As everyone considers curricula for next year - I have been thinking about math. I revisited MEP which is a great FREE program. For now I think we will finish up miquon and then supplement with MEP. My youngest might just start with MEP. I have also been thinking about the "bigger picture" of math and making sure my kiddos are equipped for it. Through a chain of events I was reading Sage Parnassus' blog and looking at her speakers for the upcoming conference (now there is a bunch worth being around as mentors). One of the biographies mentioned Mary Everest Boole as a contemporary of CM's who discussed math and science. This caught my eye. So, I have been reading her works (through google books) for the past few days.
First, Mary Everest Boole is the niece of the man that Mt. Everest is named after - he mathematical determined its height. She was also married to a mathematician and his work became the basis of "the modern digital computer" (according to wikipedia). He was her tutor before they were married. She taught in many schools around England and one of the books below includes a lecture that she gave to the PNEU on developing the scientific mind. She was a lady before her time.
I have skimmed and read parts of three of her books.
Lectures on the Logic of Arithmetic - This is a volume of short lesson to supplement any math course. Her notes to teachers caution us to think about the way we introduce concepts like negative, zero and infinity. Each chapter is basically a story and lesson plan together to help students understand a basic math concept. She does use shillings and pounds - so you'd have to translate the concept. Many of the lessons apply to studies in general and are good way to think about how children should be responsible for their own learning.
One of the key distinction she makes is that students need to be aware of what they really "know" in math (can explain) and what they have been "told" to believe. She encourages students to keep a math notebook to write down what they really know - formulas, times tables, etc. She believes that students should use these self made reference books as they work.
Philosophy and Fun in Algebra - The title itself is quite an undertaking! This is written to older students, but could easily be used by teachers, to consider some of the underpinnings of algebra. The chapters are short and cover a variety of subjects and methods - math history, logic, role of the teacher, using sewing cards to teach math, literature, the Bible. Her application of Bible stories might be a little heretical - but if an older child is reading it there is opportunity for discussion about it.
The Preparation of the Child for Science - This is the book that really got me going. In it she reminds us that the study of biology is the study of life and if we study dead things we are studying necrology! She has some strong opinions about keeping wonder in science. She does make a short argument for Latin as a great basis for later science. She also argues for allowing students to play around (under supervision) with carpentry because it is a great experiment in mathematical and scientific principles. She advocates letting kids make bows and arrows to learn more about forces, parabolas, etc. Basically, she is against stuffing kids full of science factoids for repetition and encourages them to go out and experiment for themselves with water, magnets, static electricity and the like so that they have some notion of what these concepts are. She is looking to develop men who question and think about what they observe - what real scientists do.
Some of her most interesting comments surround Euclid. She emphasizes that Euclid was meant for grown ups who were very familiar with geometric shapes. Basically, it provided the logical explanation for what they already knew "poetically" about geometry. She cautions against starting Euclid with students until they have played with geometric shapes for themselves - a lot!
In some ways, her approach made me think of some of the sensorial exercises in Montessori that are designed to give students a sense of shape, size, weight, texture, etc. In fact, geometric solids are one of the works Montessori provides.
I have only read the first half of this book (philosophy) and will make comments on the second half (practice) once I have gone through it. The second chapter of this book was an address to the PNEU.
Mrs. Boole's approach to science and math is refreshing, story based and encouraging. They are not difficult reads and they are short. They have helped me remember that science and math have to do with wonder and trying to explain real world phenomenon - not just about facts and memorization. If you have a chance to look at them I'd love to hear what you think.