Learning novel mathematical concepts in a computer-enriched environment

There is widespread belief that computers should be used for the teaching and learning of mathematics. Research indicates that computers are primarily used in mathematics classes: (1) to reinforce previously taught concepts, (2) to allow students to construct computer programs to simulate mathematical techniques known to the student and (3) to explore mathematical microworlds encompassing mathematical ideas and concepts normally known to the student. Furthermore, it is said that pre-service teachers should experience the learning of mathematical ideas and concepts of which they had no prior experience in environments in which computers are just one of the resources available for exploring and experimenting with these ideas and concepts. How should these learning environments be constructed so that pre-service teachers are sensitised to the value of doing mathematics in such environments? Is a student's understanding of novel mathematical concepts enhanced when s/he explores it in a computer-enriched environment? An experiment with pre-service teachers was carried out in a college of education for blacks in South Africa. This article describes the insights gained from this experiment.     

Scientific Inquiry in Educational Multi-user Virtual Environments

In this paper, we present a review of research into the problems of implementing authentic scientific inquiry curricula in schools and the emerging use of educational Multi-User Virtual Environments (MUVEs) to support interactive scientific inquiry practices. Our analysis of existing literature in this growing area of study reveals three recurrent themes: (1) with careful design and inclusion of virtual inquiry tools, MUVE-based curricula can successfully support real-world inquiry practices based on authentic interactivity with simulated worlds and tools, (2) Educational MUVEs can support inquiry that is equally compelling for girls and boys, and (3) research on student engagement in MUVE-based curricula is uneven. Based on these themes, we suggest that future large-scale research should investigate (1) the extent to which MUVE-based inquiry learning can be a viable substitute for the activities involved in real-world inquiry; (2) the impact of MUVEs on learning and engagement for currently underserved students, and (3) the impact on engagement and learning of individual aspects of MUVE environments, particularly virtual experimentation tools designed to scaffold student inquiry processes and maintain engagement. Additionally, we note that two identified issues with integrating scientific inquiry into the classroom are currently not addressed by MUVE research. We urge researchers to investigate whether (1) MUVE-based curriculum can help teachers meet state and national standards with inquiry curricula; and (2) scientific inquiry curricula embedded in MUVE environments can help teachers learn how to integrate interactive scientific inquiry into their classroom. This material is based upon work supported by the National Science Foundation under Grant No. 0310188. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.     

Using computer simulations to assesss hands-on science learning

Two methods of assessing student learning of a hands-on instructional unit are compared. One method involves manipulation of concrete materials, and the other method involves manipulation of icons on a computer to solve an electric circuits problem. Sixth-grade students in an inquiry-based science program completed both assessments separated by three weeks. Results indicated that although mean performance was the same for each method, individual student performance varied considerably. Implications for use of computer simulations as an alternative to hands-on assessment are discussed.This research was supported by grants from the National Science Foundation and the Office of the Vice President, University of Michigan. Opinions expressed are those of the author and not necessarily the supporting agencies.     

Computer technology and complex problem solving: Issues in the study of complex cognitive activity

Goals and plans organize much of complex problem solving behavior and are often inferable from action sequences. This paper addresses the strengths and limitations of inferring goals and plans from information that can be derived from computer traces of software used to solve mathematics problems. We examined mathematics problem solving activity about distance, rate, time relationships in a computer software environment designed to support understanding of functional relationships among these variables (e.g., distance =rate × time; time=distance/rate) using graphical representations of the results of simulations. Ten adolescent-aged students used the software to solve two distance, rate, time problems, and provided think-aloud protocols. To determine the inferability of understanding from the action traces, coders analyzed students' understanding from the computer traces alone (Trace-only raters) and compared these to analyses based on the traces plus the verbal protocols (Traceplus raters). Inferability of understanding from the action traces was related to level of student understanding how they used the graphing tool. When students had a good understanding of distance, rate, time relationships, it could be accurately inferred from the computer traces if they used the simulation tool in conjunction with the graphing tool. When students had a weak understanding, the verbal protocols were necessary to make accurate inferences about what was and was not understood. The computer trace also failed to capture dynamic exploration of the visual environment so students who relied on the graphing tool were inaccurately characterized by the Trace-only coders. Discussion concerns types of scaffolds that would be helpful learning environment for complex problems, the kind of information that is needed to adequately track student understanding in this content domain, and instructional models for integrating learning environments like these into classrooms.Members of the Cognition and Technology Group at Vanderbilt who have contributed to this project are (in alphabetical order) Helen Bateman, John Bransford, Thaddeus Crews, Allison Moore, Mitchell Nathan, and Stephen Owens. The research was supported, in part, by grants from the National Science Foundation (NSF-MDR-9252990) but no official endorsement of the ideas expressed herein should be inferred.     

