Math, MEP, Charlotte Mason, and Mastery

Sylvia posted some great food for though on her blog Homeschooling in a Bilingual Home with Mastery versus Spiral.  She discussed one educator's call for math mastery and yet wondered about MEP's spiral design.  These were my thoughts on the subject:

Interesting post, Sylvia. I suggest that given the definitions as presented, MEP is a program of mastery yet is not a Mastery Program.

Reading Liping Ma's book will help people understand what I mean. Ma makes the case, IMHO, that US teachers teach mastery of an algorithm, or the mechanics of doing problems without mastery of the mathematical concepts, while teachers in Asia have a better understanding of mathematical concepts and teach them to their students. IMHO, this was achieved by mastering concepts on a low level (1 or 2 digit numbers, using 10s, etc.) before advancing kids to greater complexity, like multiplying 37946 x 897.

My oldest is in Y4 of MEP; we switched from Math U See last year. He has not done any large or complex multiplications. He continues to master the regrouping and distributive property, though he does not call them that, by breaking larger numbers into smaller numbers and then multiplying or dividing those. He learned division through place value and no longer gets confused by "bringing down the next number." He can multiply and divide large numbers because he figured it out based on his mastery of small numbers. That is the genius of MEP.

Compare this to Math U See. By the end of Gamma my son was multiplying these large numbers because he learned mechanically how to do it, but he didn't really understand what he was doing or why. Englemann calls that Mastery. I call that Mastery of the Algorithms, while I call MEP Mastery of the Concepts. This difference is why Liping Ma got the results she did.

MEP is a true spiral program because it does not put forth a concept to cover until mastery and then move on to the next concept. But there are, what shall I call them, pseudo-spiral programs that are basically mastery programs in that they move from topic-to-topic only do so in shorter bursts. In fact, I think what we call spiral programs are really these mini-mastery programs, and are like Englemann's floating stairs. I can see why Miss Mason did not care for them. MEP then is something different entirely.

Sylvia followed up with Mastery versus Spiral (Part II)

This got me thinking not only about MEP but about education in general.  Regarding MEP:

My first comment is regarding whether MEP is a spiral program or a mastery program. My answer is: both! I currently have children in Y1, Y3, and Y4; the older two have each completed the entire previous year. What MEP does is it introduce a big subject, like multiplication and division (started together) at its simplest level, 1 digit numbers. Once that is shown and kids are doing it, MEP then presents a wide variety of different types of math concepts to which multiplication and division is used--tables, graphs, word problems, etc. In doing so, the program also slowly advances the difficulty of the multiplication and division, but never beyond small, easy-to-grasp problems.

I blogged about this here.

By this construct, MEP is teaching mastery of multiplication and division--from early in Y3 to where we are so far in year 4. It did the same thing with addition and subtraction in Y1 through the early part of Y2. Yet MEP has a spiral construct in all the other concepts to which basic arithmetic is applied. Geometry, measurement, and fractions are all scattered throughout Y2 through Y4 (in fact during the same weeks in Y3 and Y4 as I am learning with my two older sons!)

How this will work with fractions I am unsure. I know Ds#1 is ready to learn more about fractions than he does, yet because we switched to MEP later in his school years, he is only on Y4 though in 5th grade while the younger two are in MEP years that match their grades (Ds#2 being about a half year "behind" in that sense.)

I am not one to worry about keeping up with the public school kids (more about that in a subsequent post about Englemann.) I think it will be revealing as to the real strength of MEP as we do learn more about fractions, decimals, and percentages.

More important for me was the implications Englemann's approach would have on education in general, and comparing his thought to Charlotte Mason:

Again, I can't disagree with him in terms of mastery programs compared to spiral programs, but I disagree with him on the bigger picture.

For example, he states when a child does not learn, that reflects badly on a teacher. Yes, but then, in his Sweden example, he basically is saying, "If you just teach it like this then they will understand." Well, maybe not, and that's the point. A teacher has to know a topic well enough to explain it in a variety of ways to reach a variety of students. I think that is what US parents mean by having a teacher care about their children, while Englemann advocates a master teacher.

