June 21
- Three technologies:
Spreadsheet; Sketchpad; CBL
- Journals: Lucent
Automotive (Tues)
Caterpillar (Thurs)
- Wed June 30
Webboard…on line class, no face to face meeting
Present projects
- Guidelines for projects
Student (5 days)
Topic
Motivational activity
Development of lesson
Assessment
Teachers guide
Grade level
Topic--where it fits into your program
Linkage with NCTM PSSM (or science, or….) and IL Learning Standards
Materials needed
Special requirements (field trip, etc.)
Commentary on subject matter
Commentary on instructional approach(es)
Explicit linkage(s) with at least one of the field trips.
Principles and Standards for School Mathematics (NCTM)
Students’ mathematics learning can be supported:
- when instruction regularly emphasizes meaningful engagement with cognitively demanding tasks (Stein and Lane 1996);
- when teachers regularly utilize the computational, graphic, or symbolic capabilities of technological tools to develop mathematical ideas (Carpenter 1998; Heid 1988; Hiebert and Wearne 1996)
- and when teachers are supported by professional development programs that refresh and enhance their knowledge of mathematics content, pedagogy, and student learning (Campbell 1995; Cohen and Hill 1997; Fennema, et al. 1996).
Together, the principles and standards presented in this draft document can be useful for identifying directions to follow and suggesting course corrections for educators as they progress on the path of steady, incremental improvement of mathematics education.
Principles:
Equity Principle: Mathematics instructional programs should promote the learning of mathematics by all students.
Mathematics Curriculum Principle: Mathematics instructional programs should emphasize important and meaningful mathematics through curricula that are coherent and comprehensive.
Teaching Principle: Mathematics instructional programs depend on competent and caring teachers who teach all students to understand and use mathematics.
Learning Principle: Mathematics instructional programs should enable all students to understand and use mathematics.
Assessment Principle: Mathematics instructional programs should include assessment to monitor, enhance, and evaluate the mathematics learning of all students and to inform teaching.
Technology Principle: Mathematics instructional programs should use technology to help all students understand mathematics and should prepare them to use mathematics in an increasingly technological world.
The guiding principles for school mathematics programs discussed in chapter 2 provide directions to be considered in instructional classrooms, schools, districts, and beyond. They are a basis for the curricular suggestions that appear in this draft of Principles and Standards for School Mathematics. Central to these guiding principles is the question, What mathematical content and processes should students know and be able to use as they progress through school? The ten standards presented in this chapter are intended to address that question.
Societal needs for mathematical understanding have never been greater, and they will continue to increase. These needs include the following:
Mathematical literacy. The underpinnings of everyday life are increasingly mathematical and technological. Our students will live in a world where intelligent decisions often require quantitative understandings.
Cultural literacy. Mathematics is a great cultural and intellectual achievement of humankind, and our citizens should develop an appreciation and understanding of that achievement.
Mathematics for the workplace. Just as the level of mathematics needed for intelligent citizenship has increased dramatically, so too has the level of mathematical thinking and problem solving needed in the workplace increased.
Mathematicians, scientists, engineers and other users of mathematics. Equity and excellence both must be the object of school mathematics programs. By enfranchising more students, while maintaining high standards, there will be a larger number available to pursue these careers.
What Are Appropriate Mathematical Goals for Students?
The standards presented here are ambitious but necessary to achieving a society that is capable of thinking and reasoning mathematically. To be productive members of that society, all citizens must develop a common base of mathematical knowledge and skill. The standards describe the knowledge base through a connected body of mathematics understandings and competencies.
The standards address both mathematical content and mathematical processes. Roughly speaking, the content standards represent what students should know; the process standards represent ways of acquiring and using that knowledge. This separation is artificial, however. In practice, what one can do depends in important ways on what one knows and on how one can exploit that knowledge.
Five standards describe the mathematical content that students should learn:
Number and operation Patterns, Functions, and Algebra Geometry and Spatial Sense Measurement Data Analysis, Statistics, and Probability
Five standards describe the mathematical processes through which students should acquire and use their mathematical knowledge:
Problem Solving Reasoning and Proof Communication Connections Representation
It should be recognized that this set of ten standards does not neatly separate the content of school mathematics into nonintersecting subsets. Because mathematics as a discipline is highly interconnected, the areas overlap and are integrated. Some topics in data analysis, for example, could be characterized as part of measurement. Patterns and functions appear throughout geometry. Number pervades all the areas of mathematics. The arrangement of the standards is designed solely as a way of organizing the content and processes. Any method of dividing the content of mathematics will, at the top level, highlight some areas and obscure others. Consider discrete mathematics as an example. In this draft of Principles and Standards, the main topics of discrete mathematics are included, but they are distributed across the standards, rather than separated into a separate standard.
The process standards point to major aspects of student competency that are essential to students’ mathematical growth. As students learn mathematics, they will develop an increasing repertoire of problem-solving skills, a wide range of mathematical "habits of mind," and increasing sophistication in mathematical argument. Also, students should become proficient at expressing themselves mathematically, both orally and in writing, gain fluency in the language of mathematics and able to make connections within mathematics and from mathematics to other disciplines.
Aiming for Focus and Coherence: Growth Across the Grades
A significant change between the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and this draft of Principles and Standards is that there are ten standards, and each applies across the pre-K-12 grade span. Within each standard, a small number of focus areas is identified. The standards overviews that follow in this chapter are intended to describe the focus areas within each standard as they are initiated, developed, and completed across the grades. In addition, the overviews give a sense of how students’ understanding and proficiency develops in each area across pre-K-12. By organizing according to common standards across the grade levels, one can chart the growth in knowledge and sophistication of students as they progress through the curriculum. Each overview contains a summary of the main points that are elaborated in the detailed descriptions of the content at each grade-band (pre-K-2, grades 3-5, grades 6-8, and grades 9-12) that are presented in chapters 4 through 7.
Readers may wish to explore this document "by strand"—that is, by following a particular standard across the pre-K-12 span—rather than progress through the standards overviews and grade-band discussions. This can be done most conveniently in the electronic version of Principles and Standards, available on the Web at.