that are involved. The fundamental goal of the VCT project is to answer an engineering research question: "What kinds of instructional materials and learning experiences will develop effective computational thinking skills and attitudes?" The VCT project is applying a design research process involving iterative phases of development, pilot testing, and revision to produce prototype instructional materials that will be useful as stand-alone curriculum modules or when collected into different packages to support full high school courses. Project field test evaluation will provide preliminary evidence about the efficacy of the materials in developing desired student learning.

Proponents of computational thinking in STEM and STEM education have argued that it offers a powerful general approach to problem solving in discipline-specific and inter-disciplinary settings. They also argue that, when properly taught, it can provide an effective introduction and attraction to careers in computer science and other computing-intensive fields. Thus the VCT project has a long-term goal of broadening participation in computer science and related technology fields. Materials are being designed with special features to enhance their effectiveness in reaching this objective.

INK-12: Teaching and Learning Using Interactive Ink Inscriptions in K-12 (Collaborative Research: Koile)

This is a continuing research project that supports (1) creation of what are termed "ink inscriptions"--handwritten sketches, graphs, maps, notes, etc. made on a computer using a pen-based interface, and (2) in-class communication of ink inscriptions via a set of connected wireless tablet computers. The primary products are substantiated research findings on the use of tablet computers and inscriptions in 4th and 5th grade math and science, as well as models for teacher education and use.
Award Number: 
1020152
Funding Period: 
Wed, 09/01/2010 to Sun, 08/31/2014
Project Evaluator: 
David Reider, Education Design Inc.
Full Description: 

The research project continues a collaboration between MIT's Center for Educational Computing Initiatives and TERC focusing on the enhancement of K-12 STEM math and science education by means of technology that supports (1) creation of what are termed "ink inscriptions"--handwritten sketches, graphs, maps, notes, etc. made on a computer using a pen-based interface, and (2) in-class communication of ink inscriptions via a set of connected wireless tablet computers. The project builds on the PIs' prior work, which demonstrated that both teachers and students benefit from such technology because they can easily draw and write on a tablet screens, thus using representations not possible with only a typical keyboard and mouse; and they can easily send such ink inscriptions to one another via wireless connectivity. This communication provides teachers the opportunity to view all the students' work and make decisions about which to share anonymously on a public classroom screen or on every student's screen in order to support discussion in a "conversation-based" classroom. Artificial intelligence methods are used to analyze ink inscriptions in order to facilitate selection and discussion of student work.

The project is a series of design experiments beginning with the software that emerged from earlier exploratory work. The PIs conduct two cycles of experiments to examine how tablets affect students learning in 4th and 5th grade mathematics and science. The project research questions and methods focus on systematic monitoring of teachers' and students' responses to the innovation in order to inform the development process. The PIs collect data on teachers' and students' use of the technology and on student learning outcomes and use those data as empirical evidence about the promise of the technology for improving STEM education in K-12 schools. An external evaluator uses parallel data collection, conducting many of the same research activities as the core team and independently providing analysis to be correlated with other data. His involvement is continuous and provides formative evaluation reports to the project through conferences, site visits, and conference calls.

The primary products are substantiated research findings on the use of tablet computers, inscriptions, and networks in 4th and 5 grade classrooms. In addition the PIs develop models for teacher education and use, and demonstrate the utility of artificial intelligence techniques in facilitating use of the technology. With the addition of Malden Public Schools to the list of participating districts, which includes Cambridge Public Schools and Waltham Public Schools from earlier work, the project expands the field test sites to up 20 schools' classrooms.

CAREER: Teaching and Learning Social Science Inquiry and Spatial Reasoning with GIS

This research project aims to explore and understand how geographic information systems (GIS) can be used to promote and teach spatial thinking and social science inquiry skills. It addresses the research question: What are effective teaching practices using GIS to teach spatial thinking and social science inquiry in middle-school and undergraduate classrooms? This program will study the effectiveness of teaching practices for social science instruction with GIS in urban public schools for specific learning objectives.

Partner Organization(s): 
Award Number: 
0953448
Funding Period: 
Thu, 04/01/2010 to Thu, 03/31/2011
Full Description: 

This research project aims to explore and understand how geographic information systems (GIS) can be used to promote and teach spatial thinking and social science inquiry skills. It addresses the research question: What are effective teaching practices using GIS to teach spatial thinking and social science inquiry in middle-school and undergraduate classrooms? This program will study the effectiveness of teaching practices for social science instruction with GIS in urban public schools for specific learning objectives.

The research plans to develop an empirically-grounded framework for studying the ways teaching practices with GIS interact with four other foci of research: (1) learning objectives for inquiry skills and spatial reasoning, articulated across grade levels; (2) learning processes with GIS; (3) GIS curriculum designs; and (4) the design of GIS tools for learning environments. The project plans to use the GIS tools within a culturally relevant curriculum unit for diverse students of African American and Latino backgrounds.