Yet central to Charlotte Mason's homeschool philosophy is that education is the science of relations. Every child must form a relationship with some knowledge in order to learn it. Compare that with cramming for a test, or even memorizing a method. Englemann's "mastery of the method" is his definition of learning.

He is right, though, especially in math, that by knowing these methods hard and fast a child will do better in school--but that's because school assessments are designed to reward those who do! And that is why, according to Marilyn Burns, vast numbers of people have Math Phobia. For some people memorizing the algorithm simply does not work, and Englemann's answer seems to be, "Well, they just didn't master it."

This leads to the phenomenon of what I very irreverently call Stupid Human Tricks. This type of mastery creates intelligent-appearing children because they can perform all the wonderful 4 and 5 digit multiplications and divisions, spit back science and history facts, and diagram sentences with ease. They even get rewarded on tests for doing so. Yet they do not forge any relationship with the material, and so they will retain but a fraction of what they so brilliantly regurgitate. Ultimately, is that really education? Do they understand mathematical concepts? (Most do not.) Can they discuss the impact of historical events? (Most cannot.) Can they write well? (Not generally.)

Yet the science of relations should not be an excuse to avoid challenging our children, as if our child's enjoyment is the sole indicator of them forming relations. On the one hand, Miss Mason states that we should not interfere with a child's narration for they will glean what is important to them on their own terms (which is why choosing content reflecting my values is the first priority in selecting books and media.) On the other hand, she wrote the facts of a passage, say from a history text, on the board to which the children could refer while narrating. I guess there's no getting over mastering those facts, yet that should be the servant of forging a greater understanding of knowledge and not its master. In short, teach our children to think and not just to know.

Flowchart Notes

I can across this link on another list and it looked like a really neat idea for narration especially if your kids like to draw. It is simply a flowchart where you draw a picture and then write what happened below it, and when put it all together you get a story.

It is more in depth than a single picture narration and yet not as extensive as a lapbook. The idea came from this page at mrcoley.com, the web site of a fifth grade teacher. He also has a pdf available describing it. My kids' pictures won't be as nice as these but I think they will enjoy the process and improve their note-taking skills.

Response to "Unit Studies and Charlotte Mason"

Jimmie's Collage has a blog entry in the current Charlotte Mason blog carnival encouraging a discussion about Miss Mason's opinion about unit studies. Here is the quote Jimmie refers to:

"The well-intentioned, clever, hard-working teachers who create these concentrated studies have no idea that each lesson is an offense to young minds. Children are eager and capable of a wide range of knowledge and literary expression. But these kinds of lessons reduce their learning to senseless trivia and insipid, pointless drivel. They develop apathy that stays with them, and the mere mention of learning makes them anticipate boredom. Thus their minds wilt and deteriorate long before their school career ends."

Let me first define "unit studies" as the integration of multiple school subjects, such as literature, history, math, and science, based on a single unifying theme. Entire curricula are designed in this manner, the most well-known being the excellent program, KONOS. Yet even KONOS has parents supply their own separate grammar and math programs, and the science portion is weak in several units.

It is one thing to integrate topics that naturally flow together, for example drawing from your literature to create copywork, or reading historical fiction and period literature along with your history studies, or assigning writing topics based on your subject of study. Trying to make other subjects integrate, however, is like putting square pegs into round holes, and those other subjects suffer because of it.

Math and science are two subjects likely to be short-changed; this is because these are rarely the central theme of a study. Activities that integrate these subjects usually are contrived as Miss Mason observed. Creating word problems based on historical subjects does nothing to increase a child's mastery of mathematics. Science involves reading biographies or science history rather than learning scientific principles.

Today I see a different notion of "unit studies" in homeschooling circles, something that is more properly called "thematic units." We are studying Westward Expansion this year, so I have collected a variety of resources--books, movies, games, web links, lesson plans--relating to this theme. I do not try to integrate grammar, math, science, art, or any other subject into this theme. I do, however, provide a variety of approaches, including hands-0n activities, for kids to learn from, though our homeschool is child-driven in this narrow area. I give the kids an activity book and they pick out the project they want to do, or something else of their choosing, so they make their own connections rather than me giving them mine.

