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Mathematics Concept & Skill Development Lecture Series: Webvideo consolidation of site lessons and lesson ideas in preparation. Price to be determined. Bright Students: Top universities want you. While many have high fees: many will lower them, many will provide funds, many have more scholarships than students. Postage is cheap. Apply and ask how much help is available. Caution: some programs are rewarding. Others lead nowhere. After acceptance, it may be easy or not to switch. For students of reason in society, science and technology: Pattern Based Reason describes origins, benefits and limits of rule- and pattern-based thought and actions. Not all is certain. We may strive for objectivity, but not reach it. Postscripts offer a story-telling view of learning: [ A ] [ B ] [ C ] [ D ] to suggest how we share theories and practices. Site's Best LessonsFor Logic
These online chapters may amuse while leading to greater precision and comprehension in reading and
writing at home, in school, at work and in mathematics. For Arithmetic
Deciml Place Value - funny ways to read multidigit decimals forwards and
backwards in groups of 3 or 6, US-CDN, UK-German and Metric SI style. For Algebra
What is
a Variable? - this entertaining oral & geometric view
may be before and besides more formal definitions - is the view mathematically
correct? |
www.whyslopes.com >> The Math Forum and Site Content Next: [Road Safety Questions.] Previous: [Site Reviews.] [1] [2] [3][4] [5] [6] [7] The Math Forum and Site ContentFrom 1995 to the present, the Math Forum Editors in Newsletters and one Hotspot of the month have been tracking my site's content and growth. Newsletters articles - site descriptions - are quoted below, latest first. The descriptions in the Mathforum Newsletters and in other site reviews is not part of the formal peer review process met by articles appearing in mathematics and mathematics education publications. For university hiring and promotion committees, the informal reviews were not authoritative. Yet in the popularization of mathematics, or site content, they may still count. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 20 April, 2012 Vol. 17, No. 16 THE MATH FORUM @ DREXEL INTERNET NEWS Grants, Scholarships, and Awards Summer Workshops for Math Teachers | Whyslopes.Com Updated WHYSLOPES.COM UPDATED www.whyslopes.com/index.php /0400Secondary_Mathematics_-_A_Practical_Approach/ Alan Selby has added a new section to his site, entitled "Secondary Mathematics for Ages 11+, a Practical Approach." "Secondary Mathematics" provides a coherent guide to technical innovations that simplify the learning and teaching of arithmetic and number theory practices, elementary and advanced algebra, elementary and advanced geometry. The new section ends with two calculus previews with a description of a light calculus course, more descriptive than deductive, aimed at introducing the key ideas in differential and integral calculus. The appendix "Calculus with Proofs for the Keen or Gifted" describes how to reform calculus. To better reflect his site's extent and intent, Selby has also re-named his site -- originally called "Appetizers and Lessons for Mathematics and Reason," and now "Logic and Mathematics Skill and Concept Development." -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 23 December, 2011 Vol. 16, No. 51 THE MATH FORUM @ DREXEL INTERNET NEWS Effective Teaching with the Math Forum's Problems of the Week eInstruction Contest Winners | WhySlopes.com Updated WHYSLOPES.COM UPDATEDwww.whyslopes.com/index.php/ 0399Mathematics_Skill_Development_Framework/ Alan Selby recently posted a five phase framework for mathematics skill development at his site. The essay "Which Way to Go" introduces it in plain language:www.whyslopes.com/index.php /0399Mathematics_Skill_Development_Framework /0050Which_Way_To_Go.html
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18 February, 2011 Vol. 16, No. 7
THE MATH FORUM @ DREXEL INTERNET NEWS
NCTM Annual Meeting: Early Registration Discount
Whyslopes.com Revamped | Wolfram Fun Facts
WHYSLOPES.COM REVAMPED
www.whyslopes.com
Alan Selby has overhauled his website of "appetizers and
lessons for mathematics and reason." Look for the math
formulas neatly typeset with LaTeX, Flash videos, and other
rich media supported by his new content management system.
