 |
OnlineVolumes
1, Elements of Reason.
-with foreword for all volumes
1A. Pattern Based Reason
- striving for objectivity, etc
1B. Math Curriculum
Notes
inductive principles etc
2. Three Skills for
Algebra
- unifying themes + study skills
3. Why
Slopes & More Math - previews & starter lessons for
elementary & advanced calculus.
See Volume 2 and 3 if you are preparing kids for calculus.
More Site Areas
1. Help Your Child or Teen
Learn.
2. Linear Equations
& Fraction Skills - Sec I to V level
3. Fractions Ratios
Rates Proportions Units - Sec I & II
4. Euclidean
Geometry - Sec IV
5. Analytic Geometry -Sec
IV & V
6. Number Theory. Sec V
&VI
7. More Calculus Sec V
& VI
8. Complex Numbers Sec
II to VI
9. Qc Maths Education
10. Secondary IV(?) math
11.Real
Analysis College level
12. LaTeX2HotEqn College level
13. Electric Circuits Etc
Sec IV+
14 Français - Sec III +
15. www.whyslopes.com Entrance
Level Pages:
This Calculus Preview and Chapters 2 to 6 in Volume 3 offer lessons to make the hard easier at the start of calculus, or to provide a context for the study of slopes and factored polynomials before calculus.
Your IP
Address &
how to use it
Three Links for Teachers:
(i) First
Year High School Math - Lesson Plans with Fraction Focus
(ii) Second
Year High School Math - Lesson Plans with an algebra focus
(iii) Algebra Lesson
Plans
Parents: Site Area Helping Your Child or Teen Learn covers 1. Speaking Skills, 2. Reading & Writing, 3. Preparing for Science, 4. Math Work Books, 5.Books for Parents, 6. Mathematics for ages 6 to 14, 7. Having Patience -you'll need it. Chaperone your sons and daughters through jumpMath workbooks for grades 3 to 8 along side site lessons for grades 7 to college and material elsewhere. Parents and teachers need to say no for small things of little consequence to build and maintain authority to say no for larger matters. Parental authority: use it or lose it, but do not abuse it.
Lesson Plans and lessons
Secondary I - fractions
& allied concepts (decimals, percentages)
Secondary II - Algebra (arithmetic versus algebraic methods, backward
use of formulas and proportionality equations)
Secondary III - to come(?)
Secondary IV - Functions to Trig & Statistics
Algebra Lesson Notes & Ideas for All levels
Three Remarks
Previous: Foreword with Inductive Principles for Expert Instruction.
Remark 1, Fall 2005.
In the old view of mathematics education, the instructor may stand in front of the classroom writing explanations and examples on the blackboard, alone or with student help, to develop the skills and concepts, one at a time and one after another. The instructor may also collect written or walk-about the classroom to look at written work in order to correct errors in notation and understanding. The teacher is in charge of skill development and verification.
The newer view is that instructors should make mathematics attractive with activities that are fun to do in which discovery and learning of skills and concepts occurs, without the teacher standing in front of the classroom and saying directly what should be learnt.
The old and new approaches should be combined so that students can learn or discover through activities interesting to them while the instructor states learning objectives clearly and beyond that verifies that the desired skills and concepts have been mastered.
Remark 2, March 26, 2006.
Older education theory calls for course outlines and materials to set forth performance and comprehension objectives - aiming for but not always delivery, performance and understanding in a repeatable and reproducible fashion. Marks were based on performance. Students learn from course material (the theory) and from loss of marks due to the identification of errors in performance.
Modern education theory calls for students to be engaged or hooked by open-ended, course material and investigative, authentic, realistic activities with performance. Drill and practice, mastery of skills and concepts in a repeatable and reproducible manner not emphasized, not demanded, and put aside. The latter de-emphasis appears to be empirically unsound.
Remark 3. Critical Thinking
Site material here at www.whyslopes.com supports the development of critical thinking and problem solving skills, and a discovery approach to learning. Critical thinking requires the ability to follow multi-step with care, see what is available and what works, before extraordinary or out-of-the-box or lateral thinking is required.
Re-inventing the wheel is not efficient, but problem solving situations, real or artificial, in which students have to go the limit or beyond of their present body of knowledge can develop thinking skills. The extreme constructivist view that knowledge is an individual affair, not for correction, lies in contradiction with the growth and development of technical knowledge in science, engineering and mathematics. The latter seek and rely upon methods with repeatable and reproducible results. The methods are learnt by trial and error, guided by existing or extended empirical and theoretical patterns, in which nature in a behaviorist manner may allow us to learn from mistakes - what does not work and what recipes or methods do on a small if not a large scale.
While a teacher can not read the mind of a student, a teacher may see and correct mistakes, minor to major, in the content and style of student writings and further endeavors or products, so that the student may learn from his or her mistakes, and possibly learn how to make fewer mistakes. In the short span of education, several years or more, the student will meet subjects in which individual construction or organization of skills and concepts cannot in the first instance replace the early collective and refined products of many minds.
Instruction is an empirical art with value judgments and decision dependent on the subject at hand and what students produce - observable behaviors or products only. Any else is subjective - not repeatable and reproducible. In particular, the constructivist approach to instruction, despite fine calls for authentic, realistic and engaging material and practices in the classroom, calls that should be heeded and empirically supported as much as possible, in its opposition to the testing and measurement of skills and performance provide vacuous standards for instruction and undermines the sequential nature of learning in which skills and concepts at one level need to be learnt and verified before the next level begins.
Next: Chapter 1, An introduction to the problems of mathematics instruction.
1B, Mathematics Curriculum Notes, Chapters 1 to 12
Chapter 11: Primary School Mathematics
-Inductive principles for course design & delivery require a clear description of where and how skills and concepts may rest on earlier ones, so that difficulties may be explained and remedied by looking for what was missed or forgotten in earlier studies.
Mathematics is a demanding subject. All errors in notation and comprehension need to be identified and corrected. In reading, spelling and writing, students have to learn all the letters in the alphabet, not just some. and memorize spelling. Anything less implies difficulty.
Likewise in mathematics, students have to master key skills and concepts, one at a time and one after another. Anything less implies difficulty.
| for online sessions by chance when I am
online or appointment when I am off. The first session (saying hello) is
free. While talking online, we may scribble on Yahoo, MSN,
Skype or
whiteboards. The twiddla whiteboards has a built-in browser for students,
teachers and tutors in general to import webpages and explore/scribble on
them together. It also has audio in theory. [Session
length depends on supply and demand. Call during off-peak periods
for better service. ] |
|