A century of progressive domination of the American educational system has resulted in a growing number of Americans remaining mathematically illiterate. The Common Core standards are a repeat of previously failed federal policies which fail to develop academic skill making the study of mathematics needlessly boring and challenging for too many talented students. These federally supported educational policies have left our society short of talented mathematicians needed to make the American economy competitive with other nations.

Once again, the Common Core Standards are another federal policy which discourages students from memorizing multiplication facts and other basic math theories and formulas. These policies are in place to justify the emphasis on student-centered, discovery, and inquiry methods of instruction which fail because they are laborious, error-ridden, discouraging methods for introducing new concepts to young learners according to research.

The discovery and inquiry methods of instruction are useful only when a student has the basic skills needed to become “creative’ with the use of that skill. For example: when a child is asked to discover the solution to 8 X 7 instead of memorizing the fact that 8 X 7 is 56, the student uses a variety of techniques to discover the answer. Grouping of eight or seven objects, counting on fingers, etc., are the processes often used.

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When this laborious action is promoted and the memorization of facts is discouraged, solving a simple math problem becomes time consuming and error-ridden, making the learning of math frustrating and a hated task for too many students who could have become excellent mathematicians.

As a teacher, I quickly saw this flaw in the discovery and inquiry methods of instruction and refused to depend upon them in my classroom. Unfortunately, because other teachers were not requiring students to take time to memorize basic math facts, I had to spend considerable time proving to students that memorizing these facts would open the world of math to them. My approach is commonly called the direct instructional method.

I began by emphasizing the importance of learning how to memorize things; it is a skill that becomes easier with practice. Using their favorite rock stars, I pointed out that Michael Jackson, David Garrett (a crossover violinist), and Stevie Ray Vaughn play their music from memory. For a musician, memorizing the music enables fluidity. Memorizing math facts makes solving a math problem easier, faster, and more accurate.

If rock stars could memorize hundreds of songs, students could memorize 100 simple multiplication facts.

On a quiz comprised of ten basic multiplication problems and two very simple long division problems, the children who had learned long division using the discovery method during a previous school year used a dozen different methods for solving the problem. Few students obtained the correct answer using those methods. Their papers were covered with drawings and counting errors. Scores were low.

My students spent one week practicing multiplication facts in class because many parents were no longer willing to spend “family” time practicing these facts. Once the students mastered the basic multiplication facts from 0 through 10, I gave them the same quiz that I had given them earlier. Scores were improved significantly, and they finished the test in half the previous time.

Many students expressed surprise that long division problems were so much easier than they had originally thought. Some even noticed that division is the inverse of multiplication. This revelation could not have happened if they had not memorized their multiplication facts. I used this “teaching moment” to show my ten-year old students that they could now do pre-algebra. I put the following problems on the board:

3 X 7= 21

21=3 X 7

A X 7 = 21

21=3 X A

My students were amazed. I explained that, if they memorized a few basic facts, they would be able to see the relationships in numbers and the number patterns that make math a most amazing puzzle. Just as musicians must master chord progressions and a variety of techniques before they can create beautiful music, students must memorize some basic math concepts to unlock the mysteries of mathematics.

Having this basic knowledge would help students score well on an assessment test. The examples above proved to my students that they would be able to answer some basic algebra questions just because they mastered some basic math facts. Algebra is not required until the end of seventh grade in our district, but those who could answer some algebra questions on the test would rank among our highest-performing sixth-grade students.

Students became self-motivated. Knowing that improving six points on the state exam would mean one full year of academic growth, many students set a goal much higher than that for themselves. Most met those goals.

State test results proved that my special needs students made the most progress once they memorized some basic math facts. These children are doers. They are easily frustrated. They resent mind games. They see school as a place where they are set-up for failure. Once students saw that memorizing facts was the key to accuracy and success, they made impressive progress.

Professor Kilpatrick and other progressive educational experts who have been shaping federal policies and promoting the federalization of our educational system are the source of the problem because they disrespect the American student. Kilpatrick is quoted as saying, “We have in the past taught algebra and geometry to too many, not too few.” If nothing else, a student of algebra learns that what is on one side of an equation must equal whatever is on the other. Understanding this concept is essential for effective critical thinking.

Kilpatrick’s attitude is pervasive among American education experts and, therefore, prevails in federal educational policies.

It is time for civil disobedience. It is time for those who respect the intrinsic value of education and the right of every child to reach his academic potential to take back our schools at the local level.

See also here, here, here, and here.

Samuel Tennenbaum, William Heard Kilpatrick, Harper & Brothers Publishers, New York 1951. P. 105

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