Are We Using Incoherant Math Texts?
Maria Miller at Homeschool Math Blog writes:
The materials we've chosen for math in our home, Making Math Meaningful by David Quine, followed by Elementary Algebra and Geometry by Harold Jacobs, measure up to the ideas in the article in some ways. David Quine's materials for grades K-6 cover fewer topics than most US math texts I've seen. Spiraling is used, if I'm understanding the term correctly (a curriculum writer I am not!), but review is at a minimum.
Beginning algebra in jr. high, rather than spending 7th and 8th grade reviewing arithmetic further, is possible with Quine's texts as long as each level is completed in one year. I found this difficult to do until I realized that our children didn't need all the practice provided in each module. Our younger students are progressing through the books at a faster speed than our olders did.
Harold Jacobs's algebra and geometry books are focused and logical, imho. Each chapter builds on the previous work, rather than including much tedious review. I've never understood algebra and geometry as well as I do after teaching through these books. :) The beauty and mystery of mathematics is presented, as well, in the introduction/discussion of concepts (every lesson begins with a worthwhile attention-getter) and in Set IV problems, which are for extra work and are usually puzzles or brain-teasers.
On the other hand, I have not yet been successful in keeping our students on an advanced track for math courses. Our two oldest began algebra during jr. high years, but didn't finish until 10th or 11th grade. Our third daughter began algebra as a 9th grader. Our fourth daughter, now in 7th, may be able to begin during 8th grade. This is one way I can improve our plan for the 3 younger children: work harder at progressing through the math so algebra can begin earlier.
I have tended toward a relaxed attitude about math. Thus, our oldest dd will only finish algebra and geometry in high school. The second dd will have time for one more math course before graduation. Can I do better with the next four students?
As I learn more about the subject myself, I enjoy it more. I have also hoped to introduce more "living math" books to our children. Math history is intriguing, as are problem solving and logic
(a recently found author who writes logic puzzle books for teenagers on up: Raymond Smullyan). One of our daughters has picked up the hobby of Sudoku--a great way to improve one's reasoning abilities. Introducing concepts like these earlier should be a boost in the success of our family's math program.
You probably know that in international comparisons, US students don't do real well in math.
Research into curricula in the best performing countries versus US is giving us one clue as to why this is:
US curricula tend to be
- incoherent and a collection of arbitrary topics instead of focused and logical
- Average duration of a topic in US is almost 6 years (!) versus about 3 years in the best-performing countries. Lots of spiraling and reviewing is done
- Each year, US textbooks cover way many more topics than the books in the best-performing countries
The materials we've chosen for math in our home, Making Math Meaningful by David Quine, followed by Elementary Algebra and Geometry by Harold Jacobs, measure up to the ideas in the article in some ways. David Quine's materials for grades K-6 cover fewer topics than most US math texts I've seen. Spiraling is used, if I'm understanding the term correctly (a curriculum writer I am not!), but review is at a minimum.
Beginning algebra in jr. high, rather than spending 7th and 8th grade reviewing arithmetic further, is possible with Quine's texts as long as each level is completed in one year. I found this difficult to do until I realized that our children didn't need all the practice provided in each module. Our younger students are progressing through the books at a faster speed than our olders did.
Harold Jacobs's algebra and geometry books are focused and logical, imho. Each chapter builds on the previous work, rather than including much tedious review. I've never understood algebra and geometry as well as I do after teaching through these books. :) The beauty and mystery of mathematics is presented, as well, in the introduction/discussion of concepts (every lesson begins with a worthwhile attention-getter) and in Set IV problems, which are for extra work and are usually puzzles or brain-teasers.
On the other hand, I have not yet been successful in keeping our students on an advanced track for math courses. Our two oldest began algebra during jr. high years, but didn't finish until 10th or 11th grade. Our third daughter began algebra as a 9th grader. Our fourth daughter, now in 7th, may be able to begin during 8th grade. This is one way I can improve our plan for the 3 younger children: work harder at progressing through the math so algebra can begin earlier.
I have tended toward a relaxed attitude about math. Thus, our oldest dd will only finish algebra and geometry in high school. The second dd will have time for one more math course before graduation. Can I do better with the next four students?
As I learn more about the subject myself, I enjoy it more. I have also hoped to introduce more "living math" books to our children. Math history is intriguing, as are problem solving and logic
(a recently found author who writes logic puzzle books for teenagers on up: Raymond Smullyan). One of our daughters has picked up the hobby of Sudoku--a great way to improve one's reasoning abilities. Introducing concepts like these earlier should be a boost in the success of our family's math program.
posted by HowGreatADebtor @ 10:17 AM
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