Popcorn & Peanuts

Seashell Math

Original date - January 28, 1999

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This began as email discussing how to teach math, so for now I will simply paste in the messages. Later I will attempt to organize it a bit better. I will also list the books being referred to.

  • A Charlotte Mason Education by Catherine Levison. Subject by subject, how to implement the CM method. No "Twaddle" here - just quick information on HOW to do it! Many people like this one as a guide to changing their education one area at a time. Pages 46 - 49 cover how to teach math.

  • The Original Home Education Series by Charlotte Mason.
    6 fat volumes forming a reference library on teaching and parenting. Try Volume 1, Part V, chapters 4-15 for Math, and volume 6 for Reason.

  • "The Charlotte Mason Study Guide" by Penny Gardner
    A topical guide through the Series, organizing selected quotes and readings. Extremely helpful! Chapter 14 studies Math.

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    << She is having difficulty getting her daughter to memorize her multiplication tables. What is the CM method for learning multiplication >>

    We use calculadder everyday. These are timed sheets which I have laminated and take only 5-10 minutes. Eventually they learn they're way through addition, subtraction, multiplication and division. You can get the next set which goes into fractions, decimals et.

    If there is an official CM method, I would like to hear it.
    Sherie

    Hi Sherrie,

    Would you believe you are on-topic here? This is sort of a regular question.

    Series
    Volume 1, pages 263-264 on preparation
    Volume 2 page 230- "prized for the record of intellectual habits'
    Volume 3 pages 174, 234, 236 - as curriculum, but without details
    Volume 6 pages 152- 153, 230- 233 essential, purpose
    Notice - this is in the section on the Way of the Reason

    Catherine Levison's "A Charlotte Mason Education" contains sample schedules including math, and has a short Math discussion including a quote about the multiplication tables from an original 'Parent's Review', "no child should use a multiplication table until he has made one". I would consider this chapter (page 46-49) essential reading on Math.

    My son made his multiplication table using seashells on our living room floor, and did not understand them until he had made them. It took him about a week to do so, though he could already write and recite the tables without comprehension.

    Karen Andreola uses "Number" as one of the examples for her Three Period Lesson, in Chapter 20 of the Charlotte Mason Companion. This is really a Montessori concept, but is still useful.

    From my CM High School page-
    Charlotte thought 'much' math study was unnecessary. She stressed not allowing the child to focus on dry facts. Math was to be taught with a discussion, manipulatives, and a few written problems done correctly. Arithmetic for older students might include bookkeeping, checkbook balancing, and other real-life uses. Geometry would be taught by application of principles, as would algebra, but she would expect use of formal proofs. Manipulatives (models, drafting exercises) would be required. There would be two periods of each type of math per week, taught as separate subjects to stimulate the mind.

    Now, that was high school. There is no single CM math text, because there are so many needs - but I'll talk about the various ways to teach math the CM way.

    I'll start with Calculadders, because we did the whole set, K-8 plus ReadyWriter and AlphaBetter. Do you get the idea I liked them? We did try other books, but always came back to these. However, they were only the worksheet part of our math! Calculadders do not teach you HOW to teach math, they are a tool. In addition to the sheets, we used manipulatives (legos, blocks, pencil bundles, our huge seashell collection), computer games, song tapes, Wrap-Ups. For each sheet I would use the first line to teach the principle, using whatever manipulative seemed appropriate. We worked the next line together, he worked the third alone showing me each step, then he finished alone. Tomorrow he would begin the timed practices in the way intended, with the timer and the chart. My son loved seeing his score improve, and rarely needed more than 3 or 4 tries to master a page. We did not do sheets every day, so we progressed at about the rate expected.

    MMM is Cornerstone's program, and it is very CM - a few problems, lots of manipulatives and practice. The special points to consider here are that it is a scripted program, and that it was only through 8th grade. They are publishing higher levels now, I believe algebra is available and they are working on Geometry. The texts are black & white, with reproducible pages. Scripted means every word is right there in the manual - you read it to the child. If your own background is weak, this can be essential! This is the program Cindy uses and loves, and this is the program I recently recommended to a friend with a colorblind child.

