Preparing for College Mathematics
Preparation for college studies in business, engineering, mathematics,
science and further technical fields provide the motivation and context
for high school mathematics and calculus. High school mathematics may
include calculus lightly while preparing for its further
study and use at the
college level.
Calculus is a subject of slope calculation forwards and backwards for
linear and nonlinear calculations. Formulas given in
high school for areas, volumes and perimeters are justified in calculus.
Mathematical skills and concepts provides a
language for using and describing the roles of numbers in accounting,
commerce, engineering, science and technology. A knowledge of calculus
may also strengthen or enrich the mastery of skills with take-home value.
In technical subjects, the ability to use rules and patterns
represents a first level of mastery. The ability to combine rules and
patterns to arrive at further rules and patterns represents a second and higher
level. That ability can be developed in the study of mathematics.
Moreover, the computational practice and theory in technical
fields, their soundness or not, can only be understood and recognized through
mathematics and logic.
Site
sections on arithemtic, algebra, geometry and calculus include
technical innovations to make the hard easier. The proof is in the details.
In the case of arithmetic, focus on the essential material - there is
too much in that folder.
Some site elements are optional. Others are key. Identifying
which is which clearly is a site to-do. The following site reviews
are quoted to motivate site exploration.
Site Reviews
Links below lead to review locations, not site
content.
1995 -Math Forum June Hot Spot:
Three Skills For Algebra - why letters or symbols are favored in algebra
in place of numbers ... Painless Theorem Proving, What is Mathematical
Induction, Complex numbers Etc. ... How Logic or Rule-Based Reason
Appears in Math ...
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. ...
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 - Education
Planet Newsletter, top math sites:
What are the ideas behind most high school math? ... commentary and
online books ... provide a very rich guide to mathematical reasoning and
high school math to calculus. The emphasis here is on the thinking
part of math rather than the actual manipulations . ...
2002 - NSDL Scout Report for Mathematics, Engineering, Technology
-- Volume 1, Number 8 (May 24):
... 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. ...
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. ...
2005 - All.info
Science and Health - Math - Books -:
Since July 1995, this ... site has been offering ... lessons to aid and
REFORM instruction in mathematics, logic and science. ... Math-free
lessons on Euclidean Logic may lessen gullibility while developing
precision reading and writing. ...
2005 - World-Wide Web Virtual
Library Education - Canada :
... offers appetizers and lessons for math from arithmetic to calculus or
why slopes; for deductive reason (logic) and critical thinking; and for
learning in general. Included here are opinions on the communication of
skills and mathematics instruction. ... Each appetizer is different. If
one is not to your liking try another. Most are from ... books on
understanding and explaining math and reason.
Complete Record Details
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
Safety Messages and Questions: When and why should you face
traffic when walking along a road or cycle path? Is it a good
idea to hang limbs outside of cars etc? What gives more
protection in a crash: a car, motorbike or bicycle?
See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
cleaning up sets the stage for like activities or experiments in
science courses, and in developing organizational skills,
gives boys and girls a head start. Good luck. At the other
extreme, more comprehensive than light, if your motto is
McCainian: drill, drill, drill then Toronto
mathematician and actor John Mighton's jump math organization has jump math
workbooks for at least grades 3 to 8 for at-home and in-school
use - training sessions for teachers available. Jump math has
been expanding to cover older students. Jump Math Samples: plus
Fractions for
Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8
[unread - likely to be good]. and
Mathematics
Skills For Ages 3 to 14 - technical!
Skills with take
home value - A few ideas
Basic skills include
time-date-calendar Matters; money matters; map, plan and
scale diagram matters;counting, measuring and figuring;
decision making with logic and likelyhood; being careful and
being aware of the domino effect of mistakes; reading and
writing with precision.
Is your child able to add, subtract and multiply amounts
of money, work with fractions, work with clocks and calendars,
work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
arithmetic.
Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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