[Rescued from my old blog.]
I love Miquon math, but the program does feel odd to many homeschoolers, especially at first. It is so different from the math most of us grew up with that it takes time for the teacher to adjust. DJ asked for Miquon advice at a forum I frequent, but I thought enough people might find these tips useful to justify an expanded repost. If you have more advice on teaching Miquon, please chime in!
[Rescued from my old blog. To read the entire series, click here: Elementary Problem Solving Series. Photo by Studio 757 via Flickr (CC BY 2.0).]
You can begin to teach your children algebraic thinking in preschool, if you treat algebra as a problem-solving game. Young children are masters at solving problems, at figuring things out. They constantly explore their world, piecing together the mystery of how things work. For preschool children, mathematical concepts are just part of life’s daily adventure. Their minds grapple with understanding the three-ness of three blocks or three fingers or one raisin plus two more raisins make three.
Wise homeschooling parents put those creative minds to work. They build a foundation for algebra with games that require the same problem-solving skills children need for abstract math: the ability to visualize a situation and to apply common sense.
Continue reading Elementary Problem Solving: The Early Years
Well, I didn’t get any takers with the last story problem challenge. But school is in full session now, and we’re doing story problems in Math Club this Friday, so I thought I’d try again.
Here’s the challenge: Can you and your students make up some original math problems?
In Math Club, we always start by reading part of the book Math by Kids for inspiration. I can’t print those stories here, however, because of copyright rules, so I’ll share some of the stories my past students have made, arranged in roughly increasing order of difficulty. After you solve a couple of these problems with your children, encourage them to try making some of their own.
And please, share their gems with us!
The problems below are now available as a printable handout: Story Problem Challenge.
[Rescued from my old blog.]
Percents are one of the math monsters, the toughest topics of elementary and junior high school arithmetic. The most important step in solving any percent problem is to figure out what quantity is being treated as the basis, the whole thing that is 100%. The whole is whatever quantity to which the other things in the problem are being compared.
Comments by W. W. Sawyer, in his wonderful, little book, Mathematician’s Delight:
Earlier we considered the argument, ‘Twice two must be four, because we cannot imagine it otherwise.’ This argument brings out clearly the connexion between reason and imagination: reason is in fact neither more nor less than an experiment carried out in the imagination.
[Rescued from my old blog.]
Paraphrased from a homeschool math discussion forum:
“I am really struggling with percents right now, and feel I am in way over my head!”
Percents are one of the math monsters, the toughest topics of elementary and junior high school arithmetic. Here are a few tips to help you understand and teach percents.
[Rescued from my old blog.]
Marjorie in AZ asked a terrific question on the (now defunct) AHFH Math forum:
“…I have always been taught that the order of operations (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) means that you work a problem in that order. All parenthesis first, then all exponents, then all multiplication from left to right, then all division from left to right, etc. …”
Many people are confused with order of operations, and it is often poorly taught. I’m afraid that Marjorie has fallen victim to a poor teacher — or at least, to a teacher who didn’t fully understand math. Rather than thinking of a strict “PEMDAS” progression, think of a series of stair steps, with the inverse operations being on the same level.
[Rescued from my old blog.]
Division of fractions is surely one of the most difficult topic in elementary arithmetic. Very few students (or teachers) actually understand how and why it works. Most of us get by with memorized rules, such as:
Ours is not to reason why;
just invert and multiply!
[Rescued from my old blog.]
For young children, mathematical concepts are part of life’s daily adventure. A toddler’s mind grapples with understanding the threeness of three blocks or three fingers or one raisin plus two more raisins make three.
Most children enter school with a natural feel for mathematical ideas. They can count out forks and knives for the table, matching sets of silverware with the resident set of people. They know how to split up the last bit of birthday cake and make sure they get their fair share, even if they have to cut halves or thirds. They enjoy drawing circles and triangles, and they delight in scooping up volumes in the sandbox or bathtub.
[Rescued from my old blog.]
Well, my computer is still being rebellious, so I’m at dh’s office again to check e-mail while the kids are gone to karate. But I thought it was high time I got another entry up on the blog…
One of my favorite activities for Math Club is to have my students write their own story problems. Then we pass the problems around so everyone can try to solve them. With all the discussion of problem solving on the math forum lately, I thought it would be fun to extend the challenge to you all. Can you come up with a word problem for us to practice our problem-solving skills on?
Denise Gaskins' Let's Play Math 