Instructional Materials: Math
Students often find it helpful to review mathematical
concepts repeatedly or from multiple points of view. The Center
for Learning Enhancement has a variety of materials presenting concepts
in various ways by different instructors. If one resource isn't
particularly helpful, alternatives are almost always available. To
locate a math resource which is stored on the Center's open shelves, go
to .
To get access to CDs and other instructional software, see a CLE
staff member.
Arem, C. (1993). Conquering math
anxiety: A self-help workbook. Pacific
Grove, CA:
Brooks/Cole.
Smith, R. M. (1991). Mastering mathematics: How to be a great math
student (2nd ed.).
Belmont, CA: Wadsworth.
Tips on how to adjust your attitude toward math, how to study most
effectively, and how to prepare for math tests.
Studying the Content Areas, Mathematics
(H&H
Publishing, 1988, 35 min.videos + workbook + audiocassette)
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These materials address basic study skills useful in any math
course. |
1. Surveying Textbooks (~17 min.)
2. Surveying Textbook Chapters (~17 min.)
3. Reading and Marking Textbook Chapters (~18 min.)
4. Using Maps, Diagrams, Graphs, and Tables (~18 min.)
5. Solving Word Problems (12 min.)
6. Taking Tests (19 min.)
7. Using the Library (21 min.)
Basic Math
Basic Mathematics
(Accelerated Learning Systems, 1987,
video)
Designed as a stand-alone telecourse, the ALS series is a carefully
sequenced and detailed explanation of basic mathematics.
Diagnostic tests of content mastery are included. The video
cases of the ALS basic math tapes are coded with a pink dot.
1. Addition
facts (45 min.)
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Basic Mathematical Skills
(PWS/Educational Video Resources, 1994, 25 min.videos)
This instructional series is helpful to students currently
enrolled in a basic mathematical skills course or a pre-algebra
mathematics course, or for anyone wanting to review basic
mathematical skills. Elayn Martin-Gay from the
University of New Orleans teaches a variety of topics
common to most basic courses. For a detailed description
of each module, |
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1001. Whole
numbers- place value, addition, subtraction, rounding
1002. Whole
numbers- multiplication order of operation
1003. Whole
numbers- division
1004.
Factors and multiples
1005.
Fractions, equivalent fractions, and mixed numbers
1006.
Fractions- multiplication and division
1007.
Fractions- least common denominators, addition
1008. Decimals-
addition, subtraction, multiplication and rounding
1009.
Decimals- division, converting to fractions
1010. Percent
and applications
1011.
Percent and application II
1012.
Perimeter and area
1013.
Operations with signed numbers
1014.
Solving equations
1015.
Exponents
1016. More
exponents and introduction of radicals
1017.
Estimating
1018.
Applications with fractions
1019.
Ratios and proportions
1020. Applications
of proportions
1021.
Comfortable with percents
1022. U.S.
customary system
1023.
Metric system
1024.
Thinking metric
1025. Order
of operations
1026.
Introduction to variables
1027.
Applications of linear equations
Bobrow, J. (1995). Basic math and pre-algebra
(Cliff's Quick Review Series).
Lincoln, NB: Cliffs Notes.
Brooks, L.D. (1991). Math for workplace success:
General business. Eden
Prairie, MN: Paradigm.
Lerner, J.J., & Zima, P. (1985). Theory and
problems of business mathematics
(Schaum's Outline Series). New
York: McGraw-Hill.
Rich, B. (1977). Review of elementary mathematics
(Schaum's Outline Series).
New York: McGraw-Hill.
Slater, J. (2000). Practical business math
procedures (Brief 6th ed.). Boston:
Irwin.
Studying the Content Areas/Mathematics: Solving
Word Problems (H&H
Publishing, 1988, 35 min.video)
Word problems are presented as written
text and diagrams as the narrator explains how to work through the
logical processes needed to solve them.
Westbrook, P. (1999). Mathsmart for business:
Essentials of managerial
finance (The Princeton Review Series).
New York: Random House.
Wheeler, R.E., & Wheeler, E.R. (1995). Modern
mathematics (9th ed.). Pacific v Grove, CA: Brooks/Cole.
Wheeler, R.E., & Wheeler, E.R. (1995). Instructor's
manual for
Modern mathematics (9th ed.). Pacific Grove, CA:
Brooks/Cole.
Wood, M.M., & Capell, P. (1995). Developmental
mathematics (5th ed.).
Boston: PWS.
Wood, M.M., & Capell, P. (1995). Instructor's manual
for
Developmental mathematics (5th ed.). Boston: PWS.
MathQuest (PWS, 1995, software)
DOS-based interactive software corresponding to the 5th edition of Developmental
Mathematics by Wood & Capell. Feedback is given for correct and incorrect answers.
Developmental
Mathematics (College
of Charleston, n.d., video series)
Designed to accompany the Wood & Capell text, this set of short
videos demonstrates key concepts in Math 0096 and Math 0097. Hope
Florence, Director of the Math Lab at the College of Charleston, works
through a series of math problems illustrating fundamental math topics.
Vol.
1: Arithmetic
Vol.
2: Polynomials
Vol. 3: Linear equality and inequality
Vol. 4: Graphs and systems of equations
Vol. 5: Intermediate algebra
Algebra
Basic Algebra (Accelerated Learning
Systems/Learned & Tested, 1987, video series)
Designed as a stand-alone telecourse, the ALS series is a carefully
sequenced and detailed explanation of basic algebra. Diagnostic
tests of content mastery are included. The video cases of the ALS
algebra tapes are coded with a blue dot.
1. Introduction to integers and
rational numbers (60 min.)
Beginning Algebra: Series II
(Dekalb College, 1988, video)
A videotape series showing faculty teaching the various topics
listed below. Preferred over ALS videos by some people
with math anxiety because of the human element included in the
instruction. Less detailed than the ALS video series and
no mastery tests are provided. Content spans Math
0096-Math 0099 courses. The video cases of the Dekalb
algebra tapes are coded with a yellow dot.
Older versions of the Dekalb tapes are coded with an orange dot.
1.(558) Reducing, Multiplying, and
Dividing Fractions (14 min.)
2. (559) Adding and Subtracting Fractions (14 min.)
3. (560) Algebraic Symbols (13 min.)
