Parents: Site Area Helping
Your Child or Teen Learn covers 1.
Speaking Skills, 2.
Reading & Writing, 3.
Preparing for Science, 4.
Math Work Books, 5.Books
for Parents, 6.
Mathematics for ages 6 to 14, 7.
Having Patience -you'll need it Parents and teachers need to
say no for little things, keep in practice, otherwise the authority to say
no for big things will vanish. Parental Authority: Use it or
lose it.
Students: Take charge of your learning. Try
to read like
a lawyer
for better work & study skills, but do not take
everything literally. In
particular, two
logic puzzles are keys to site content, and to greater work and study
skills.
Welcome. If you like chapters 1 to 12, 14, 16 & 17 in Volume 2,
Three
Skills for Algebra, site exploration
is recommended. If not, more experience in work and study may help
lead you to a greater liking.
Teachers & Tutors: If you are mathphobic,
start with Three
Skills for Algebra. Site pages stems from self-contained inductive principles and
standards for training, coaching and the direct development of observable skills.
In support of the latter, site
folders and how-TOs
offer smaller steps, more steps and alternative
steps to aid instruction. Skill development may require natural
talent, but should do so in a minimal manner. Form
a group of mathematics teachers & tutors for collecting and sharing
methods for observable skill development. That is a professional duty. Invite
speakers to offer those steps. As a group talk about critical path
analysis, about the ends and values of instruction. If you have a great
method for skill development, invite colleagues into your classroom to observe
and refine it. If you a difficulty with one part of skill development, invite a
colleague to discuss the matter. Do not be shy. Think of the long-term benefit.
Difficulties in
education are not private matters. Difficulties in mathematics education
are common. Exposure is needed for resolution. Mathematics education/training should include food for thought, but it should also provide and emphasize observable and measurable
skills and talents. Do not waste student time with the former when observable
skills and talents are weak or absent. Where course design and curriculum
looks like spaghetti, object.
See sites mathsisfun.com,
purplemath.com and themathpage.com for
more help Multiple views are better than one.
A Secret - Written Work is Every Thing:
For a pair of decimals with too many digits to keep in your mind,
imagine the task of adding them without the aid of a calculator. You
would write the decimals, one above the another, with place values
aligned, and then add them digit by digit with carries
as needed. That provides a first example of how written methods
aids and shows work. Mathematics mastery is
largely an on-paper activity with steps drawn or written to obtain results
and to record what was done, so that your mastery of mathematics
is observable and correctable. Mental skills are helpful, but for ease and better performance, learn how to write
or draw ideas and steps on paper to do and record mathematics. Anything less will lead to
difficulties. Good luck.
Where is Mathematics? ask what would happen if
numbers, geometry and algebra was to disappear. Numbers and geometry
are part of daily life. Decimals appear in telling and tracking time, distance,
speed, mass or weights, measures, costs and revenues. Geometry
appears in life like drawings, plans and maps. Algebra too appears as
formulas describing calculations that may be done forward first and backwards
later. Mathematics education includes and may cover first practical and
concrete skills and concepts before and then beside preparation for
calculus. That we hope, can be done in a way that serves other ends for
mathematics.
What is Mathematics Mastery? If you want to learn mathematics well you
need to have a strong work ethic. You need to watch for and master
methods and practices for writing and thus recording and doing work on paper in
a step-by-step manner that can be seen and understood by others. While you
may get credit for right answers, answers that you arrived at in your
head, there is still a great need to show work on paper. While you may think or hope that
showing work is not needed, the ability to record steps in arithmetic,
geometry and algebra on paper allows us to develop and follow the onger and longer
chains of reason that mathematics mastery requires.
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Calculus is the college or senior
high school mathematics subject required for college or
university studies in accounting, business, money matters,
science, engineering and health.
Calculus is very demanding.
Half the students who take college calculus fail. Try to
be in the other half.
Calculus employs at full
strength earlier elements of high school mathematics,
namely functions, trig, algebra (including
polynomials), mathematical induction, more logic,
geometry and exact arithmetic. But preparation
for calculus should not be the only end for secondary school
mathematics. other shorter term ends need to be included to
provide a motivation and a context. Preparation for
calculus could be buried in quantitative skill development
for daily life and for numerical and geometric methods
there-in.
