Chapter 11
“Technology in Mathematics and Science Instruction”
1. What Does TPACK Look Like in Science and Math Education?
A. The union of the 3 knowledge domains (content, pedagogy, technology) to develop a lesson base from which a teacher can view a lesson and understand how technology can enhance the learning opportunities and experiences for students while also knowing the correct pedagogy to enhance the learning content
B. For example, when teaching about magnetic north, instead of simply lecturing on the differences between geographic north and magnetic north, the teacher might have students use a magnetic field sensor and data collection software to monitor the magnetic field intensity as they identify magnetic north
2. Issues and Problems in Mathematics Instructions
A. Accountability for Standards in Mathematics
i. Principles and Standards for School Mathematics
à Released in 2000 by the National Council of Teachers of Mathematics
à Serves as the primary resource and guide for all who make decisions that affect the mathematics education of students in pre-K through grade 12
à Achievement of the vision of the document requires, “solid mathematics curriculum, competent and knowledgeable teachers who can integrate instruction with assessment, education policies that enhance and support learning, classrooms with ready access to technology, and a commitment to both equity and excellence.”
à Calls for a common foundation of mathematics to be learned by all students; the following six principles address the critical issues:
- Equity
- Curriculum
- Teaching
- Learning
- Assessment
- Technology (is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning)
à Develops 5 content standards for pre-K through 12th grade
- Numbers and operations
- Algebra
- Geometry
- Measurement
- Data analysis and probability
à Develops 5 process standards for pre-K through 12th grade
- Problem solving
- Reasoning and proof
- Communication
- Connections
- Representations
B. Challenges in Implementing the Principles and Standards for School Mathematics
i. Adapting for special needs
ii. Research points to three implications for the selection and use of technology related to mathematics education
à (1) Teachers should consider an appropriate combination of off- and on-computer activities
à (2) Teachers should view technology as a mathematical tool as opposed to viewing technology as a pedagogical tool
à (3) Teachers should view technology as a tool for developing student thinking
iii. Software and applications should be incorporated in a way that can be extended for long periods of time across many topics to engage students in meaningful problems and projects
iv. Research points to the positive influence of technology on student achievement in mathematics—programs that promote experimentation and problem solving enable students to embrace key mathematical concepts that are otherwise difficult to grasp
3. Technology Integration Strategies for Mathematics Instruction
A. Using Virtual Manipulatives
i. Elementary level: teachers can display models for numbers and operations on the computer screen so the students can derive and construct their own meaning for mathematical concepts
ii. Secondary level: teachers can use software models to make abstract concepts more concrete
iii. Benefits
à Supports hands-on activities for learning mathematics
à Offers flexible environments for exploring complex concepts
à Provides a concrete representation of abstract concepts
iv. Resources & Activities
à National Library of Virtual Manipulatives for Interactive Mathematics at Utah State University; http://matti.usu.edu/nlvm/index.html
B. Fostering Mathematical Problem Solving
i. Problem solving: “…engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process they will often develop new mathematical understandings. Solving problems is not only a goal of learning mathematics, but also a major means of doing so.” (NCTM, 2000)
ii. Benefits
à Helps students gather data to use in problem solving
à Provides rich, motivating problem solving environments
à Gives student opportunities to apply mathematical knowledge and skills in meaningful contexts
iii. Resources & Activities
à CBLs
à Software; The Learning Company’s Zoombinis: Thinkin’ Things
à Programing languages
à Texas Instruments Educational Technology Download Center; http://education.ti.com/educationportal/sites/US/sectionHome/download.html
C. Allowing Representation of Mathematical Principles
i. Mathematics is, by its nature, an abstract subject—our understanding of mathematical ideas and concepts is closely tied to how we represent the abstractions of mathematics
ii. Benefits
à Makes abstract mathematical concepts more visual and easier to understand
à Gives student environments in which to make discoveries and conjectures related to geometry concepts and objects
iii. Resources & Activities
à Graphing calculators
à Software; Geometer’s Sketchpad, KaleidoMania
à Spreadsheets
à Key Curriculum Press Software; http://www.keypress.com/x6475.xml
D. Implementing Data-Driven Curricula
i. Benefits
à Provides easy access to multiple data sets
à Provides real statistics to support investigations that are timely and relevant
à Supports development of student knowledge and skill related to data analysis
à Allows for exploration and presentation of data in graphical form
ii. Resources & Activities
à Software; Fathom, Tabletop, Tabletop Jr.
