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Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

Index

A

AAAS, see American Association for the Advancement of Science

Abstraction, 15, 90, 107-110, 132, 159

Academic education

vocational education and, 11, 12, 15, 24-29, 164

ACT, 61, 69, 71

Adult learners, 11

Advanced Technological Education program, 3, 165

Aesthetic value of mathematics, 4, 35, 36

Agriculture, 26, 27, 39

Algebra, 2, 12, 31-34, 35-41, 69

curricular design, 94-95, 98-100, 103, 104-105

mental mathematics, 83-86

representations, 39-40, 55, 80-82, 87-90, 105, 109-110, 111-114, 124, 133

school-to-work experiences, 2, 12, 37-40

spreadsheets, 32, 80-82, 87-90, 94-95, 105, 111-112, 133, 158

tasks, 32, 33-34, 54-56, 76, 80-82, 83-86, 87-90, 98, 99, 100, 109-110, 111-114, 117, 118, 121-122, 123-124, 133, 158

Algorithms and procedures, 9, 64, 69

adult learners, 11

algebra, 37, 39, 83-86

concepts and understanding, relation to, 32-34, 54, 59, 95, 134

curricular design, 94, 99-100, 102-103, 104-106

mental mathematics, relation to, 83-86

problem solving, relation to, 11, 97

recursion, 62, 75, 76, 80-82, 87-90, 105, 111-114

similarities among, for abstraction, 62, 90, 132

AMATYC, see American Mathematical Association of Two-Year Colleges

American Association for the Advancement of Science, 60

American College Testing, see ACT

American Mathematical Association of Two-Year Colleges, 60

see also Two-year colleges

Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

Annuities, 109, 111-114

Apprenticeships, see Vocational education

Area, geometry, 16, 38, 39, 47, 131, 145-146

Assessment, 3, 16, 59-90, 138, 165

ACT, 61, 69, 71

adequacy for purposes, 61, 70-71

curriculum, influence by, 61-62, 70-74

eighth grade test, national voluntary, 59, 69

international context, 75-76

item development, 97-98

NAEP, 62, 73, 77-79

parents, concerns of, 61, 70 74

SAT, 61, 71-74

standards, relation to, 59, 61

teacher development, role in, 130, 141-144

TIMSS, 4, 95

see also Standards

ATE, see Advanced Technological Education program

Attitudes, see Motivation

Automobiles

car purchase, 105, 131, 140, 153

driving, braking distances, 123-124, 125

traffic control, 147-152

B

Back-of-the-envelope estimates, see Estimation

Baseball, 116, 158

Benchmarks for Science Literacy, 60

Body proportions, 125, 145-146

Business applications, 11-13, 30, 32

tasks, 18-23, 45, 46-47, 49-53, 76, 83, 84-86, 119-121

see also School-to-work experiences;

Tasks, mathematical, by context

C

Calculations, mental, see Mental mathematics

Calculators, see Computers and calculators

Calculus, 69

high school, in, 31, 104

international context, 75-76

NCTM standards, role in, 28

preparation for, 3, 28, 60, 95, 108, 131, 145

student performance on an algebra problem, 33

tasks, 54-56, 121-122, 145-146

California, 59

Careers, preparation for, 2, 4, 9, 10, 30-31, 34, 67-69, 107-110, 158

see also Business applications;

School-to-work experiences;

Tasks, mathematical, by context;

Vocational education

Carl Perkins Vocational and Technical Education Act, 29

Center for Education Research (Wisconsin), 26

Charts and tables, see Graphical representations and tables

Clinton, William, 59, 69

Coalition of Essential Schools, 25

Collaborative learning, see Group learning

Colleges and universities, see Post-secondary education;

Two-year colleges

Commission on Achieving Necessary Skills, see Secretary's Commission on Achieving Necessary Skills

Communication skills, 1, 27, 30, 32, 34, 54, 107, 130, 138, 140

standards, 60, 62, 64, 66, 68, 69, 78-79, 137

see also Group learning

Computers and calculators, viii, 1, 10, 30, 34, 36, 80-82, 87, 105, 109, 133, 135, 153

see also Spreadsheets

Conceptual understanding, 2, 9, 10, 30, 37, 62, 95, 159

skills and procedures, relationship with, 9-11, 24-26, 32-34, 54, 59, 62, 66, 68, 75, 79, 83, 107-109, 132-134, 138, 157-158

