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First we need to define our terms. Spiral learning is based on behaviorism, which says we are programmable machines and we need endless repetitions to master something. Spiral curriculums cover the same material year after year in ever widening circles, with the anticipation that increased exposures will eventually lead to mastery of the basics. The number of topics covered is broad, but they never go deep. It is more of an exposure philosophy.
Mastery approach curriculum builds sequentially. This philosophy states that there is no need to move to the next step until the preceding one is mastered. Therefore, lessons may take many days or even weeks if necessary for students to master the facts. Fewer topics are covered. Pre-testing and post-testing are done to assure mastery. Both approaches have some validity as well as some drawbacks.
The way the brain works is that it attaches new information to something already known. The more ways information is attached in the brain, the better it is learned. Children need more than one exposure and one way to learn a topic, but repeated exposures to the same material are not enough for mastery.
Thomas E. Clark, author of VideoText Algebra, defines the goal of arithmetic as finding an answer, but the goal of mathematics as solving a problem. We need to teach students to be problem solvers. Therefore, RightStart™ Mathematics introduces a large number of topics, but they are built sequentially for greater understanding. Students need to be challenged by many topics in order to see the interconnectedness in mathematics. For example, one of the goals of mathematics instruction is that students be fluid in their basic facts. So, students learn strategies for mastering the facts. They master them by playing games, which gives them a reason for learning the facts.
In RightStart™ students learn techniques for thinking mathematically. Dr. Cotter has systematically introduced principles of mathematics that lead students to self-discovery through the well-designed lessons.
Understanding is stressed throughout. The primary manipulative is the AL Abacus. Necessary repetition is provided through math card games.
The RightStart™ program is complete in itself. It is not a supplement nor does it need other supplements. Math card games are interwoven into the RightStart lesson plans. The games are often used as a supplement for other math programs. RightStart™ also includes the other branches of mathematics required from kindergarten on, such as geometry, algebra, probability, and statistics.
A more serious limitation of rods 6-10 is that they cannot be visualized, or seen in the mind, because they are not grouped in fives. Try to imagine 8 apples in a row without any grouping–virtually impossible. Now imagine 5 apples as red and 3 as green–this you probably can do. The Romans grouped in fives (8 as VIII), and composers used two groups of five lines for writing music. Money and clocks group in fives.
The purpose of a manipulative is not only to see the concept, but to help the learner construct a mental model, for example, to learn the facts. Note also that adding two rods does not immediately give the sum.
Any concept that can be taught with colored rods can be taught with the AL Abacus without the bother of little pieces.
The AL Abacus, grouped in 5s and 10s, is designed to teach adding, subtracting, multiplying, money, and other concepts. The second side emphasizes trading: that 10 ones is 1 ten, 10 tens is 100, and 10 hundreds is 1000. As with all good manipulatives, children use it less and less as they construct their mental models.
The Slavonic Abacus, used in the UK, Australia, and New Zealand, is the same as the front side of the AL Abacus, but it does not have a reverse side.
The second edition program uses more materials. The Book Bundles will provide the lessons and worksheets. The RS2 Math Set provides all the materials you will need for RS2 Levels A through F. The RS2 Math Set will be a one time investment.
We recommend implementing VideoText Interactive Algebra Module A about half way through the Geometric Approach, doing about a lesson a week. You may purchase this individually or include in the Deluxe Starter Kit G and save a bit.