4. (561) Introduction to Exponents (6 min.)
5. (562) Order of Operations (10 min.)
6. (563) Variables: Evaluating Algebraic Expressions (7
min.)
min.)
35. (592) Dividing Polynomials and Monomials (12 min.)
36. (593) The Quotient of Two Polynomials (19 min.)
37. (594) Factors and Prime Factored Form (11 min.)
38. (595) Greatest Common Factors (20 min.)
39. (596) Factoring by Grouping (15 min.)
40. (597) Factoring Trinomials: Part I (21 min.)
41. (598) Factoring Trinomials: Part II (16 min.)
42. (599) Factoring: Difference of Two Squares/Perfect Square
Trinomials (14 min.)
43. (600) Factoring: Sum and Difference of Cubes (13 min.)
44. (601) Steps in Factoring (14 min.)
45. (602) Solving Quadratic Equations by Factoring (16 min.)
46. (603) Applications of Quadratic Equations (13 min.)
47. (604) Reducing Rational Expressions (16 min.)
48. (605) Multiplication and Division of Rational Expressions
(23 min.)
49. (606) Least Common Denominators (15 min.)
50. (607) Addition and Subtraction of Rational Expressions (22
min.)
51. (608) Complex Fractions (16 min.)
52. (609) Equations Involving Rational Expressions (22 min.)
53. (610) Ratio and Proportion (12 min.)
54. (611) Applications of Rational Expressions: Part I (14
min.)
55. (612) Applications of Rational Expressions: Part II (9
min.)
56. (613) Linear Equations in Two Variables: Ordered Pairs
(14 min.)
57. (614) Graphing Ordered Pairs (13 min.)
58. (615) Graphing Linear Equations: Part I (17 min.)
59. (616) Graphing Linear Equations: Part II (13 min.) |
Bobrow, J. (1994). Algebra I (Cliffs Quick
Review Series). Lincoln, NB: Cliffs
Notes.
Johnson, M. (1976). How to solve word problems in
algebra: A solved problem
approach. New York: McGraw-Hill.
The Math Tutor: Algebra Series
(Video
Tutorial Service, 1998, video)
A five-part video review of algebra for students who want to refresh
their understanding of material learned in the past. Particularly
helpful for
students who had algebra courses in high school and who are preparing for placement exams.
Part 1. Algebraic terms and operations (50 min.)
Part 2. Solving algebraic equations of the first degree and inequalities
(60 min.)
Part 3. Factoring and solving quadratic equations (30 min.)
Part 4. Solving simultaneous equations and inequalities algebraically
and
geometrically (30 min.)
Part 5. Verbal problems and introduction to trigonometry (45 min.)
Mini-Courses in Math: Algebra Series
(Educulture, 1974, audiocassettes + workbook)
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Each modular lesson uses a cassette tape and a response manual to help
students learn and review. The format is to listen, read a little, |
answer questions or work exercises, and find out whether the answers are
right or wrong. Interaction with the material is required, promoting
active learning. |
Module
1. Polynomial arithmetic
Module 2. Factoring I
Module 3. Factoring II
Module 4. Algebraic fractions I
Module 5. Algebraic fraction II
Module 6. Exponents and radicals
Module 7. Linear equations and inequalities in one variable
Module 8. Quadratic equations and inequalities in one variable
Module 9. Functions, relations, and inverses
Module 10. Graphs and variations
Module 11. Linear relations
Module 12. Quadratic relations
Module 15. Logarithms
Module 16. Sequences and series
Module 17. Probability
Module 19. Field axioms and elementary proof
Kohn, E. (1995). Algebra II (Cliffs Quick Review
Series). Lincoln, NB: Cliffs
Notes.
Mayes, R.L., & Lesser, L.M. (1998). ACT in
algebra: Applications, concepts, and technology in learning algebra.
New York: WCB/McGraw-Hill.
This text emphasizes expressing and analyzing relationships in real
world situations. Readers will critically analyze data, induce
patterns, discover relationships, and define modeling functions. The
TI-92 graphing calculator and computer algebra systems are used as
tools for exploring mathematical concepts and
relationships.
Ross, D.A. (1996). Master math: Algebra.
Franklin Lakes, NJ: Career Press.
Intermediate Algebra by McKeague 4/e
(Harcourt, 2002, 4.5 hour video)
The core concepts for each of the first seven chapters of Intermediate
Algebra: Concepts and Graphs, 4/e, are presented by the author,
Charles P. McKeague. This instructional presentation is divided
into 50 problem-solving lessons useful in preparing for class,
clarifying homework problems, and reviewing for tests.
Intermediate Algebra by McKeague 4/e
(Harcourt, 2002, CD-ROM)
This CD which accompanies the textbook of the same name is a clearly
organized set of video lessons by Charles McKeague. The author
systematically works through specific problems correlated with each
chapter of the text.
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Intermediate Algebra by
McKeague 3/e
(Saunders, 1999, videos)
These instructional materials correspond with material included in the
McKeague textbook used in Math 0099. McKeague is currently a
full-time writer of college level math textbooks, having written
a total of ten math textbooks ranging from basic mathematics
through trigonometry. In addition to writing, he teaches at
Cuesta College in San Luis Obispo, California
1.
Basic definitions and properties
2.
Equations and inequalities in one variable
3.
Equations and inequalities in two variables
4.
Rational expressions
5.
Rational exponents and roots
6.
Quadratic equations
7.
Systems of linear equations in two variables
8.
Exponential and logarithmic functions
9.
Sequences and series
10. Conic
sections
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Intermediate Algebra by McKeague
(Saunders, 1994, videos)
These are older instructional materials which roughly correspond with material included in the
McKeague textbook used in Math 0099. McKeague is currently a
full-time writer of college level math textbooks, having written
a total of ten math textbooks ranging from basic mathematics
through trigonometry. In addition to writing, he teaches at
Cuesta College in San Luis Obispo, California.
1.
Basic properties and definitions
2. Linear equations and inequalities in one variable
3. Exponents and polynomials
4. Rational expressions
5. Equations and inequalities in two variables
6. Rational exponents and roots
8. Systems of linear equations
9. Relations, functions, and conic sections
10-11. Logarithms/Sequences and series
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Intermediate Algebra:
Concepts & Graphs by McKeague
(Saunders, 1998, 4 hr.
video)
The core concepts for each of the first seven chapters of Intermediate
Algebra: Concepts & Graphs, Third Edition, are presented
by the author. This video may be used to prepare for
class, to clarify homework problems, or to review for tests.