    At this point I am going to mention Saxon, which no one asked about. Saxon in the new K-3 levels seems very CM, with lots of manipulatives. I haven't tried it, so I'm not sure. From 54 on up Saxon is a program with lots of repetition, a few new problems of a new type in each lesson followed by lots of review. It is a very visual, abstract way of studying math. It is possible to skip volumes 76 and/or 87 completely and go directly into Algebra 1/2.
    (My daughter did Saxon 1/2 in 7th grade and onward, and did very well because she is a very abstract thinker. We tried my son in Saxon several times, and he never did well - he is a kinesthetic learner, and was greatly frustrated by reviewing concepts he already knew. We returned to Calculadders.)
    Geometry is included in the algebra and Advanced Math volumes, instead of being a separate course, and formal proofs are not greatly used. If your child is going on to a technical college field you may want to use a separate Geometry book with formal proofs.

    The reason for all that is to help describe MUS. Steve Demme was a Saxon teacher with a problem - one of his homeschooled sons is a Downs, who needed manipulatives. Demme took Saxon and using the same basic outline teaches all concepts with colorful manipulatives, visual overlays, and a video. MUS goes all the way through High School (the only manipulative program that does so). The advanced math and Geometry does include using formal proofs.

    I have mentioned before that Dr. Jay Wile, author of the excellent Apologia high school science texts, previously recommended either Saxon or MUS, but no other math program as being thorough enough for college-bound students. I am told he now prefers an algebra video program titled "VideoText Algebra", but I have not seen it.

    I have also had Mortenson's Moving With Math described to me as being excellent and very CM (I think Donna-Jean uses it) but I have not seen it myself.

    Now back to the Way of the Reason. Did you see my note of where the most useful math comments are found? Smack in the middle of the High School chapter on Reason! (Book 1, chapter IX) The next section is in chapter X, on curriculum, but instead of how-to's we get pithy comments such as, "In a word our point is that Mathematics are to be studied for their own sake and not as they make for general intelligence and grasp of mind. But then how profoundly worthy are these subjects of study for their own sake, to say nothing of other great branches of knowledge to which they are ancillary! Lack of proportion should be our bete noire in drawing up a curriculum, remembering that the mathematician who knows little of the history of his own country or that of any other, is sparsely educated at best." p 232
    and
    "Mathematics depend upon the teacher rather than upon the textbook and few subjects are worse taught ; chiefly because teachers have seldom time to give the inspiring ideas ... which should quicken imagination." p 233

    Mathematics belongs to the discussion of Reason because mathematics is a language of symbolic Logic. The Logic games we were discussing are math games. The games provide something essential to a true understanding of math, they provide an application. My son could not understand the multiplication tables until he applied them to something he could touch. When we added the shells, the computer games, the Wrap-Ups - then his math applications became real in a way that no drill sheet could.

    Math also belongs to Reason because Math is without morals, without a knowledge of right or wrong. Calculating a geometric trajectory does not involve whether you are calculating the orbit for a manned rocket or for a bomb. The math is the same. Thus, CM gives us instruction on how and why we need to include applications and History with our abstract studies.

    Lynn H

    Second email post, continuing the discussion...

    I'm not being able to visualize the seashells. Could you explain - draw me a picture or something?Thanks,
    Dia

    > My son made his multiplication table using seashells on our living room
    > floor, and did not understand them until he had made them. It took him
    > about a week to do so, though he could already write and recite the
    tables without comprehension.

    Seashells? Calcium carbonate exoskeletons of assorted marine life forms... clams, snails, bivalves, univalves, starfish, Angelwing, a few chunks of coral... all possible sizes and colors from cowry to conch? Ours have been rubbed with mineral oil to bring out the colors and preserve them.

    OK, no snowballs, please! I think I understand! You want to know how my son made his table using shells, right?