Playing with computers,playing with ideas

In this article I react to the thoughts of Hennessey, addressing mainly the student, and Esquivel, addressing mainly the teacher. These authors present complementary, interesting, and consistent pictures of creativity education. Here I comment on a few issues that are less clear and discuss implications of these authors' work for computers in education. I conclude that teachers need to play with ideas about how they might use computers to build a culture that promotes deep, meaningful, and creative learning.Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.     

Active classroom participation in a Group Scribbles primary science classroom

A key stimulus of learning efficacy for students in the classroom is active participation and engagement in the learning process. This study examines the nature of teacher–student and student–student discourse when leveraged by an interactive technology—Group Scribbles (GS) in a Primary 5 Science classroom in Singapore which supports rapid collaborative knowledge building (RCKB). We envisaged nine design principles for RCKB in the design of lessons and postulated a logic model that links and explains the effects of our design principles to the ultimate goal of learning efficacy. We presented a case study of a GS lesson which shows that GS affordances leveraged by good lesson and activity design could enable the students to have more epistemic agency. Students had opportunities to participate spontaneously in class discussions by fully expressing their ideas without inhibition. The technology effect is used to support instant formative feedback and interactions among students effectively.     

Middle Grade Teachers’ Learning through Students’ Engagement with Modeling Tasks*

We report on how two middle-grade teachers supported their students’ mathematical reasoning within the context of a novel modeling task in data analysis. We examine how the task features supported the development of teachers’ knowledge as their students engaged with the task. Analyses of the teachers’ practices suggest that the task features enabled teachers: (a) to develop new understandings of the mathematical content and the ways in which student ideas develop and are represented; (b) to adopt new roles in their interactions with the students, including a focus on listening and observing, and on asking questions for understanding and clarification; and (c) to engage in forms of interpretative listening that shifted the role of evaluation from the teacher to the student. This material is based upon work supported by the National Science Foundation (NSF) under Grant No. 9722235 and by the Australian Research Council (ARC).     

Finding the Hook: Computer Science Education in Elementary Contexts

The purpose of this study was to investigate how elementary teachers with little knowledge of computer science (CS) and project-based learning (PBL) experienced integrating CS through PBL as a part of a standards-based elementary curriculum in Grades 3–5. The researchers used qualitative constant comparison methods on field notes and reflections to describe the teachers' participation in professional development to create CS-infused projects to be implemented with their students. Categories that emerged included standards integration, student autonomy, and challenges of infrastructure and time. The data are from the first 6 months of a 3-year, National Science Foundation-funded project. (Keywords: computer science, project-based learning, integration, elementary curriculum)     

Training elementary mathematics teachers using interactive multimedia

Two studies were conducted wherein an interactive, multimedia-based instructional system was piloted with preservice elementary school teachers. Mathematics methods classes experienced conventional instruction with a new interactive technological-instructional system as supplemental course material. An analysis of interview data indicated that students were more likely to incorporate the knowledge they acquired from the system into their teaching repertoire. Many students thought that this mode of presentation enhanced their learning of mathematics teaching methods and their teaching in other fields.This project was supported, in part, by a grant from the National Science Foundation (Award # TPE-8950317) and International Business Machines.     

IDEA: Identifying design principles in educational applets

The Internet is increasingly being used as a medium for educational software in the form of miniature applications (e.g., applets) to explore concepts in a domain. One such effort in mathematics education, the Educational Software Components of Tomorrow (ESCOT) project, created 42 miniature applications each consisting of a context, a set of questions, and one or more interactive applets to help students explore a mathematical concept. They were designed by experts in interface design, educational technology, and classroom teaching. However, some applications were more successful for fostering student problem-solving than others. This article describes the method used to mine a subset (25) of these applets for design principles that describe successful learner-centered design by drawing on such data as videos of students using the software and summaries of written student work. Twenty-one design principles were identified, falling into the categories of motivation, presentation, and support for problem solving. The main purpose of this article is to operationalize a method for post hoc extraction of design principles from an existing library of educational software, although readers may also find the design principles themselves to be useful. This project was funded by a seed grant from the Center for Innovative Learning Technologies funded by the National Science Foundation (REC # 9720384), and was partially supported by Educational Testing Service. Any opinions expressed in this publication are those of the authors and not necesarily of Educational Testing Service.     

