A number of teachers have shared with me that they've had some success using math journals with their students. Personally, it's not a strategy I've tried when I was teaching. However, I do feel strongly about having students explain their mathematical thinking either verbally or in writing. To be able to explain solutions and strategies usually means there is deeper understanding of the concept. When a student isn't able to explain how they attacked a math problem, it may be that they're relying on a guess method with minimal strategies and it just happened to work.

Some great questions for math classes are:

• How do you know?
• What would happen if?
• What strategies did you use and why?

Of course, you don't always have time in those busy math classes to have all students share their thinking, so journals may just be the right tool for you. To find out how to do math journal and the kinds of writing your students can do, read on.

When you're in a pinch and don't really feel like stepping out to grab the graph paper you need, look no further! You'll find isometric paper of varying sizes, coordinate grids with and without numbers, various sizes of graph paper and dot paper. For whatever your need, I'm sure you'll find it here.

The downside?

You need blank paper and a printer!

Some teachers require students to memorize the formulas and some don't. Some standardized testing allow formula sheets (referred to as cheat sheets by some) and some don't. It doesn't seem to matter who you ask, the answers always vary. I've gone both ways myself depending on the concept I'm addressing. For what's it's worth, I'm sitting on the fence with this one as I think there are certain formulas worth committing to memory and others that are always available at your fingertips.

Check out what our users say about the value of memorizing (or not) formulas.

Just to clarify: once upon a time, I would only use the word formulae when referring to the plural of formula. However, with the ever evolving and changing language, both are completely acceptable according to most dictionaries.

To stimulate mathematical thinking, many teachers provide a problem of the week, some even do it daily. The problems are to stimulate extended thinking and problem solving. When you think about it, it makes great sense! Do you have a favorite? Why not share it.

If not, here are a few to get you started:

• Pails of Water
• The Pig Pens
• Shorther Than you?
• The Horse Problem

Not sure about problem solving? Here are some strategies to help you get started.

Regardless of what curriculum your jurisdiction is working on, it's still important that students commit the multiplication facts to memory. Let me say that again, YES, it's still important that young learners commit the math facts to memory. Long ago, teachers had the time to help students commit the facts to memory. However, we are in the information age and when I look at the math curricula in various jurisditions, I don't see time for memorizing the basics. Therefore, this task will fall directly into the parents laps. It's been a long time since I've been in school, but my parents too were determined that I would commit the facts to memory and much to my demise (at the time) I did. Things really haven't changed too much. This is a task that still needs to happen and for the most part, it needs to happen at home.

The American Mathematical Society (AMS) has an oustanding career section for those interested in pursuing careers in mathematics. Not only will you find the job listings but you'll also find a wealth of information pertaining to early prep., issues great advice for new PHDs and programs. If you haven't visited the AMS site before, it's well worth a bookmark.

Check out the scientific notation worksheets with answers on the 2nd page of the PDF. After all, practice makes perfect, or at least improves learning!

Not sure about Scientific Notation? It's really just a method of writing very large or very small numbers in a form of shorthand. Scientists developed this method many years ago to provide them with a method to save time by easily representing numbers by using less characters. See more.

The year was 1956, Martin Gardner who had never taken a math course since high school left his job with Humpty Dumpty and began writing recreational math for Scientific American. Mr. Gardner just turned 95 and has now published 70 books! He has probably turned more people on to the joy of math than anyone else! Why? Because he makes math fun! "He has turned thousands of children into mathematicians, and thousands of mathematicians into children." Ronald Graham, University of California.

Many teachers use Gardner's puzzles as part of the problem solving in their math program. Making math fun should be the goal for all math teachers. Learn more about Gardner in the NYT article.

See also, some fun recreational math activities.

Why is it that this tiny country scores so high in mathematics? Is it their curriculum? Is it their superior approach to teaching math? Do Singapore students actually have superior ability?

Something they're doing is working and it sure would be nice to know just what is working. Other countries could certainly learn from and benefit from whatever it is that is working there, I would think.

Note: The Singapore Math Curriculum and the actual core math curriculum/program used in Singapore are NOT the same. As a result of Singapore's success, the Singapore Math Curriculum is getting a great deal of attention. However, even if it is their curriculum, every curriculum has its drawbacks. Curriculum tends to be implemented differently, sequenced differently and taught by teachers who have varying levels of expertise with math. It's also known that many districts have tried Singapore Math, only to drop it later. Why didn't it work for them? Singapore Math is a curriculum/framework that was developed based on some of the findings about how math is taught in Singapore. And, as I mention earlier, Singapore is doing something right. Here are some of the research articles about Singapore Math:
Singapore Math Research

Research in PDF

Be sure to post your experiences and/or opinions about Singapore Math, it's a popular topic.

The order of operations is taught usually in the 7th grade and is used immensely for many grades beyond. Usually the problem with teaching the order of operations is that it becomes a task for memory. Hence, it's more important that students understand why there is order.

Be sure to use manipulatives and basic questions when starting out with the order of operations. Here are some great basic worksheets to start with.

See also, how to solve the classic algebra age problem questions that tend to appear in most math text books.