Math Chat: What Does it Mean to be “Good at Math”?

The Never Ending Math Problem Some years ago, I taught an evening course at a community college that catered to working adults. The students varied in age from 20 to 60, but they all shared one thing in common. They all had a huge amount of math anxiety. They were all absolutely convinced that they were not “good at math.” This class, with the innocuous name of “General Mathematics for Non-Mathematicians,” was designed to bridge the gap between the skills the students were supposed to have mastered in middle school and high school and where they needed to be. After the mastery of skills in this class and two other prerequisites, the goal was for them to excel in their future mathematics classes and graduate to become clean-room technicians, health workers, machinists, electricians, and dental hygienists.

I remember one woman in particular who came up to me at the beginning of the school year and was literally trembling because she needed the class to graduate and she was so afraid she wouldn’t pass. I promised her that she would do well and would even grow to like math. She looked at me as if I were from Mars.

So what does it take to be “good at Math” and what can we do as educators and parents to foster this mastery in our children? The beginning steps to understanding any subject and to delve into its inner workings further is curiosity. Without intellectual curiosity and a desire to explore there can be no progress into a deeper level of learning. Adults who have had little success with mathematics have already labeled themselves with the “I’m NOT good at math label.” One of the keys is to explain to students that mathematics is challenging for everyone.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” –Albert Einstein
Adopting a spirit of exploration by pulling numbers apart, going down blind alleys with trial and error, playing number games, and teaching students how to self-check their own work can help their fears subside. A student who has been shown varying techniques for skill mastery and concept understanding has a greater chance for success in mastering mathematics at all levels. Our job as teachers, educators, and parents is to help foster this type of high-level engagement and interest.

Everyone makes mistakes. It’s OK to make mistakes. The first time I tried to bake a loaf of bread, I did something wrong with the yeast. My bread turned out to be a lethal weapon instead of something palatable. The next week I tried again. The second loaf of bread was even worse than the first. But my parents and my teachers taught me not to give up so easily. With any new skill, my expectation was, and is, that it may take me some time to master it. The third time, I spent a lot of time focusing on the details of the proper yeast proofing. The resulting loaf was almost as tasty as my Mom’s home-baked bread. Those bites of bread tasted especially flavorful to me because the success was hard won.

The student who is “good at math” doesn’t give up too easily. He or she realizes that there are usually several different ways to solve any mathematics problem. If one pathway doesn’t work or is arduous, there might be a pathway to a clearer process around the corner. There are over 400 proofs of the Pythagorean Theorem. They all achieve the same goal but they vary greatly in length and complexity. The details of each proof matter. Those details are what make that particular proof viable.

I have made this letter longer than usual, only because I have not had the time to make it shorter. –Blaise Pascal

Just like Chinese, Italian, or the acronyms associated with a particular industry, mathematics is a unique language. The use of symbols in mathematics helps to communicate precisely and in a relatively short length. However, just as it takes mastery to be fluent in a language, it takes careful thought, time, and effort to become masterful with mathematical language. But here’s the joy in it…we can write “x + 7 = -25” and it will be understood around the world. Fluency in any language requires practice and the language of mathematics is rich in visual symbols. Once a student understands those symbols, they become second nature and a very complex thought or relationship can be summarized in a very short space.

So, let’s think about how we can represent what it means to be “good at math.”

a = intellectual curiosity
b = a spirit of exploration and play
c = persistence when faced with challenges
d = a toolkit of different techniques to try
e = the ability to pay attention to details
f = fluency in the language of math
g = “good at math”

a + b + c + d + e + f = g

The good news is that these are qualities that we can foster in our children and students. We can also work on these qualities in ourselves as we improve our own mathematical abilities as educators.

My adult student who was trembling at the beginning of our math class went on to become the best student that quarter. She said to me “I wish I had realized how much I could enjoy math. I never would have been afraid to try when I was younger.” That poignant comment stuck with me and influenced my view of the role of mathematics educator ever since.


Teaching With Technology: Jenny David

Welcome to Teaching with Technology! This series of guest posts asks educators to share how they integrate technology in their classrooms. These posts are written by a very special group, CK-12 Foundation’s Champions.

Today’s guest post is by Jenny David. Jenny is a Special Education Teacher with the TCSOS Nexus Program in Jamestown, CA.

How do you currently integrate technology in your classroom (e.g., products used, devices, etc.)?
I am a special education teacher for students in 5th-8th grades who have EBD (Emotional Behavior Disorders). Many students are not at grade level. I utilize the CK-12 grade 6 math book for all students, with modifications based on individual levels. I also use Raz-Kids as a supplement to the SRA Corrective Reading Program.

What have been the advantages and disadvantages of using technology in the classroom?
My students seem less threatened by it than by being handed a big textbook. Also, today’s math books have a lot of information and graphics on each page, which many of my students find too distracting and overwhelming. The CK-12 math format is more focused without many distractions.

The disadvantage is, although I have been teaching for 24 years, my technology skills need to get caught up to today. I continue to take every workshop that is offered and try using all the latest in technology, but it takes time! Also I don’t have a budget to buy some of the items that could be helpful in the classroom, e.g., more up-to-date computers, iPads, and e-readers.

How have your students benefited from technology?
They are able to practice skills at individual levels and get immediate feedback.

If money were no object, what would you like to see happening in your classroom with respect to use of technology?
I would have more computers available, along with e-readers and iPads.

We hear the phrase “21st Century Skills” often with respect to technology and education. What are “21st Century Skills?”
Utilizing today’s technology to learn, communicate and create. In a way we are returning to the Renaissance of learning when people had broader knowledge of a variety of disciplines around a common theme of study, instead of intense specialization where people do not see interconnections.

Describe the “classroom of 2040.” What’s different? What’s the same?
Hopefully we do a better job of meeting individual needs so that all students can reach their full potential.


Teaching With Technology: Philip Lacy

Welcome to Teaching with Technology! This series of guest posts asks educators to share how they integrate technology in their classrooms. These posts are written by a very special group, CK-12 Foundation’s Champions.

Today’s guest post is by Philip Lacy. He is the Director of Instructional Technology at Niles Township Community High School District 219 in Illinois.

How do you currently integrate technology in your classroom (e.g., products used, devices, etc.)?
We have a Ubuntu based 1:1 program using Free and Open Resources wherever we can: Moodle, Open Office, NROC content, other OER.

What have been the advantages and disadvantages of using technology in the classroom?
Change is always difficult. Helping teachers and administrators see the value and quality of OER content, in addition to the whole paradigm shift teachers must experience and embrace to enable a new instructional model to evolve in which technology becomes a seamless tool.

How have your students benefited from technology?
Just-in-time access to materials, equal access to computers/technology in the house and at school.
Increased opportunities for authentic learning, supplemented by the access to information facilitated by ubiquitous access to technology.

If money were no object, what would you like to see happening in your classroom with respect to use of technology?
1:1 student/family and faculty access to devices with universally available, platform-agnostic interactive and engaging content.

We hear the phrase “21st Century Skills” often with respect to technology and education. What are “21st Century Skills?”
Learning how to learn. Technology based research, analysis, and collaboration skills are becoming more valuable than rote memorization. Knowing and understanding which tools to use and how to use them (or where to find the information to do both) are increasingly important in a world predicated on change.

Describe the “classroom of 2040.” What’s different? What’s the same?
Students would have individual, non-standardized devices. The curriculum would be competency-based, with rolling enrollment and blended or virtual access. There would be no classroom per se, as anywhere two or more people meet to learn would be a “classroom”.