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) 

Resource Roundup: Math

Math Resources
Here is a roundup of all of my favorite resources for math instruction, practice, games, and exploration. Included are links to the math curriculums that I recommend, my favorite math stories, my go-to resources for practice and games, and more. Enjoy! 

Math Curriculum 

The math curriculum that I most highly recommend is MEP. 
From using several math programs and extensively reviewing many, I have formed the opinion that MEP can be used by nearly everyone and is extremely conducive to a living education. Here are the reasons I love MEP.
1. It is a brilliant blend of the mastery and the spiral approaches to math instruction. It provides mastery based material with a variety of exercises and types of practice.
2. Because of its format it is very versatile. You can skip portions of the books, moving forward at a faster pace. You can go through the material very slowly, not using the entire year and still find opportunity to master new material and build upon previously mastered material from the previous year. You can use only portions of the books or all of them. (Because it is free, you can do this without incurring any cost)
3. It is perfect for a Charlotte Mason education because the lessons can be kept short, the written practice is not extensive, and the material promotes mathematical reasoning.
Other Programs I Recommend:
1.Life of Fred- Mason didn't use math stories to teach math material and I do realize that some would label the Fred stories as twaddle. However, I think they are brilliant and the concepts are explained very well. The written work is very minimal, fitting Mason's heavy lean upon oral work in the younger years. There is also a huge focus on mathematical reasoning, and the stories and questions naturally form relations between math and the rest of life.
2. Khan Academy- I LOVE the videos on Khan Academy, and I think they are a great math supplement or great math lessons themselves. The videos are short, the instruction is straightforward, and the exercises are the perfect length and helpful to understanding.
3. Math Primers- I love out of print math primers from the public domain. I often take a concept from a math primer and build short lessons following the format of introduce, demonstrate, narrate, practice. I also use math primers to help me progress through math concepts in lessons that I form myself, giving me a list and an idea of what concepts are included in a thorough math education.
(There are a few math books linked here, in my Public Domain Roundup Post)
4. Singapore Math- Singapore is a mastery based program that mimics Mason's approach to math concepts by following a concrete-pictorial-abstract progression. However, lessons must be shortened and written work must be decreased. Narration of concepts should also be added, along with math games to encourage mathematical reasoning.
5. Art of Problem Solving by Beast Academy
6. Under the Home- uses Ray's Arithmetic, which are classic Math Primers that build strong computational skills and mental calculation, and include many word problems. You can use grades 1-4 for free on UTH (with more to come), broken down into daily lessons and with a free lesson guide. Or, you can purchase all of Ray's on CD for a great price from  Dollar Homeschool.
7. Purple Math is a free online algebra program that is straightforward and easily adapted. 
      There are other programs that I believe can be adapted to fit into a Charlotte Mason education (such as Teaching Textbooks and Math on the Level). These programs (and any others) need to be adapted to fit into short lesson times, and the repetition of practice needs to be decreased. Math games should also be added.
      There are also programs which I believe have no place in a living education (such as Math U See and Saxon). It is important to understand the principles of a living approach to mathematics, so that you can quickly identify the programs that can be easily adapted to fit those principles, and those that are foundationally different.

       The underlying principles for choosing and adapting a math program are to ensure that lessons are short, written work is purposeful and not repetitious, oral work is prioritized, mathematical reasoning is built, exercises are varied, concepts are narrated, facts and formulas aren't drilled without understanding, and mastery of concepts is built upon.

Math Stories 

My absolute favorite Math Stories are the Charlesbridge Math Adventures .

A few other favorites: 
Anno's Counting Series (These are so fun.)
Bunches and Bunches of Bunnies
Sea Squares
One Grain of Rice
Elinor J. Pinczes series.
David M. Swhartz series. (We LOVE these books and have read them over and over.)

Huge Index of Math Stories for All Ages: 
Living Math Stories Index

Books About Math Itself: 

String, Straightedge and Shadow (for older kids) 
Number Stories of Long Ago (Mason sometimes used this book) 
Growing Patterns
Wild Fibonacci
The Golden Ratio (high school and adults) 

Books About Mathematicians: 
The Librarian Who Measured the Earth
Mathematicians are People Too

Math Practice 
Bedtime Math Series and Bedtime Math Apps (we LOVE Bedtime Math, and use the apps regularly)

Doodling in Math Class Videos 

Greg Tang Math Riddles (these are favorites!) 

Great Estimations

Mission: AdditionSubtraction Action and other books by Loreen Leedy

Hershey's Math Series

The Math Chef

The Painless Math Series (middle school or high school, depending on child) 

Two Plus Two is Not Five and Five Times Five is Not Ten
(I don't recommend using the heavy number of problems in these books, but the tricks are extremely helpful, and a few problems can be completed for practice) 

Math Reference(These books are like Math Encyclopedias, useful for looking up a concept to understand it better or to simply explore Math and its huge impact on our life and world)
How Math Works

Go Figure!

Math GamesGames and Manipulatives from Triumphant Learning (we love ALL of the math products from Triumphant Learning- so affordable, so useful, so user-friendly, so flexible, so fun!)
Two favorites from Triumphant Learning: 
Time to Tell
Place Value Calendar

Let's Play Math

Math Games with a Pack of Cards, from Practical Pages

Family Math and Family Math 2 (Family Math is a staple in our curriculum!) 

Pizza Fractions

Games for Math

For Mom(A few reads for any mom who is wanting to understand Math in general, Mason's approach to it, the teaching of it, and its proper place in our curriculum.) 
Afterthoughts Math Week (blog series)

Living Math Blog

The Math Myth

Arithmetic for Parents

2020 Book Club Book List

Delightfully Feasting Book Club


Book List

Here is the Book List for the 2020 Delightfully Feasting Book Club.
        (if you haven't registered yet, you can register here.)
Happy Book Buying, Friends!

February- March

Educational Philosophy 




Book Club 2020 Registration

Delightfully Feasting Book Club 2020

Join us for a year of reading accessible and beneficial to all readers. Whether you're a novice reader or a seasoned bibliophile, the DF Book Club is for you. Whether you plan to read much in 2020, or you just want to ensure that you read something, the DF Book Club is for you. The book choices, the structure, the's all designed to meet YOUR needs, no matter where you are starting or where you plan to go in your reading life in 2020.

After you have registered, request to join the Book Club Group here


Retreat Registration: Principles, Papers and Planning

Join us for the Principles, Papers and Planning Retreat, held on February 21st from 10 am to 5 pm. The retreat is held in Alvin, Texas. As always, your registration fee covers a full coffee bar, your educational materials and all retreat sessions. Your optional meal package covers your breakfast and your lunch.

See inside the registration form for more info on retreat sessions, or follow along in the Delightfully Feasting Facebook community for details. 

Facebook Event Link is here.

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