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Guidance from Expert Panels
NCTM's Principles and Standards
NCTM has released a series of statements over the past decade that offer increased direction for schools about the use of technology in mathematics education. For example, in the most recent version of their position statement, The Use of Technology in the Learning and Teaching of Mathematics (2003), we read:
Position: Technology is an essential tool for teaching and learning mathematics effectively; it extends the mathematics that can be taught and enhances students’ learning.
Rationale: In the context of a well-articulated mathematics program, technology increases both the scope of the mathematical content and the range of the problem situations that are within students' reach. … Teachers must be prepared to serve as knowledgeable decision makers in determining when and how their students can use these tools most effectively.
Reflecting this same perspective, the NCTM’s Principles and Standards for School Mathematics (2000) pays significant attention to technology. The document emphasizes the importance of every student having access to technology and to a teacher skilled in its use:
In the mathematics classrooms envisioned in Principles and Standards, every student has access to technology to facilitate his or her mathematics learning under the guidance of a skillful teacher. (p. 24)
This general statement is elaborated in the Technology Principle. Each of the six principles included in the Principles and Standards is intended to guide educators in shaping mathematics instruction in schools. The Technology Principle, in particular, contains a rich description of the role of technology in mathematics instruction.
From this description, we have extracted seven qualities of technology (listed below). In constructing the Mission:Algebra website, we have used these qualities as guidance for the creation of the Standards-based Classroom Examples. Each of the classroom examples includes a section titled “The Value of This Technology” which draws on these qualities in analyzing the role of technology for enhancing middle grades mathematics teaching and learning.
Qualities of Technology that Support
Good Learning Practices in Mathematics
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With calculators and computers, students can examine more examples or representational forms than are feasible by hand, so they can make and explore conjectures more easily.
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The graphic power of technological tools affords access to visual models that are powerful but that many students are unable or unwilling to generate independently.
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The computational capacity of technological tools extends the range of problems accessible to students and also enables them to execute routine procedures quickly and accurately, thus allowing more time for conceptualizing and modeling.
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Technology provides a means of viewing mathematical ideas from multiple perspectives.
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Students’ learning is assisted by feedback, which technology can supply (e.g., dynamic geometry software).
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Technology provides a focus as students discuss with one another and with their teacher the objects on the screen and the effects of the various dynamic transformations that technology allows.
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Technology offers teachers options for adapting instruction to special student needs.
—Adapted from the text of The Technology Principle (NCTM, 2000, p. 24-27)
Principles and Standards also includes five Process Standards that are intended to inform mathematics practice across the full range of grade levels, Pre-K to grade 12. These include Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. These five Process Standards guided us in creating the kinds of learning we portray in the Standards-based Classroom Examples.
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