This goes back to my own philosophy about phantom "holes" I used to worry so much about. We are learning about vast subjects, like history and science, of which we could never master all there is to learn. The notion of "core knowledge" is an illusion when we consider all that we leave out of curriculum standards. And when we forget more than we learn of trivial facts, then what our children retain through the relationships they form with a topic is as worthy as what anyone else has formed. Our task as teachers is to provide the framework that reflects our world view and the resources that instill our moral values; our children will then forge their own knowledge relationships.

This reminds me of a G. K. Chesterton quote (who married a woman that worked for the P.N.E.U. by the way) that is at the bottom of my left sidebar:

"The present collapse of this country began when education was regarded as a substitute for culture, or rather when instruction was regarded as a substitute for education, or rather when getting facts by teaching was regarded as a substitute for getting truth by tradition."

That is where KONOS has it right--by centering their themes around Christian virtues. In that sense, our entire homeschool is one continuous unit study centered on the Truth of Jesus Christ.

My Charlotte Mason

I certainly consider myself a Charlotte Mason homeschooler, though I am just as certain that I do not exactly follow her methods. It appears this is not uncommon among CMers.

What I have embraced fundamentally, as the title of this blog reflects, is that "education is the science of relations." Those relations are lifelong pursuits when education is an atmosphere, a discipline, and a life. They are best formed through living books and materials. The rest is an eclectic mix of educational material to achieve these goals.

While Ambleside Online and Mater Amabilis are outstanding programs, I wanted to combine my children in several subjects, so the separate yearly schedules made that very difficult. I refer to and recommend them frequently. I also view books like This Country of Ours and Apologia Science as textbooks compared to the many other books available about specific aspects of history and science.

Having said that, our school is not void of all curricula; instead we have an eclectic mix of living educational material that best works for our family. Here is an overview of My Charlotte Mason educational program:

Religious Education: I spend one day a week for each child teaching Faith and Life using the teacher's manual after they have done the reading in the student book. Other days they are reading the Bible and the Saints.

Math: we all love M.E.P. I set aside 40 minutes per child to teach it 3 days a week. We do various living math 2 days a week.

Language Arts: Each child works independently. Ds#1 is on year 2 of 3 in Intermediate Language Lessons, while Ds#2 is on year 2 of 2 in Primary Language Lessons. These books have a wonderful mix of grammar, picture study, dictation, and copywork. Ds#3 needs to solidify his reading, so I will continue Hooked on Phonics with him (a program I've had for 7 years now.) He'll also be doing copywork.

Literature: Ds#1 and Ds#2 read independently while I read aloud to Ds#3; art study they read and view independently. They work on Rosetta Stone Italian separately. I may try and fit in some basic Latin, too, though I am not sure if I will do this with Ds#1 only or all 3.

Everything else I combine, starting with the Program for Achieving Character Education (P.A.C.E.) I get poetry and copywork from it; the stories from William Bennett's The Book of Virtues and The Moral Compass we read aloud together.

Shakepeare and tales we read together, and we do art projects together. I even do Writing together, though each are of course working on their own pieces.

U.S. History, World History, Science, and Nature I approach in a similar way using the CONNECT method as described in the Connecting With History program. I introduce and discuss whatever topic we are covering to all of them. Each week we have short readings from our "spine" and work on timelines, cultures, famous people, and experiments together. Beyond that I give them individual books to read (or to have read to them) at their own levels, and they narrate (written or oral) what they have read. They also each pick projects to work on throughout the weeks; these are presented at the end of each topic. Everything gets put into notebooks or lapbooks.

We start at 8 am and finish by noon, with additional time in the afternoon for them to work on their projects. It is not what Charlotte Mason described, with children reading all morning, their attention kept by the wonderful books and that they may be called upon to narrate; and then long afternoons outdoors for masterly inactivity and nature study. Yet through My Charlotte Mason I am striving to meet that fundamental principle: Education is the Science of Relations.