Cost analysis

business plan, 20-23, 68

car purchase, 105, 131, 140, 153

credit, 87-90, 105

optimization, 53

procurement, 45, 46-47, 119-121

sales tax, 99

schooling costs, 16

see also Tasks, mathematical, by context

Credit, 62, 87-90, 105

see also Financial applications

Crossroads in Mathematics: Standards for Introductory Mathematics Before Calculus, 60

Curriculum and curricular design, 1, 2, 3, 4, 10, 93-126, 157-158, 159

academic/vocational education related, 11, 12, 15, 24-25

algebra, 94-95, 98-100, 103, 104-105

algorithms, 94, 99-100, 102-103, 104-106

Bruner's spiral, 95

calculus, 28

computers and, 10

defined, 93

geometry, 100, 104, 109

habits of mind, 94, 102-106

modeling, 93-94, 99-101, 104

Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

post-secondary education preparation, 93, 107-110

problem solving, 97, 98, 100, 103

standards, 60-62, 63-66, 95, 104, 107-108, 137

tasks, inclusion in, 94-95, 97-101, 104, 108-110, 138, 159

teaching, relationship to, 129-130, 132-133

testing, influence on, 61-62, 70-74

tracking, educational, 11, 12, 15, 24-29, 73

see also Tasks, mathematical, by content

Curriculum and Evaluation Standards for School Mathematics, 60, 65, 137

D

Data analysis, 4, 12, 21, 22, 68, 75

tasks, 16, 18-23, 27, 42-44, 56, 64, 71-74, 115-116, 153

see also Graphical representations and tables;

Spreadsheets;

Tasks, mathematical, by content

Data representation, see Graphical representations and tables

Department of Education, 3

Department of Energy, 56

Department of Labor, 3

Developmental education, 3, 15, 35, 36

Diagrams, see Graphical representations and tables

Discrete mathematics, 158

E

Economic factors, see Cost analysis;Employment and employers;Financial applications; Wages and salaries

The Education Imperative, 2

Employment and employers

academic/vocational tracking, 25

see also Business applications;

Careers, preparation for;

School-to-work experiences;

Wages and salaries

Energy conservation, 13, 33, 54-56

Engineering, 3, 37-38, 47, 77

Environmental science, 27, 31, 32, 47, 49

Equity issues, 11, 73, 116

Error of measurement, 22, 119, 145, 146

Estimation, 12-13, 21, 30, 31, 76, 131, 145

tasks, 37-38, 45-48, 119-122, 123-126, 139, 145-146

Evaluation, see Assessment; Standards

Everybody Counts, ix, 9, 103

Exponential functions, 4, 76, 99, 109-110, 111

F

Federal government

assessments, 59, 62, 69, 73, 77-79

legislation, 3, 26, 29, 60

see also Carl Perkins Vocational and Technical Education Act;

School-to-Work Opportunities Act of 1994;

headings beginning ''Department of …"

