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General References

References on Specific Topics

Research Projects and Centers

Mainly these are projects and centers receiving funding from US Federal Government Agencies.

Center for Innovative Learning Technologies (CILT)) [Online]. Accessed 2/10/02: Quoting from the Website:
The Center for Innovative Learning Technologies (CILT) is a distributed center designed to serve as a national resource for stimulating research on innovative, technology-enabled solutions to critical problems in K-14 learning. Our approach is to foster and conduct collaborative research and development in areas that we believe promise significant advances in learning.

Center for Talented Youth at the Johns Hopkins University [Online]. Accessed 2/26/02:

This Center is especially known for its many years of work with mathematically gifted students. However, it works with a broader range of students. Quoting from the first part of the Mission Statement:
Conduct national and international talent searches which identify, assess, and publicly recognize outstanding academic talent.

Provide challenging and innovative learning opportunities in mathematics, science, and the humanities, through:

- summer programs that meet the highest instructional and residential standards;

- rigorous distance education programs which are independent of time and location; - conferences that explore diverse and exciting educational topics and encourage broad-based, life-long learning programs. - awards ceremonies that affirm and nurture respect for intellectual abilities.

Center for Technology in Learning [Online]. Accessed 2/10/02:

This center is a component of SRI, International located in California. It is headed by Barbara Means and Roy Pea. Quoting from the Website:
By the early 1990s, it became very clear that technology was to play an increasingly important role in the education of children, youth, and adults. The issues of how to effectively use technologies to support learning were considered to be so important that the Center for Technology in Learning (CTL) was established at SRI. The Center was established within SRI's Policy Division, where it is closely allied with ongoing education and health research programs

National Science Foundation: Research on Learning and Education (ROLE) [Online]. Accessed 2/10/02: . Quoting from the Website:

Synopsis of Program: This program seeks to capitalize on important developments in a variety of fields related to human learning and to education. It will support research along a four-quadrant continuum that includes 1) brain research as a foundation for research on human learning; 2) fundamental research on behavioral, cognitive, affective and social aspects of human learning; 3) research on science, technology, engineering and mathematics (STEM) learning in formal and informal educational settings; and 4) research on STEM learning in complex educational systems. ROLE seeks gains at the intersections of these areas, where issues arising from research and educational practice can be reconciled, and hypotheses generated in one area may be tested and refined in others. The ROLE Program aims to advance the knowledge base in and across these multidisciplinary areas.

National Science Foundation: Research on Learning and Education (ROLE) Initial Round of Awards and Base "Quadrant"
. Quoting from the Website that lists Round 1 funding:

Carnegie Mellon University Tracking the Course of Mathematical Problem Solving, Anderson, John.
0087396 Whang I-II-III The goal of this project is to improve our ability to track how students solve mathematical problems. This research will use eye tracking to make real-time inferences about what the student is thinking and fMRI imaging to make inferences about different styles of problem solving. This research is done in the context of both the ACT-R theory of human cognition, which allows us to produce computational models of cognition, and a series of cognitive tutors for mathematics education, which are based on the ACT-R theory. The ACT-R theory is a theory of how the cognitive system adaptively uses procedural and declarative knowledge to achieve its goals. The research will focus on the algebra tutor that is currently in use in high schools and is being adapted for use in middle schools. The research will be concerned with the effect of different mathematical representations on problem solving and with different strategies for mathematical problem solving. There will be three lines of research. One, involving eye movements, will document the instructional opportunities associated with eye movements in the context of the cognitive tutors. It will particularly focus on the eye movements associated with competent use of graphical, tabular, and symbolic representations of functions. The second line of research, involving fMRI brain imaging, will study brain activation markers of the course of mathematical problem solving. It will particularly focus on distinguishing between students who use an informal, verbal form of reasoning with students who use a symbolic, visual form of reasoning. This line will also look at how we can merge information from imaging and eye scanning to make both methodologies more effective. The third line of research will study how one can use the information from fMRI scanning and eye tracking to produce more effective instruction. The three lines of research will converge on a culminating study that attempts to improve the effectiveness of the middle school tutor. It will first use fMRI imaging to identify the learning strategies of individual students and then collect real-time eye movement to guide instruction as students are learning. This will demonstrate how we can use some of the new emerging sensing technology to improve mathematics education.

