About Teaching Mathematics – A K-8 Resource
by Marilyn Burns


After a quick browsing of Burn's book, I knew I wanted About Teaching Mathematics in my library. Here's why. It addresses the need of the teacher in five areas.

Part 1 – Raising Issues

The first topic she addresses is "You Can't Teach What You Don't Understand." Basically, her point is teachers should explain why a particular algorithm works. However, that is not possible if the teacher does not understand. For example, teach "why does canceling zeros in the fraction 10/20 produce an equivalent fraction, but not in the fraction 101/201?"
A few other valuable topics discussed -

Understanding Common Arithmetic Errors
Incorporating Writing into Math
Managing Classroom Instruction
Teaching Vocabulary

If any teacher has not tried incorporating writing in math, I strongly recommend it. It forces students to slow down and think about what they are doing. It gives the teacher insight into every students understanding and misconceptions. Burns gives ideas on how to get started such as sharing prompts to use.

Part 2 – Instructional Activities for the Content Standards
Section two gives examples of problem-solving activities for the NCTM standards. Each teacher will have to read through the many activities because grade levels are not given. However, the math activities are suitable for independent and small group learning unless it specifically states it's a whole class activity.

Part 3 – Teaching Arithmetic
Here's a section to refresh your coffee or tea, and spend a little time. The thought "teaching for understanding is essential" sums up this section. Results of classroom research are shared. Burns shares the limits of learning rules, multiple strategies for computing, how to develop an understanding of arithmetic, and other topics. Also, you may find more answers in the "Questions from teachers". However, the majority of Teaching Arithmetic offers ideas for teaching arithmetic. The topics include

Beginning Number Concepts
Place Value
Addition and Subtraction
Multiplication
Fractions
Division
Extending Multiplication and Division
Fractions
Decimals
Percents

The author does not leave you wandering how to implement her suggestions. She includes whole class lessons, independent activities and suggestions to assess the students' understanding.

Part 4 Mathematical Discussions
Earlier in the book, Burns shared her thoughts on teachers being unable to teach what they don't understand. In these next several pages she attempts to do something about it. Thus, teachers with" a limited mathematics background can learn more about specific areas of mathematics and, in general about thinking mathematically." If you have more mathematical experience, you may find other ways to approach a particular problem. Also, she goes in depth about probability and statistics, geometry, patterns, functions, and algebra problems. There is a question and answer section too.

Part 5 – Questions Teachers Ask
This section differs from other questions in earlier sections because they are pedagogical in nature. Also, unlike the other questions, the author does include grade levels. The questions range from organizing math centers to relating fraction and decimals to assigning homework grades.
Lastly, the book includes blackline masters for over 20 handouts.
Without a doubt, this is a resource definitely written with the teacher in mind.

Buy About Teaching Mathematics: A K-8 Resource, 3rd Edition from Amazon