Math: A Mountainous Land

                                     Principles of Math Instruction 

     Math instruction is one area in which I consistently see moms struggle to know if they are applying Mason's principles "properly", worry if they've made a good choice of curriculum, and fear for the future. However, I believe that math instruction is one of the areas of a CM curriculum that has the most freedom and should cause the least stress. I wrote here about my recommendations for math curriculum, and I truly believe that a mother should feel free in her choice of math curriculum (avoiding only those which are entirely formulaic or contrived in nature), and should focus more upon applying general principles and practices of math instruction to the work at hand than she should upon finding the elusive "perfect" math curriculum. 

     The ideal instruction for mathematics in a living education could be summed up as that which is logical, clear, promotes mathematical reasoning, proceeds at a pace reasonable for the child, includes written work that is intentional and meaningful, prioritizes oral work, includes games, approaches each concept from a variety of angles, and is straightforward. Mason called math a "mountainous land", giving us the idea of a worthy struggle. The mountain of math is a vigorous, and challenging climb but it is one that should be invigorating and rewarding. 

     We can provide this type of mathematical effort and reward by keeping in mind the following principles and practices that Mason lays before us for math instruction: 
1. Keep Motives in Mind:
Reasoning Powers, Insight, Readiness, Accuracy, Intellectual Truthfulness, Observation, Attention to Detail, Judgment, Neatness, Beholding the Beauty of Absolute Truth (v1 pg 254/ v6 pg 230)
2. Math Lessons are Dependent Upon the Teacher, not the Textbook (v1 pg 254/ v6 pg 233)
3. Rules Must be Contextual (v1 pg 254)
4. Choose Problems Intentionally- as opposed to random pages of problems (v1 254-255, v6 pg 231)
5. Use Word Problems Liberally (v1 pg 255)
6. Demonstrate Everything (v1 pg 255)
7. Prove Every Rationale {Don't Allow Work on Anything that Isn't Understood} (v1 pg 255)
8. Use Natural Manipulatives, Never Contrived or "Special" (v1 pg 256)
9. Do Manipulative and Oral Work Before Written Work (v1 pg 256)
10. Follow the Progression of Concrete, Pictorial, Abstract (v1 pg 256)
11. Introduce, Demonstrate, Narrate, Practice (v1 pg 258)
12. Work Gradually (v1 pg 257-258)
13. Make Principles Clear (v1 pg 259)
14. Use Tools (weights, scales, rulers, etc) (v1 pg 260)
15. Let Child Build Own Tables and Charts and Use Own Judgement (v1 pg 260)
16. Don't Correct Wrongs (v1 pg 261)
17. Excite Enthusiasm of Concentrated Attention (v1 pg 261/ v6 pg 233)
18. Base all Instruction on the "Evidence of Sense" (v1 pg 261)
19. Promote Mathematical Reasoning (v1 pg 262)
20. Don't "make the illustration occupy a more prominent place than the thing illustrated"
(v1 pg 262)
21. Don't Over-Prepare a Math Lesson (v1 pg 264)
22. Don't Over-Teach, but Instead Trust the Affinity and Capacity of the Child (v1264)
23. Don't Give Math More Prominence than Everything Else (v6  pg 231)

For Your Research
Mason discusses mathematical instruction primarily in the following locations:
Volume 1: Home Education pgs 253-264
Volume 6: Towards a Philosophy of Education
pgs 110-112, 151-152, 230-231
(Keep in mind the idealism present in Volume 1, and apply these principles in freedom, not in perfectionism or legalism) 

A Program of Math 
Updated for Today from the PNEU 
(This is a basic program of mathematics that I have taken from various programmes and updated for today's student) 

Form 1- 
Oral and Manipulative Arithmetic
Math Stories
Math Games/ Puzzles

Form 2- 
Oral, Manipulative, Written Arithmetic
Practical Geometry
Math Games/Puzzles
Math Stories (if desired) 

Form 3-
Oral and Written Arithmetic
Pre-Algebra (if ready) 

Form 4- 
Written Arithmetic
Oral Drills
Algebra (if ready) 

Form 5-6
Consumer Math
Advanced Math (if needed and desired) 

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