Primary- and Pre-School Mathematics
As infants with full use of their senses turn into young children, they
learn to talk and they learn to recognize key people and key shapes in
their environment. The key shapes may include doors and windows,
chairs and tables, spoons and forks, and so on. Parents may
introduce pre-school students to the daily use of time and clocks - when
to sleep, rise, eat and wash, and beyond that how long to wait.
Like Shapes and Angles (Similarity): The ability to read and write
is based on the child ability to recognize, draw and name letters of the
alphabet, digits and further common shapes such as squares, rectangles,
triangles and circles, in all or part. The primary or pre-school child
may recognize alphabet, digits and further common shapes and even angles
from a a concept of like or similar shape independent of size.
Indeed in moving about a room with shapes in it, or in moving a piece of
paper with shapes on it, letters and digit included, the child may see
and recognize like shapes and angles at changing distances and angles. So
before formal definition or characterization of similarity of
triangles and polygonal figures in high school mathematics,
children acquire and exhibit a larger (?) operational command of similar
or like shapes. Later high school mathematics simple serves to codify
that comprehension and command in a partial manner, first in two
dimensions and then perhaps in three.
Parents in introducing pre-school students to the daily
use of time and clocks - when to sleep, rise, eat and wash, and beyond
that how long to wait. - are taking advantage of the child ability to
recognize the value of figures on an digital clock display or the
position and orientation of hands on an analogue clock. The orientation
of a clock hand with respect to positions around the clock is based on
angle sense.
Spatial Sense: Primary school students from ages 5 to
8 may learn to understand and even apply spatial relations such as
above, below, before, behind, left of, right of, in the middle of
etc.
Decimals: Primary school students may also learn to
recognize groups of 2 to 9 objects, singleton sets and empty sets,
and associate all the latter with the digits and numbers 0 to 9. In this
association, sets of 0 to 9 may appear using dots, tally marks, rocks,
coins, chalk marks, and in printed pages, cute objects such as ducks,
sheep, dogs, cats and so on. While the alphabet may learnt by rote and in
sequence, children may learn to write and count from 0 or 1 to 9, then
10, then 20 and then higher without and then perhaps with a partial or
full comprehension of decimal place value. With variation due to
the use of different currency systems in different parts of the globe,
children may also learn the values of coins and paper currency:
pennies, dimes, quarters, dollars and beyond. There decimal notation with
decimal point may be met and learnt for monetary amounts varying from a
penny to ten dollars, and then beyond. Before, besides and in school
students may learn how to handle coins and paper in buying and selling
small items in local markets or shops. All the foregoing provides an
operational command and context for decimal notation and a partial
command of decimal notation in writing numbers alone or along side common
units of weight, measure and value. Relatives and teachers may
deliberately encourage students to understand more and more about the
latter.
Order Sense: When a sequence of letters or numbers is to be
met and master, joining the dots to draw a path or image can help
students recognize or memorize such sequences forwards and
backwards. The use of scales, rulers and tape measures with unit
length markings and division of the unit length into tenths or hundredths
further introduces and re-enforces decimal skills and
comprehension.
Counting Process: A set of tally marks or a set of pennies,
one each object in a set, may serve to record and track the presence of
each element. By grouping the tally marks or pennies (or real
objects) into units, tens, hundreds, and further powers or multiples of
ten, decimal notation may be serve as a shorthand record for describing
how elements are present. The conversion of ten plus multiples
of
Primary Mathematical Scenarios:
- At a store (several types)
- On a bus
- At the bus or train station
- In a taxi
- Traveling with Maps
- Working with plans
- Hiring help
- Working for Wages
- Carpentry (Work Working)
- Metal Working
- Redecorating
- Cabinet Making, Shelf Making.
- Model Material Usage
- At the Garage
- In the kitchen - Weights, Measures, Fractions & Proportionality
(Scale Factors) in the Kitchen.
- Concrete Making
Multiplication - Physical and Decimal View
Subtraction - Physical and Decimal View
Division and Fractions - Physical and Decimal View - Quotient &
Remainder Views.
Working With Decimals - Forwards and Backwards - Billions, Trillions,
Billionths and Trillionths.
Exact Arithmetic Operations on Fractions
Optional: Justification of Decimal Point Shifting.
Arithmetic With week, days, hour and second mixed measures of
time: addition, subtraction, multiplication by a whole
number,
Arithmetic with units.
Counting Principles: Order does not matter:
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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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