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McKeague, C.P. (1998). Intermediate algebra:
Concepts and graphs (3rd ed.)
Orlando, FL: Saunders/Harcourt
Brace.
Garlow, J. (1998). Student solutions manual to
accompany
McKeague's Intermediate algebra: Concepts and graphs (3rd
ed.). Orlando, FL: Saunders/Harcourt Brace.
McKeague, C.P. (1998). Instructor's answer
manual to accompany
McKeague's Intermediate algebra: Concepts and graphs
(3rd ed.). Orlando, FL: Saunders/Harcourt Brace.
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Intermediate Algebra by Larson & Hostetler
(Heath,
1992, video)
Dana Mosely, the video instructor, has over fifteen years
of classroom teaching experience and twelve years of video
teaching experience, from junior high school through junior
college levels. Dana's teaching style is relaxed and easy to
understand. He has a knack for explaining difficult math topics
using living room conversation, and in so doing he takes the
anxiety out of the most intimidating topics. The
video cases are coded with a small red
dot on a larger blue dot.
1. Introduction to algebra
2. Linear equations and inequalities
3. Polynomials and factoring
4. Rational expressions
5. Radicals and complex numbers
6. Quadratic expressions and inequalities
7. Introduction to analytic geometry
8. Functions and mathematical models
9. Systems of equations and inequalities |
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Larson, R.E., & Hostetler, R.P. (1992). Intermediate
algebra. Lexington, MA: D.C.
Heath.
Vidrine, G.C. (1992). Complete solutions guide to
Larson/Hostetler's Intermediate algebra. Lexington, MA:
D.C. Heath.
Martin-Gaye, K.E. (1997). Intermediate algebra (2nd ed.,
Annotated
instructor's ed.) Upper Saddle River, NJ: Prentice
Hall.
Intermediate Algebra
(PWS/Educational Video Series, 1994, 25-30
min.videos)
This series is helpful to students
currently enrolled in an intermediate algebra course, reviewing
before enrolling in a college algebra course, or for anyone
wanting to refresh their intermediate algebra skills. Elayn
Gay-Martin from the University of New Orleans teaches a variety
of topics common to most intermediate
algebra courses. Many of the
topic titles are the same as for the beginning algebra series,
but at a level consistent with intermediate algebra courses.
The video cases are coded with a small green dot on a larger yellow dot.
For a detailed description of each module,
3001.
Solving linear equations
3002.
Applications that lead to linear equations
3003.
Solving linear equations
3004.
Solving absolute value equations
3005.
Compound inequalities
3006.
Solving absolute value inequalities
3007.
Exponents
3008.
Addition, subtraction, and multiplication of polynomials
3009.
Greatest common factor and factoring trinomials
3010.
Factoring binomials
3011.
General factoring
3012.
Solving quadratic equations by factoring
3013.
Multiplication and division of rational expressions
3014.
Addition and subtraction of rational expressions
3015.
Complex fractions
3016.
Division of rational expressions
3017.
Equations involving rational expressions
3018.
Applications that lead to equations involving rational expressions
3019.
Rational exponents
3020.
Simplifying radicals
3021.
Addition and subtraction of radical expressions
3022.
Multiplication and division of radical expressions
3023.
Radical equations
3024.
Miscellaneous quadratic equations solved by factoring
3025.
Solving quadratic equations by completing the square
3026.
Solving quadratic equations by the quadratic formula
3027.
Applications that lead to quadratic equations
3028.
Intercepts, distance, midpoint
3029. Slope
and equations of straight lines
3030.
Functions and graphs of linear inequalities
3031.
Simultaneous equations |
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Streeter, J., Hutchison, D., & Hoelzle, L. (1998). Intermediate
algebra (3rd ed.).
Boston: WCB/McGraw-Hill.
Wood, M.M., Capell, P., & Hall, J.W. (1982). Intermediate
algebra. Boston:
PWS-Kent.
College Algebra
(Prentice Hall, 1988,
video)
This series of videos is explicitly designed to supplement classroom
learning in Math 0099 and Math 1101. Roger Breen is currently a math
professor at the Florida Community College at Jacksonville. The video cases are coded with a reddish
dot.
1A. Introduction/Uses of interval notation
1B. Introduction to relations and functions
2A. Inverse exponential and logarithmic functions
2B. Graphing rational functions
3A. Circle, ellipse, hyperbola
3B. Systems of equations
4A. Matrices and determinants
4B. Solving systems of equationa using matrices and determinants
5A. Introduction to theory of equation
5B. Sequences and series
Algebra Lessons for the Deaf (Math
Learning Center, 1992, video)
Paul Peterson signs selected algebra lectures for deaf students in this video
series.
VF-464-3 Solving literal equations
VF-465-3 Key number factoring of trinomials
VF-466-3 Addition and subtraction of algebraic fractions
VF-467-3 Introduction to graphing (Algebra 2B Modules 1, 2,
3)
Aufmann, R.N., & Nation, R.D. (1995).
Solutions manual with instructor's
resource manual.
Boston: Houghton Mifflin.
Computer Tutor: College
Algebra and Trigonometry 2/e
(Houghton Mifflin, 1993, DOS
3.5" disks)
These software disks provide exercises with feedback corresponding to
topics covered in the Aufmann, Barker, & Nation College Algebra
and Trigonometry 2/e textbook.
Barnett, R.A., Ziegler, M.R., & Byleen, K.E.
(2000). College algebra: A graphing
approach.
Boston: McGraw-Hill.
Hall, J.W. (1992). College algebra
with applications (3rd ed.). Boston: PWS
Publishing.
Interactive Tutorials for
Mathematics: Earth Algebra-College Algebra with Applications to
Environmental Issues
(HarperCollins, 1995, 3.5" disks)
These tutorials allow students to review important concepts in
mathematics and to practice problem-solving. The use of randomly
generated numbers allows students to use the tutorials repeatedly to
obtain as much practice as they need. Full solutions are provided
for all problems, and students may print out a record of the work they
have done on each section.
Kime, L.A.,& Clark, J. (1998). Explorations
in college algebra. New York:
Wiley.