Project on scope,sequence, and coordination: A new synthesis for improving science education

The Project on Scope, Sequence, and Coordination of Secondary School Science (SS&C) is a major national project designed to reform science education, K-12. Based on research on learning science, the project includes provision for hands-on experience, sequencing over time at successively higher levels of abstraction, and taking account of student preconceptions. Associated with SS&C is a performance-based student assessment project which incorporates compact-disc interactive (CD-I) technology. The SS&C project and its assessment component were initiated by the author and have become projects of the National Science Teachers Association (NSTA) funded by the National Science Foundation and the U.S. Department of Education. Projects are underway in California, North Carolina, Iowa, Puerto Rico, Texas, and Alaska.     

Student Use of Scaffolding Software: Relationships with Motivation and Conceptual Understanding

This study was designed to theoretically articulate and empirically assess the role of computer scaffolds. In this project, several examples of educational software were developed to scaffold the learning of students performing high level cognitive activities. The software used in this study, Artemis, focused on scaffolding the learning of students as they performed information seeking activities. As 5th grade students traveled through a project-based science unit on photosynthesis, researchers used a pre-post design to test for both student motivation and student conceptual understanding of photosynthesis. To measure both variables, a motivation survey and three methods of concept map analysis were used. The student use of the scaffolding features was determined using a database that tracked students’ movement between scaffolding tools. The gain scores of each dependent variable was then correlated to the students’ feature use (time and hits) embedded in the Artemis Interface. This provided the researchers with significant relationships between the scaffolding features represented in the software and student motivation and conceptual understanding of photosynthesis. There were a total of three significant correlations in comparing the scaffolding use by hits (clicked on) with the dependent variables and only one significant correlation when comparing the scaffold use in time. The first significant correlation (r = .499, p < .05) was between the saving/viewing features hits and the students’ task value. This correlation supports the assumption that there is a positive relationship between the student use of the saving/viewing features and the students’ perception of how interesting, how important, and how useful the task is. The second significant correlation (r = 0.553, p < 0.01) was between the searching features hits and the students’ self-efficacy for learning and performance. This correlation supports the assumption that there is a positive relationship between the student use of the searching features and the students’ perception of their ability to accomplish a task as well as their confidence in their skills to perform that task. The third significant correlation (r = 0.519, p < 0.05) was between the collaborative features hits and the students’ essay performance scores. This correlation supports the assumption that there is a positive relationship between the student use of the collaborative features and the students’ ability to perform high cognitive tasks. Finally, the last significant correlation (r = 0.576, p < 0.01) was between the maintenance features time and the qualitative analysis of the concept maps. This correlation supports the assumption that there is a positive relationship between the student use of the maintenance features and student conceptual understanding of photosynthesis. This material is based upon work supported by the National Science Foundation (REC9980055). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.     

Developing interactive mathematical talk: investigating student perceptions and accounts of mathematical reasoning in a changing classroom context

In recent years there has been an increased focus on the need for teachers to develop learning communities where all students have opportunities to engage in interactive discourse. However, there are few studies that focus on student perceptions and accounts of mathematical reasoning in classrooms with interactive mathematical talk as a focus of reform. A framework of teacher actions to develop classroom and mathematical practices was developed from classroom observations. Photo-elicitation interviews were used to investigate student perception and accounts of mathematical explanations and reasoning. The professional development programme, shifts in the teacher actions, and subsequent shifts in student perception and their recall of their own and peers’ mathematical reasoning over a school year are highlighted. Developing interactive dialogue in the classroom took considerable time and attention. Facilitating change to the way students both participated and understood their obligations required constant, ongoing attention to both the classroom and mathematical practices.     

