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Showing posts from August, 2010

### Carnival time: Math Teacher's at Play

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Head on over to Math Teachers At Play #29 carnival to read a nice assortment of posts on math education!

### The equal sign problem

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An interesting piece of research has just come out on the misconceptions with the equal sign (=).

Students' understanding of the equal sign not equal

According to the research, US students exhibit this misconception much more often than students in other countries. It has to do with thinking of the = sign as an operator. Kind of like thinking that = means "to do" the operation.

For example, a student with that misconception tends to solve the problem

7 + 6 = ____ + 2

by adding 7 + 6, and placing the answer on the empty line.

The correct way is of course to think of the equality: 7 + 6 equals 13, so the other side has to equal 13 too. 11 fulfills this little equation:

7 + 6 = 11 + 2

I have known of this problem for years, and have tried to include problems in my Math Mammoth books to help children NOT to develop this wrong idea. For example, children solve

200 + 50 + 6 = ____ + 200 + 50 in the place value section.

Or, I use problems where they have to put either <, >…

Students' understanding of the equal sign not equal

According to the research, US students exhibit this misconception much more often than students in other countries. It has to do with thinking of the = sign as an operator. Kind of like thinking that = means "to do" the operation.

For example, a student with that misconception tends to solve the problem

7 + 6 = ____ + 2

by adding 7 + 6, and placing the answer on the empty line.

The correct way is of course to think of the equality: 7 + 6 equals 13, so the other side has to equal 13 too. 11 fulfills this little equation:

7 + 6 = 11 + 2

I have known of this problem for years, and have tried to include problems in my Math Mammoth books to help children NOT to develop this wrong idea. For example, children solve

200 + 50 + 6 = ____ + 200 + 50 in the place value section.

Or, I use problems where they have to put either <, >…

### Math Mammoth Geometry 2

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I have just finished writing the material for Math Mammoth Geometry 2 book. The material in it is suitable for grades 6-7. Download price is $5.80.

The main topics in the book include:

* angle relationships

* classifying triangles and quadrilaterals

* angle sum of triangles and quadrilaterals

* congruent transformations, including some in the coordinate grid

* similar figures, including using ratios and proportions

* review of the area of all common polygons

* circumference of a circle (Pi)

* area of a circle

* conversions between units of area (both metric and customary)

* volume and surface area of common solids

* conversions between units of volume (both metric and customary)

* some common compass-and-ruler constructions.

I've included several complete lessons from the book as samples (PDF). Feel free to download these and use with your students!

Angles in Polygons

Review: Area of Polygons, 1

Surface Area

Besides those, there are two other sample pages:

Area and Perimeter Problems

…

The main topics in the book include:

* angle relationships

* classifying triangles and quadrilaterals

* angle sum of triangles and quadrilaterals

* congruent transformations, including some in the coordinate grid

* similar figures, including using ratios and proportions

* review of the area of all common polygons

* circumference of a circle (Pi)

* area of a circle

* conversions between units of area (both metric and customary)

* volume and surface area of common solids

* conversions between units of volume (both metric and customary)

* some common compass-and-ruler constructions.

I've included several complete lessons from the book as samples (PDF). Feel free to download these and use with your students!

Angles in Polygons

Review: Area of Polygons, 1

Surface Area

Besides those, there are two other sample pages:

Area and Perimeter Problems

…

### Review of Harold Jacobs Geometry

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I have just posted a comprehensive review of this book that is popular among homeschoolers for a high school geometry course. Click to read:

Review of Harold Jacobs Geometry book

Review of Harold Jacobs Geometry book

### Math assessment and placement

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My daughter just completed the end-of-year math test for 4th grade. She scored 82%. She missed doing one question (just forgot), made a few careless mistakes, and then missed several in the measuring unit section because she didn't remember how many ounces are in a pound or how many grams in a kilogram. So we need to review some of that.

But overall, I am happy with the results, because (and I knew this beforehand too) she understands the concepts well! That is the most important thing. It's always easy to review some forgotten facts (such as measuring units), but when child has not understood the main concepts, the "patch-up" work is more tedious.

I have provided these Math Mammoth end-of-year tests on my site as free downloads so that people can use them as placement tests or for general math assessment. I often have people email me about their kids' results, and based on that, I feel those tests are working fine.

I have also collected a few other math assessme…

But overall, I am happy with the results, because (and I knew this beforehand too) she understands the concepts well! That is the most important thing. It's always easy to review some forgotten facts (such as measuring units), but when child has not understood the main concepts, the "patch-up" work is more tedious.

I have provided these Math Mammoth end-of-year tests on my site as free downloads so that people can use them as placement tests or for general math assessment. I often have people email me about their kids' results, and based on that, I feel those tests are working fine.

I have also collected a few other math assessme…