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Protest: The site author, a McGill University,
1983 Ph. D in mathematics, failed a McGill Faculty of Education B. Ed pgm 2003-5
due to
YOU are better than YOU think. Show
yourself how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study
Learn to read notes and textbooks like
a lawyer, so that no nuance, no subtlety and no clause escapes your
attention. |
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
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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.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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In deciding which teacher certification program to follow in a school or
faculty of education, or in a teacher training college, you need to know if the
certification process is well-balanced and well-defined. In a teacher
certification program there will be invariably be practicums or field
experiences course in which you interact with a host teacher and field
experience supervisors Those personnel and the structure of the practicum or
field experience, along with the preparation and support you will get for
the field experience are critical. Your success in the teacher
certification program, its evaluation of your suitability for becoming a primary
or secondary school instructor, will be based on those experiences.
Question - pointing to or calling for best practices
- Are host teachers screened for their class-room management and
subject expertise?
If host teachers are not screened, the field experience is
become a lottery. In the worse case, a host teacher may base your
direction in the field expeirenc and the judgment of your suitability for
becoming a high school instructor on his or her substandard practices?
Ideally, the host will be a master teacher, familiar with the nuances and
quirks of the local curriculum and course material.
- Are there any guidelines for the host teachers?
If there are no guidelines, if any thing the host teachers
wants is satisfactory in the certification program, the degree
of support and direction is not governed, and what is provided and
sanctioned may depend on the host teacher inclination. Since host teacher
varies, the ease or difficulty of your certification journey will depend on
chance.
- How are the field experiences structured?
In some teacher certification programs, a field experience is
a random event. You are assigned a host teacher at random, and two or
three days after arrival in the host teacher classroom, you are expected to
deliver lesson plans and lessons. And in that randomness, the subjects meet
may be one of 5 plus, and you will not have time to prepare. In other
field experiences, you will meet the host teacher before the start of the
school year and collaboratively plan or anticipate your interaction while
building up trust and identifying far in advance the subject or topics in
which you will have to plan and deliver lessons. The latter represents a
best practice.
- What is the certification program field experience policy with respect to
students knowledgeable in teachable subject without being familiar with
the local course materials and practices?
If there is no policy that indicates the teacher education
program in question may fail to give you the support you need and so let you
fail. So If you are an older student starting a teacher certification
program, go the program office which monitors student teaching
and ask what will happened when a student teacher, familiar in general with
a subject is not familiar with the current course materials and
practice? That question is important. If there is no special
consideration for that circumstance, there may be tacit assumption that you
are familiar with the current course materials and practices.
- Are field experience supervisors expert, master teachers, in
the course material in which your practicum or field experience will occur?
The certification program needs to provide access to a master
teachers familiar with the course material and its nuances or quirks to
provide a check or balance on the host teacher's expectations practices. The
assumption that a certified or qualified teacher is course material and
delivery expert often fails in secondary schools where compulsory subjects
like mathematics have to be given regardless of whether or not the subject
is in the zone of comfort of the host teacher. I have met cases where
substandard textbooks or course material are approved and
required. If your first encounter with such substandard texts is in a
field experience, and master teachers are not available to provide aid, your
do-or-fail field experience may end in a disaster.
- Does the teacher certification program provide instruction on classroom
management?
With the advent of compulsory school attendance in
authoritarian societies, instruction was teacher and subject centered, in a
way that manners and good behaviors was required. Otherwise, there might be
stiff penalties. In that environment, students were afraid to misbehave. But
in societies which are granting and recognizing more and more freedom for
their youth, school attendance may be required while the consequences of not
cooperating with the schools and their instructors become less and less. In
many societies today, school attendance is compelled while poor
manners and behaviours are not enforced. So teachers have to artfully employ
the limited means at their disposal for classroom and hallway order and
management. That being said, your participation in school activities and
your teaching a course in a way that maintains or develops students will to
cooperate and participate in their own education minimizes the need for
display of fairness and firmness. Repeatedly providing students
opportunities for success is one way to encourage the will to learn
and work in each. Tat being said, you will sooner or latter give a course in
which the motivation of most if not all, is success in the final
examination. Good luck. You will be meeting students, students likely
to be well-mannered later on, who are in your face rude. In all
interactions, look for a path or intervention in which the student or
students decide that cooperation is in their best interest.