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Advanced Level Help: Volume
3, Why
Slopes and More Math offers starter and preview lessons
for calculus to make the hard easier. These arithmetic
review problem with hints of algebra may catch a few
weaknesses at the start of calculus or in earlier instruction.
More Mid-Level Help: Talking about three
skills for algebra and what
is a variable introduces more words into understanding
and explaining algebra. In mathematics, the question of what does it mean to use a formula or
rule forwards and
backwards (link for students) identifies with words a recurring
pattern or unifying theme (link for tutors-teachers).
Mid-Level Help
Seeing
the difference between one and two-way implication rules
may provide lawyer like, precision reading skills needed for
success and self-defense in studies, in work and in
making agreements. Besides that, put mathematics aside
and see if you can enjoy the leading math-free
logic chapters in Volume 2. You know not
studying leads to poor marks. If you decide to study,
take some time to master logic. That exercise and logic
mastery together will lead to better study skills.
Good luck.
Base Level Help: Arithmetic Flash
Video Lessons review and explain operations with
decimals and integers in great depth - perhaps too
deeply. Solving
Linear Equations lightlyconnects (i) algebra with geometry and fractions
- fractional operations on line segments), connects (ii) word
problems with systems of equations in essentially one unknown
- let algebra make the hard easier. For a further
review and explanation of arithmetic with fractions see the site folder
on Fractions
etc. If you are adult or older
teen, the lesson here should be a review and should make
what was hard in the past, easier - and the review should
unify and connect the ideas and skills, half of which or more,
you have seen before.
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Site Reviews
kindest first
- Magellan, the McKinley Internet Directory,
1996: 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
Current Location: Volume 2, Three
Skills for Algebra - for the most part.
-
The
World-Wide Web Virtual Library Education by Country - Canada,
Nov. 2005: This online classroom 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. The logic appetizers are math free. Each
appetizer is different. If one is not to your liking try
another. ...
-
The
NSDL Scout Report for Mathematics Engineering and Technology--
Vo. 4, No. 4 (Feb.
2005) [A new] section of the website,
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. Links to related [online] chapters ... are
also provided.
Location: Site Folder. Solving
Linear Equations 04-2005. The
stick diagram approach was
invented during a third high school teaching practice in that
program and posted online just before the fourth.
-
The
NSDL Scout Report for Mathematics, Engineering, &
Technology -- Vol. 1, No. 8 (May 2002) 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, [ouch] the site is
not well organized. This does not take away from the quality
of the information, though.
Remark: Six year later,
November 2008, the site has been reorganized. Site pages are
now (we hope) clearly and properly organized into books or
folders with chapters or lesson groups.
-
Education
Planet Newsletter, top math sites, 2001: ... The
commentary and online books available at this site 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 themselves. There is also
information here for parents as well as teachers. Now you can
help your students gain insight into mathematics rather than
just helping them memorize formulas.
Current Locations: Volume 2, Three
Skills for Algebra: and Volume 3, Why
Slopes and More Mathematics, Help.
your. child. or. teen.study and Volume 1B, Math
Curriculum Notes. The entrance page to site folder
Mathematics
Education Essays includes a long article on the thinking
part of mathematics and how it may have to co-exist with rote
learning (or postponed explanations).
-
Math Forum News Letter: Aug, 2001.
...
new sections on Complex Numbers and the Distributive
Law for Complex Numbers offer a short way to reach and
explain:
Current Location: In Euclidean
Geometry & Complex No, and Complex No. Folders
Original & Current Locations:
Volume 3, Why
Slopes and More Mathematics for complex numbers & Site
Folder :
Complex Numbers More on the short way to reach the
latter using complex numbers. Since 1996 introductions of
complex numbers have appeared in Volume 3, alone in a
single 2001 page on complex
numbers, then in the Analytic
Geometry/Functions folder and, saving the best for last,
in Euclidean-Geometry
folder.
-
Math Forum News Letter, November 25,
1996 .... mathematics appetizers range over
arithmetic review problems, notions of what variables are,
skills leading to algebra, painless theorem proving, complex
numbers with some trig, the importance of slope (some
calculus), a decimal perspective of error control and
continuity (more calculus), and renaming the greater than sign
(back to algebra). // Advice on how to read, how to
learn, why go to school, etc. ... included. The tone is
sometimes funny, and the writing is dense, rich, and
intriguing. There are reflections on teaching, so these
materials can be used in the classroom and as a place for
teachers to learn. // ... explanations of mathematical
concepts using words and stories are particularly strong. ...
