by Douglas E. Newton

According to the Oregon Department of Education, “The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so…upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict…White supremacy manifests itself in the focus on finding the right answer.”

Not to be outdone, the state of Virginia is discussing a document with the Orwellian name of “Virginia Mathematics Pathways Initiative” to teach “Mathematics Education Through the Lens of Social Justice,” which dumbs down mathematics education for all in the name of racial equity.

Why such hatred toward mathematics?

In a postmodern, relativistic worldview, one of the worst things to perpetuate is objectivity. Absolute truth is the enemy. Denial of absolute truth pervades literally every school subject today.

One of the last bastions of absolute truth is mathematics. However, with its walls under siege and weakening, the truth of mathematics may, too, fall. All because our society has forgotten what mathematics is all about.

For millennia, the primary purpose of teaching mathematics was to train the mind in deductive, logical thinking. It was seen as a cousin to logic, philosophy, and religion. In the classical mindset, mathematics is to intellectual education what stretching, and push-ups are to physical education. The direct application in the sciences and everyday life was only a secondary purpose of mathematics.

Today, not only mathematics is under assault, but also deductive, logical thinking and ultimately absolute truth.

Initially, this attack was indirect and subversive. It began with the inverting of the purpose of mathematics. Teachers have emphasized the practical nature of mathematics and minimized, or even denigrated, the value of training the mind.

Students ask, “How am I going to use this in the real world?”

Instead of explaining the real purpose of mathematics, teachers try to make it more “relevant.” To increase relevancy, curriculum writers have dumbed down mathematics. After all, who will need to do geometry proofs in the real world?

Now we see direct assaults on the very nature of mathematics.

What can parents do to reverse this incorrect view of mathematics?

Following are some suggestions I have developed over the years. They apply primarily to the upper grades, but some pertain to the lower grades as well.

Avoid Memorization

Memorization is an important brain function, yet it differs from deductive reasoning. Save memory work for history or Bible classes. Trust me, your children will not fail in life because they don’t memorize the multiplication table. I haven’t.

I remember my third-grade teacher holding up multiplication facts flashcards one-on-one with students and expecting each to recite the answers. Here’s the kicker, we had to answer quickly. If we took too long, we had to start over until we could do it fast enough.

Sorry, Mrs. Hadley, but that is the wrong approach.

If a student takes time to answer the question, is obviously working on it, and gets it right, that should be celebrated.

On the other hand, if the student answers 24 immediately when asked what is 4×6, that should be cause for concern. Does she really know the answer, or is it rote memorization? Make sure she can explain why 4×6 = 24.

Sure, some memorization work is helpful. For example, students should memorize the associative, commutative, and distributive properties. However, it is more important that the student can illustrate the concepts than quote a definition or theorem word for word.

Rule of thumb: if you can derive it, there is no value in memorizing it.

Use Manipulatives with Discernment

The tactile nature of manipulatives can increase a students understand of mathematical concepts. But don’t let them become a crutch.

For instance, arrange 24 cubes into four rows by six columns and have the student tell you how many there are. Now turn the set of cubes 90 degrees, so there are six rows by four columns. Then ask the student how many there are. The student may roll his eyes, but you can explain that you have just illustrated the commutative property of multiplication. Manipulatives help explain concepts, but your student shouldn’t rely on the manipulatives to solve arithmetic problems.

Be Prudent with Repetition

Repetition enhances learning, but don’t overdo it.

Mathematics builds on itself. For the most part, what you learn in chapter 3 will be used in chapter 4. On the flip side, the concepts you learned in chapter 3 will become more apparent as you work on chapter 4.

Make sure the student understands each concept. But as soon as he gets it, move on, but be ready to review a concept if you need to. Be aware of the difference between understanding a concept and mastering it. One can understand a math concept while still fumbling when using it.

To illustrate, I learned to type in early high school and immediately used the skill to write papers. If I had waited until I could get my speed up to 50 error-free words per minute before I turned in typewritten reports, I probably still wouldn’t be up to that speed. Today, I type about 70 wpm precisely because I moved forward and used the skill even though I hadn’t yet mastered it.

If you drill a concept until the student has mastered it, you run the risk of boring him, and you waste valuable time. If you move forward too quickly, you run the risk of frustrating the student. You must find a balance between over-drilling and moving forward too quickly.

Be Liberal with Partial Credit

This doesn’t often apply to the lower grades. A problem such as 4×6 = 24 can’t be partially correct. However, as your student advances in math, the problems will become more complex with multiple steps and have more places to make errors.

Let’s say you have a word problem worth 10 points such as two trains leaving opposite sides of the country, traveling towards each other at different speeds. When and where do they meet? There is a lot of setup and calculations involved. If the student sets up the problem correctly, does most of the calculations accurately, but at one point adds 3 and 4 to get 5, don’t give zero points. It may be worth eight points.

The curriculum I used with my children did not have prescribed points for assignments and tests. So, I would count how many steps it took to arrive at the correct answer, and that number would be the possible score. If the student had the right answer, he got full credit.

If he did not get the correct answer, I looked at his work, counted how many checkpoints he got right, and gave him partial credit.

Proofs Are Important

Some people will hate me for this one. But in geometry, proofs are essential. In fact, I would say that they are the main point of geometry.

Earlier, I mentioned how students ask, “How will I ever use this in the real world?” Well, let me turn it back on them.

Let’s face it, most students will not end up in a mathematics-intensive field. They probably won’t use 95 percent of what they learn in geometry.

Yet, what if the student wants to become a police detective. Why would she need to know the properties of an Isosceles triangle? Solving a case by looking at the evidence and reasoning it out sounds an awful lot like the thinking process one uses for a geometry proof.

What if the student wants to be a social worker who helps families in need? How will he ever use the Pythagorean theorem? Will he have all the applicable laws and available programs memorized? Probably not, but he will be familiar with them and know how to look up the specifics and logically use them to meet the particular family’s needs. Sounds similar to how one would do a proof in geometry.

Your student may not ever use the details of geometry in the “real world,” but he will use the principles of proofs no matter what career he chooses.

Remember the Purpose of Mathematics

Above all, keep in mind the primary purpose of mathematics: to train the mind in logical, deductive thinking.

A few of us are lucky enough to use advanced mathematics in our careers. If you have a student who is leaning in that direction, by all means, bring out the pragmatic aspects of mathematics. But everybody, no matter what career, needs training in deductive, logical reasoning.

Mathematics is like wisdom. It teaches you how to use the knowledge you learn from other subjects.

Doug Newton is a homeschooling father living in Clinton, Washington, with his wife, Lorinda, and their trade-school son and high school daughter. He has a BS in Computer Science and Mathematics and works on a financial projection model for life insurance companies at an actuarial consulting firm. He is currently working on a Master’s in Theological Studies.