- For the subjects you plan to teach, will the teacher certification program
besides describing or exhorting best classroom practice, describe what
is done as well?
If a teacher training program focuses on what should be
rather than what is, you will missing some necessary preparation for
the field experiences and lesson planning.
Teacher education programs may exhort you to act in a certain
manner and say what should be without focusing on what is? Besides
course on pedagogy, you may need a course from a master teacher familiar
with the current course materials in a primary and secondary subject
program, mathematics, science, history or a language such as English or
French or the language of instruction. For example in mathematics or
science, a master teacher at the elementary level or secondary level, would
describe the ends and means of each year of instruction, course by course,
to identify how later skills and concepts are erected on earlier ones in a
linear or spiral (repetitive) manner. A master teacher would also describe
the benefits and limitations of current course materials, and identify
nonsense in them. Nonsense can appear and continue in course materials if
the latter are generated, approved and required in the absent of a master
teacher or subject master to object.
- For the subjects you plan to teach, does the college education library
keep on it shelves or computers, full set of course materials (textbooks and
governmental course definitions and final examinations) for student-teachers
and Professors of Education to consult?
The presence of course materials - what you will meet in the
classroom or in your field experiences - will allow you to get a headstart.
And if the course materials or government documentation are not clearer
complete, access to several, preferably a dozen, recent final examinations
may define course content for you. That is important for subjects or
school courses which you have not followed in your school days due to their
newness or because you followed another path in school days, while or before
current materials were in use.
- What are your withdrawal rights for the practicum's or field
experiences? Do they exist? What are the penalties?
In many college or university courses, there is a penalty-free withdrawal
period. So if you do not like the courese or its instructors, you can
withdraw. However, withdrawal in teacher certification may be deemed a
failure. But the right to withdraw without penalty may be very precocious in
field experiences where host teachers and/or field supervisors and
everyoneelse in the chain of command are not master teachers in the subject
at hand.
- If you fail a field experience due to unanticipated difficulties
with course practices and materials in subject will you be allowed to
continue the program at later date after studying the subject in question in
greater depth?
This may be important if you discover you subject knowledge
is not a great as thought.
- If you fail a field experience due to classroom management difficulties,
will the certification program allow you to re-enter in a few years time to
try again?
With the passage of time, maturity and out-of-school
experience in the workforce may provide the pose and greater maturity needed
for classroom management?
- If you fail and make an appeal, in the appeal process itself, will there
be a master teacher in your teachable subjects, so that any subject related
aspects of your appeal are heard?
- Does the teacher certification program or host institution provide insurance
cover for the possible hazards met in primary and secondary schools, gentle
to tough?
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www.whyslopes.com
Mathematics Education Essays,
57 or so
Area Entrance & Hub
Ideas for Better Instruction
4 Ways to Improve Reform
Theory of Knowledge
Peer Review
The Trouble With Algebra
Course Design and Delivery
How Letters Appear
Sit Down & Study
Modern Education
Key Notes and Themes
Site Lesson Plans
How This Site Differs
Site Origins
Math & Logic Puzzles
Comments on site content.
Words For Instructors
Inductive Principles
Fairness Principles
Apprentices & Masters
Three Remarks
For a Leaner Curriculum
Mixed Maths Curricula
Cultivating Intelligence
Reason - 3 kinds in maths
Logic in Mathematics
Science Education
Maths Instruction in General
Operational View & Values
Standards
Ends and Values
Goals & Unifying Themes
Algebra Lesson Plans
Algebra, Geometrically
Mathematics Curriculum Shifts
Teaching Tips - Fractions to Calculus
Math Ed Perils
Talk the algebra talk
Sec I - Fraction Focus
Sec II - algebra focus
Sec III - Focus on Slopes
Maps-Plans-Drawings
Math Wall Posters
Education, Empirical Art
Damage Reversal
North American Math Curriculum
Managing Reform
Essay January 2007
Educational Follies
Contructivism Incomplete
Missing the Point I
Mathematics in Context
What and When, A Challenge
Grouping Students
Teacher Certification
Education of Math Ed. Professors
Site Eurekas
Links
Help Me Learn/Teach;
- Algebra
words before symbols
- direct &
indirect use of formula, numerical versus algebraic solutions - what
is a variable (more words)
- Arithmetic
- 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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