Homeschool Math Newsletter, Vol. 5
January 22, 2007
It's Maria Miller, from HomeschoolMath.net and MathMammoth.com.
In this month's newsletter:
1. Fractions - visually
2. Geometry - by drawing
3. Interview from space?
4. Tidbits
5. HomeschoolEstore
1. Fractions - visually
Why are fractions so difficult to many kids? I feel one of the big reasons is that kids are not allowed to spend enough time on the "representational" level (or however you want to call it) - doing problems with manipulatives or pictures, working with visual models.
Most math books DO show pie charts for fractions in their teaching section, and in a few other problems. But all too often the book soon - too soon - turns to numeric calculations. So what follows is the kids maybe memorize the procedure, the 'how' to do it, but forget it in a few months.
I feel kids need to first add and subract fractions using pie pieces or other manipulatives, before embarking upon the calculations without them. They should first be able to do problems such as 1/6 ÷ 2 or 4 × 1/8 using the pie pieces, visually.
Then, as the student is confident with that, he/she starts doing the numerical problems.
In my Math Mammoth fractions workbooks, I've strived to teach all fraction operations visually using plenty of picture exercises.
I just got feedback about this a few days ago, from a teacher:
"These books fill the gap between using manipulatives (concrete level) and abstract (symbolic) level. Too often students are expected to make that leap from the concrete level without spending time at the representational level."
The fraction books have recently been updated. They look much better now and have some new lessons and problems. Download the free sample worksheets for your lessons!
Geometry - drawing
On a similar note, I feel students need to draw to learn elementary geometry. For example, consider the following problem:
Draw a parallelogram with a 3-inch side and a 47° angle.
When doing this problem, the student will soon notice that he does not have all the information. What is missing? Can you calculate the missing information, or just make it up? Can you draw one, or several parallelograms that fit the description?
After drawing the figure and thinking the situation through, the student has learned the truth about parallelogram's angles much more profoundly than just reading it in a book.
Such problems abound in my Geometry 1 ebook.
3. Interview from space?
No, not really from space, but it was an astronomer talking. I recently conducted an 'email' interview of the astronomer Dr. Sten Odenwald who is heavily involved in math and science education.
Sten has been writing weekly space-related math problems for grades 9-11, which are quite interesting.
4. Tidbits
Trigonometry: Finding the value of sine Pi/3.
Cute circle terminology song
Can Less Equal More? - Proposal to teach math students fewer concepts in greater depth has divided Md. educators.
The site DoubleDivision.org shows you an alternative long division algorithm, which takes the guessing away from estimating how many times the divisor goes into what needs divided. Also called 1-2-4-8 division.
At MathLogarithms.com you can download an ebook by Dan Umbarger explaining logarithm how's, why's, and wherefore's in all detail for students.
5. HomeschoolEstore
Most of my Math Mammoth books are now also available at HomeschoolEstore.com. The site also has lots of other downloadable educational books as well. I even saw Miquon Math there.
They also employ a special promotional measure where each publisher has one of his/her products for a free download one week during the year. So at all times there is at least one, if not several, free downloads at HomeschoolEstore.com.
Till next time,
Maria Miller
How did you like this month's newsletter? Is there any topic you'd like to see in the next one? Contact me.
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