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K-8 Full report - SEPUP

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K-8 Full report - SEPUP

    Teaching and Learning K8 Mathematics and Science

    through Inquiry: Program Reviews and Recommendations

    Marcia C. Linn

    Cathy Kessel

    Kristen Lee

    Janet Levenson

    Michelle Spitulnik

    James D. Slotta

    October 31, 2000

    Metiri Group

    122 Ocean Park Blvd. #306

    Santa Monica, CA 90405

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    Table of Contents

    Table of Contents __________________________________________________________ iii

    1. Introduction ____________________________________________________________ 1

    Contemporary views of teaching and learning science and mathematics _________________ 2

    Promising uses of technology in learning and instruction ____________________________ 10

    Evolving uses of technology in science and mathematics _____________________________ 15

    Criteria for selecting exemplary instructional programs _____________________________ 17

    Mandatory Criteria ___________________________________________________________________ 18

    Pedagogical criteria __________________________________________________________________ 19 II. Caveats_______________________________________________________________ 22

    III. Program Reviews ______________________________________________________ 24

    Program Categories ___________________________________________________________ 25

    Recommendations of Exemplary Programs _______________________________________ 25

    1. Comprehensive Courses _____________________________________________________ 26

    Comprehensive Courses Reviewed ______________________________________________________ 28

    Reviews of Exemplary Comprehensive Curricula ___________________________________________ 29

    Connected Mathematics ____________________________________________________________ 29

    Investigations in Number, Data, and Space______________________________________________ 33

    MMAP: Middle School Math through Applications Project _________________________________ 35

    Science Education for Public Understanding Program (SEPUP) _____________________________ 38 2. Project-Based Curricula and Collaborative Projects ______________________________ 42

    Project-Based Curricula and Collaborative Projects Reviewed _________________________________ 43

    Reviews of Exemplary Project Based Curricula and Collaborative Projects _______________________ 44

    Global Lab_______________________________________________________________________ 44

    IMMEX (Interactive Multi-Media Exercises) ____________________________________________ 47

    The Adventures of Jasper Woodbury __________________________________________________ 51

    Model-It ________________________________________________________________________ 55

    One Sky Many Voices______________________________________________________________ 58

    The Web-based Integrated Science Environment: WISE ___________________________________ 60 3. Activities and Skill Acquisition ________________________________________________ 66

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    Activities and Skill Acquisition Projects Reviewed__________________________________________ 68 Reviews of Exemplary Activities and Skill Acquisition Projects _______________________________ 70

    Building Perspective _______________________________________________________________ 70

    Logical Journey of The Zoombinis ____________________________________________________ 73

    Millie's Math House _______________________________________________________________ 76

    National Council of Teachers of Mathematics Electronic Examples __________________________ 79

    Science Court ____________________________________________________________________ 81

    The Factory/The Factory Deluxe _____________________________________________________ 84

    Thinkin' Things All Around FrippleTown ______________________________________________ 85 4. Computational and Representational Tools _____________________________________ 89

    Computational and representational Tools Reviewed ________________________________________ 92 Reviews of Exemplary Computational and representational Tools ______________________________ 93

    AgentSheets _____________________________________________________________________ 93 Description __________________________________________________________________ 93

    Geometer’s Sketchpad______________________________________________________________ 98

    SimCalc MathWorlds _____________________________________________________________ 100

    STAGECAST Creator _____________________________________________________________ 103

    StarLogo _______________________________________________________________________ 106 5. Resource Web Sites (links to reviewed sites and online resources) __________________ 108

    Resource Web sites Reviewed _________________________________________________________ 109 Reviews of Resource Web sites ________________________________________________________ 109

    Math Forum _____________________________________________________________________ 109

    National Council of Teachers of Mathematics Web Resources _____________________________ 111 IV. Next steps ___________________________________________________________ 113

    V. References ___________________________________________________________ 115

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1. Introduction

    This report offers guidance for those shaping policy and designing elementary and middle school science and mathematics courses that prepare students to be lifelong

    users of scientific and mathematical ideas.

    We have reviewed programs designed to improve elementary and middle school students‘ understanding of science and mathematics by incorporating instructional

    technology effectively into the curriculum. Using criteria backed by research on

    learning and instruction, we have selected exemplary programs from among those

    reviewed.

    We emphasize the teaching of science and mathematics as a process of inquiry in which students learn to solve complex problems and critique scientific and

    mathematical arguments. We look for uses of computer and communications

    technology that help students become lifelong science and mathematics learners who

    are prepared to meet all sorts of challengesfrom computing their income taxes to

    interpreting data on global warming to assessing the risk of a medical procedure.