Tailoring National Standards to Early Science Teacher Identities: Building on Personal Histories to Support Beginning Practice

Individual recommendation plans (IRP) for student teaching practice were co-constructed with two methods students based on the select application of National Science Teachers Association’s National Standards for Science Teacher Preparation. Methods students completed a resume, an interview on pedagogical preferences, and a learning styles survey to determine the reform-based standards and pedagogical approaches that better fit their personal histories and identity formation as science teachers. Each case was unique with one student better meeting the Standards of “Issues” and “Science in the Community” and the other student better meeting the standards of “Inquiry” and the “Nature of Science”. Student teachers planned and taught lessons based on their IRP and were mostly successful in meeting their prescribed standards and utilizing their preferred pedagogies. However, their success in use of specific strategies supporting their approach was highly dependent upon classroom context. The use of the IRP process as a reflective tool strengthening identity formation and early practice is discussed.     

Using Handheld Computers to Support Improved Classroom Assessment in Science: Results from a Field Trial

A variety of handheld applications and curricular materials have been developed to support inquiry science learning in recent years, but there are few handheld-supported assessment activities available to teachers. In Project WHIRL, researchers from SRI International worked in partnership with teachers from Beaufort County School District (SC) to develop a suite of handheld software applications that could be used to support classroom assessment in upper elementary and middle school science classrooms. In this paper, we will analyze results from a field trial conducted in 2003–2004 with 18 teachers in the district, focusing on how teachers’ enactment of handheld-supported assessment activities altered the frequency and quality of their assessment practices.This material is based in part on work supported by the National Science Foundation under Grant Number REC-0126197. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.     

如何创立以学生为中心的英语课堂教学

随着语言教学不断向交际化方向发展,传统的教学模式受到挑战,逐渐转变成以学生为中心的课堂教学模式。本文从转变教学观念和学习观念,确定英语课堂教学中的教师作用和学生地位,营造民主平等的教学氛围,培养学生自主学习,尝试小组合作、开展互动教学等方面来阐述如何创造“以学生为中心”的英语课堂教学。     

Delivering Food Safety Education to Middle School Students Using a Web-Based, Interactive, Multimedia, Computer Program

ABSTRACT:  More than 76 million persons become ill from foodborne pathogens in the United States each year. To reduce these numbers, food safety education efforts need to be targeted at not only adults, but school children as well. The middle school grades are ideal for integrating food safety education into the curriculum while simultaneously contributing to national and state education standards in science, technology, and family and consumer sciences. For this project, a multimedia, self-paced online resource for delivering a food safety curriculum to middle school children was developed. Animated characters were used to deliver the lesson content. The application also included video segments, quiz feedback, and interactive games and activities. The effectiveness of the Web site was evaluated using validated cognitive and attitudinal assessment tools, and by comparing student cognitive gains to individual student learning styles. Participants were recruited from 6 middle schools in 5 states, totaling 217 students (20 sixth graders, 157 seventh graders, and 40 eighth graders). The results show that students had statistically significant modest gains in pretest to posttest knowledge and enjoyed using the Web site. The 6th grade students had significantly lower pretest to posttest improvement compared to 7th and 8th grade students, suggesting that this program may not be appropriate for this grade level. Furthermore, the results indicate that this Web-based computer application meets the needs of varying individual student learning styles.     

An investigation on the effects of using interactive digital video in a physics classroom on student learning and attitudes

Interactive digital video provides students with control of computer visualization techniques and allows them to collect, analyze, and model two-dimensional motion data. Activities that use these techniques were developed for students to investigate the concept of frames of reference in various real-life situations. This investigation examines the effect on student learning and attitudes of using these materials in an introductory college physics course. The study measured students' computer attitudes and found improvement in students' feelings of comfort in using computers after completion of the activities. We found students' prior computer experience did not influence their perceptions of the activities. The majority of participants perceived discussion and the computer visualization techniques as being very effective in helping them learn, Students' understanding of the physics concepts were assessed and the participants' scores were compared with nonparticipants' scores. Although analysis of variance statistical procedures revealed no significant differences between the two groups, the results of this study indicate that sophisticated instructional video software can be perceived as easy to use and effective by students who are novices and experts in using computers. Thus, interactive digital video tools and activities have the potential to provide physics teachers with the latest technology to bring the active process of learning physics to their classroom. © 1997 John Wiley & Sons, Inc. J Res Sci Teach 34: 467–489, 1997.