Monday, August 19, 2019

Every Word Matters in a Mathematical World

Recently, I had the pleasure of listening to Dr. Concepcion “Como” Molina at a company-wide conference. I was vaguely familiar with his teaching concepts, however never had the pleasure of seeing him present. I am always interested in learning and crave new techniques that can save me time and effort.

What happened next, I was not prepared for. Dr. Molina spoke about the language of teaching and learning. How one word can change the meaning in a sentence or can be interpreted in several different ways. For instance, during a lesson on addition, a teacher may verbally ask students to add up numbers in a problem. What does this actually mean? How do students interpret the concept or define what is meant by “add up?”  

Conceptual understanding of various math topics is not as straight forward as you might think. Some students might interpret the concept of “add up” to literally mean place the sum of the numbers at the top of the problem. Thus, adding the numbers in the direction of “up” or at the top of the problem. I found myself stunned and hanging on every word. I wasn’t the only person in the room that had a personal “aha” moment.

Interpretation of adding the sum of an equation “up”.

Dr. Molina continued by explaining the little things that can be done when teaching students at all different levels. He was excited to introduce us to the idea of teaching pre-algebra in grades one through seven because there's so many things that can be taught as far as algebra through arithmetic. The fundamental practice of teaching mathematics, for the most part, is taking things apart, putting them together, or reorganizing them.

I started questioning things and as I looked around the room…I could see the mathematicians’ eyes questioning the concepts as well. I watched as several teachers in the audience were seriously studying his interpretation of what the math equations and symbols COULD mean. You see, Dr. Molina showed us in a very clear and concise way what it is like to read a math problem when you have limited or no English language skills and honestly even students who are native English readers. He shows us how to come at math from a completely different point of view that provides more context and meaning to what you are learning.

Dr. Molina explains that to really understand mathematics you must pay a lot of attention to the language and the symbolism. “We really have to do a better job of increasing the content knowledge of elementary teachers, because as I say, you can't teach what you don't know. It's more about the methods. It's like you're teaching someone to fish as opposed to giving them the fish. You know, if you teach them how to fish then they [teachers] can create a lot of their own stuff and really do a better job of teaching the math that kids need to know,” comments Dr. Molina. It’s about visualization, concrete modeling, approaching it from different perspectives. Teaching is about being mindful of the instructional language that is being used because it’s very easy to change one word in defining a concept that can lead to “adding up.”

Every single one of us comes from somewhere. We all experience different events in our lives that shape who we are. Our families, friends, educators, and everyone in our social circle. This starts at a very young age. We can easily agree that we are all unique individuals with diverse needs. So, with this in mind, why would we expect kids to learn in the same manner? Additionally, understanding our differences and creating a language of learning that includes ALL students is key to providing equality in education. When everyone understands the language, symbolism, and representation of math concepts, teaching and understanding become easier.

“The Problem with Math is English” is Dr. Molina’s new book. He shares his story with humor and wit. His book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism. The idea about mathematics and the language connection really is not just about EL students, it’s about ALL students.

"In this easy to read book, Como Molina—with rare humor, insight and thoughtfulness—shares many of the lessons he has learned while providing professional development for mathematics teachers in U.S. public schools. Como delightfully challenged my own understandings of the important relationships between mathematical ideas and the language we commonly use to teach them."
—Dr. Stephen Marble, 
Associate Professor of Education, Southwestern University, 
Georgetown , TX

His examples can be profound “aha” moments in your classroom. Decide for yourself and give it a try. As you’re building your curriculum plans for the school year, consider adopting some of his concepts.

I hope you share some of you “aha” moments this fall. Let’s continue to inspire each other. Our passion for education matters and the language of learning continues in every word we speak.

About the Author
Concepcion Molina, Ed.D., is a program associate with SEDL, a private, nonprofit education research, development, and dissemination corporation based in Austin, Texas. Dr. Molina supports systemic reform efforts in mathematics and works to assist state and intermediate education agencies in their efforts to improve instruction and student achievement.

Written by Jody Jepson, Senior Communications Coordinator, Assessment Technology, Incorporated