Mathematics Concept & Skill Development Lecture Series:
Webvideo consolidation of site
lessons and lesson ideas in preparation. Price to be determined.
Bright Students: Top universities
want you. While many have
high fees: many will lower them, many will provide funds, many
have more scholarships than students. Postage is cheap. Apply
and ask how much help is available.
Caution: some programs are rewarding. Others lead
nowhere. After acceptance, it may be easy or not
to switch.
For students of reason in society, science and technology:
Pattern Based Reason describes
origins, benefits and limits of rule- and pattern-based thought and
actions. Not all is certain. We may strive for objectivity, but not
reach it. Postscripts offer
a story-telling view of learning: [
A ] [
B ] [
C ] [
D ] to suggest how we share theories and practices.
These online chapters may amuse while leading to greater precision and comprehension in reading and
writing at home, in school, at work and in mathematics.
1 versus 2-way implication rules - A different starting point - Writing or introducting
the 1-way implication rule IF B THEN A as A IF B may emphasize
the difference between it or the latter, and the 2-way implication A IF and ONLY IF B.
Deductive Chains of Reason - See which implications can and cannot be used together
to arrive at more implications or conclusions,
Mathematical Induction - a light romantic view that becomes serious.
Responsibility Arguments - his, hers or no one's
Islands and Divisions of Knowledge - a model for many arts and
disciplines including mathematics course design. Site Theme: Different entry
points may be easier or harder for knowledge mastery.
Deciml Place Value - funny ways to read multidigit decimals forwards and
backwards in groups of 3 or 6, US-CDN, UK-German and Metric SI style.
Decimals for Tutors - lean how to explain or justify operations.
Long division of polynomials is easier for student who master long
division with decimals.
Primes Factors - Efficient fraction skills and later studies of
polynomials depend on this.
Fractions + Ratios - See how raising terms to obtain equivalent fractions leads to methods for
addition, comparison, subtraction, multiplication and division of
fractions.
Arithmetic with units - Skills of value in daily life and in the
further study of rates, proportionality constants and computations in
science & technology.
What is
a Variable? - this entertaining oral & geometric view
may be before and besides more formal definitions - is the view mathematically
correct?
Formula Evaluation - Seeing and showing how to do and
record steps or intermediate results of multistep methods allows the
steps or results to be seen and checked as done or later; and will
improve both marks and skill. The format here
allows the domino effects of care and the domino effects of mistakes
to be seen. It also emphasizes a proper use of the equal sign.
Solve
Linear Eqns with & then without fractional operations on line segments - meet an visual introduction and learn how to
present do and record steps in a way that demonstrate skill; learn
how to check answers, set the stage for solving word problems by
by learning how to solve systems of equations in essentially one
unknown, set the stage for solving triangular and general systems of
equations algebraically.
Function notation for Computation Rules - another way of looking
at formulas. Does a computation rule, and any rule equivalent to it, define a function?
Axioms [some] as equivalent Computation Rule view - another way for understanding
and explaining axioms.
Using
Formulas Backwards - Most rules, formulas and relations may be used forwards and backwards.
Talking about it should lead everyone
to expect a backward use alone or plural, after mastery of forward use. Proportionality
relations may be use backward first to find a proportionality constant before being
used forwards and backwards to solve a problem.
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whyslopes.com >> Parent Center >> 17 Math Booklets for children and young teenagers Next: [18 Math Booklets for children and young teenagers Details.] Previous: [16 Secondary Mathematics Tips.] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18][19]
Pre-School and Primary Skill Development Steps
For students before high school, the following inexpensive booklets
on arithmetic, geometry and word problems develop skill and
concepts with value in daily and adult life, while pointing to a
strong base for high school mathematics. Just buy them and use them
from your local bookstore, if possible, and online, if need-be.
Booklet inspection is recommended before any purchase. Later versions when available are
likely to be better than early ones.
To
see which the recommended booklets fit your needs is to visit a
bookstore that stocks them.