Fermi problems, see Estimation

Financial applications, 87-90, 98, 99, 105, 109-110, 111-114, 124-125, 133

Foreign countries, 18-23, 76-78

Formulae, 9, 16, 69, 81, 84-86, 87-88, 90, 112, 113, 117, 121-122, 146, 151

rules of thumb, 39, 95, 123-126

Fractals, 146

Functions, 22, 39, 40, 56, 75-76, 98-99, 110, 112-113, 158

concept of, 37

exponential, 4, 76, 99, 109-110, 111

linear, 33-34, 54-56, 78, 95, 98, 99, 105, 108, 113, 123-126, 133, 147-152, 158

quadratic, 32, 69, 95, 99, 121, 124

trigonometric, 12, 31, 75, 109

G

Gender issues, see Equity issues

Geometry

area calculations, 16, 38, 39, 47, 131, 145-146

curricular design, 95, 100, 104, 109

fractals, 146

representation, 65, 77, 95, 117-118, 119-122, 147-152

mapmaking, 110, 146

ordered pairs, 95, 120

tasks, 39, 64-65, 76, 77, 109, 110, 117-118, 119-122, 145-146, 147-152, 158

topology, 104

vectors, 95, 117-118

Germany, 76

The Goals 2000: Educate America Act, 29(n.5), 60

Government role, see Federal government; State government

Graphical representations and tables, 30, 37, 76, 108, 133-134

algebra, 39-40, 55, 80-82, 87-90, 105, 109-110, 111-114, 124, 133

data analysis, 12, 21, 42-44, 115-116, 153

geometry, 65, 77, 95, 117-118, 119-122, 147-152

modeling, 49-53, 55

Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

Group learning, 1, 12, 25, 32, 49, 68, 69

assessment of, 61

business planning, 18-23

teacher involvement, 135-136, 139-140

H

Habits of mind, 94, 102-106

Health care, 12, 26, 30, 62

tasks, 39-40, 42-44, 80-82, 115-118, 145-146

Higher education, see Post-secondary education

I

Incentives, see Motivation

Interactive Mathematics Program, 73

International issues, see Foreign countries

Interpersonal skills, see Communication skills

J

Japan, 18-23, 76-78

L

Legislation, Federal, 3, 26, 29, 60

Life by the Numbers, 30

Linear functions, 33-34, 54-56, 78, 95, 98, 99, 105, 108, 113, 123-126, 133, 147-152, 158

M

Mapmaking, 110, 146

Mathematical Preparation of the Technical Work Force, ix, 2

Mathematical Sciences Education Board, ix, 9

Mathematical tasks, see Tasks, mathematical

Measuring Up, ix

Medicine, see Health care

Memorization, 15, 95, 134

see also Algorithms and procedures;

Conceptual understanding

Mental mathematics, 62, 83-86

see also Conceptual understanding;

Habits of mind;

Rules of thumb

Minority groups, see Equity issues

Models and modeling, 11, 13, 22, 64

curricular design, 93-94, 99-101, 104

energy conservation, 13, 33, 54-56

linear, 54, 133-134

optimization, 49-53

problem solving, 98-99

solar system, 64-65

trigonometry, 31

see also headings beginning "Tasks …"

Motivation

aesthetic value of mathematics, 4, 35, 36

science, connection with, 25, 26, 64, 66

students, 10-11, 36-37, 77, 79, 98, 108, 113

negative, 12, 15, 24, 36

teachers, 134-135, 136, 140, 141-144

N

NAEP, see National Assessment of Educational Progress

National Assessment of Educational Progress, 62, 73, 77-79

National Center for Restructuring Education, Schools, and Teaching , 25-26

National Council of Teachers of Mathematics, 28, 137

standards, 28, 61, 63-64, 137

National Science Education Standards, 60, 64-66

National Science Foundation, 3, 168

National Skills Standards Board, 29(n.5), 60

A Nation at Risk, 25, 60

NCTM, see National Council of Teachers of Mathematics

NSES, see National Science Education Standards

O

Open-ended problems, 12, 25-26

assessment using, 61, 70-71, 78

standards, 63-64

teacher involvement in assessment, 130-131, 141-144

Optimization problems, 49-53

Ordered pairs, 95, 120

Order of magnitude, 45

P

Partitioning, 145

Post-secondary education, 2, 3, 16, 107-110, 164

admissions tests, see ACT; SAT

preparation for, 93, 107-110

school-to-work experiences and, 12

vocational education and, 24-29

see also Two-year colleges

Preparing for the 21st Century: The Education Imperative, 1

Probability, 21, 76, 95, 104, 115-118, 119-122, 158

Problem-centered teaching, 9-11, 12, 33, 130, 132-140

research support, 11, 73

Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

Problem solving, 1, 3, 10-11, 12, 16, 27-28, 31, 79, 132

assessment of, 61

business/marketing application, 18-23

classroom environment, 139

curricular design, 97, 98, 100, 103

difficulty level, 138, 139

mental mathematics, 83-84

research support for problem-centered teaching, 11, 73

skills, relationship with, 59, 95, 97, 103

standards, 60, 61, 64, 68

teacher involvement, 130, 132-140

theory, relationship with, 103

types of problems, 98-99

see also Algorithms and procedures;

Open-ended problems;

Word problems;

headings beginning "Tasks …"

Procedures, see Algorithms and procedures; Conceptual understanding

Professional education, see Teacher education

Professional Standards for Teaching Mathematics, 130

Proportional reasoning, 4, 38, 54-56, 78, 94, 104, 115-118

Psychological factors, see Motivation

Q

Quadratic functions, 32, 69, 95, 99, 121, 124

R

Rates, 62, 78, 80-82, 87-90, 95, 100, 110, 111-114, 115-118, 147-152

Reasoning, see Conceptual understanding; Habits of mind; Mental mathematics; Problem solving