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September 24, 2010 Vol. 15, No. 39
THE MATH FORUM @ DREXEL INTERNET NEWS
Macalester Problem of the Week | Whyslopes.com Updated
Mathematical Creativity and Giftedness
WHYSLOPES.COM UPDATED
Since we last featured the complex numbers section of
Alan Selby's site "Appetizers and Lessons for Mathematics
and Reason" in March this year, he has added a new section,
Mathematics Education Revisited:
www.whyslopes.com/mathematics_education_essays/
Selby has also included a section called POMME: Progressive
Observable Motivated Mathematics Education, which he
describes as "a two-level program for practical
mathematics instruction." Read more about it here:
www.whyslopes.com/#POMME
Postscript: Now in Archives Directory
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March 26, 2010 Vol. 15, No. 13
THE MATH FORUM @ DREXEL INTERNET NEWS
Math Awareness Month
Capturing Teacher Knowledge Study | Complex Numbers
COMPLEX NUMBERS
www.whyslopes.com/complex.html
Since we ... featured the fractions section of Alan Selby's
site "Appetizers and Lessons for Mathematics and Reason" in
January this year, he has revised and expanded the section
on complex numbers, organizing it under these topics:
- Addition and Multiplication [of vectors]
- What Are Complex Numbers?
- Addition and Multiplication Properties
- Second Way to Compute Products
- Consequences of Two Ways to Compute Products
These pages provide a way to introduce complex numbers
before the study of periodic (unit-circle based)
trigonometric functions.
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January 8, 2010 Vol. 15, No. 2
THE MATH FORUM @ DREXEL INTERNET NEWS
Math Forum Online Workshop: Algebraic Reasoning
Math Forum Online PD Courses
2010 Census | Fractions, Ratios, Proportions
May 30 2005 Vol. 10, No. 22
FRACTIONS, RATIOS, PROPORTIONS
www.whyslopes.com/etc/fractions/
Since we last featured Alan Selby's site "Appetizers and
Lessons for Mathematics and Reason" in 2005, he has revised
and greatly expanded the section on fractions and ratios,
organizing it under these topics:
- Fractions
- Fractions with Units (arithmetic and algebra with units)
- Ratios and Fractions (or ratios versus fractions)
- Proportionality Relations Forwards and Backwards
- Links
For all of Selby's pages on high school mathematics and
calculus topics, see:
www.whyslopes.com/
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May 30 2005 Vol. 10, No. 22
THE MATH FORUM @ DREXEL INTERNET NEWS
MathMem | Fractions and Ratios | Math-A-Thon
FRACTIONS AND RATIOS
www.whyslopes.com/etc/fractions/
Alan Selby has added a new section called Fractions and
Ratios to his site "Appetizers and Lessons for Mathematics
and Reason." This new area "offers a thought-based
development of fractions, what they are, how to compare,
add, multiply and divide them."
Selby organized his pages under these topics:
1. What is a Fraction
2. Multiplication I: Unit Fraction of Unit Fraction
3. Multiplication II: Unit Fraction of a Simple Fraction
4. Multiplication III: Simple Fraction of a Simple
Fraction
5. Equivalent Fractions
6. Mixed Numbers
7. Comparison of Fractions
8. Addition and Subtraction I: Case of Like Denominators
9. Addition and Subtraction II: Case of Unlike Denominators
10. Addition and Subtraction III: Efficiency Matters - Use
of LCDs
11. Multiplication IV: Efficient Ways to Multiply Fractions
12. Division of Fractions
13. Two Term Ratios
14. Implied Ratios
15. Multiple Ratios
The earlier site area on solving linear equations visually
reinforces Selby's concept of fractions and arithmetic
operations on them, while geometrically introducing algebra.
www.whyslopes.com/etc/solvingLinearEquations/
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21 February 2005 Vol. 10, No. 8
THE MATH FORUM @ DREXEL INTERNET NEWS
What the US Can Learn from Singapore's Mathematics System
Geometry Module | Solving Linear Equations
SOLVING LINEAR EQUATIONS
www.whyslopes.com/etc/solvingLinearEquations/
Alan Selby has added a new section called Solving Linear
Equations to his site "Appetizers and Lessons for
Mathematics and Reason." The section introduces stick
diagrams as a way to "provide a concrete context for many
of the rules or patterns for solving equations -- a context
that may develop equation solving skills and confidence
informally before the algebraic statement of the rule and
patterns for solving equations."