Arithmetic Skill Development
The arithmetic booklets include examples and explanations before
each group of exercises to show parents how to check and develop
the skills and abilities of their children. That makes their
arithmetic skill development parent or teacher friendly. Since these works come from
different publishers, there is some overlap. Their
development of arithmetic skills and practices is usually in
sequence.
-
Title:: Little Critter, Numbers and Counting,
PreSchool
ISBN 0-7696-5199-2 , School Specialty Publishing, OH
43240-2111,
SchoolSpecialityPublishing.com
-
Title: MATH - 101 Things First Graders should know about
math, Ages 5+
Author: Peg Hall
ISBN-13: 978-1-4127-1235-4 & ISBN-10: 1-4127-1235-1
Publisher: Active Minds, IL 60712 USA
-
Title: Time, Money and Fractions, Grades 1-2
Author: Barbard Bando Irvin, Ph. D.
ISBN- 0-938256-44-0
Publisher: School Zone Publishing Company, P.0. Box 777,
MI 49417, USA
-
Title: Math Basics, Grades 2, An I Know It! Book.
Author: Barbard Bando Irvin, Ph. D.
ISBN- 0-978-088743-138-8
Publisher: School Zone Publishing Company, P.0. Box 777,
MI 49417, USA
-
Title: Math Grade 2,
Authors: T.J. Richards & M. D. Freeman
ISBN 1-5776802-3
Publisher: McGraw-Hill Children's Publisheing
www.littlecritter.com
I would prefer the term rewriting instead of renaming in
the discussion of conversion, carries, borrows in decimal
method for addition and subtraction. Chapters 4 to 6 are
well-done, Chapter 4 especially.
-
Title: Math Basics, Grades 2, An I Know It! Book.
ISBN- 1-896477-46-1
Publisher: Popular Book Company (Canada) Ltd www.popularbook.ca
Distributed in Canada by Monarch Books: www.monarchbooks.ca
-
Title: Multiplication and Division, Grades 3- 4, An I
Know It! Book.
Author: Barbard Bando Irvin, Ph. D.
ISBN- 0-938256-34-3
Publisher: School Zone: www.schoolzone.com
The next booklet also includes multiplication and division
questions. The introduction in it is simpler than the
previous one - Cover first.
-
Title : Math Basics, Grade 4,
Author : B. Bando Irvin, Ph. D
ISBN 0-938256-33-5
Publisher: School Zone Publishing Company.
P.O. Box 777, Grand Haven MI49417, USA
Website: www.schoolzone.com
-
Title: Math Grades 4, 150+ pages
Author: Thomas J. Richards.
ISBN 1-57768-404
Publisher: McGraw Hill Children Publishing. 1999
-
Title: Math Grades 5, 158+ pages
Author: Thomas J. Richards.
ISBN 1-57768-405-2
Publisher: McGraw Hill Children Publishing. 1999
Each lesson begins with a worked example that a parent may
follow and explain. Some children may be able to follow by
themselves. The text is strong on explaining the mechanics of
operation by example.
-
Title: Math Basics, Grade 5
Author: B. Bando Ivin, Ph. D
ISBN 0-978-088743-1412-8
Publisher: School Zone Publishing Company.
P.O. Box 777, Grand Haven MI49417, USA
Website: www.schoolzone.com
-
Title: Math Grades 6, 150+ pages
Author: Thomas J. Richards.
ISBN 1-57768-406-0
Publisher: McGraw Hill Children Publishing. 1999
-
Title: McGraw-Hills Math - Grade 6
Author:
ISBN 0-778-0-7-174730-1
Publisher: McGraw-Hills
Website: www.mhprofessional.com
-
Title: McGraw-Hills Math - Grade 7
Author:
ISBN 0-978-0-7-174863-3
Publisher: McGraw-Hills
Website: www.mhprofessional.com
Kumon Work Books
The inexpensive Kumon Geometry and Measurement booklets and the
Word Problems booklets below complement the counting and arithmetic
work books above. The Geometry and Measurement Books develop
length, area and volume measurement and calculation skills. They do
not cover mass and weight measures. Nor they cover the use of maps,
plans and diagrams drawn to scale.