College Algebra by Larson & Hostetler 2/e
(Heath,
1991, video)
With over fifteen years of classroom teaching experience
and twelve years of video teaching experience, from junior
high school through junior college levels. Dana Mosely's
teaching style is relaxed and easy to understand. He has a knack
for explaining difficult math topics using living room
conversation, and in so doing he takes the anxiety out of the
most intimidating topics. These videos
roughly correspond with the material covered in Math 0099.
The video cases are coded with a red dot.
1.
Review of fundamental concepts of algebra
2.
Algebraic equations and inequalities
3.
The Cartesian plane and graphs of equations
4.
Functions and graphs
5.
Finding zeroes of polynomial functions
6.
Exponential and logarithmic functions
7.
Systems of equations and inequalities
8.
Matrices and determinants
9.
Sequences, counting principles, and probability
10.
Sections 4.3-4.4 |
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Larson, R.E., & Hostetler, R.P. (1989). College
algebra (2nd ed.). Lexington, MA:
D.C. Heath.
Larson, R.E., Hostetler, R.P., & Edwards, B.H. (1993). Algebra and trigonometry:
A
graphing approach. Lexington, MA: D.C. Heath.
Edwards, B.H., & Zook, D.L. (1993). Study
and solutions guide for
Larson, Hostetler, & Edwards' Algebra and trigonometry: A
graphing approach. Lexington, MA: D.C. Heath.
Schaufele, C., & Zumoff, N. (1995). Earth
algebra: College algebra with
applications to environmental issues.
New York: HarperCollins.
Schaufele, C., Zumoff, N., & Straley, T.H. (1995). Instructor's guide
to Earth algebra: College algebra
with applications to environmental issues. New York:
HarperCollins.
Schmidt, P. (1991). 2500 solved
problems in college algebra and trigonometry
(Schaum's Solved Problems
Series). New York: McGraw-Hill.
Spiegel, M.R. (1991). Theory and problems of college algebra
(Schaum's
Outline Series). New York: McGraw-Hill.
Wells, D., & Schmitt Tilson,
L.(1997). College algebra: A view of the world
around us.
Upper Saddle River, NJ: Prentice Hall.
Wells, D., & Schmitt, L. (1996). College
algebra: A view of the world around us
(preliminary ed.). Upper
Saddle River, NJ: Prentice Hall.
College Algebra: In Simplest Terms
(Annenberg/CPB, 1991, 30 min.videos)
Series host Sol Garfunkel explains why the algebra branch of mathematics is
necessary for solving real-world problems. With this "textbook on
film," repeated exposure to concepts and visually oriented
presentations improve comprehension. The series includes applications in
geometry and calculus instruction.
1: Introduction. Introduces several
mathematical themes and emphasizes why algebra is important in today's
world.
2: The Language of Algebra. Examines the
vocabulary of mathematics, properties of the real number system, and
basic axioms and theorems of algebra.
3: Exponents and Radicals. Explores
properties and equations of rational numbers and square roots and
their applications to positive numbers and the Pythagorean theorem.
4: Factoring Polynomials. Discusses how the
distributive property is used to factor common monomial factors, the
difference of two squares, trinomials as a product of two binomials,
sum and difference of two cubes, and regrouping of terms.
5: Linear Equations. Covers how solutions are
obtained, what they mean, and how to check them using one unknown.
6: Complex Numbers. Complex numbers and their
use in basic operations and quadratic equations are the focus of this
program.
7: Quadratic Equations. Stresses the
quadratic formula--how it is used to complete a square, and how it is
expressed as the difference or sum of two squares.
8: Inequalities. Develops the basic
properties and examines how to solve inequalities using polynomial and
rational expressions.
9: Absolute Value. Defines this concept,
enabling students to use it in equations and inequalities.
10: Linear Relations. Linear equations are
used to develop and give information about two quantities. Their
applications to the slope of a line are also shown.
11: Circle and Parabola. Using conic
sections, this episode takes a detailed look at circles and parabolas.
Terminology and formulas for equations are discussed for each.
12: Ellipse and Hyperbola. Discusses the
equations for ellipses and hyperbolas, and demonstrates graphically
how to develop the equation from each definition.
13: Functions. Defines a function, develops
an equation from real situations, and discusses domain and range.
Cryptographic functions--such as Caesar's code--and DNA codes are
explored.
14: Composition and Inverse Functions.
Graphics are used to introduce composites and inverses of functions as
applied to cost and production level.
15: Variation. Many types of variation are
covered, including direct, inverse, and joint variation with
applications from chemistry, physics, astronomy, and the food
industry.
16: Polynomial Functions. How to recognize,
graph, and determine all of the intercepts of a polynomial function,
as applied to banking, medicine, and energy production.
17: Rational Functions. The properties of
rational functions are developed by investigating several graphs to
determine the intercepts, symmetry, and asymptotes. Applications
demonstrate double time for simple interest, average cost function,
and tax rates.
18: Exponential Functions. Covers graphing
and developing the equation for an exponential function. Applications
include bacteria growth, population growth, and radioactive decay.
19: Logarithmic Functions. Understanding the
logarithmic relationship, the use of logarithmic properties, and the
handling of a scientific calculator are addressed. How radiocarbon
dating and the Richter scale depend on the properties of logarithms is
explained.
20: Systems of Equations. Elimination and
substitution methods are used to solve problems with systems of
studying linear and nonlinear equations. Their applications to supply
and demand and to cost and revenue are demonstrated.
21: Systems of Linear Inequalities. This
program sets up a problem, finds a solution, develops linear
inequalities, graphs these solutions, and forms a region of feasible
solutions.
22: Arithmetic Sequences and Series. Uses
applications such as linear depreciation and fixed annual raise to
develop the basic properties and formulas for arithmetic sequences.
23: Geometric Sequences and Series. Focuses
on these concepts and determining the sum of their functions.
Calculating the size of retirement savings illustrates their use.
24: Mathematical Induction. This segment
exhibits special cases, looks at patterns of numbers that develop,
relates the patterns to Pascal's triangle and factorials, and develops
the general form of this theorem.
25: Permutations and Combinations. Techniques
for counting the number of ways that collections of objects can be
arranged, ordered, and combined are demonstrated.
