Teachers First: Gain A Deeper Conceptual Understanding in Math

A sure-way to create anxiety in many teachers is to ask them to lead a math workshop. Faced with the task of explaining math concepts to peers, even teachers who lead math classes every day may run from the challenge.

Math: the language many teachers fear

Many schools and early learning centers across the country employ teachers who hated math as young people, struggled with it in college, and are currently faced with making sense of it for the next generation. In the past, traditional math classes taught an algorithm or formula to solve a math problem without requiring students to understand the reasoning behind the process. To many, math was equal to a foreign language that was difficult to comprehended.

Research on language learning suggests that anxiety and fear of failure can stand in the way of effective language acquisition. Stephen Krashen, a former linguistics professor and current emeritus professor of education at the University of Southern California, hypothesized that students with low motivation, low self-confidence, and high anxiety can raise an affective filter and form a mental block that impedes effective language learning.

In the language of mathematics, early failure at understanding math concepts can destroy a student’s sense of self-confidence. This results in a high level of anxiety as the student continues to encounter new math concepts. Foundational math concepts form the building blocks for higher levels of mathematics. Without intervention, early failure in math creates problems for teachers who are expected to nurture the next generation.

Research based math-teaching strategies

Elizabeth Green, co-founder and editor-in-chief of Chalkbeat, tells of Takeshi Matsuyama, a Japanese elementary teacher and college teacher trainer who used math teaching theories developed in the United States. Takeshi focused on using the language of math in discussions. Students came to understand the concepts of math and were drawn to its challenges by discovering principles and properties of math for themselves. Instead of dreading math instruction, students were highly motived and engaged in exploring mathematical concepts.

Yet, Green wrote in a New York Times excerpt from her book “Building a Better Teacher,” through the years our U.S. schools have not embraced the results of our own research. Generally, traditional teaching methods prevailed. Teachers tended to teach the way they were taught, which left little room for innovation and exploration in mathematical thinking.

College and Career Readiness Standards expect a rigorous level of conceptual understanding

With 21st-century college and career standards, teachers must now face their fear of math and find ways to engage their own understanding before they can begin to open this world of numbers to the next generation.

The college and career readiness standards expect students to understand multiple ways of arriving at solutions to problems. Accepting the viability of multiple paths to a correct solution ensures that students are developing conceptual understanding. Teachers who feared straying from the teachers’ manual for the “right” process and answer must now seek additional training and support to better embrace their own mathematical understanding.

Professional development in math: Find the right environment

Taking additional college courses or attending workshops may not always solve the problem for teachers. As in learning other languages, high levels of anxiety and low self-confidence can block effective acquisition of concepts.

A college professor told a teacher faced with failing a required math course that she should reconsider teaching because of her failure to understand numbers. However, instead of giving up, the teacher was challenged to retake the course under another professor. The second professor worked with the teacher to help her understand the way numbers work and introduced her to the language of mathematics in a low-anxiety situation. The teacher reported, “Through my own struggles and my new understanding, I now have the knowledge to show students different avenues to understand numbers.”

The problem is not that we cannot understand the language of mathematics; the problem is that we were not always taught to understand. To effectively learn any new language, including math, levels of anxiety must be reduced. Once solid learning occurs, levels of confidence naturally rise.

Teachers can seek out programs and workshops where the presenter offers appropriate developmental support without judgment of a participant’s struggle to understand. Use of appropriate hands-on materials to manipulate ideas can also help teachers see the reasoning behind the concepts. Once a teacher gains a deeper conceptual understanding of mathematics, she will be excited to share this new understanding with her students.

With over 35 years in administration and teaching in K-12 and higher education both in the U.S. and internationally, Dr. Nancy Cardenuto strives to cultivate creative and innovative learning paths. She is an adjunct professor in the master’s program at Concordia University – Portland, where she teaches courses in support of the Common Core State Standards.

Learn More: Click to view related resources.