Concord Consortium From Videogames to Science: A Design Study of BioLogica. Horwitz, Paul.

0087579 Sloane III This project will attempt to combine the excitement and interest students evince when allowed to interact with open-ended, exploratory computer models, with the structure and explicit pedagogy many require to succeed at linguistically oriented, paper-and-pencil tests. Using BioLogica, a software environment we have developed on a prior NSF grant, we will present students with a sequence of "web labs," or computer-based, guided investigations, that will introduce them to multi-level reasoning in the domain of genetics. The web labs will provide the students with challenges of increasing difficulty, monitoring their work, offering feedback and soliciting responses as appropriate. Each will present students with information and questions regarding situations or problems analogous to the ones they have just worked on, offering metacognitive prompts designed to promote transfer from the computer activities to a broader understanding of the underlying scientific concepts

University of Chicago Understanding and Teaching Spatial Competence Huttenlocher, Janellen.

0087516 Whang I-II Spatial competence is a fundamental aspect of intelligence, important to successful functioning. A high level of spatial skill is critical to the achievement of a technologically sophisticated work force for the twenty-first century. Spatial intelligence plays a major role in effective education in mathematics, science and engineering. The interdisciplinary research we will carry out focuses on understanding of spatial intelligence and establishing methods for maximizing the development of spatial skills. We will study spatial competence at different levels of analysis. At the biological level, we will will investigate the neurological foundations for spatial growth. We will examine the growth and organization of neural connections in areas of the brain that underlie the processing of spatial information. At the behavioral level, we will investigate the mechanisms that are involved in the mental representation of the spatial aspects of the world. We also will study the ways in which children come to understand spatial symbols such as maps and models. We will study how acquisition of these symbol systems affects the development of spatial intelligence. This work will include computational modelling of spatial intelligence. Finally, at the level of educational application, we will investigate the educational input responsible for the differential gains in spatial skill levels children achieve in school. We plan to identify specific teacher practices that are associated with high gains in student achievement. Our research team has expertise in a variety of relevant fields, including neural science, cognitive psychology, developmental psychology,computer science, education, and statistics. This research team has worked together for the past three years on research that has identified core elements of spatial functioning. Our goal now is to further our understanding of how the development of spatial competence can be enhanced .

 Carnegie Mellon University Dynamic Scaffolding to Improve Learning and Transfer of Hidden Skills. Lovett, Marsha

0087632 VanderPutten II Failure to learn hidden skills is a persistent obstacle to students in science, math, and engineering domains. Hidden skills, which include problem categorization, feature detection, and planning, are critical to solving problems in a domain but do not have any immediate, external product for students to see. Unfortunately, it is unclear how best to identify and teach these difficult-to-learn skills. Instructional scaffolding is a popular and effective technique for providing targeted support and guidance while students learn to solve problems in a new domain. Scaffolding has great potential for improving hidden-skill learning. However, the reasons it works and how best to implement it are largely unknown. The proposed research will explain the effectiveness of instructional scaffolding in terms of hidden skill learning. Several hypotheses about the relationship between scaffolding and hidden skills will be tested, and new scaffolding designs will be evaluated. This will lead to a systematic approach to teaching hidden skills that improves students' learning and transfer. The four specific aims of this project are: (1) Develop a systematic, efficient method for identifying hidden skills. While methods currently exist for analyzing domain-specific knowledge, these methods are not robust for identifying hidden skills, and they tend to be difficult and slow. This project will develop and test an automated method that combines logistic regression models and heuristic search algorithms to infer where hidden skills lie. (2) Develop a theoretical explanation for why scaffolding works. Although instructional scaffolds often lead to better learning, there has been little theoretical progress in explaining when and how scaffolding works. A sequence of experiments will be conducted to test three hypotheses that offer increasingly concrete levels of explanation for how scaffolding benefits learning and transfer. (3) Develop practical guidelines for the design of effective instructional scaffolding. Three critical questions for scaffolding design will be examined: What level of scaffolding support is sufficient to achieve its main benefit? When and how should scaffolding support be built and faded? And how can human instructors (i.e., TA's) best complement a computerized scaffolded learning environment? (4) Develop novel applications of our results on scaffolding hidden skills. There are at least two novel applications of this work, beyond the scope of learning theory and instructional design. First, the scaffolding designs from Specific Aim 3 will be used to develop new on-line assessments of students' understanding. Second, the results from Specific Aim 1 will be used to develop tools that train instructors to "see" the hidden skills in complex problems and thus better anticipate students' learning difficulties.