26: Probability. Beginning with
games-of-chance, shows how the subject of probability has evolved to
include application in such areas as genetics, social science, and
medicine.
Lindstrom, P.A. (1992). Study guide for the television course
College Algebra: In simplest terms. Lexington, MA: COMAP.
Geometry
Coxeter, H.S.M., & Greitzer, S.L. (1967). Geometry
revisited. New York:
Random House/Singer.
Geometry: Right Triangles (Educational
Video Resources, 1992, 28 min.video)
The Geometer's Sketchpad
(Key Curriculum
Press, 1993, Windows + reference manual).
The student is able to explore geometry through logical abstractions
(words) as well as with pictures (graphs).
The Math Tutor: Geometry Series
(Video
Tutorial Service, 1998, videos)
Selected topics in geometry, designed for students who want to refresh
their understanding of material learned in courses taken in the past.
Part
1. Introduction to geometric terms, angles, and triangles (35 min.)
Part 2. The geometry of parallel lines, geometric figures, the
parallelogram, and
circles (38 min.)
Statistics
Against All Odds: Inside Statistics
(Annenberg/CPB, 1989, 30 min.videos + telecourse study guide)
With an emphasis on "doing" statistics rather than on
passive learning, this series goes on location to help uncover
statistical solutions to the puzzles of everyday life. You learn how
data collection and manipulation--paired with intelligent judgment and
common sense--lead to greater understanding of the world.
1: What is Statistics? Discover how this
complex discipline has evolved.
2: Picturing Distributions. Construct
stemplots and histograms, and understand the importance of pattern
deviation.
3: Describing Distributions. Examine the
difference between mean and median and learn of quartiles, box-plots,
interquartile range, and standard deviation.
4: Normal Distributions. Shows the
progression from histogram to a single normal curve for standard
measurement.
5: Normal Calculations. Emission standards
and cholesterol studies give examples of normal calculations at work.
6: Time Series. Statistics identify patterns
over time, answering questions about stability and change, as seen in
the stock market.
7: Models for Growth. Topics include linear
growth, least squares, exponential growth, and straightening an
exponential growth curve by logic.
8: Describing Relationships. Scatterplots,
smoothing scatterplots of response versus explanatory variables by
median trace, and least squares regression lines are covered.
9: Correlation. How to derive and interpret
the correlation coefficient using the relationship between a baseball
player's salary and his home run statistics.
10: Multidimensional Data Analysis. This
program recaps the data analysis by showing computing technology at
Bell Communications Research.
11: The Question of Causation. The
relationship between smoking and lung cancer is examined, and a study
of admissions data illustrates Simpson's paradox.
12: Experimental Design. Distinguish between
observational studies and experiments, and learn the basic principles
of design, including comparison, randomization, and replication.
13: Blocking and Sampling. Understand random
sampling and the difference between single-factor and multi-factor
experiments.
14: Samples and Surveys. Stratified random
sampling is explained. A 1936 Gallup election poll yields information
about undercoverage.
15: What Is Probability? Distinguishes
between deterministic phenomena and random phenomena.
16: Random Variables. Topics covered include
independence, the multiplication rule for independent events, and
discrete and continuous random variables.
17: Binomial Distributions. Calculate the
mean and standard deviation of binomial distributions, and see a
representative example of binomial distribution.
18: The Sample Mean and Control Charts.
Roulette and business demonstrate the use of the central limit
theorem, control chart monitoring of random variation, creation of
x-bar charts, and definitions of control limits.
19: Confidence Intervals. Explains the
confidence interval using population surveys to show how margin of
error and confidence levels are interpreted.
20: Significance Tests. A hiring
discrimination case illustrates the basic reasoning behind tests of
significance.
21: Inference for One Mean. Study inference
about the mean of a single distribution, with an emphasis on paired
samples and the t confidence interval and test.
22: Comparing Two Means. Learn to recognize a
two-sample problem and to distinguish it from one- and paired-sample
situations.
23: Inference for Proportions. See confidence
intervals and tests for comparing proportions applied in government
estimates on unemployment.
24: Inference for Two-Way Tables. The
chi-square test and the relationship between two categorical variables
are covered.
25: Inference for Relationships. Understand
inference for simple linear regression, emphasizing slope, and
prediction.
26: Case Study. See planning data collection,
collecting and picturing data, drawing inferences, and evaluating
conclusions.
Moore, D.S. (1993). Telecourse study guide for Against all
odds:
Inside statistics and introduction to the practice of statistics
(2nd ed.). New York: W.H. Freeman.
Aliaga, M., & Gunderson, B. (1998). Interactive statistics:
Preliminary edition.
Upper Saddle River, NJ: Prentice
Hall.
Aliaga, M., & Gunderson, B. (1998). Interactive
statistics. Prentice Hall; Upper
Saddle River, NJ.
Brase, C.H., & Brase, C.P. (1995). Understandable
statistics: concepts and
methods (5th ed.). Lexington, MA: D.C.
Heath.
Farber, E. (1995). Study and solutions guide for Brase/Brase
Understandable statistics (5th ed.). Lexington, MA: D.C.
Heath.
Brase, C.H., & Brase, C.P. (1995). Technology guide to
accompany
Understandable statistics (5th ed.) Lexington, MA:
D.C. Heath
Exercises using TI-82 graphics calculator and MINITAB.
ConStatS: Software for Conceptualizing
Statistics
(Prentice-Hall, 1997, 3.5" disks + manual).
Designed to be used as a supplement in one-semester statistics courses,
ConStatS requires only high school algebra as background. The
program includes four units on representing data, two on probability,
three on sampling, two on the elements of statistical inference, and one
on conducting experiments.
Freund, J.E., & Simon, G. A. (1997). Modern elementary
statistics (9th ed.).
Upper Saddle River, NJ: Prentice Hall.
Hanke, J. E., & Reitsch, A. G.
(1994). Understanding business statistics (2nd
ed.,
instructor's edition). Burr Ridge, IL: Irwin.
Hartman, W., & Van Ness, P.D. (1994). Study
guide for use with
Hanke & Reitsch Understanding business statistics
(2nd ed.). Burr Ridge, IL: Irwin.
Kazmier, L.J. (1988). Theory and problems of
business statistics with computer
applications (2nd ed., Schaum's
Outline Series). New York: McGraw-Hill.