    We discuss:

    ? Contemporary views of teaching and learning science and mathematics ? Promising uses of technology in learning and instruction

    ? Evolving uses of technology in science and mathematics

    ? Criteria for selecting exemplary instructional programs

    ? Reviews of programs that meet our mandatory requirements, organized by category ? Recommendations of exemplary programs

    ? Next steps

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Contemporary views of teaching and learning science and

    mathematics

    Cognitive and social research clearly indicates that educational programs should

    challenge students to link, connect, and integrate their ideas and to learn in authentic contexts, taking into account their perception of real world problems. (Baumgartner & Reiser, 1998; Bransford, Brown and Cocking, 1999; diSessa, 2000; Linn & Hsi, 2000; Slotta & Linn, 2000). Too often our science and mathematics curricula present ideas in isolation, fail to encourage students to link their ideas, settle for the regurgitation of facts rather than the connection of ideas, and fail to prepare students to solve the personally relevant, everyday problems they will encounter throughout their lives. Instead, we should be educating students to be lifelong learners of science and mathematics by engaging in the process of inquiry that is the very nature of these fields.

    National groups have recently set standards for learning and teaching in science and

    mathematics that emphasize inquiry. In science, two reports detail standards for instruction in elementary and middle school. The Project 2061 benchmarks from the American Association for the Advancement of Science, (AAAS, 1993) and the National Research Council Science Education Standards (NRC, 1996) both offer a philosophy of instruction as well as specific topic suggestions for each grade level. The National Council of Teachers of Mathematics (NCTM) revolutionized thinking about

    mathematics instruction with the publication of standards (NCTM, 1989). These reports emphasize the need for understanding the scientific process as well as the integrated nature of science and mathematics. They advocate problem-based instruction as well as assessments that are integrated with instruction.

    NCTM called for significant increases in approaches to teaching and learning that foster mathematical inquiry, such as problem solving, critiquing, and project work. These standards influenced the development of many NSF-funded curriculum projects during the '90s. NCTM published an update and elaboration of its standards in 2000 that

    incorporated new research on teaching and learning (NCTM, 2000). NCTM

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recommended that all high school students receive four full years of mathematics

    instruction and identified specific instructional strategies for fostering a thorough

    understanding of mathematics. NCTM‘s updated report pays greater attention to the

    role of instructional technology. The NCTM maintains a Web site with materials that

    meet the new criteria and ―e-examples‖ that illustrate the current standards, as we describe below.

    The NCTM sees clear advantages for technology, commenting, ―Students can learn

    more mathematics more deeply with the appropriate use of technology (Dunham and

    Dick 1994; Sheets 1993; Boers-van Oosterum 1990; Rojano 1996; Groves 1994).

    Technology should not be used as a replacement for basic understandings and

    intuitions; rather, it can and should be used to foster those understandings and

    intuitions‖ (NCTM, 2000, p. 25).

    The NCTM sees technology as enhancing opportunities for students with special

    needs. For example, the NCTM notes, ―Technology can help students develop number

    sense, and it may be especially helpful for those with special needs. For example,

    students who may be uncomfortable interacting with groups or who may not be

    physically able to represent numbers and display corresponding symbols can use

    computer manipulatives. The computer simultaneously links the student's actions with

    symbols. When the block arrangement is changed, the number displayed is

    automatically changed. As with connecting cubes, students can break computer base-

    ten blocks into ones or join ones together to form tens‖ (NCTM, 2000, p. 81).

    The NCTM identifies specific uses of technology for inquiry (e.g., place-value

    concepts can be developed and reinforced using calculators). The NCTM emphasizes

    using calculators to identify patterns, pointing out, for example, that, in ―a challenging

    calculator activity for second graders…students begin at one number and add or

    subtract to reach a target number. By having students share and discuss the different

    strategies employed by members of a class, a teacher can highlight the ways in which

    students use place-value concepts in their strategies‖(NCTM, 2000, p. 81).

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    Computers and scientific or graphing calculators permit middle-grade students to deal with "messy," authentic problems. Combined with electronic data-gathering

    devices, such as calculator-based laboratories these tools allow students to gather and analyze data on such topics as the water quality of a local stream. The NCTM points out, ―For example, students might be interested in investigating whether it is cost-effective

    to recycle aluminum cans at their school, or they might explore weather patterns in

    different regions. Graphing calculators and easy-to-use computer software enable

    students to move between different representations of data and to compute … with

    messy numbers, both large and small, with relative ease― (NCTM, 2000, p. 258).