A range of research methods will be used to study teaching and learning, focused on a common topic: American Migrations of African American and Latino populations over time, using GIS-mapped census data. Research will be conducted in three phases: (1) design experiments iteratively developing a theoretical framework, curriculum, and instructional strategies; (2) case studies of effective instruction at two levels; and (3) curriculum evaluations. Findings on effective teaching and learning in middle school classrooms, with undergraduate college students, and pre-service elementary teachers via GIS based-curriculum, will be presented.

Mathematics for Teaching: A Problem-based Resource for Teachers

This project will produce, publish and disseminate a strong mathematics content curriculum for in-service secondary mathematics teachers and prepare a group of specialized teacher-leaders to deliver this curriculum across the country. Important components of this project are that expert teachers will ensure that the mathematics is relevant to the professional lives of secondary teachers and mathematicians will be core members of the development and review team.

Lead Organization(s): 
Award Number: 
0554309
Funding Period: 
Thu, 06/15/2006 to Wed, 05/19/2010
Full Description: 

This project builds on a very successful program of summer institutes for mathematics teachers, graduate students and university faculty at the Park City Mathematics Institute (PCMI) run by the Institute for Advanced Study and supported in part by Boston University and EDC. In this project they will produce, publish and disseminate a strong mathematics content curriculum for in-service secondary mathematics teachers and prepare a group of specialized teacher-leaders to deliver this curriculum across the country. The program works on the theory that an immersion experience moves teachers to a higher order of understanding; formality and precision are crucial in mathematics; and teachers thrive in a mathematical community. Important components of this project are that expert teachers will ensure that the mathematics is relevant to the professional lives of secondary teachers and mathematicians will be core members of the development and review team. The materials produced for these courses contain ingredients for a problem-driven curriculum connecting advanced mathematical knowledge with the mathematics used by secondary teachers, in and out of their classrooms. Mathematics courses that connect upper-division university mathematics to secondary mathematics are not typically available to teachers. This program uses very well respected mathematics and mathematics educators to prepare content rich materials that will be tested at a prominent facility with teachers. They will also be working with presenters at this time to prepare facilitators guides for the materials. The developers currently have five three-week courses. The proposal will allow them to 1) add exposition and detailed commentary for facilitators; 2) add courses where there may be gaps in the mathematical topics and 3) prepare teachers who will work with mathematicians to develop and teach the materials to their colleagues using the PCMI professional development approach.

Mathematics and Culture in Micronesia: Integrating Societal Experiences (Macimise)

Founded on ethnomathematics research findings, this project aims to increase the mathematics learning of first-, fourth-, and seventh-grade elementary school Micronesian students. Plans are to develop and field-test culturally and linguistically sensitive grade-level curriculum units in specific mathematics topics, such as number and counting, division of whole numbers and fractions, and elements of geometry, focused on the indigenous mathematics learning experiences of eight distinct islands in the Pacific region.

Project Email: 
Award Number: 
0918309
Funding Period: 
Tue, 09/01/2009 to Sun, 08/31/2014
Project Evaluator: 
Joan LaFrance
Full Description: 

Founded on ethnomathematics research findings, this project--a collaborative research and development effort between Pacific Resources for Education and Learning and the University of Hawaii-Manoa--aims to increase the mathematics learning of first-, fourth-, and seventh-grade elementary school Micronesian students. Plans are to develop and field-test culturally and linguistically sensitive grade-level curriculum units in specific mathematics topics, such as number and counting, division of whole numbers and fractions, and elements of geometry, focused on the indigenous mathematics learning experiences of eight distinct islands in the Pacific region. A team of mathematicians, mathematics educators, mathematics teachers, graduate students, curriculum and assessment experts, and quantitative and qualitative methodologists will develop and implement approximately 24 curriculum units (8 for each grade level).

The hypothesis that inclusion of indigenous ways of knowing into the mathematics curriculum may enhance students' NCTM standards-based mathematics learning and meaning making drives the proposed scope of work. Thus, the main research question is: Does knowledge of recovered culturally based mathematics significantly improve indigenous student scores on standardized mathematics tests at grades 1, 4, and 7? The specific setting of the study comprises eight islands included in the Federated States of Micronesia, the Marshall Islands, the Commonwealth of the Northern Mariana Islands, Palau, and American Samoa. Participants include 2,304 first- , fourth- , and seventh-grade students: 24 experimental and 24 control groups, two of each grade level on each of the eight U.S.-affiliated islands of the Pacific region.

Qualitative data gathering strategies, such as interviews with local informants, teachers, and students; and classroom observations are used to document indigenous ways of knowing, mathematical content, assessment practices, and cultural practices. Quantitative data gathering and interpretation strategies using pre-and post-test scores, as well as scores from standardized assessments, will include statistical analyses to determine the effect of the curricular units on participating students' grade-level mathematics achievement.

The evaluation plan comprises both formative and summative components, including implementation evaluation and progress evaluation. Grade-level curriculum units, three publications on findings, a professional development model for teachers through graduate courses, and a cadre of masters' and doctoral degrees in mathematics education are among the main products of this effort.

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