à Spreadsheets
E. Supporting Math-Related Communications
i. Expressing ideas in written form is essential; therefore, students must be able to convert their mathematical ideas/thinking into words
ii. Benefits
à Allows easy contacts with experts
à Promotes social interaction and discourse about mathematics
à Allows teachers to reach other teachers for the exchange of ideas
iii. Resources & Activities
F. Motivating Skill Building and Practice
i. Even though the current emphasis is on learning higher order mathematics skills, many students need more resources to support the practice of basic skills
ii. Benefits
à Provides motivating practice in foundation skills needed for higher order learning
à Provides guided instruction within a structured learning environment
à Delivers instruction when the teacher may not be available
iii. Resources & Activities
4. Websites for Mathematics Instruction
A. National Council of Teachers of Mathematics
5. Issues and Problems in Science Instruction
A. Accountability for Standards in Science
i. American Association for the Advancement of Science (AAAS)
à Science for All Americans (1989)
à Set out recommendations for what all students should know and be able to do in science, mathematics, and technology by the time they graduate from high school
à Challenges science teachers to ensure that all students are scientifically literate so that all children can participate in the everyday science discourse
ii. The National Research Council (NRC)
à National Science Education Standards (1995)
à Outlines the content that all students should know and be able to do
à Provides guidelines for assessing student learning in science
à Provides guidance for science teaching strategies, science teacher professional development, and the support necessary to deliver high-quality science education
à Describes the policies to bring coordination, consistency, and coherence to science education programs
iii. Many of the state standards documents have drawn their content from The Benchmarks for Science Literacy (AAAS, 1993) and/or The National Science Education Standards
iv. U.S. Department of Education and the National Science Foundation endorse mathematics and science curricula that “promote active learning, inquiry, problem solving, cooperative learning, and other instructional methods that motivate students.”
v. National Committee on Science Education Standards and Assessment (1992) state that “school science education must reflect science as it is practiced and that one goal of science education is to prepare students who understand the modes of reasoning of scientific inquiry and can use them.”
vi. Inquiry-Oriented Instruction
à The basis for inquiry-oriented science instruction is developing opportunities for students to learn science process skills:
- Collecting, sorting, and cataloging
- Observing, note taking, and sketching
- Interviewing, polling, and surveying
à Research has shown that inquiry-based instruction is effective in developing the following:
- Scientific literacy
- Understanding of scientific process
- Vocabulary knowledge
- Conceptual understanding
- Critical thinking
- Positive attitudes towards science
- Construction of logico-mathematical knowledge
à Research has identified 4 major ways technology is utilized in the successful inquiry-based science classroom:
- As a productivity tool: technology aides in accomplishing tasks with greater efficiency, allowing students to spend more time on tasks that are more supportive of learning; for example, students spend less time on data management and calculations and more time interpreting and understanding the scientific concepts related to those data
- Communicating ideas and information: students do not have to spend time constructing illustrations, graphs, and pictures, they can let the software format them, etc.
