Educational Follies

Appetizers and Lessons for Mathematics and Reason (www.whyslopes.com) \|\|Définition d'une variable \|\| Algèbre \|\| Arithmetique \|\| Logique \|\|La raison basée sur les règles et modelés\|\|
Online Volumes 1, Elements of Reason. 1A. Pattern Based Reason 1B. Math Curriculum Notes 2. Three Skills for Algebra 3. Why Slopes & More Math (Optional Book Orders)	More Site Areas 1. Help Your Child or Teen Learn 2. Solving Linear Equations 3. Fractions Ratios Rates Proportions & Units 4. Euclidean Geometry 5. Analytic Geometry/Functions 6. Number Theory. 7. More Calculus	More Site Areas 8. Complex Numbers 9. Qc Maths Education 10. Secondary IV(?) maths 11. Real Analysis 12. LaTeX2HotEqn: 13. Electric Circuits Etc 14. Français 15. Algebra, Odds & Ends, Etc	More Site Areas 16. Math Education Essays 17. Telling & Working with Time 18. Maps, Plans & Drawings 19. Quantitative Skills for home, shopping and work 20. Statistics Useful, or Not. Test the Twiddla Whiteboard
[Site Entrance & Hub][ Back ] [ Area Entrance & Hub ] [ Next ][Site Exit] Educational Follies

Education Follies

Learning by Discovery Incomplete, Not Enough Time

Educational theories calling for students to discover and master skills and concepts through activities instead of direct instruction lead textbooks be designed and chosen for their incompleteness. Then their readers are left to discover what is not said in critical parts of a subject or its development. That invite confusions, especially when teachers new to a field or appointed at the last minute are two pages ahead of the students in course delivery. Deliberate gaps or deliberate incomplete make learning and teaching difficult

While learning by discovery can lead to deep understanding, learning by discovery when incomplete leads to key skills and ideas being missed.

Post modern education theory holds that comprehension is deeper if it follows from individual discovery instead of direct explanation. However, prior this pedagogy and its introduction of further vagueness, the direct explanation and development of mathematical skills and concepts was incomplete. So this additional deliberate vagueness compounds difficulties with earlier developments of modern mathematics.

Students of present-day science and technology are meeting empirical bodies of knowledge (rules and pattterns) built on the earlier efforts of others. The history or development of these bodies of knowledge need to be mentioned while the rules and patterns are presented, so that students are aware of the origin and limitations of the rules and patterns, the circumstances in which they may apply, and of the needs to check prediction made with these rules and patterns. That being said, an operational command of these rules and patterns has to be taught directly as it is extremely unlikely that a student has the time and ability to discover and verify the rule and patterns in their present refined form by individual construction or discovery.