# A MATH PROBLEM

*By Sharon Hillestad*

I started my career as an educator in 1966 with 22 third graders in a Wisconsin public school. Modern math was a new way to teach math. I just had to follow the teacher’s guide and do what it said. It was “teacher proof.” All my students were to do the same lesson at the same time.

I offered to teach two chapters a day from the math textbook to students who wanted more math. It was double work and five third graders who loved math jumped at the chance. The rest of the students thought one lesson a day was plenty.

Then there was Julie who not only did double math lessons, but also did every extra credit problem in the back of the textbook. She was in a group by herself.

**Testing at the end of that school year revealed that the fast motivated students, even Julie, knew very little more math than the regular students.** Shouldn’t students who get through the entire Modern Math textbook know more than those who did a little over half the lessons? I became suspicious of those textbooks.

**As Foundational Math Instruction disappears from Grade School, Students able to do Advanced Math disappear from High School.**

I only taught in that school district for two years. However, eight years later I spoke to a teacher who had been teaching in that district for nearly ten years. **In 1968 this math teacher taught five classes of advanced math students. By 1977 he had only one advanced class.** This high school math teacher had to teach basic math skills to students who had gone through Modern Math lessons during grade school. His morale was as low as his students’ math scores.

Several years later I met an outstanding math teacher by the name of Stan Hartzler. His high school students had won awards. His other claim to fame was that he researched the history of math textbooks. **His study included examining copies of textbooks dating from the time of Thomas Jefferson to the time of Ronald Regan**.

## Textbooks Making Math Harder

We could expect that the textbooks would change somewhat during those decades 1800 to 1980, but who would suspect that **textbooks would gradually make teaching and learning math more difficult.**

**This was done by teaching math concepts and skills out of sequence and by not mastering foundational math skills.** This was happening even when I was in grade school. In 1953, my 4th grade teacher skipped around in the arithmetic textbook. She knew what skills needed to be taught first. Experienced teachers taught around the textbooks, adjusting the lessons as needed. Novice teachers, such as myself, adjusted to the textbooks and followed the teacher guides to the letter.

In the 1960s, with the advent of modern math, arithmetic skills (addition, subtraction, multiplication, division, fractions, decimals and percents) took a big hit. The Teacher’s Guide did not include practicing the addition facts or multiplication facts in third grade. But I sure spent a lot of time teaching “sets and subsets.” The students had pages of “greater than and less than.” These symbols were a big deal in third grade and not even mentioned in fourth grade. I have never seen them used in life. I didn’t know then that math textbooks couldn’t be trusted.

**I taught useless math concepts instead of teaching basic arithmetic skills.** Stan discovered that these changes first occurred in the 1920s. This was just after compulsory education to age 16 became the law throughout the US. **It appeared to Stan that the textbooks were written to limit the number of students who would eventually master advanced math.**

Stan did not sit on his discovery that math was purposely being made hard to learn. He presented these findings to the American Mathematics Society and the National Council of Teachers of Mathematics. These people regulated the math curriculum and the training of math teachers.

The rationale of the math instruction regulators was that there are jobs in society that need to be done, but that no one really wants to do. **It is easier to find workers for less desirable jobs if there are large numbers of people who are convinced that they are not capable or qualified to do the more desirable jobs.**

After one of his presentations, a professor approached Stan Hartzler and said, “We don’t want too much of a good thing Stan. Can you imagine what kind of a job we would have if everyone was as good at math as you and me?”

**Math curriculum was designed to be understood by the upper 5 to 10 percent of the class.** Elitism created and is still creating an expanding working lower class of Americans.

That cleared up the mystery of the math textbooks when I was a public-school teacher. It also explains the convoluted math homework that I’m dealing with now as a private tutor. Multiplication and division “strategies” make learning these concepts difficult and hateful. I am helping students drill “rounding numbers” and “estimating answers.” Students are being taught to guess.

What should I tell the 8-year-old boy when he asks, “Why is multiplication so hard to learn?”

The problem: the boy’s parents are paying me to help him master the homework. The truth is that the curriculum/homework has been designed to keep this student from getting good at math. Not doing the homework may cause him to fail 4th grade. Not being properly taught arithmetic will make it harder for him to support himself, to be successful, maybe even to be happy.

What should I tell him and his parents? What would you tell them?

Sharon Hillestad, Educator

January 2023

Whiteboard from a recent tutoring session. To solve the problem 362 times 47, my student was taught to break the numbers apart in the manner shown on the right. He kept getting the wrong so I demonstrated the “old” way for him on the left.