How Shall We Teach Fractions?

Posted on by Denise Gaskins

How did you fare on the Frustrating Fractions Quiz? With so many apparent inconsistencies, we can all see why children (and their teachers) get confused. And yet, fractions are vital to our children’s test scores — and scores are important to college admissions officers. What is a teacher to do? Must we tell our children, “Do it this way, and don’t ask questions”?

Parents and teachers are tempted to wonder if the struggle is worth it. After all, how often do you divide by a fraction in your adult life? If only we could skip the hard stuff…

Continue reading How Shall We Teach Fractions?

What Do We Mean by “Assume”?

Posted on by Denise Gaskins

Almost all math problems call for the student to assume one thing or another. Without assumptions — definitions, postulates, axioms, common notions, or whatever you want to call them — mathematics of any kind is impossible. Tony at Pencils Down (who plans to be a math teacher when he grows up) reminds us that, necessary though it may be, we are stepping on dangerous ground when we assume:

Random Samples: Making an Ass of You and Me

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Ben Franklin Math: Elementary Problem Solving 3rd Grade

Posted on by Denise Gaskins

The ability to solve word problems ranks high on any math teacher’s list of goals. How can I teach my students to solve math problems? I must help them develop the ability to translate “real world” situations into mathematical language.

In two previous posts, I introduced the problem-solving tools algebra and bar diagrams. These tools help our students organize the information in a word problem and translate it into a mathematical calculation.

Working Math Problems with Poor Richard

This time I will demonstrate these problem-solving tools in action with a series of 3rd-grade problems based on the Singapore Primary Math series, level 3A. For your reading pleasure, I have translated the problems into the life of Ben Franklin, inspired by the biography Poor Richard by James Daugherty.

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While I Was Distracted…

Posted on by Denise Gaskins

After a hectic couple of weeks, I finally found a little time to sit at the computer and browse — and boy, was I amazed to see what I had missed! If you have not yet read Dave‘s interview with Prof. Lynn Arthur Steen about the state of math education reform, click over and check it out: Part I here, and Part II here.

According to the intro, Prof. Steen “has been a driving force for the reform of school mathematics for many years and was on the development team that produced NCTM’s Curriculum and Evaluation Standards for School Mathematics. For the last few years, he has been involved in Achieve’s commitment to developing world-class mathematics standards for K-8 and ADP’s similar commitment to secondary mathematics.” He has some interesting things to say, although many of his statements are open to various interpretations, and at times he seems determined to provoke a hot-headed response. For instance:

Continue reading While I Was Distracted…

Reading to Learn Math

Posted on by Denise Gaskins

[Photo by Betsssssy.]

Do you ever take your kids’ math tests? It helps me remember what it is like to be a student. I push myself to work quickly, trying to finish in about 1/3 the allotted time, to mimic the pressure students feel. And whenever I do this, I find myself prone to the same stupid mistakes that students make.

Even teachers are human.

In this case, it was a multi-step word problem, a barrage of information to stumble through. In the middle of it all sat this statement:

…and there were 3/4 as many dragons as gryphons…

My eyes saw the words, but my mind heard it this way:

…and 3/4 of them were dragons…

What do you think — did I get the answer right? Of course not! Every little word in a math problem is important, and misreading even the smallest word can lead a student astray. My mental glitch encompassed several words, and my final tally of mythological creatures was correspondingly screwy.

But here is the more important question: Can you explain the difference between these two statements?

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Penguin Math: Elementary Problem Solving 2nd Grade

Posted on by Denise Gaskins

The ability to solve word problems ranks high on any math teacher’s list of goals. How can I teach my students to reason their way through math problems? I must help my students develop the ability to translate “real world” situations into mathematical language.

In a previous post, I analyzed two problem-solving tools we can teach our students: algebra and bar diagrams. These tools help our students organize the information in a word problem and translate it into a mathematical calculation.

Now I want to demonstrate these problem-solving tools in action with a series of 2nd grade problems, based on the Singapore Primary Math series, level 2A. For your reading pleasure, I have translated the problems into the universe of one of our family’s favorite read-aloud books, Mr. Popper’s Penguins.

UPDATE: Problems have been genericized to avoid copyright issues.

Continue reading Penguin Math: Elementary Problem Solving 2nd Grade

Writing to Learn Math

Posted on by Denise Gaskins
2009 Challenge - Day 72: Pencil
Image by ☼zlady via Flickr

Have you considered experimenting with writing in your math class this year? It seems that math journals are a growing fad, and for good reason:

Writing is how we think our way into a subject and make it our own.

—William Zinsser
Writing to Learn

Math journal entries can be as simple as class notes, or they can be research projects that take hours of experimentation and pondering. Students may use the journal to store their thoughts as they work several days to solve a challenge problem of the week, or they might jot down quick reflections about what they learned in today’s math class.

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Elementary Problem Solving: The Tools

Posted on by Denise Gaskins

[This article begins a series rescued from my old blog. Moving has been a long process, but I’m finally unpacking the last cardboard box! To read the entire series, click here: elementary problem solving series.]

Most young students solve story problems by the flash of insight method: When they read the problem, they know almost instinctively how to solve it. This is fine for problems like:

There are 7 children. 2 of them are girls. How many boys are there?

As problems get more difficult, however, that flash of insight becomes less reliable, so we find our students staring blankly at their paper or out the window. They complain, “I don’t know what to do. It’s too hard!”

We need to give our students a tool that will help them when insight fails.

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Quotations XIII: Mathematics Education Is Much More Complicated than You Expected

Posted on by Denise Gaskins

Registrations have been rolling in for our homeschool co-op, and the most popular classes are full already. Math doesn’t seem to be a “most popular” class. I can’t imagine why! Still, many of my students from last year are coming back for another go, and I am getting spill-over from the science class waiting list.

Anyway, I have started planning in earnest for our fall session. As usual, I look to those wiser than myself for inspiration…

Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.

— Paul Halmos

Continue reading Quotations XIII: Mathematics Education Is Much More Complicated than You Expected