Mathematics Skills Year by Year
Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
Ages 3 plus to 4 plus
Ages 4 plus to 5 plus
Ages 6 to 7
Ages 7 to 8
Ages 8 to 9
Ages 9 to 10
Ages 10 to 12 Arithmetic
Ages 10 to 12 Geometry
Ages 12 to 14 Arithmetic
Ages 12 to 14 Geometry
Ages 12 to 14 Skills with take home value
"Would you tell me, please, which way I ought to go from here?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't much care where--" said Alice.
"Then it doesn't matter which way you go," said the Cat.
"--so long as I get SOMEWHERE," Alice added as an explanation.
"Oh, you're sure to do that," said the Cat, "if you only walk long
enough."
(Alice's Adventures in Wonderland, Chapter 6)
From Practice to Theory- Weaving A Web
In general, the aim of primary and secondary mathematics education
for those who want skills with take home value is to provide a
consistent web of inter-related and interdependent skills,
practices, rule and patterns, with an emphasis on showing work for
the sake of observable and verifiable abilties and results, with
explanations given as needed for the latter to occur. Following
that, after an initial development of logic, algebra and geometric
skills and practices, the deductive or axiomatic organization of
the web may be introduced and developed, with some practices
familar or self-evident through experience taken as axioms -
assumed patterns. There-in lies an alternate vision for mathematics
education, one that teachers and education committees needs to
learn and take as a lower bound for instruction. Within this
framework, there is room for discussion of what content or skills
to include in developing decimal skills and beyond. It the
objective is to provide an operatinal command, a spanning subset of
the skills and practices may be sufficient for most, with study and
skill perfection left aa an option, one supported in pages offline
and on.
Use Site Ideas With Caution
Each year of mathematics instruction has skill and practice
development objectives. Those objectives may vary with the school
or college program followed. Students, tutors and teachers may
guide their efforts by identifying from course outlines and
previous final examinations which skills and practices, which rules
and patterns need to be mastered. The aim of studies and
instruction is not to identify skills and practices not alone but
with methods for showing mastery. In mathematics especially, the
ability to do and record steps of methods and practices in a ways
that can be seen and corrected as done or later by the doer, a
fellow student or instructor sets the stage for observable and
verifiable skill development. In this matter it is cruel to be
kind. Parents, tutors and teacher need to tell students, we can not
see nor check what is in your mind, you need to show work for marks
and more importantly for your skill to be seen and confirmed or
corrected. Skill needs to be seen.
Site material contains many ideas and lessons for skill
development. Site description of mathematics skills for ages 3+ to
14 provides a model for what might be taught and when. The model
itself is a guideline. It pacing and selection of material is
likely to conflict with some or many elements of your school
requirements for each age level. Do not replace local skill
development aims and requirement by site suggestions for each.
Different school systems will cover the same or similar material at
rates. You task is to identify site ideas and lessons that might
assist the meeting locally needs.
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Primary and Junior High School Mathematics
Folder webpages essentially provide a year-by-year model of what might be
taught and when. The key idea is that earlier provide a base for later
ones. Respecting that dependence, and not rushing instruction since that
may overwhelm students appears to tbe main constraint. In each year of
arithmetic and other areas, the accumulation of skills implies more
variation in content is possible in the following years. The distribution
of skills among age groups is an estimate based on a reading of other
course designs and common work exercise booklets available in Montreal
and Toronto. Hopefully the model will do no harm.
Since my teenager years, I have been attracted by the deductive and
axiomatic development of mathematics or its subjects. But in retrospect,
my education in primary school mathematics was incomplete in that I met
and learnt methods without fully understanding why they worked. That
attraction, the idea that mathematics instruction should be deductive
motivated the thought-based development and exploration of mathematics in
site pages.
Until recently, whenever I entered the mathematics classroom, I felt my
instruction was incomplete if I did not explain why the mathematical
methods met in a course held. But mathematics can be mastered at two
levels. The higher level consists of comprehension, in all or part, of
why mathematical work. The base level consists of a mechanical mastery of
methods, by rote, in a way that leads to calculations and figuring that
can be done and recorded step by step for confirmation or correction.
Before any efficient, deductive and algebraic Euclidean style, axiomatic
development of mathematics, students have to master deduction and
algebra. Thus an Euclidean account is inaccessible without mastery and
appreciation of both deduction and algebra.
The first several years of mathematics instruction may focus on skill and
practice mastery, with full comprehension optionals, but with mastery
being observable and when applied without errors, leading to repeatable
and reproducible steps and results. In this skill and practice
development, methods to follow may be instroduced or shown by example.
Over time, the inter-relationships between methods may be seen, with some
implying others. In general, an operational and empirical command of a
subject does not require a lean axiomatization of the subject, with skill
and concept derived from a minimal set of rules and patterns.
For common needs and the common person in the street, when the aim is an
operational command of a subject, instruction and course design may aim
to present a web of consistent rules and patterns, a web clearly
described and easily understood and repeated, a web that does not have to
be derived from a minimal collection of assumed rules and patterns. Such
derivation may be left to those students willing to adopt some of the
ends and values of pure matheamtics.
The web we want to weave in mathematics will however set the stage for
such a derivation while focusing on common needs first, and others needs
such as preparation for college studies, second. The axiomization of an
art or discipline with prior empirically developed rule, patterns or
practices, may elevate some practices to the state of axioms for the sake
of an deductive codification and arrangement of islands and bodies of
knowledge within a web or subweb.
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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.
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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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