Recursion, 62, 75, 76, 80-82, 87-90, 105, 111-114

Remedial education, see Developmental education

Research

science/math integration, 64

supporting problem-centered teaching, 11, 73

Reshaping School Mathematics, ix, 10

Rote learning, see Memorization

Rounding off, 76, 90, 95, 119-122

Rules of thumb, 39, 95, 123-126

S

Salaries, see Wages and salaries

Sampling, 19-20, 22, 44

SAT, 61, 71-74

SCANS, see Secretary's Commission on Achieving Necessary Skills

Scholastic Aptitude Test, see SAT

School-to-work experiences, 3, 10, 12-13, 26-27

algebra, role in, 2, 12, 35-41, 94

interdisciplinary collaboration, 26, 27

sources of, 164

see also Tasks, mathematical, by context

School-to-Work Opportunities Act of 1994, 3, 26

Science education, 10, 47

basis for careers, 1, 9, 12, 30, 34

mathematics, relationship with, 3, 24, 25-27, 31, 75-77

standards, 60, 63-66

tasks, 64-65, 80-82

TIMSS, 4, 95

Secretary's Commission on Achieving Necessary Skills, 60-61, 67-69

Simpson's paradox, 95

Skills, see Algorithms and procedures; Communication skills; Conceptual understandings; Memorization

Spreadsheets, 32, 68, 80-82, 87-90, 94-95, 103, 105, 111-112, 133, 153, 158

Standards, 3, 59-90

academic/vocational education integrated, 28

assessments, relation to, 59, 61, 141-144

calculus, 28

communication skills, 60, 62, 64, 66, 68, 69, 78-79, 137

curricular design, 60-62, 63-66, 95, 104, 107-108, 137

definitional issues, 60

national, 59, 61

National Skills Standards Board, 29(n.5), 60

NCTM, 28, 61, 63-64, 137

NSES, 60, 64-66

parents' role in standardized testing, 61, 70, 74

problem solving, 60, 61, 63-64, 68, 130, 137-138

SCANS, 60-61, 67-69

State government role, 59, 60

teaching methods, 130, 137-140, 142

technical education, 2

see also Assessment;

Curriculum and curricular design

State government

assessment and standards, 59, 60

local support for teachers, 130

State-to-state comparisons, SAT testing, 71-74

Statistics, 4, 74, 75, 100, 115-116, 158

sampling, 19-20, 22, 44

Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

tasks, 18-23, 42-44

see also Data analysis;

Estimation;

Probability

Successive approximation, 75, 145

T

Tables and charts, see Graphical representations and tables

Tasks, mathematical, 4, 9

curriculum, selection of, 94-95, 97-101, 104, 108-110, 138, 159

source of, 163-166

see also Open-ended problems;

Problem solving;

Tasks, mathematical, by content;

Tasks, mathematical, by context

Tasks, mathematical, by content, 4, 9

algebra, 32, 33-34, 54-56, 76, 80-82, 83-86, 87-90, 98, 99, 100, 109-110, 111-114, 117, 118, 121-122, 123-124, 133, 158

calculus, 54-56, 121-122, 145-146

data collection and analysis, 16, 18-23, 27, 42-44, 56, 71-74, 115-116, 153

estimation, 37-38, 45-48, 119-122, 123-126, 139, 145-146

fractals, 146

geometry, 39, 64-65, 76, 77, 109, 110, 117-118, 119-122, 145-146, 147-152, 158

optimization, 49-53

probability, 21, 76, 115-118, 119-122, 158

proportional reasoning, 38, 54-56, 78, 115-118

rates, 78, 80-82, 87-90, 100, 110, 111-114, 115-118, 147-152

recursion, 80-82, 87-90, 105, 111-114

representation, 39-40, 42-44, 49-53, 109-110, 115-118, 119-122, 133, 147-152

statistics, 18-23, 42-44

vectors, 117-118

weighted averages, 115-118

see also Functions;

Open-ended problems;

School-to-work experiences;

