The following article in quoted in full from the online
publication
Speaking of Learning of the Writing Center in Owens Community College. It refers to four
things a student should know once posted online in the site entrance
page.
Speaking of Learning…
Teaching, Learning, and Writing
Across the Curriculum
at Owens Community College
WHAT WORKS FOR ME IN THE CLASSROOM
Volume 2, Number 1 Fall 2001
MATHEMATICS: Reality Checkup: Learning
requires Effort,
by Jennifer Sawyer and Elsie Newman
One problem that some students encounter in learning mathematics is the
misguided belief that a skill has been mastered without actual written
practice. These students assume that skill mastery is based solely on
the ability to understand solutions, which are modeled during classroom
presentations. Without instructor intervention, these students often
learn of their lack of total mastery after a poor test score. The goal
of the instructor is to circumvent the notion that learning occurs
without actual written skill practice before it results in student
failure
Alan Selby, author of the website http://whyslopes.com, explains that students must be made
to understand four things about learning math:
- Learning takes time and effort.
- Notes and work for doing problems must be written on paper and must
be written precisely. Ideas or work written incorrectly will be a
source of error later – at the time of reading or further
reasoning.
- Use of the electronic calculator for decimal computations does not
provide the exact answers that are needed for derivations of formulas
in algebra and beyond. For true understanding of concepts beyond
arithmetic, students must be able to perform operations with
fractions.
- To completely master a mathematical concept, one must be able to
write calculations precisely and exactly on paper. Errors of notation
create misinterpretations which when read later on lead to
misunderstanding or errors of further reasoning.
Collecting student work frequently to check for correct notation is one
way to identify errors early on. This also encourages students to
engage in written skill practice prior to graded assignments or
tests.
These frequent checks, referred to as "attendance verification,” do not
have to be lengthy: 2 - 4 problems is a convenient length because
completion does not require too much class time and prompt grading is
possible. Grading is not based on "percent correct"; instead it is an
opportunity for students to receive feedback on their individual levels
of understanding, so that errors of precise notation and calculation
can be noted and corrected prior to a test or graded assignment.
Complete attendance for the class session is awarded to all students
who provide written effort.
Remark, October 13, 2007: The phrase referred to as
"attendance verification,”- indicates I wrote and echoed a muse
about the use of start of class work to provide attendance. Let me
explain. Attendance checks takes time in the classroom. So in place
of formally taking attendance at the start of a class, give an opening
set of question in the first few or fifteen minutes and insisting all
students present hand in at least one answer with their name on it serves
the dual purpose of (i) collecting written work for feedback (and grades
too) and (b) providing a record of attendance. In that way, collecting
work frequently may serve as an attendance check. An alternate way
to take attendance quickly is to have a seating chart established by the
teacher or by student habits. Then empty desks correspond to an
absent student. Chart use requires students to go to their places at the
start of class.
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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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