TERC, Inc. Math in Motion: Investigating the relationship between formal mathematics and body action. Nemirovsky, Ricardo

0087573 Zia II The aim of this proposal is to investigate new approaches to nurture and cultivate the mathematical imagination of all students. Mathematics as a science to imagine-with is not incompatible with memorizing the multiplication tables, number facts, or shortcuts to operate fractions, but it changes what these memories are part of. It is about imagiining space and time: shapes, patterns, or trajectories; it is about envisioning houw things could be; it is about discriminating the finite and infinite, the discrete from the continuous, and dthe possible from the impossible. The main conjecture of this proposal is that cultivating mathematical imagination is deeply related to enriching bodily action/perception. The research we propose intends to investigate this thesis through a series of studies with high school students and pre-service teachers. 

MIT The Role of Emotion in Propelling the SMET Process. Picard, Rosalind

0087768 Whang II-III Exploring the Role of Emotion in Propelling the SMET Learning Process The proposed research aims to build a computerized Learning Companion that will be sensitive to the affective aspects of learning and that will work with the child to facilitate the child's own efforts at learning. Learning complex ideas in science, math, engineering, and technology and developing the cognitive reasoning skills these areas demand often involves failure and a host of associated affective responses. When learning proceeds via human-human interaction, it is often improved by communication of affective cues (such as frustration, confusion, or interest), and by adaptation of the learning experience to such cues (adjusting pace of presentation, interjecting motivation, offering an additional view, etc.). When learning involves human-machine interaction, the human communication about when, where, how, and how important it is to adapt also often involves emotional information; however, today's computers largely ignore this information. Affective computing has the potential to expand human-computer interaction by extending computing to include emotional communication together with appropriate means of handling affective information. The proposed research aims to bring new tools of affective computing into the reach of educators, to begin to change computer-based learning from a style that ignores emotions to a style that can begin to respond appropriately to student emotions. The initial focus is on building a system that (1) helps students increase their awareness and mastery of the important role that emotions can play in learning and (2) facilitates the child's learning, by occasionally prompting with questions or feedback, and by watching and responding to the affective state of the child-watching for signs of frustration and boredom that may precede quitting, for signs of curiosity or interest that tend to indicate active exploration, and for signs of enjoyment and mastery, which might indicate a successful learning experience. Tools developed for the Learning Companion should also be useful for intelligent tutoring systems, and should help give insight into new theories of motivation and emotion in teaching; however, the Learning Companion is not a teacher or tutor that knows the answers, but a player on the side of the student. The companion will be sensitive to the learning trajectory of each student, helping him or her learn, and in so doing, learn how to learn better. At the same time, the Learning Companion will serve as an interactive system for helping researchers identify and better understand ways in which emotion is expressed, communicated, and handled in successful science, math, engineering, and technology learning experiences.