Spreadsheets

Tasks, mathematical, by context

agriculture, 39

automobiles, 105, 123-124, 125-126, 140, 147-152, 153

baseball, 116, 158

body proportions, 125, 145-146

business, 18-23, 45, 46-47, 49-53, 76, 83, 84-86, 119-121

construction, 37-38, 39, 109

cooking, 125

energy conservation, 33, 54-56

environmental science, 27, 31, 32, 47, 49

finance, 87-90, 98, 99, 105, 109-110, 111-114, 124-125, 133

health care, 39-40, 42-44, 80-82, 115-118, 145-146

hypothetical, 139

mapmaking, 110, 146

mathematics, 76, 77, 83, 84, 105, 121-122, 158

piano tuning, 45

police protection, 47

salaries, 45, 115, 116

school and education, 16, 33-34, 45, 46, 71-74, 116-117

science, 64-65, 80-82

tax, 47-48, 78, 99, 125

wages and salaries, 45, 115, 116

Tax calculations, 47-48, 78, 99, 125

Taxonomy of Educational Objectives, 97

Teacher education, 3, 4, 127-153

inservice teachers, 141-144

preservice teachers, 130, 134-135, 137, 139

Teachers, 3, 4

assessment, involvement in, 130, 141-144

attitudes, 134, 140

communication skills, 134, 139-140

local support for, 130

motivation, 134-135, 136, 140, 142-143

problem solving, 132-140

student interactions, 10, 129, 135-136, 139-140

Teaching, 3, 14-15, 129-153

curricular design, 129-130, 132-133

feedback, 129, 139

interdisciplinary collaboration, 26, 27

memorization, 15, 95, 134

standards, 63-64, 130, 137-140, 142

see also Curriculum and curricular design;

Group learning;

Memorization;

Models and modeling;

Problem solving;

Tasks, mathematical

Technical applications, see Tasks, mathematical, by context

Technical education, 2, 3, 164

Tests and testing, see Assessment

Theory, relationship with problem solving, 103

Third International Mathematics and Science Study, 4, 95

TIMSS, see Third International Mathematics and Science Study

Tracking, vocational/academic, 11, 12, 15, 24-29, 73

Trigonometry, 12, 31, 75, 109

Two-year colleges, 2, 3, 15, 26, 27, 29, 60, 140, 164

Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

U

Uncertainty, 20, 21, 23, 25

error of measurement, 22, 119, 145, 146

Universities and colleges, see Post-secondary education;Two-year colleges

University of Chicago School Mathematics Project, 99

V

VATEA, see Carl Perkins Vocational and Technical Education Act

Vectors, 95, 117-118

Visual aids, see Graphical representations and tables

Vocational education, 2, 109, 164

academic education and, 11, 12, 15, 24-29, 164

see also Technical education

W

Wages and salaries, 26

tasks, 45, 115, 116

Weighted averages, 115-118

What Work Requires of Schools, 60, 67, 68-69

Word problems, 15, 32-33, 69, 98, 108

see also Tasks, mathematical, by content;

Tasks, mathematical, by context

Workplace, see Careers, preparation for; Employment and employers; School-to-work experiences

Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
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Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
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Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
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Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
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Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
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Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
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Suggested Citation:"Index." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×
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Traditionally, vocational mathematics and precollege mathematics have been separate in schools. But the technological world in which today's students will work and live calls for increasing connection between mathematics and its applications. Workplace-based mathematics may be good mathematics for everyone.

High School Mathematics at Work illuminates the interplay between technical and academic mathematics. This collection of thought-provoking essays--by mathematicians, educators, and other experts--is enhanced with illustrative tasks from workplace and everyday contexts that suggest ways to strengthen high school mathematical education.

This important book addresses how to make mathematical education of all students meaningful--how to meet the practical needs of students entering the work force after high school as well as the needs of students going on to postsecondary education.

The short readable essays frame basic issues, provide background, and suggest alternatives to the traditional separation between technical and academic mathematics. They are accompanied by intriguing multipart problems that illustrate how deep mathematics functions in everyday settings--from analysis of ambulance response times to energy utilization, from buying a used car to "rounding off" to simplify problems.

The book addresses the role of standards in mathematics education, discussing issues such as finding common ground between science and mathematics education standards, improving the articulation from school to work, and comparing SAT results across settings.

Experts discuss how to develop curricula so that students learn to solve problems they are likely to encounter in life--while also providing them with approaches to unfamiliar problems. The book also addresses how teachers can help prepare students for postsecondary education.

For teacher education the book explores the changing nature of pedagogy and new approaches to teacher development. What kind of teaching will allow mathematics to be a guide rather than a gatekeeper to many career paths? Essays discuss pedagogical implication in problem-centered teaching, the role of complex mathematical tasks in teacher education, and the idea of making open-ended tasks--and the student work they elicit--central to professional discourse.

High School Mathematics at Work presents thoughtful views from experts. It identifies rich possibilities for teaching mathematics and preparing students for the technological challenges of the future. This book will inform and inspire teachers, teacher educators, curriculum developers, and others involved in improving mathematics education and the capabilities of tomorrow's work force.

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