Khazanie, R. (1990). Elementary statistics in a world of
applications (3rd ed.).
New York: HarperCollins.
Mason, R.D., & Lind, D.A. (1996). Statistical
techniques in business and
economics (9th ed.). Chicago: Irwin.
Mason, R.D., & Lind, D.A. (1996). Study
guide for use with Mason
& Lind's Statistical
techniques in business and economics (9th ed.). Chicago: Irwin.
McClave, J.T., & Sincich, T. (1997). A first course in
statistics (6th ed.). Upper
Saddle River, NJ: Prentice Hall.
Shafer, N.J. (1989). Solutions manual for McClave &
Dietrich, A
first course in statistics (3rd ed.). San Francisco:
Dellen.
McClave, J.T., Dietrich, F.H., & Sincich, T. (1997). Statistics
(7th ed.). Upper
Saddle River, NJ: Prentice Hall.
Moore, D.S. (1992). Statistics: Decision through data video
applications
library. Lexington, MA; COMAP.
Moore, D. S. (1997). The active practice of statistics: A text
for multimedia
learning. New York: W.H. Freeman. (Text for use with ActivStats CD-ROM.)
Moore, D. S. (2000). The basic practice of statistics (2nd
ed.). New York: W. H.
Freeman.
Moore, D. S., & McCabe, G. P. (1993). Introduction to the
practice of statistics
(2nd ed.). New York: W. H. Freeman.
Moore, D.S. & McCabe, G.P. (1999). Introduction to the
practice of statistics
(3rd ed.) New York: W. H.
Freeman.
Rossman, A.J. (1996). Workshop statistics: Discovery with data.
New York:
Spring-Verlag.
Spiegel, M. R. (1988). Theory and problems of statistics
(2nd ed., Schaum's
Outline
Series). New York: McGraw-Hill.
Statistics, Unit I: Descriptive Statistics and
Probability Distributions (Educulture, 1979, audiocassettes +
workbooks)
|
The Statistics series is written especially for students who require a
knowledge of statistics but do not have a strong background or |
ability
in mathematics. Abstraction and symbolism are kept to a minimum,
yet the series is not a "cookbook" course. All concepts,
generalizations, rules, and processes are well-motivated and
well-illustrated. Teaching is done inductively and in the context
of ongoing problem-solving. Modular tests and scoring keys are
provided. |
1. Intro to frequency distributions and graphs
2. Special frequency distributions and frequency polygons
3. Measures of central tendency
4. Measures of variability
5. Basic probability
6. The binomial distribution
7. The normal distribution
Statistics, Unit II:
Inferential Statistics (Educulture,
1979, audiocassettes + workbooks)
|
The Statistics series is written especially for students who require a
knowledge of statistics but do not have a strong background or |
ability
in mathematics. Abstraction and symbolism are kept to a minimum,
yet the series is not a "cookbook" course. All concepts,
generalizations, rules, and processes are well-motivated and
well-illustrated. Teaching is done inductively and in the context
of ongoing problem-solving. Modular tests and scoring keys are
provided. |
8. Sampling and sample statistics
9. Hypothesis testing
10. Estimation of population parameters
11. The t distribution
12. Linear correlation
13. Linear regression
Statistics: Decisions Through Data
(COMAP, 1992, 60 min.videos + workbooks)
|
This video series is an introductory statistics course which unravels
the statistical arguments behind surveys, polls, experiments, and |
product claims. Each episode begins with a documentary segment that
engages students' interest, and then teaches skills to gather data,
analyze patterns, and draw conclusions about real-world issues. |
Hour 1: Basic Data Analysis
Unit 1. What is Statistics?
Unit 2. Stemplots.
Unit 3. Histograms and Distributions.
Unit 4. Measures of Center
Unit 5. Boxplots
Unit 6. The Standard Deviation
Hour 2: Data Analysis for One Variable
Unit 7. Normal Curves
Unit 8. Normal Calculations
Unit 9. Straight-Line Growth
Unit 10. Exponential Growth
Hour 3: Data Analysis for Two Variables
Unit 11. Scatterplots
Unit 12. Fitting Lines to Data
Unit 13. Correlation
Unit 14. Save the Bay
Hour 4: Planning Data Collection
Unit 15. Designing Experiments
Unit 16. The Question of Causation
Unit 17. Census and Sampling
Unit 18. Sample Surveys
Hour 5: Introduction to Inference
Unit 19. Sampling Distributions
Unit 20. Confidence Intervals
Unit 21. Tests of Significance
Understanding Business Statistics
(Irwin, 1994, videos)
This 5-video lecture series, given by Dr. Arthur Reitsch, Professor of
Decision Science well known for his work in business forecasting, is
designed to supplement the first 10 chapters of the textbook by Hanke
& Reitsch. These lectures are intended to help students become
better decision-makers and better managers.
Technical Mathematics
Austin, J.C., Gill, J.C., & Isern, M.
(1988). Technical mathematics (4th ed.) Philadelphia:
Saunders.
Includes an assortment of applied math topics, including: applied
geometry, basic algebraic operations, linear equations, factoring,
exponents and scientific notation, roots and radicals, quadratic
equations, logarithms, and trigonometry.
Calter, P. (1979). Theory and problems of technical mathematics
(Schaum's
Outline Series). New York: McGraw-Hill.
Davis, L. (1990). Technical
mathematics. Columbus, OH: Merrill.
Davis, L. (1990). Study guide to
accompany Technical
Mathematics. Columbus, OH: Merrill.
Dossey, J.A., Otto, A.D., Spence, L.E., & Vanden Eynden, C.
(1993). Discrete
mathematics (2nd. ed.). New York:
HarperCollins.
Trigonometry
Ayres, F., Jr., & Moyer, R.E. (1990). Theory and problems
of trigonometry (2nd
ed., Schaum's Outline Series). New York:
McGraw-Hill.
Bittinger, M.L., Beecher, J.A., Ellenbogen, D., & Penna,
J.A. (1998).
Trigonometry: Graphs and models. Reading, MA:
Addison-Wesley.
Penna, J.A. (1998). Student's solutions manual for
Trigonometry:
Graphs and models. Reading, MA: Addison-Wesley.
Penna, J.A. (1998). Graphing calculator manual for
Trigonometry:
Graphs and models. Reading, MA: Addison-Wesley.