    This has everything to do with Mama catching on, not the boy. When my son was small we did a lot of oral math, in the car as we drove to our very multiple activities. Somewhere around the middle of third grade he could recite the tables through the 13's perfectly. (Our goal here was the 25's by 6th grade.) I decided it was time for a little pencil work before we went on to simple division, so I pulled out the Calculadder sheets and did a brief instruction on the symbols. That was where things got rough - because my son had no idea what to do. 2x2=? He had no clue that those digets had anything to do with the tables. It didn't take much investigation to discover he also had no clue what the tables meant - they were simply something he could recite. OUCH!

    So, we did Calculadders every day, often painfully slowly. After about a year (it seemed like) he could write the pages in the time required. Some of them gave him constant trouble, and it was clear they still didn't mean anything!

    That was when this Mama caught on. He was playing on the living room rug, and I was in the study looking for something when my eyes fell on one of the tubs of shells on my science shelf. I picked up the tub, marched into the living room, and dumped the whole thing recklessly on the floor beside him. I asked him to give me 6x8 shells (one of his tough problems). He looked at me as though I had lost it completely, but began to count out 48 shells. I stopped him and said I had asked for 6x8, and what I meant was I wanted 6 piles of 8 shells. Another "strange Mama" look, and then he complied. I asked him how many shells were there - he didn't know. What is 6x8? 48. How many shells do you have there? Duh..., so I let him count them out. He was really surprised there were 48!

    Then I pushed the extra shells aside and asked him to count me out 8x6. He said he would need more shells - I told him to try it and see how far he got. He was truly surprised when he had enough! I asked how many were there, and you could SEE the light begin to come on! He counted them to be sure! That afternoon he worked through the 6's and 8's, by the end of the week he had worked completely through the 13s. We had rows of piles of shells - 5,5,5,5.. then 6,6,6,6.. and so on. We skip-counted by groups - 5, 10, 15, 20, and then counted a few to be sure we had the right totals. We could count across 6 rows and down 8, then add up all the shells in the two rows where they met and SEE that they were equal!

    It made a lot of rows of shells, but we have a big room and a big rug and a LOT of shells. At the end of a very fun week he knew the tables, knew the numbers and exactly what they meant! (He was also pretty good at identifying shells!)

    Now, I am sure that we did this in a very confused order. Catherine Levison's math section with the information from the 1893 Parent's Review would have been a lot of help! This section describes a several month process, including oral math, counters or beans, and working out the tables in sections. I am sure they mean the production of a handwritten table like the one I made in 7th grade. We did use all the sections and activities with my son, but I was dense and didn't do the manipulatives until the end. Dumb me! I knew my son was a kinesthetic learner, but because he recited so well I took a while to realize he didn't know what he was saying! He could "Reason", that is he could follow in order, but it had no meaning, no application.

    After the shells week I had him do a couple more Calculadders, just to be sure. He zoomed through them.

    finis
    We did Calculadders all the way through their 8th level, including their "ReadyWriter" penmanship program (lots of fun) in the beginning, and the "Alphabetter" reference program in 7th. At several points I tried other texts such as Saxon 65, but he had trouble with their abstract thinking. We also used many other resources as enrichment and as the manipulative part of our program: "WrapUps!, several felt math games, computer games and drills, skip counting and multiplication table tapes, blocks, paper clips, graph paper, money, activity books, dot-to-dots, and some children's math videos. Whatever fitted, we did it. When we finished the 8th level in the Fall of his 8th grade year, I put him into the Saxon 76 (which I already had) to keep him busy while we decided on what to do for Algebra. He had no trouble at all with this Saxon book, except for disliking the mixed problem sets.

    It has since been suggested that part of his problem with textbook programs may have been having to copy out the problem sets. Worksheet programs, including Calculadders, and computerized drill programs provide the assignments without the child having to copy by hand. This can bypass certain dyslexic language disorders affecting writing, and physical disabilities. Some computerized math programs can be done with speech recognition software, if this is your child's difficulty.

    You DO need to choose the program to suit the child. This boy's older sister was very much an abstract thinker who enjoyed the Saxon books. She was often able to pick up a concept and skip several problem sets at a time. She was also good at the Logic games and "Critical Thinking Skills" books we tried.

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