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Mathematics: An Instrument For Living Teaching
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I purchased this book today and I really enjoyed it. Last year was a great math year but this year has started off for the worse. We started using a curriculum a lot more and I got bogged down in feeling like we needed to do it all. This book was a breath of fresh air for me and caused me to reevaluate our math. Thanks!
I have one question about the scope and sequences – which one is best to follow? I see that one is newer and includes things like weights and measures for younger children. Is this to better align with today’s standards? I was just a little confused. Forgive me if I missed that answer. I’ve only read it through once and looked back through but didn’t see an explanation.
Tara
Hi Tara,
We’re so glad you enjoyed the handbook and hope it will be used to breathe some life into your math lessons.
At the end of the chapter on Arithmetic you will find the Scope and Sequence that goes along with the detailed information found in the chapter. This is the Scope and Sequence I would recommend using if you want to really free yourself from a curriculum that might not be truly CM-friendly, being sure to move at your child’s pace, including lots of hands-on and oral practice and ensuring your child has proven the facts before memorizing the tables, etc.
I included the four different S&S variations for Form I for a variety of reasons. This was the history of the PNEU schools and show exactly what was scheduled for each form. The first programme is taken from the ABC of Arithmetic, the book we are most familiar with from Charlotte’s Vol. I on Home Education. As Charlotte continued to use this book and observed the children, they found some problems with it. Among them was 1)that children formed an ironclad association with the special apparatus used and math facts and 2)children taught in this manner were good at the analysis of a number but couldn’t relate it to problems outside of their Numbers class. The next two S&S were used at the same time and are based on two different textbooks – whichever one a class had. I say based because throughout my research it is clear that the goal in Charlotte’s classes was never merely to “get through” a book and be on to the next. They took their time, worked according to the students’ needs, they skipped whole chapters as well as skipping long and tedious calculations.
The math textbooks seemed to be utilized mainly to provide examples a teacher would give orally to her class. Charlotte seemed to use the best she could find available then structure it according to her methods. When Irene Stephens was a guest lecturer at Ambleside she even commented that ABC of Arithmetic should not be used in the way the authors presented the material but could be handy for examples. It would be difficult for us to use the textbooks Charlotte used today for our examples because they were written in pre-decimalized British currency and so many examples just don’t relate to our children, ie, balancing a “stone” or weighing a “gill.”
Sorry, long story short: the S&S found at the end of the chapter on Arithmetic – the final S&S in the Appendix.
Hope that answers your questions.
Richele
I just looked over the sample for the book. I noticed that there are chapters on Algebra and Geometry and there is also a chart showing CM math across the grades. Does the book address the topic of upper level math for high school age? For example, how to accomplish CM style math and get the credits for Algebra 1, 2, and Geometry, etc.?
@Tara, you’re welcome. Our first son had lost his initial love of math and regained it when I was able to bring the “life” back into it. Our second son has had the hapiness of starting out with CM’s methods in math. He is a completely different type of learner Charlotte’s methods happily work well for them both.
@Mrs. K, this is an interesting question. Though Charlotte’s methods do not “teach to the test” it appears that her programmes of study for high school ensured the requirements were met for college matriculation at the time. We stopped with high school Arithmetic, Algebra and Geometry because that was the course of study until Charlotte’s death in 1923. Trigonometry was later added to the PNEU programmes but whether that was due to the Matriculation Board’s changing requirements or the change in the leadership of PNEU I am not sure.
Anyhow, the handbook lays out how pre-Algebra, Algebra and Geometry were taught in her schools and how much time was given to each. Her approach to Geometry really blew me away and my husband had commented that if he’d been taught that it is really the art of measurement he would have loved it. Credits will have to be determined by you and your child’s goals and interests. Charlotte’s curriculum remained generous and well-balanced.
Joanna gave an indepth forum post regarding math and the goals of college, maybe college and no college.
Let me know if that answered your question.
Best,
Richele
Thank you Richele. That does help. I also read the post you referenced from Joanna. Great post! It actually helped confirm for me a decision I have been trying to make with math for my daughter. So thanks for mentioning her post.
