The ability to count and all of the ramifications of being able to do so is critical in our present world. Counting leads to measuring. It allows us to predict. It permits us to define the world around use in terms other than our own subjective beliefs. “I know my first 10 letters of the alphabet.” “I know all 400 words in my basic reader.” “I am learning 5 new words each day.” “I read one book each week this summer.” When will you be empowered to the point (exhibit mastery) that cramming for and taking NCLB standardized tests will be, “just a waste of time?”
I learned my math on a sheet of paper. A large square was drawn. The square was divided into four squares. Each of these was marked off with four horizontal and four vertical lines. I could count to 100 by filling in the cells. I could count by 2s, 3s, 4s, and 5s, which was really multiplying by 2, 3, 4, and 5. I could count backwards, which was subtracting. I learned to estimate the answer to any math question so I had some judgment if I might not be right (I actually spotted a failing Marchant calculator. One of the wheels failed to stop at nine when it should have, but continued on to four). Later I learned square and square root. And finally logarithms, where addition is multiplication and subtraction is division (to three significant digits on a slide rule). The experience of learning the multiplication tables not only is essential in math but also carries over into learning other things that are not as limited and well defined. Hand calculators allow students to skip the basics and suffer the consequences.
The oldest, time tested, math downloadable listed by the Educational Software Cooperative teaches counting, addition, and subtraction. Next multiplication was included. Educational games and puzzles have always been popular, I think in part, because the authors have fun creating them. In a free enterprise economy, a successful game can support the author and a business is born. Those who directly benefit pay the cost of development rather than taxpayers or a non-profit that obtained its funding from a taxable free enterprise activity.
Word problems for grades 1-8 can now be presented by software. Unique calculator and statistical software are available to supplement the myriad of hand calculators. Some of this software is free. The same is true for graphing calculators. All of these are under listings and math downloadables.
Fractions and algebra are still available as downloadables from Merit Software even though these are much further developed in its online software. Evallutel Multimedia presents algebra and geometry, and more. Math downloadables are listed under classroom tests, educational games, math, and teaching aids. The online offerings in the prior two posts on reading and writing; vocabulary, phonics and spelling; also include math.
All of these lessons in software are designed to free teachers to teach, and students to learn, the subject rather than to spend time trying to memorize answers to questions they guess will be on a standardized test. Use this software to give students the opportunity to develop the sense of responsibility needed to learn at all levels of thinking. They will then be ready for Knowledge and Judgment Scoring, quantity and quality, and as also in Winsteps and Amplifier.
With subject mastery at the proper levels of thinking, there should be very little concern about passing current NCLB standardized tests that are scored at the lowest levels of thinking. IMHO it is failure on the part of school administrators to understand this miss match that locks many failing schools into continued failure. Preparing for a lower level of thinking scored test using lower level of thinking experiences dooms students to failure now and even more so in the future. In math especially, students need to be able to do and to understand, not just be aware of what a teacher has presented.
Students functioning at lower levels of thinking are dependent upon their teacher for maintaining their knowledge and skill levels. Students functioning at higher levels of thinking are capable of relearning as needed. They need a teacher for direction and for the expansion of their abilities, not for the maintenance of their knowledge and skill. The more you develop students, the easier it is to teach and to learn. This is the reason that well prepared third graders survive and flourish.