# Back to school: Let's make mathematics more interesting | Opinion

Now that the school year has begun and students are slowly acclimating to live instruction, teachers are once again present in the classroom where one of their chief responsibilities is to make their instruction exciting and motivating. When we think back about how we selected our life’s area of interest, very often it goes back to a highly motivating teacher who extended her subject beyond the textbook. All too often, when I am in a social setting meeting new people, they may ask about my profession and when I mentioned the word mathematics the most frequent response I receive is, “Oh my gosh. I struggled through mathematics in school and I’m glad it’s behind me.”

Unfortunately, too many mathematics teachers are more concerned about “teaching to the test” than making the subject truly interesting.

At this point, you might be asking how does one make mathematics more interesting? Yes, it requires going beyond the textbook. When working with elementary school students where teachers expect students to realize that a number ending in an even digit is divisible by 2, why not extend that and say that when the number formed by the last two digits is divisible by 4, then the original number is divisible by 4. This, of course, could be extended to the last three digits determining whether a number is divisible by 8. Or showing students that by merely looking at a number and adding the digits, they can determine whether is divisible by 3 or 9, that is, if the sum of the digits is divisible by 3 or 9 then the number itself is divisible by 3 or 9. And so there are lots of rules for divisibility that are not part of the textbook and yet can make students truly appreciate arithmetic.

Telling a relevant historical story can also enhance mathematics instruction. For example, when in 1787 the famous German mathematician Carl Friedrich Gauss at age 10 was in a class with a teacher who wanted to keep the class busy for a period of time, asked the class to add the numbers from 1 to 100. No sooner had the assignment been given that young Carl Friedrich raised his hand with an answer. The teacher ignored him and found at the end of the half-hour that he was the only one with the correct answer. Instead of adding the numbers in sequence, he saw that adding 1 +100, 2 +99, 3+98 allowed him to merely multiply 50×101 = 5,050. This provided both the teacher and the class with a fresh view of arithmetic.

When thinking back to the high school geometry class most people recall that it consisted largely of doing geometric proofs. Unfortunately, not enough attention was given to exploring some of the astonishing results that we can visualize in geometry. For example, suppose you take any 4-sided figure (quadrilateral) and locate the midpoint of each of the four sides. By joining these midpoints consecutively, regardless of the shape of the original quadrilateral, the result will always be a parallelogram. Taking this a step further, a teacher could use this scheme to ask students under what circumstances will this resulting parallelogram be a square, rectangle, or a rhombus?

We are currently inundated with daily statistical reports about the COVID-19 pandemic. Understanding these reports is very important. Related to this is the topic of probability, which is being taught more in the schools now than in previous years, and yet too often teachers do not properly motivate students by employing some of the spectacular results that can be garnered in everyday life situations. For example, the probability of two students in a class of 30 students having the same birth date is astonishingly 71%. In a group of 50 students, it’s almost 100%. Having mentioned that, most students would be eager to find out how that was arrived at. What could be a more motivating way of introducing probability than that?

It is clear that we are struggling to get back to some form of normality in school settings by providing students with the excitement of socialization and the richness of on-site instruction, for which there is no learning parallel. After this isolating hiatus, wouldn’t it be great if we opened up, as well, a new leaf for our instructional techniques, making the return to school feel even more consequential and stimulating. For the mathematics teacher, there is the opportunity to motivate students to explore mathematics concepts and ideas through activities that extend beyond the textbook, creating math enthusiasm through real-time examples. Invoking interest in math is not only a meaningful task for mathematics teachers but for parents, who can encourage students to study mathematics without apprehension and with an appreciation for its relevance in their own lives.

Let’s make sure that the next generation, growing up in a more technological world than in the past, will genuinely appreciate the power and beauty of mathematics.

*Alfred S. Posamentier is a lecturer and professor emeritus of mathematics education at The City College of New York.*