    Science and mathematics educators have also stressed the importance of age-appropriate instruction. Piaget (1929), Vygotsky (1978) and others have identified

    developmental trajectories and their impact on learning, stressing that instruction

    builds on what students know and is regulated by the developmental process. Recent

    research has established that student trajectories vary depending on a huge range of

    factors, including prior schooling, family experience, and personal interest. Rather than setting definite age-appropriate tasks, it has become important to test instruction with the intended students and tailor instruction to student ideas. If the instruction is to succeed, it must address the ideas students already have about scientific or

    mathematical topics. For example, most students come to science class with the idea

    that heat and temperature are the same thing, since the terms can often be used

    interchangeably. Instruction must take this confusion into account and address it

    directly (Linn & Hsi, 2000). Many of the technological environments reviewed in this

    report enable teachers to customize instruction to their students and to regularly update their own versions of activities as they gain more insight into the student audience.

    At the same time that educators and others are becoming aware that technology can improve instruction, a large body of national and international test results has revealed weaknesses in students‘ preparation and in their understanding of both basic and

    advanced scientific and mathematical ideas. Large numbers of students have difficulty

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solving complex problems in science and mathematics and fail to understand the

    process of inquiry. American students fall further and further behind their international

    counterparts as they progress through the educational system. The Third International

    Mathematics and Science Study (TIMSS) reports that, by eighth grade, American students

    have fallen from near the top in fourth grade to around the middle among the more

    than 40 countries studied, when their scientific and mathematical accomplishments are

    compared (Schmidt, McKnight, & Raizen, 1997; Schmidt et al., 1999; Stigler & Hiebert,

    1999; U.S. Department of Education & National Center for Education Statistics, 1999).

    These results, as well as other research about how students learn, have motivated

    teachers, schools, policy analysts, and concerned citizens to call for reform of instruction.

    Because education is a complex interconnected system, change is difficult. Many

    attempts at innovation succumb to the pressures of the status quo, becoming

    indistinguishable from the programs they seek to replace. For example, an innovative

    approach to problem solving may evolve into just another electronic ―drill and kill‖

    program by the time it becomes available to educators as a product. In this report, we

    look for exemplary programs that help to transform the teaching of science and

    mathematics based on current research studies.

    Current research offers guidelines for taking advantage of what we know about how

    people learn. A recent National Academy of Sciences committee has produced How

    People Learn, an extremely clear and powerful summary of research on student learning

    (Bransford, Brown, & Cocking, 1999) that emphasizes weaknesses in the current

    educational system as well as research results pointing to reforms that could improve

    student outcomes.

    Comparing the teaching of middle school mathematics in Japan with instruction in

    the United States underscores some of the shortcomings of American education. In a

    report synthesizing classroom observations conducted as part of the TIMSS study,

    Stigler and Hiebert (1999) noted that over 95% of American in-class work requires only

    that students apply an approach demonstrated by the teacher. Less than half of the class

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    time in Japan is devoted to this sort of work. In contrast, Japanese students spend far more time on complex science and mathematics and generally start a topic by inventing a strategy for solving novel problems. American students study less demanding topics and generally start by reading about or listening to the correct way to approach the problem. In the 1980s, Stevenson, Stigler, and their colleagues studied first and fifth graders in Japan, Taiwan, and the United States using tests and individual interviews (Stigler, Lee, & Stevenson, 1990). On average, Japanese students outperformed Taiwanese students and Taiwanese students outperformed U. S. students on these tasks. Essentially, the Japanese curriculum offers students more opportunities for scientific and mathematical inquiry, while the American curriculum asks American students to spend most of their time learning established approaches.

    The TIMSS analysis of the textbooks used in American science and mathematics courses supports the classroom investigations from the TIMMS research. The U.S. curriculum, as reflected in recent textbooks, is ―a splintered vision‖ (Schmidt, McKnight, & Raizen, 1997). Project 2061 (Kulm, 1999; Rosemary, Kesidou, Stern & Caldwell, 2000) recently released an analysis of middle school textbooks for science and mathematics and rated most as falling short of emphasizing inquiry and helping students develop cohesive understanding. Textbooks did not offer sufficient opportunity for students to understand science and mathematics so that they could apply the ideas to novel and complex problems. These analyses coincide with complaints from the workplace that American students lack preparation for jobs requiring scientific and mathematical thinking.

    Science and mathematics instruction in the elementary and middle school has often

    resulted in fewer opportunities for females and members of various cultural groups. Two factors contribute to this problem. First, stereotyped beliefs about who can succeed in science and mathematics deter some from participating in the discourse of mathematics and science (AAUW, 1998; Fenema & Leder, 1990; Hyde, Shibley, Fennema, Ryan, Frost, & Hoop, 1990; Martin, 2000; Sadker & Sadker, 1994). Second, and

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