- Investigating with technological tools: technology can aid in the fundamental practice of scientific investigation by collecting information and representing information appropriately; the most commonly used technological processes are simulation and data-gathering tools such as probes
- Creating knowledge products: the use of technology can allow students to synthesize knowledge in more challenging ways through computer-generated graphs, pictures, hyper-links, etc.
vii. Integration of technology in the science classroom is dependent on an understanding of the definition of technology in the context of scientific teaching and learning
à Benchmarks for Science Literacy, AAAS, 1993: “Technology once meant knowing how to do things—the practical arts or the study of the practical arts. But it has also come to mean innovations such as pencils, television, aspirin, microscopes, etc., that people use for scientific purposes, and it refers to human activities such as agriculture or manufacturing and even to processes such as animal breeding or voting or war that change certain aspects of the world.”
à National Science Education Standards, NRC, 1996: “The central distinguishing characteristic between science and technology is a difference in goal: the goal of science is to understand the natural world, and the goal of technology is to make modifications in the world to meet human needs. Technology as a design is included in the Standards as parallel to science inquiry.”
B. The Narrowing Pipeline of Scientific Talent
i. A trend has been identified in the declining number of students (especially females and minorities) pursuing studies in math, science, and engineering fields
ii. As a result of the declining numbers of students entering the STEM (science, technology, engineering, mathematics) fields, America is facing a growing crisis in a lack of leadership in these areas
iii. One of the first reports on the issue: Fueling the Pipeline: Attracting and Educating Math and Science Students (EMC Corp., 2003)
C. Increasing Need for Scientific Literacy
i. The science benchmarks reflect a growing need for all citizens to be scientifically literate
ii. The economic and environmental welfare of the country depends on the character and quality of the science education that the nation’s schools are providing
D. Difficulties in Teaching K – 8 Science, Study Conducted by Educational Testing Service
i. Research has compared the SAT scores of teacher candidates passing the Praxis II exam with the average scores for all college graduates
ii. Conclusions: the elementary education candidates have much lower math and verbal scores than other college graduates do
iii. The teaching of science for understanding has become difficult due to the lack of deep understanding on the part of the teacher
iv. The Eisenhower National Clearinghouse offers a guide to improving professional development in the areas of math, science, and technology; http://www.goenc.com/
E. New Emphasis on and Controversies about Scientific Inquiry
i. Scientific inquiry: approaching problems scientifically
ii. When learning with technology focuses on inquiry-based learning, the following approaches are commonly adopted:
à Technology is viewed as a tool, much like a pencil or pen, only more powerful
à Use of technology is primarily taught in the context of solving a problem
à Students help each other with the mechanics of the technology—in many classrooms, it is the students that are the experts
à Talking about and around the technology is as important as the technology itself; just as talk about how information can be applied is as important as the information itself
à Technology is used to augment the communication by expanding the audience and the expressive options
iii. The National Science Teachers Association recommends a combination of direct instruction and inquiry-based learning
F. Adapting for Special Needs
6. Technology Integration Strategies for Science Instruction
A. Supporting Authentic Science Experiences
i. The American Association for the Advancement of Science challenges teachers and schools to engage their students in actually doing science rather than just hearing about it or seeing demonstrations of it
ii. Further, authentic science involves not only hands-on science, but also connecting the science to students’ lives and life experiences
iii. Authentic science instruction is supported by both constructivist learning theory and cognitive apprenticeship concepts
iv. The GLOBE Project
à An environmental science project that utilizes remote sensing and ground-based observations to study local environments—weather, land cover, soil, and hydrology
à Students use GPS (global positioning system), GIS (global information system), and information technologies to collect and analyze data
v. GoNorth! Adventure Learning Series
à Driven by the adventure learning model of online learning
à Adventure learning
- Hybrid distance education approach that provides students with opportunities to explore real-world issues through authentic learning experiences within collaborative learning environments
- Based on a combination of inquiry-based learning and experiential learning
- Students’ learning processes involve pursuing answers to their own questions rather than memorizing rote facts
vi. Webquests
à Designed to connect students with a reasonable sample of Internet resources where they, on their own, decide which resources to use
