Methods in Math

Math Philosophy
My experience with math instruction has been extensive. It spans from Korea to America for over two decades. Yet, the experience has been very similar in both countries – dry and uninteresting. As a future educator, I would like to explore the way I used to view math instruction and the way I view it now after being exposed to effective math instructions that can promote deep understanding and student engagement. This paper attempts to outline the change in my math philosophy before and after the mathematics methods course.
My first encounter with math began in Korea. There, I was forced to master many rote skills such as the multiplication tables and quick mental math. The teachers used physical and emotional pressure to ensure my mastery. With the solid background in math algorithm, my family brought me to America when I was eight. The math classes in the American schools were very simple compared to what I was used to in Korea. It followed the traditional method of instruction: check homework, review the past lesson, introduce the new lesson, do the book problems, and assign homework. As an English language learner, I found working with numbers and algorithm to be easy. I was in honors math since middle school, and I passed my AP Calculus before entering college.
Being unchallenged and bored in high school math made me lazy. Maybe that’s why I struggled through college advanced math classes. I didn’t realize that math required additional skills besides learning the rules and applying them to find the right answer. I didn’t have the deep understanding of mathematical concepts to appreciate the advanced calculus. I didn’t know how to apply higher thinking skills (such as evaluations, investigation, analysis, and synthesis) that were required in college math. Even now, I spend a lot of time using paper and pencil to do the most basic, everyday calculations because I don’t understand the basic numbers sense and estimation.
I do not want my students to take the misguided journey that I did. I want my students to find math to be meaningful in their everyday lives, to learn to comprehend math concepts concurrently with the many skills, to explore different tools such as computers and graphs in mathematics, and to take ownership in their own learning.
Before taking a mathematics methods course at Trinity, I never really criticized the traditional role of math instructions. I thought that math was a discipline that required teachers to be the masters of information. After the direct instruction, math teachers would ask students, rhetorically, if they understood a certain algorithm or problem. If the student answered the problems correctly, then the teacher would go on. They would call on another student if the answer was incorrect. Some teachers may ask students to work out a problem on the board or tell the class answer.
In the traditional math classroom, students didn’t need to understand as much as need to know what appropriate skills to use to arrive at a designated answer. Similarly, the homework assignments and tests were very algorithm-oriented. Even the problem-solving questions were just solving for the problem (not really investigative with multiple approaches to diverse solutions). In addition, independent work was emphasized in the traditional classrooms.
Conversely, the new methods introduced to me at Trinity are different from the traditional math instructions. In an effective math class, teachers should create and maintain a classroom norm that fosters student understanding, reflection, articulation, ownership, and critical thinking. This type of classroom norm mandates teachers to be engaging, hands-on, masters of questioning, and reflective.
Instead of emphasizing the algorithms, math instruction should foster higher-level thinking skills. Instead of providing one single, correct answer to a problem, students should learn to compare different strategies and approaches to problem solving. Instead of textbook problems, students should learn to solve real, meaningful, and relevant problems. It should provide the understanding of how mathematical thinking affects our everyday lives.
Math instruction should be about student understanding. In order to foster that, teachers must provide authentic learning and promote the ownership of learning. That means, embedding math instruction across the curriculum. Math should be integrated with art, sports, literature, social sciences, and other sciences. This is a natural way to engage with the students.
Another engaging instructional method is through the art of asking questions. The way teachers ask and the questions they ask are powerful in creating an effective classroom. For example, teachers can use a “fist to five” questioning method to check for individual understanding. Then, they could ask a student who has mastered the concept to explain it to the student who doesn’t understand. Furthermore, another student can be asked to explain the concept another way.
Just as in our everyday lives, students should collaborate and help each other. Ninety percent of learning is retained when students teach another student. Instead of busy work, the math instruction should promote active participation of all students. By working together with others, students can articulate their understanding and learn from others.
The real learning and understanding occur when teachers encourage the why’s and how’s of math concepts instead of the what’s. If the why’s and how's are genuinely explored with the students, then they will take ownership of their own learning. Along with understanding and ownership, students should work with hands-on tools, such as educational games, and integrate technology (eg. internet and graphing calculator). They cater to different learning styles and can engage all students.
Math is an understanding of relationships. It’s not only about numbers but about all relationships in our everyday lives, including numbers and time. By understanding relationships, we can make wise decisions in our everyday lives such as the amount of tip after a meal and balancing the checkbook. This is my philosophy of math. As a future teacher, I will try to create and maintain a classroom norm that fosters student understanding, reflection, articulation, ownership, and critical thinking. I will do that by being engaging, hands-on, master of questioning, and reflective.