Mastery Learning Systems has developed the Discover the Basics math series to get right to the core of the subject. The Adding & Subtracting edition focuses on fundamental concepts and builds a firm foundation in math. This course covers simple addition and subtraction of single digits with numbers up to 100. More specifically, topics include counting, plus and minus, fact families, doubles and doubles plus one. The use of dimes and nickels is also included. Upon completion, students will know all facts up to 9+9 and 18-9. Regrouping is not part of this book. 

Adding & Subtracting is suitable for grades one and two, and would be useful for remedial work for third grade through adult. The text comes in a three ring binder and consists of 208 pages, including pre-tests, post tests, and an answer key. There is also a thorough explanation of how to use the book, which in itself is a very interesting read. 

Mastery Learning Systems has a distinct approach that allows children to experience math concepts through guided discovery. This approach consists of three steps: count (experience), notice, and remember. First, children construct and experience the math problem for themselves by using paper manipulatives. This enables them to form an accurate mental image of the math concept and to notice the relationship between numbers. Further practice requires additional thinking about the concept, which in turn leads to remembering. 

This comprehensive program helps students build confidence and fluency. The goal is to have children understand the actual meaning of addition and subtraction so that they can then solve problems. The introduction states, "This book always begins with establishing an understanding of the idea at hand, and then proceeds to memory development." This is important because some math texts do not provide enough practice problems, while others do not give clear enough models so that children can understand the concept. Discover the Basics: Adding & Subtracting does both. 

This series provides a lot of multi-sensory repetition without the use of extra materials. Children write answers and work with paper money and number lines with their hands. They are also instructed to speak answers at various times. This provides plenty of practice, which develops fluency. Eventually, children will be able to instantaneously remember the facts presented in this book. 

The text is not divided into set lessons, meaning you will not find lesson one on pages 1-3 and then lesson two and so on. However, it does move through concepts logically and activities are sensibly grouped together. Twenty to thirty minutes of work each day is recommended, and the user may proceed as quickly or slowly as necessary. 

This series begins with the basics: counting. Students familiarize themselves with the order of numbers, learning what comes before and after. They then move quickly to plus and minus one. The first lessons with plus and minus involve using one-dollar bills (fake ones provided in the text). I thought this was an excellent way to expose children to the value of money while learning about addition and subtraction. Dimes and nickels are used when learning about 10s and 5s. 

Two features that are consistently used in this program are number lines and partner pages. A few different types of number lines are presented and are frequently utilized by the student as they familiarize themselves with the sums. These lines are covered with blank paper, which is then moved to find the answer. By doing so, children are able to avoid frustration and quickly gain confidence. Since this is used often, it does not take long before kids know the facts without it. 

The number line is also used in conjunction with the partner pages, which are designed to help students practice addition and subtraction sums with a partner. Students are encouraged to work with speed, as they circle the time it took to complete the page on the progress chart. This worked wonders with my 8-year-old, who usually gets flustered with anything mathematical. She actually began to enjoy trying to beat the clock and was very proud when she did. 

I believe this could be a stand-alone math curriculum or extra practice for struggling students. I was able to begin the first lessons with my 5 year old and also use it with my 8-year-old, who is having trouble understanding math. This program would be excellent in a homeschool or classroom environment and would also be appropriate for one-on-one tutoring. 

I liked this program and enjoyed using it with my children. I feel it has helped my "math resistant" child, and I will continue to work with her from this book. The focus on understanding instead of rote memorization impressed me. The text is presented in a way that enables children to feel successful quickly, which is a big plus for a child who has difficulty with mathematics. My only criticism would be that some things seemed a little tedious, like having the child check off each step in a particular problem. But I am not convinced that it is not helpful, it may very well be. 

My family is very happy with Discover the Basics: Adding & Subtracting. If I had to describe this program in two words they would be "comprehensive" and "thorough." The simple, straightforward approach is sure to help many struggling students build a strong foundation in math.

Product review by Stacy Kalisz, The Old Schoolhouse® Magazine, LLC, March 2010