Mini-Courses in Math:
Trigonometry
(Educulture, 1975, audiocassettes + workbooks)
|
Each modular lesson uses cassette tapes and a response manual to help
students learn or review. Students listen, read a little, answer |
questions or work exercises, and find out whether they are right or
wrong. |
1.
Circular functions
2.
Graphs of circular functions
3.
Identities and proofs
4.
Inverse functions and conditional equations
5.
Right angle trigonometry
6.
The solution of right triangles
7.
Polar coordinates and parametric equations
8.
Vectors
9.
Complex numbers
Trigonometry (GPN, University of Nebraska-Lincoln,
1990, <30 min.videos)
Award-winning mathematics
instructor Elayn Gay and Dr. Maurice Dupre give students the opportunity
to master mathematical skills in this video series which helps seventh-grade through college students review and learn
difficult mathematical concepts.
Angles, degrees, and
radians
Introduction to trigonometric functions
Trigonometric functions of general angles
Evaluating trigonometric functions
Graphing trigonometric functrions I
Graphing trigonometric functions II
Trigonometric equations
Right angle applications
Precalculus
Schmidt, P. (1989). 3000 solved problems in precalculus
(Schaum's Solved
Problems Series). New York: McGraw-Hill.
Varberg, D., & Varberg, T.D. (1995). Precalculus: A
graphing approach.
Englewood Cliffs, NJ: Prentice Hall.
Varberg, D., & Varberg, T.D. (1995). Instructor's solution
manual
for Precalculus: A graphing approach. Englewood Cliffs,
NJ: Prentice Hall.
Varberg, D., & Varberg, T.D. (1995). Student solutions
manual for
Precalculus: A graphing approach.
Englewood Cliffs, NJ: Prentice Hall.
Calculus
Anton, H. (1992). Calculus (4th ed.). New York: John Wiley.
Barker, W. H., & Ward, J. E. (1992). The calculus companion to
accompany Anton's Calculus with analytic geometry (4th ed., Vol. 1).
New York: John Wiley.
Barker, W. H., & Ward, J. E. (1995). The calculus companion to
accompany Anton's Calculus with analytic geometry (5th ed.). New
York: John Wiley.
Herr, A. (1992). Student's solutions manual to accompany Anton's
Calculus with analytic geometry (4th ed.). New York: John
Wiley.
Bradley, G.L., & Smith, K.J. (1995). Calculus (Instructor's
Edition). Englewood
Cliffs, NJ: Prentice Hall.
Smith, K.J. (1995). Student mathematics handbook and integral
table for Bradley & Smith's Calculus. Englewood Cliffs, NJ:
Prentice Hall.
Calculus
(GPN, University of
Nebraska-Lincoln, 1990, <30 min.videos)
Award-winning mathematics instructor Elayn
Gay and Dr. Maurice Dupre give students the opportunity to master
mathematical skills in this video series which helps
seventh-grade through college students review and learn difficult
mathematical concepts.
Limits of Continuity
1. Definition of limit (16 min.)
2. The limit theorem (14 min.)
3. Limits at infinity (13 min.)
4. Continuity (16 min.)
The Derivatives
5. The tangent problem (12 min.)
6. The derivative (13 min.)
8. Product and quotient rules for derivatives (17 min.)
9. The chain rule for derivatives (18 min.)
Applications of Derivatives
13. Derivatives and curve sketching (20 min.)
14. Maximum-minimum problems (24 min.)
The Integral
17. Implicit differentiation (14 min.)
20. Velocity, acceleration, related rates (17 min.)
21. Antiderivatives (20 min.)
22. The indefinite integral (26 min.)
23. The area problem (21 min.)
24. Definite integrals and areas (18 min.)
Carpenter, L.L. (1997). Instructor's guide with complete answer
key to
accompany Calculus concepts: An informal approach to the
mathematics of change (preliminary ed.). Lexington, MA: D.C.
Heath.
CD Calculus for Windows (Wiley, 1994, CD-ROM)
The CD is a complete textbook and a wealth of additional learning
material. The electronic study environment lets the student design
and create her own custom study system.
Connally, E. Hughes-Hallett, D., Gleason, A. M. et al. (2000). Functions
modeling
change: A preparation for calculus. New York: John
Wiley.
Dowling, E.T. (1990). Theory and problems of calculus for
business, economics,
and the social sciences (Schaum's Outline Series).
New York: McGraw-Hill.
Hughes-Hallett, D., & Gleason, A.M., et al. (1994). Calculus.
New York: Wiley.
Ching, K., Connally, E., Mallozi, S. A., Mitzenmacher, M., &
Wang, A.
H. (1994). Student solutions manual to accompany
Hughes-Hallett, D., & Gleason, A.M., Calculus. New York: John
Wiley.
LaTorre, D.R., Kenelly, J.W., Fetta, I.B., Harris, C.R., &
Carpenter, L.L. (1995).
Calculus concepts: An informal approach to
the mathematics of change (preliminary ed.). Boston: Houghton
Mifflin.
LaTorre, D.R., Kenelly, J.W., Fetta, I.B., Carpenter, L.L., &
Harris, C.R. (1998).
Calculus concepts: An informal approach to
the mathematics of change (brief 1st ed.). Boston: Houghton
Mifflin.
Lial, M.L., & Miller, C.D. (1989). Calculus with
applications (4th ed.). Glenview,
IL: Scott, Foresman.
Lial, M.L. (1993). Student's solution manual to accompany
Calculus with applications (5th ed.) New York: HarperCollins.
Lial, M.L. (1993). Instructor's answer manual to accompany
Calculus with applications (5th ed.) New York: HarperCollins.
Lial, M.L. (1993). Instructor's guide and solutions manual to
accompany Calculus with applications (5th ed.) New York:
HarperCollins.
Mazur, J. (1994). How to study calculus. Dubuque, IA:
Wm. C. Brown.
Mendelson, E. (1985). Theory and problems of beginning calculus
(Schaum's
Outline Series). New York: McGraw-Hill.
Mendelson, E. (1988). 3000 solved problems in calculus
(Schaum's Solved
Problems Series). New York: McGraw-Hill.
Stewart, J. (1998). Calculus: Concepts and contexts. Pacific
Grove, CA: Brooks/Cole.