University of Maryland College Park Learning How to Learn Science: Metacognition in post-secondary physics education for bioscience majors. Redish, Edward

0087519 $946,855 II-III In this project, a cross-disciplinary team of the University of Maryland Physics Education Research Group (UMD-PERG) and an advisory team of biologists and biology-oriented education specialists is carrying out basic research in science learning among college-level bioscience students. An emphasis on meta-learning frames the approach of the team. This includes metacognition, epistemologies, expectations, and the construction of broad and powerful mental models; in short learning that goes beyond content and helps students understand what it means to learn science and how to learn it effectively. The project is studying student learning of fundamental issues in thinking about science; modifying current best-practices learning environments to make them effective tools for teaching meta-learning in a large-lecture environment; and developing survey tools to permit the documentation and evaluation of the state of student meta-learning attitudes and skills in large classes. The "laboratory" for this research effort is an algebra-based physics course, and the project builds on earlier work of the UMD-PERG in studying student meta-learning in high school and calculus-based university physics classes

MIT Sources of mathematical thinking. Spelke, Elizabeth

0087721 Whang I-II To understand mathematical cognition both as it develops in the young child and as it is taught in school, one must understand the cognitive systems from which it is constructed and the processes by which those systems are coordinated to produce new concepts and skills. Based on previous research, we hypothesize that elementary school mathematics builds on three representational systems: a system for representing exact small numerosities, a system for representing approximate large numerosities, and natural language with its system of number words and other quantifiers. The proposed research investigates each of these building block systems and their interactions through experiments on human infants, non-human primates, preschool children learning counting, elementary school children learning arithmetic and fractions, and adults. To study the building block cognitive systems directly, experiments investigate spontaneous number representations in human infants and in untrained adult monkeys, using in each population the same three converging behavioral measures: looking time to arrays of different numerosities and to addition or subtraction events (building on the finding that both infants and monkeys look longer at novel arrays or unexpected events), manual search (building on the finding that the number of times that an infant or monkey will search in a container depends on the number of objects it represents within the container), and locomotor approach to containers with different numbers of attractive objects (building on the finding that infants and monkeys will approach the container with the greater number of objects). Further experiments investigate how preschool children assemble these components in learning number words and the counting routine, by using verbal and pointing tasks to assess developmental changes in children's understanding of number words and counting procedures. To uncover the neural substrates underlying mathematical cognition, both behavioral and neuroimaging experiments investigate whether and how human adults use each of the three representational systems in performing numerical comparisons and elementary arithmetic. Finally, experiments investigate number concepts and arithmetic learning in elementary school children. Training studies in which children are taught new facts or concepts and then are tested on a range of related problems will serve to investigate the subsystems involved in this learning, to probe the processes by which those subsystems are assembled to meet new educational challenges, and to explore ways of enhancing mathematics learning in elementary school. This research promises to shed light on the teaching and learning of mathematics through coordinated, laboratory-based studies in which monkeys, infants, children and adults are given the same stimuli and often the same tasks. This coordinated effort should provide a broad portrait of the sources of mathematical thinking, from its phylogenetic and ontogenetic origins to its culmination in educated adults.

University of California - Berkeley Modeling, Developing, and Assessing Scientific Inquiry Skills Using a Computer-Based Inquiry Support Environment. White, Barbara

0087583 Suter III This study investigates cognitive models of scientific inquiry skills in middle school science. It creates pedagogical approaches that enable students to develop widely applicable cognitive skills needed for collaborative inquiry and reflective learning. It would investigate a number of hypotheses concerning how to achieve these objectives. The study expects to result in creating a learning theory that links metacognition and reflective practices to the development of expertise in scientific inquiry. The central hypothesis is that scientific inquiry can be taught, or facilitated, through computer tools that support cognitive modeling and reflective practice. The investigators would create a support environment that houses several software advisors that can give strategic advice and guide students as they conduct research projects in science and reflect on their processes of investigation. Also, the investigators would create assessments of students' expertise and evaluate the use of these models increases their understanding and performance of scientific inquiry.

