Every math teacher has encountered the question. Midway through a lecture the hand goes up and the query is posed: “When will we ever have to use this stuff?” The response a teacher gives to that class can have a profound impact on not only that lesson but the course of those students’ math careers.
Because of that precise educational moment of truth one of the main points of emphasis with the Common Core State Standards (CCSS) for mathematics is the requirement to show real world applications of the material being taught. This objective, if fully embraced, will result in a significantly altered the approach to teaching math, especially at the elementary level. In order to create the connections necessary to clarify for students the power, potential, and prevalence of the curriculum they are being taught, the teacher must have a solid mathematical background and experiences which will allow him or her to dramatically illustrate the place of mathematics in a student’s environment.
The wrong answer
In too many classes the answer to “Why do we have to learn how to factor” is “Because you will need to know it.” This is what I refer to as “the why/because rationale for mathematics” and it is one of the primary reasons so many individuals either dislike or fear math at an early age. Enter the CCSS math philosophy.
Mel Riddile recently sent me an article on five steps that need to be taken to effectively implement the new standards. The changes were:
- Combine content and practice.
- Don’t rely solely on the textbook.
- Make connections across the standards.
- Create a classroom environment where students feel free to invent strategies.
- Engage students in rich mathematical discussions.
As I read those strategies, I realized that they had been employed for many years in my own classroom.
A fresh start for everyone
I began every course I taught with a subject the students had not previously encountered. For years I had heard students complain about learning “order of operations” for the fifth consecutive year. Consequently, in Algebra 2 I would start with sequences and series. In Pre-Calculus, the initial topic was probability.
The strategy was simple—on the first day of school the playing field in the room was level for all students and the material was instantly challenging. Regardless of whether a student had earned a B+ in Honors Algebra 2 or a C- in regular Algebra 2, both were starting with the same knowledge base in probability. Instead of being instantly behind their more successful classmates, weaker students were beginning at the same starting line. Those with strong backgrounds could not coast through a mind-numbing review. There was always a loud gasp on that initial day of school when it was announced that chapter 11 would be the first to be studied. The message was clear—this was one math class that was not going to follow the sequence of a textbook.
Math is cool and all around you
I love math because in a world full of unpredictable events, it is a constant source of reliability. On the first day of probability, I would have each of the 25 students in the room write a number between 101 and 200 on a piece of paper. Then I would pose the question “With 100 numbers to choose from and 25 being selected, what do you think is the chance that any of you have chosen the same number?” In theory each student could have written four numbers and still not have had a match. The typical answer was either zero or one. We would then have the selections read aloud. Much to their astonishment, at least four pairs would be a match. The process was repeated with numbers between 201 and 300. The same results would occur. I would then explain to them that this was the expected outcome due to probability. The educational hook had been set.
Sometimes the truth is more interesting than fiction
Math teachers can create lesson plans as interesting as “Myth-Busters” and far more educational. Ask a student what are the chances of flipping a coin and it landing heads and most will say 50-50. Then have every student flip a coin twenty times. A show of hands reveals that very few had ten heads and ten tails. Normally, out of 25 students only two or three would have such a result. But then combine the total of all 500 tosses and the average is stunningly close to 10 of each. A teacher knows that their math classes are making an impact when their students are telling their friends what they have “discovered” in the class. Lessons like the coin toss and picking a number will create just such a buzz.
In sequences and series we learned how to determine the seating capacity for a rock concert; derivatives could find max and min points which allowed the class to find the price point for maximizing profits at that concert.
A “tangent to a curve”(also found with the derivative) is a line that intersects a curve at only one point. The concept sounds pretty boring until it is demonstrated that it would be a wonderful piece of information for finding the precise trajectory of radiation treatment for a tumor on a kidney. The treatment would attack only the cancer. Throw open to the class what other uses would be possible. (Targeting a missile attach is an inevitable response)
Such approaches to math are especially critical in elementary school when everyone is beginning to first learn the subject and many negative views of mathematics are planted as the result of failure. Rote learning with little connection to the world around them will create too many negative attitudes toward the subject. Only a teacher with an expansive knowledge of math can engender the necessary enthusiasm for the actual subject.