If I remember correctly, CM would have a couple of strands of math going at the same time. For example, they might work on Arithmetic 3 days a week, Euclid’s 1 day, and Algebra 1 day. Is that correct? MEP is like that from what I can tell. You cover Arithmetic, Algebra, Geometry, etc. all woven together throughout the course of study.
Sorry Mrs.K, I have no answer for your strands Q above.
I just want to chime in on this thread and say:
I am 30+ pages into this book and LOVE IT. SO very happy I got it and recommend it fully. What a refreshing encouragement in a subject that has never been my strong point. My children will be thrilled with a new breath in this area.
Thank you Richele and SCM for such a valuable resource.
I got on to post a very similar message. I’m on page 28 and am really enjoying this book. I took a year long math class last year on how to teach math (from a non-textbook approach). This book has really solidified for me what I learned in that class. Thank you!
Thank you @cedargirl and @pollysoup and everyone so much for the good reviews. It’s doubly encouraging coming from women on the forum that I admire and respect.
@Mrs.K, in about 5th grade, Practical Geometry (no proofs) would take the place of the Arithmetic lesson on Friday. In about 9th grade, Algebra would take the place of Wednesday’s Arithmetic lesson. You can see exactly how that looked and how it increased by grade in the appendices in the back of the handbook.
How MEP compares, I’m afraid I can’t answer fully as I’ve never reviewed it. Charlotte insisted upon Mastery and I’ve heard MEP is a spiral program that moves at a quick pace. Charlotte’s lessons were very carefully graduated and her teachers really wanted the students to get into math not just through it. Each year Charlotte’s upper classes would return to rules studied and mastered before for review and more complex problems were then taken. I remember Jeanne, a CM schooler, at A Peaceful Day reviewed MEPS and you can search her blog for a thorough review. I believe a lot of new things are presented in the SCM handbook though that you may want to take into account when looking at any program.
HTH,
Richele
I have read the book and am now going back to analyze it. As I am making notes, I have a few questions.
1. Addition and subtraction tables are mentioned in the early section of arithmetic where the children are exploring the numbers in grade 1. It is mentioned again in the four rules and tables section. Addition and subtraction are not in the grade 1 S&S. Is the intention of the tables in grade 1 to familiarize them with the numbers, but not necessarily memorize the table? Or should they be able to complete an addition table at the end of grade 1?
2. Did I read correctly that grade 1 lessons include 5 min of rapid mental math. Grades 2 & 3 those 5 minutes become work on the addition and multiplication tables? When do you continue to work on mental math problems in grades 2 & 3? During lesson time or an additional 5 min?
I have been confused by constructing the multiplication tables with beans. Would they focus on one number such as 6, lay out rows of six beans and add/skip count them as they say 6×1 is 6, etc? Then work on a different table another day for a different number?
Is the written table demonstrated on page 35 only three rows? Each number would have its own three row table? Once they can complete this table they can fill in a traditional multiplication table (numbers across the top and down the sides and fill in where they meet)?
@cjwagner77 – Great questions and my hope is to be able to respond this evening if someone hasn’t posted before then. -Richele
I’m going to add some more questions. 🙂
1. Is the main difference in grades 2 and 3 that grade 2 is learning the concept and beginning mastery. The goal of grade 3 is to master the tables through more practice? Would the lessons in grade 3 consist mostly of working through problems? And lesson time during grades 2 & 3 consist of working on the rules and tables?
2. Page 19 does not have anything listed on the geometry row for grade 4. Should that be a continuation of outdoor geography or move into practical geometry?
3. On the grade 4 S&S, it lists multiplication by a product and division of one quantity by another. I thought the answer of a multiplication problem was the product. And the definition of division is division of one quantity by another. Are these just another way of listing these concepts?
4. Is there a place that lists the rules to help get multiplication and division sums right? And why would this not be listed until grade 4? To make sure they understand what to do and how to do it and not take a short cut?
Hi cjwagner:
I’ll print your latest questions out and add them to the rest. We don’t have internet at home so I’ll have to ask for your patience as I am unable to fully respond at the moment and am leaving our business – so I’ll try to write the answers out fully tonight and post them as soon as I am able.
Best,
Richele
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