-
Title: Are You Ready for Kindergarten - Pencil
Skills, Kumon Ages 4-5. Publisher's Pitch: Inroduce your
child to pencil-control activities to develop motor ... skills
... .
-
Title: Are You Ready for Kindergarten - Scissor
Skills, Kumon Ages 4-5. Publisher's Pitch: Inroduce your
child to paper-cutting activities to develop motor ... skills
... .
-
Title: Geometry and Measurement, Grade 1, Kumon
Math Workbooks. Publisher's Description: This workbook will
introduce ... shapes and their basic attributes (that is,
properties).
-
Title:Word Problems, Grade 1, Kumon Math
Workbooks. Publisher's Description: This workbook will
introduce ... word problems dealing with early addition and
subtraction.
-
Title: Geometry and Measurement, Grade 2, Kumon
Math Workbooks. Publisher's Description: This workbook will
... improve .. understanding of measurement concepts.
-
Title: Word Problems, Grade 2, Kumon Math
Workbooks. Publisher's Description: This workbook will
introduce ... word problems dealing with multiple-digit
addition and subtraction.
-
Title: Geometry and Measurement, Grade 3, Kumon
Math Workbooks. Publisher's Description: This workbook will
introduce your child to concepts ... perimeter, area, symmetry
and other attributes (properties) of shape and improve their
understanding of measurement concepts.
-
Title:Word Problems, Grade 3, Kumon Math
Workbooks. Publisher's Description: This workbook will
introduce ... word problems dealing with advanced addition and
subtraction, and early multiplication and division.
-
Title: Geometry and Measurement, Grade 4, Kumon
Math Workbooks. Publisher's Description: This workbook will
help your child to understand ... lines, circes and angles, as
well as to solve problems concerning area, perimeter, volume
and elapsed time.
-
Title: Word Problems, Grade 4, Kumon Math
Workbooks. Publisher's Description: This workbook will
introduce ... word problems dealing with multiple-digit
multiplication and division as well as early... table and
graphs.
-
Title: Geometry and Measurement, Grade 5, Kumon
Math Workbooks. Publisher's Description: This workbook will
help your child understand and apply more advanced concepts
regrading lines, angles and symmetry, and will introduce ...
measurement formulas for area, perimeter and volume.
-
Title: Word Problems, Grade 5, Kumon Math
Workbooks. Publisher's Description: This workbook will
introduce ... word problems dealing with multiplying and
dividing decimals and fractions, as well as continued (that is,
more) work with table and graphs.
-
Title: Geometry and Measurement, Grade 6, Kumon
Math Workbooks. Publisher's Description: This workbook will
introduce ... advanced properties of circles, the concepts of
symmetry and ratio, as well as how to calculate the volume of a
geometric solid among other applied measurement problems.
-
Title: Word Problems, Grade 6, Kumon Math
Workbooks. Publisher's Description: This workbook will
introduce ... word problems dealing with adding, subtracting,
multiplying and dividing fractions with unlike denominators, as
well as working with the concepts of ratio, average, speed and
proportion.
John Mighton's Efforts
For parents well-versed in secondary mathematics, John Mighton's
jump math organization has
workbooks for at least grades 3 to 8 for at-home and in-school use
- training sessions for teachers available. Jump math is expanding
to cover older students and to support home instruction. Jump Math
Samples: plus Fractions for Grades 3-4
& Grades 5-6 are not bad. Its Free Resources grades 1 to 8
which I have yet to read - likely to be good]. Jump math is writing
mathematics books for home-schooling in British Columbia. Where I
prefer a lighter approach for home- and school skill development
because many parents and instructors may find their time and own
skills insufficient for a heavier approach. Less may be better. The
Jump math author John Mighton is a mathematician turned actor. So
his live presentation skills are better or more flexible than mind.