Stewart, J. (2001). Calculus: Concepts and contexts (2nd ed.)
Pacific Grove, CA:
Brooks/Cole.
Burton, R., & Garity, D. (2001). Study guide for Stewart's
Single
Variable Calculus: Concepts and contexts (2nd ed.). Pacific
Grove, CA: Brooks/Cole.
Cole, J.A. (1998). Student solutions manual for Stewart's
Calculus: Concepts and contexts. Pacific Grove, CA:
Brooks/Cole.
Clegg, D. (1998). Student solutions manual for Stewart's
multivariable Calculus: Concepts and contexts. Pacific Grove,
CA: Brooks/Cole.
Integrated
Content
Britton, J.R., & Bello, I. (1989). Topics in contemporary
mathematics (4th ed.). San Francisco: Dellen.
Topics covered include: sets; logic; numeration systems; rational
numbers; the metric system; equations, inequalities, and problem
solving; functions and graphs; geometry; matrices; probability and
statistics; and consumer math.
For All Practical Purposes
(Annenberg/CPB,
1987, 30 min.videos)
Real-life examples help teach a basic understanding of mathematics and
its relationship to other areas of study. Mathematical problem solving
is shown to influence everything from the success of savvy entrepreneurs
to the fairness of voting practices. Examples are pulled from management
science, social science, design, and computer science. The modular
construction of the series is useful across the curriculum.
1: Overview. Examines how management science
concepts help our society run more efficiently.
2: Street Smarts. Cities and towns can make
best use of their limited resources by graphing an "Euler
circuit" to find the most efficient routes.
3: Trains, Planes and Critical Paths. Various
algorithms introduced can aid in solving complex routing problems.
4: Juggling Machines. List processing
algorithms and bin-packing, or how to use the least space to
accommodate the most objects, are discussed.
5: Juicy Problems. Linear programming
techniques such as the corner principle, the simplex method, and the
Karmarkar algorithms are covered.
6: Overview. This program explains how to
understand what data is and how it is collected, organized, and
analyzed.
7: Behind the Headlines. Statisticians
demonstrate the use of random sampling methods and randomized
comparative experiments.
8: Picture This. Graphs, histograms, and box
plots reveal changes and patterns that help define mean, median,
quartile, and outlier.
9: Place Your Bets. Techniques of sampling
distributions, normal curves, standard deviations, expected value, and
the central limit theorem are examined.
10: Confident Conclusions. Explains
statistical inference and how it is based on calculations of
probability.
11: Overview. Mathematics makes our decisions
quantifiable in areas as diverse as game theory and social choices.
12: The Impossible Dream. Not all voting
methods are fair, as seen by looking at five different methods.
13: More Equal than Others. Mathematics and
statistics are key to issues of weighted voting and winning
coalitions.
14: Zero Sum Games. Game theory offers
strategies to resolve disputes, and zero sum games and game matrices
provide mathematical solutions to real problems.
15: Prisoner's Dilemma. The games of
"chicken" and "prisoner's dilemma" illustrate
issues in corporate takeovers and labor relations.
16: Overview. This program draws upon
historical examples of geometric applications.
17: How Big Is Too Big. Geometric similarity
and scale help mathematically balance the tensile strength of the
materials with the size of the structure.
18: It Grows and Grows. How population grows
mathematically and the importance of calculating growth.
19: Stand up Conic. The use and importance of
conic sections in the design of twentieth-century inventions.
20: It Started in Greece. The mathematical
tool of Euclidean geometry explains the congruence of triangles, the
Pythagorean theorem, and similarity.
21: Overview. The history of the computer
points out the relationship and interdependence between mathematics
and computers.
22: Rules of the Game. Computer users must
understand algorithms to analyze, choose, and apply the best type for
a given problem.
23: Counting by Twos. Computers store,
process, and reproduce information via codes.
24: Creating a Code. Encoding information for
a computer requires the best and most efficient code.
25: Moving Picture Show. Visit Symbolics,
Inc., to let the experts explain computer graphics.
26: Summing Up. Emphasizes the real-world
applications of mathematics in today's society and the mathematical
models that can be built from them.
For all practical purposes: Introduction to
contemporary mathematics (2nd ed.).(1991). New York: W.H.
Freeman.
The text correlated with the Annenberg/CPT video series, this book
addresses topics in management science (street networks, linear
programming, planning and scheduling, and vertices), statistics, social
choice and decision-making, population growth, patterns, and computer
codes.
Savage, S.H. (1991). Instructor's guide to
accompany For all
practical purposes: Introduction to contemporary
mathematics (2nd ed.). New York: W.H. Freeman.
Learning Plus (Educational Testing Service, 1995?, 3.5" disks)
Originally developed to insure preparation for the Praxis I teacher education test, Learning Plus is
designed to confirm (or remediate) skills in reading, writing, and
mathematics. The software may be installed on a student's notebook
computer for a fee. Individuals who would like access to Learning Plus
should contact Sharon Stufflebean, Coordinator of Assessment Services, at
770/961-3445 or .
Lerner, M. (1996). Math smart:
Essential math for these numeric times (Princeton Review Series).
New York: Random House.
Topics include: numbers, fractions, ratios and proportions, exponents
and roots, algebra, geometry, and statistics.
Miller, C.D., Heeren, V.E., & Hornsby, E.J. (1997). Mathematical
ideas (8th ed.). Reading, MA: Addison Wesley.
Topics include: sets; logic; number theory; basic concepts of algebra;
functions and graphs; counting methods; probability and statistics;
consumer math; and matrices.
Miller, C.D., Heeren, V.E., & Hornsby, E.J. (1997). Study
guide and
solutions manual for Mathematical ideas (8th ed.).
Reading, MA: Addison Wesley.
Research and Education Association. (1976).
Algebra & trigonometry: A complete
solution guide to any
textbook (REA's problem solvers series). Picataway, NJ: REA.
Mathematics for Modern Living
(Magna Systems, 1980, ~30 min.videos + workbooks)
|
The video course has minimal prerequisites and can be used by adult
learning centers, community colleges, and other educational |
facilities.
The course covers a variety of topics relevant to society. Modules
are designed to be stand-alone so that students can study only selected
topics or can work through the entire series. Study guides include pretests, post-tests, activities to be completed
after viewing a video, and a glossary. |
|