|
YOU are better than YOU think. Show yourself how:
|
-/[]\- Logic chapters 1 to 5 re- appear not in sequence, as is or longer, in Volume 1A, Pattern Based Reason, Bon Appetite. Logic
Mastery 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;
|
-/[]\- 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. |
Remark 1, Fall 2005. Direct and Indirect Instruction Combined: 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 (engaging for) 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. Empirical Flaw in Indirect Instruction (Constructivism) 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 - A Call in Constructivism that ain't clearly supported. 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. |
www.whyslopes.com
|
|
[Top of this Page][
|