Kansas State University Technology & Model-Based Conceptual Assessment: Research in Students' Applications of Models in Physics & Mathematics. Zollman, Dean

0087788 Zia III To improve the communication between students and teachers, particularly in large classes, many universities have begun using technology-based response systems. These systems enable an instructor to pose questions and see, within a few minutes, the students' responses to those questions. Another similar approach is to assign homework that is submitted, graded and returned quickly via the World Wide Web. Both of these technology-based systems offer instructors the opportunity to record each student's responses in a database. Thus, the instructor can track students' understanding much more completely than with traditional homework and quizzes and can use the resulting data to investigate more deeply how students understand the scientific and mathematical concepts. In addition to seeing the present level of each students understanding the instructor can learn how the students change their thinking by making comparisons of responses throughout the learning process. A present, the analyses of these responses generally tell instructors when the students are obtaining the right answers. However, for students who are not answering correctly, the present systems do little more than indicate that the student is not applying the scientific theories and models correctly. Still missing is an analysis tool that is based on contemporary educational research and can provide robust quantitative information on the students' difficulties with the underlying scientific models and theories, and can track how the students' understandings of these models change during instruction. These tools must go beyond correct answer analysis and analyze students' incorrect answers by incorporating theories of learning into the systems. This project will begin with a model for students' conceptual learning processes and with existing work on assessing students' conceptual understanding in physics and mathematics. Then, research will be conducted on students' applications of scientific models and mathematical concepts, on how the students' thinking and applications change during instruction, and methods to present the results of these assessments to teaching faculty who are using in-class, real-time response or on-line homework systems. By constructing sets of questions in which incorrect answers provide insights into the scientific and mathematical models that students are applying, the project's results will lead to a deeper understanding of students' abilities to learn physics and mathematics and the contexts in which that learning occurs most effectively. The analysis will also provide insight into students' abilities to transfer knowledge between physics and mathematics courses. The major objectives of the project are to measure, with real-time feedback, students' understanding of fundamental concepts and the application of those concepts, trace changes in those understandings and applications during instruction, investigate how students' conceptual understanding depends on the context in which a new concept is studied, create analysis tools that can be used effectively in many educational environments, provide information about the transfer of knowledge between physics and mathematics, and investigate how students and instructors interact with this teaching environment. The result of reaching these goals will be a system that will have a large impact on the teaching of science and mathematics. The impact will be particularly great in large enrollment classes where instructors are often very detached from their students because, frequently, such information becomes available only after students take an exam. Of particular importance for the instructors is knowledge of when students have begun to change their thinking but still sometimes revert to pre-instructional applications of scientific or mathematical concepts-- a mixture of understanding and a lack of understanding. Such situations are recognized to be an important intermediate step in the learning process. By knowing the extent of this mixture the instructors can plan the next step in the learning process based on the students' present physical or mathematical understanding and the contexts which aid fundamental change in students' thinking. Thus, the project will provide both information and tools to help science and mathematics instructors learn about the present knowledge of their students and how to use that present knowledge constructively to improve the students' scientific and mathematical thinking skills.

Stanford Center for Innovation in Education. Accessed 7/14/03: Quoting from the Website:

Stanford faculty and students from many schools and departments collaborate on SCIL programs and projects, since complex learning issues are by their very nature multidisciplinary. The Stanford Learning Lab, established in 1997 and now merged with SCIL, has added its accomplished staff and formidable international research base to further the Center's objectives.

SCIL resides in Wallenberg Hall, a showcase facility with path-breaking technology, learning, and research spaces located in the front of the Quad on the Stanford campus. Wallenberg Hall was built with generous support from the Knut and Alice Wallenberg Foundation, which has maintained a long and auspicious affiliation with Stanford University's educational mission.

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