à Designed for all students from elementary to secondary
vii. Project FeederWatch
à Designed by Cornell University
à Provides students with a bird identification key, information for sticking a bird feeder, gathering data, and submitting information to the site
à How the teachers/students choose to use the information and the site is up to them
à Provides numerous opportunities to use spreadsheet data and carry out geographic information system analyses
viii. Virtual Field Trips
à Relies on the Internet to allow students to visit an informal learning setting
ix. Benefits
à Provides resources needed for doing each phase of authentic science activities
à Some internet projects provide environments that support all phases of an authentic science project
x. Resources & Activities
B. Supporting Scientific Inquiry Skills
i. Locating information to investigate scientific issues and questions
à National Science Foundation has funded the creation of digital libraries for science to serve as a go-to resource for students and teachers
à The Digital Library for Earth System Education (DLESE) is a community of educators, students, and scientists working to improve the teaching and learning about the Earth system at all levels
à Digital libraries provide the critical starting point for the investigation of scientific questions
ii. Collecting data
à Data collection and archiving are important parts of the scientific inquiry process—science bases its conclusions on data
à Calculator or computer based laboratory (CBL) are ideal for middle through high school students
iii. Visualizing data and phenomena
à Computer simulations differ from pictures in that students can manipulate computer simulations—they allow students to visualize macroscopic phenomena that are difficult to understand because they cannot be seen directly (i.e., phases of the moon)
à Visualization tools can also be used to see microscopic phenomena that are otherwise difficult/impossible to see (i.e., molecular structure or cellular growth)
à Another use of visualization tools is the ability to rotate images to view them from various vantage points
iv. Analyzing data
à Spreadsheets
à GIS—allows students to analyze factors in an image by removing or adding attributes and looking for connections among the various attributes
v. Communicating results
à Standard word processing software
à Digital images/photographs
à E-mail collaboration
à Webcasts
vi. Benefits
à Helps students locate and obtain information to support inquiry
à Makes data collection and analysis easier and more manageable
à Makes it easier to visualize and understand phenomena
à Supports communicating results of inquiry
vii. Resources & Activities
C. Supporting Science Concept Learning
i. Scientific concepts are easier to understand when they are presented via simulation or animation as opposed to simple text and static picture
ii. Virtual chemistry and physics labs save money and increase student safety
iii. Virtual dissections allow students to conduct dissections without coming into contact with the animal or the preservation chemicals
iv. Benefits
à Allows simulating and modeling of scientific processes
à Provides opportunities to engage in problem-solving activities
v. Resources & Activities
D. Accessing Science Information and Tools
i. The internet allows access to up-to-date science information for both teachers and students
ii. The internet also allows access to content knowledge and professional development that may not be available locally
iii. Benefits
à Allows access to unique tools and collections of information
à Expands opportunities for learning
iv. Resources & Activities
E. Barriers to Integrating Science and Technology
i. Teacher resistance to technology use in the science classroom
à The National Science Education Standards advocate professional development for teachers with an emphasis on technology
à Information from the National Center for Educational Statistics (2004) show that public school teachers still feel that there is little time to learn about, plan, and implement instructional technology in their everyday lessons
ii. Equity to access to technology
à There are still gaps in the availability of educational technology among demographic groups
7. Top 10 Strategies for Integration of Technology in Math & Science Instruction
A. Mathematics
i. Graphing calculators give student hands-on practice in solving mathematical problems
ii. Interactive geometry software such as the Geometer’s Sketchpad make abstract concepts easier to understand
iii. Spreadsheets help students carry out “what-if” problem solving
iv. Students use the Internet to obtain useful, math-related information
v. Reasoning and skill-building software increases students’ fluency with prerequisite sub-skills while developing logic and comprehension
B. Science
i. The GLOBE program offers opportunities for doing authentic science activities
ii. NASA internet sites keep students in-touch with scientific events
iii. Calculator-based labs give students hands-on practice with scientific data analysis
iv. GPS and GIS tools let students make observations and analyze data to support scientific investigations
v. Digital imaging tools and simulations slow down or speed up processes for easier observation
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