Selby organized his pages under these topics:
- Letters and Lengths
- Stick Diagrams
- Beyond Sticks
- Almost One
- Binary Systems
- Larger Systems
The earlier online chapter 15, Linear Equations, offers
further information and examples for the development of
algebraic reasoning skills in the solution of linear
equations.
www.whyslopes.com/etc/ThreeSkillsForAlgebra/ch15.html
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13 August 2001 Vol. 6, No. 33
THE MATH FORUM INTERNET NEWS
Complex Numbers and Trig - Alan Selby | NASA CONNECT
Dare to Fly with Class
COMPLEX NUMBERS and TRIG - Alan Selby
www.whyslopes.com/complex.html
In an expansion of "Appetizers and Lessons for Mathematics
and Reason," Alan Selby has added new sections on Complex
Numbers and the Distributive Law for Complex Numbers. They
offer a short way to reach and explain:
- trigonometry
- the Pythagorean theorem
- trig formulas for dot- and cross-products
- the cosine law
- a converse to the Pythagorean Theorem
www.whyslopes.com/freeAccess/distributiveLaw.html
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19 March 2001 Vol. 6, No. 12
THE MATH FORUM INTERNET NEWS
String Figures, Mathematics, Origin - Probert
Appetizers and Lessons for Math and Reason - Selby
2001 Regional Conference - Mid-Atlantic Eisenhower
Consortium @ RBS
APPETIZERS AND LESSONS FOR MATH AND REASON - Alan Selby
www.whyslopes.com/
Alan Selby's 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). Intended for the learning and teaching of
mathematics at the high school and college level, the site
also offers some reflections that support teachers' use of
the materials for their own learning.
Sections include: ...
- Pattern Based Reason (Vol 1A)
www.whyslopes.com/volume1a/index.html
A book in eighteen chapters that describes the origins,
benefits and limits of rule- and pattern-based thought
and processes in daily life, society, science and
mathematics.
- Applet
www.whyslopes.com/freeAccess/applet.html
Shows how to multiply and add complex numbers (vectors
in the plane).
...
- Helping Your Child Learn
www.whyslopes.com/ParentCenter/index.html
Suggestions on how to help children aged 7-16 learn in
school.
A version in French is also available:
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25 November 1996 Vol. 1, No. 8
Alan Selby's Appetizers | Dynamic Algebra | NCTM-L Archive
THE MATH FORUM INTERNET NEWS
www.mathforum.org/
FEATURED INTERNET RESOURCE: ALAN SELBY'S 'MATH APPETIZERS'
www.cam.org/~aselby/lesson.html#math
ALAN SELBY's 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. is 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.
Alan's explanations of mathematical concepts using words
and stories are particularly strong. Don't miss his
Appetizers and Lessons for Logic, also on this site.
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Math Forum June Hot Spot of the Month in
www.mathforum.org/library/hotspots/95.html
Alan Selby's Lessons and Appetizers for Math and Logic
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 Etc. - 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;
VNR Concise Encyclopedia of Mathematics. Also Appetizers
on Other WWW Pages.
www.whyslopes.com >> The Math Forum and Site Content Next: [Road Safety Questions.] Previous: [Site Reviews.] [1] [2] [3][4] [5] [6] [7] |
Road Safety Messages for All: When walking on a road, when is it safer to be on the side allowing one to see oncoming traffic? Site Reviews1996 - Magellan, the McKinley Internet Directory: 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. 2000 - Waterboro Public Library, home schooling section:
CRITICAL THINKING AND LOGIC ... Articles and sections on topics such as
how (and why) to learn mathematics in school; pattern-based reason;
finding a number; solving linear equations; painless theorem proving;
algebra and beyond; and complex numbers, trigonometry, and vectors. Also
section on helping your child learn ... . Lots more!
2001 - Math Forum News Letter 14,
... new sections on Complex Numbers and the Distributive Law
for Complex Numbers offer a short way to reach and explain:
trigonometry, the Pythagorean theorem,trig formulas for dot- and
cross-products, the cosine law,a converse to the Pythagorean Theorem
2002 - NSDL Scout Report for Mathematics, Engineering, Technology -- Volume 1, Number 8
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, it is somewhat poorly organized. This does not take
away from the quality of the information, though.
2005 - The NSDL Scout Report for Mathematics Engineering and Technology -- Volume 4, Number 4
... section Solving Linear Equations ... 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. ...
For Geometry
Maps + Plans Use - Measurement use maps, plans and diagrams drawn
to scale. For Calculus
Why study slopes - this fall 1983 calculus appetizer shone in many
classes at the start of calculus. It could also be given after the intro of slopes
to introduce function maxima and minima at the ends of closed intervals. |