Current Locations: Volume 2, Three
Skills for Algebra: and Volume 3, Why
Slopes and More Mathematics. What does it
mean to use a formula forwards
and backwards
-
Cornell
Theory Center, Fall1995. Several puzzles and short
discussions to help students understand algebra and proofs. If
you don't like the first one you look at, try another; they're
all quite different.
The Cornell Theory Center and the Math Forum provided the
first two links to this site.
-
-
Math Forum June
1995 Hot Spot: Three Skills For Algebra (a
first image of mathematics after arithmetic - why letters or
symbols are favored in algebra in place of numbers); Two logic
puzzles to show the difference between a one-way and a two-way
rule; Painless Theorem Proving; Longer Chains of Reason: What
is Mathematical Induction?; Complex numbers - A geometrical
story based on the addition and multiplication of arrows in
the plane; Chains of Reason - math-free examples of rule-based
reasoning; How Logic or Rule-Based Reason Appears in Math;
...
Current Location: Volume 2, Three
Skills for Algebra:
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Entrance Level
[ Next ]
Adopt whyslopes.com/search/
for internet searches.
Pages for Students
Home
How to Improve Marks
Grades 7 to 12 Guide
1. Arithmetic Lessons
2. Algebra How-TOs
3. More Algebra How-TOs
4. Geometry Steps Into
5. More Geometry
6. Calculus How-TOs
7. Logic in Math
Proper notation & format
makes the hard easier.
Pages For Teachers
Home
Notes for Instructors
Vol 1, Elements of Reason
Sec I Objectives
Sec II Objectives
Sec III Possibilities
Permissions
A Site Map
Show a student how to learn and that helps one. Show a
teacher or tutor how to make skills and concepts easier for students and
that helps many.
Miscellaneous
Your IP Address & how to use
it
Three Links for Teachers:
(i) First
Year High School Math - Lesson Plans with Fraction Focus
(ii) Second
Year High School Math - Lesson Plans with an algebra focus
(iii) Algebra
Lesson Plans
What may be learnt and when depends on how skills and
concepts are developed. Making the hard easier and clearer will allow earlier
& richer development of skills and concepts.
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YOU are
better than YOU think. Show yourself how:
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Take
greater charge of your work or studies: Read like
a lawyer
for better work & study skills, but do not take
everything literally. |
| In
particular, two
logic puzzles are keys to site content, and to greater work and study
skills. See if you agree. |
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Help Me Learn/Teach;
- Algebra
words before symbols
- direct &
indirect use of formula, numerical versus algebraic solutions - what
is a variable (more words)
- Arithmetic
-new Arithmetic
Folder
- exercises
- with fractions
-
videos on primes, lcm, gcm,lcd, square roots etc
- Calculus - geometric
preview, algebraic
preview,
3 study guides,
much more
- Complex numbers
-starter lesson with java applet - easy
consequences for trig & vectors in the plane
- Education
- Empirical Course
Design & Delivery
- Fractions
- alone
- by rote
- with
algebra
- videos
- Functions - introduction
hindsight
- composition aka
substitution -
- Geometry, Euclidean - Correspondence
of triangles, Triangle
construction, duplication & Isometry - Failure
of ASA & the // line postulate - angle
sum in triangles -//
grams - Triangle
Similarity
- Geometry-
Analytic - functions, polynomials, complex numbers, unit circle
trigonometry
- Logic
- First Steps -
Symbols in
Logic -
Occurrence
& Truth Tables - Indirect
Reason -Indirect
Reason More
- Proportionality
- Definition
- Direct & Indirect Use - Numerical versus Algebraic Solutions
- Real Analysis
- Decimal View of concepts
and of proofs
- Rules &Patterns in Science, Technology & Society
- Pattern Based Reason
- Mathematical Reasoning, empirical, inductive or deductive
- Units
- in rates & slopes
& (?) derivatives
- in ratios
& proportions - slopes & rates included
- Complex Numbers & Vectors & Trig
- trig expression for
dot & cross - cosine
law
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