Mighton's philosophy for skill development is similar to mine. That
is, skill and concept development steps should be fully described
and documented, or a least provided by explanations and exercise in
ways easily understood and repeated by instructors and tutors. We
differ on the extent of skill development. His booklets cover more
than I recommend. That is, I favour a lighter approach, especially
in the case where one or both parents did not do well in
mathematics. However, sooner or later his work is likely to provide
yet another route for skill and concept development at home and in
school. Skill development using his methods is likely to be strong.
whyslopes.com >> Parent Center >> 17 Math Booklets for children and young teenagers Next: [18 Math Booklets for children and young teenagers Details.] Previous: [16 Secondary Mathematics Tips.] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18][19]
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Road Safety Messages
for All: When walking on a road, when is it safer to be on
the side allowing one to see oncoming traffic?
Site Reviews
1996 - Magellan, the McKinley
Internet Directory:
Mathphobics, this site may ease your fears of the subject, perhaps even
help you enjoy it. The tone of the little lessons and "appetizers" on
math and logic is unintimidating, sometimes funny and very clear. There
are a number of different angles offered, and you do not need to follow
any linear lesson plan. Just pick and peck. The site also offers some
reflections on teaching, so that teachers can not only use the site as
part of their lesson, but also learn from it.
2000 - Waterboro Public Library, home schooling section:
CRITICAL THINKING AND LOGIC ... Articles and sections on topics such as
how (and why) to learn mathematics in school; pattern-based reason;
finding a number; solving linear equations; painless theorem proving;
algebra and beyond; and complex numbers, trigonometry, and vectors. Also
section on helping your child learn ... . Lots more!
2001 - Math Forum News Letter 14,
... new sections on Complex Numbers and the Distributive Law
for Complex Numbers offer a short way to reach and explain:
trigonometry, the Pythagorean theorem,trig formulas for dot- and
cross-products, the cosine law,a converse to the Pythagorean Theorem
2002 - NSDL Scout Report for Mathematics, Engineering, Technology
-- Volume 1, Number 8
Math resources for both students and teachers are given on this site,
spanning the general topics of arithmetic, logic, algebra, calculus,
complex numbers, and Euclidean geometry. Lessons and how-tos with clear
descriptions of many important concepts provide a good foundation for
high school and college level mathematics. There are sample problems that
can help students prepare for exams, or teachers can make their own
assignments based on the problems. Everything presented on the site is
not only educational, but interesting as well. There is certainly plenty
of material; however, it is somewhat poorly organized. This does not take
away from the quality of the information, though.
2005 - The
NSDL Scout Report for Mathematics Engineering and Technology -- Volume 4,
Number 4
... section Solving Linear Equations ... offers lesson ideas for
teaching linear equations in high school or college. The approach uses
stick diagrams to solve linear equations because they "provide a concrete
or visual context for many of the rules or patterns for solving
equations, a context that may develop equation solving skills and
confidence." The idea is to build up student confidence in problem
solving before presenting any formal algebraic statement of the rule and
patterns for solving equations. ...
Maps + Plans Use - Measurement use maps, plans and diagrams drawn
to scale.
Euclidean Geometry - See how chains of reason appears in and
besides geometric constructions.
Coordinates - Use them not only for locating points in the plane
or space.
Complex Numbers - Learn how rectangular and polar coordinates may
be used for adding, multiplying and reflecting points in the plane,
in a manner known since the 1840s for representing and demystifying
"imaginary" numbers, and in a manner that provides a quicker,
mathematically correct, path for defining "circular" trigonometric
functions for all angles, not just acute ones, and easily obtaining
their properties. Students of vectors in the plane may appreciate the
complex number development of trig-formulas for dot- and
cross-products.
Lines-Slopes [I] - Take I & take II respectively assumes no
knowledge and some knowledge of the tangent function in
trigonometry.
What is Similarity - another view of using maps, plans and
diagrams drawn to scale in the plane and space. May buildings in
space are similar by design.
Why study slopes - this fall 1983 calculus appetizer shone in many
classes at the start of calculus. It could also be given after the intro of slopes
to introduce function maxima and minima at the ends of closed intervals.
Why factor polynomials - this 1995-96 lesson introduces calculus
skills and concepts. It may also may be given to introduce further function maxima
and minima both inside and at the ends of closed intervals.
Check Arith. Skills - too many calculus and precalculus
students do not have strong arithmetic and computation skills. The
exercises here check them while numerically hinting at
equivalent computation rules.
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