The Art of Teaching Math

Measuring math ability by thinking more deeply vs working more quickly

Barb Corna, Instructional Coach, Northwood Elementary School
Published on May 10, 2018

Timed math tests create math anxiety

“Okay, everybody! Put away your books and get ready for our weekly, timed math test.” Do the words, ‘timed math test’ make your stomach clench just a little? Those words often bring back memories of math anxiety along with a long-term fear of math.

Somewhere along our elementary school journey, teachers, parents, and our educational system have instilled in kids that it’s okay to be bad at math. Collectively, we have given kids “a pass” on mathematics because we have the misconception that students are either intrinsically “math people” or not — and the reality is, that’s simply not true. The beginning of that downhill slide could be that age-old, fear-instilling, timed math test.

Using manipulatives helps students visualize math

Visualizing math with a new mindset

Arriving at the realization that it really doesn’t matter if it takes one student a few seconds to come up with the right answer and another one a minute of deeper thinking and mulling it over has led Napa Valley Unified School District to adopt a math curriculum called “Bridges” along with a new approach to teaching it. In its third year, students are learning math concepts with confidence and a new math mindset. Instead of memorizing algorithms and completing worksheets of problem sets, you see teachers setting up a situation for students to construct solutions based on their own learning styles. Math is no longer a passive activity where kids sit and follow along with the teachers — the students are actively involved. Working in teams, they share ideas and clarify with each other what they’ve learned. They’re building their knowledge together and teachers are facilitating the learning process.

Students continue to memorize formulas and algorithms just like before, but it’s not for memorization sake. It’s memorization with the knowledge that backs it up. As kids progress through each grade, they need to know how to resolve algorithms and use addition and subtraction and multiplication because that’s the most efficient way to solve problems; however, they don’t blindly solve them step-by-step. Now, they understand why they’re doing what they’re doing, as well as how.

While the Bridges curriculum opens up new learning experiences for students, it also provides teachers with opportunities to inspire their students. All teachers want to motivate their students and they crave those “ah ha” moments when they see a child’s face light up with comprehension. Teachers also want to make sure students leave their classrooms prepared and with a positive attitude about math. They see the difference that this curriculum makes but they also need support as they transition their teaching practices. This is where a new program that I’m involved in from NapaLearns called Accelerate Math enters the picture.

Accelerate Math: Supporting teachers through coaching and video-based feedback

NapaLearns is helping to accelerate the teacher learning curve by implementing a new coaching model that incorporates online demonstration lessons by experts, teacher goal-setting, and video-based observation and feedback for participating teachers. It’s a three year long program and includes four schools. One day a week, I mentor a cohort of 30 other teachers from Snow, West Park, Yountville or my own school, Northwood Elementary School. Our goal in supporting these teachers is to accelerate student achievement in math.

students solve problems in teams
Students work in teams to share ideas and solve problems

On a routine basis, I conduct demonstration lessons, appraise videos of teachers conducting a lesson, or meet with Professional Learning Community (PLC) teams. We strategize on “how do you incorporate workstations in the lesson?” Or, “how do you meet your struggling students?” Instead of doing a “one size fits all” approach, my goal is to meet everybody where they are. Some people don’t need to meet with me very often because they’re feeling really comfortable with Bridges; they’ve got it and they’re good. But I will spend more time with teachers who need help understanding certain concepts. Many have stated that they wish they had been taught this way!

“I eat math!”

We are starting to see a difference and I believe it’s a combination of the new curriculum and our teachers becoming more comfortable in this new teaching practice. West Park Elementary had a goal of a 10% improvement in the Math Inventory test at the end of this year. Their students have already surpassed that goal.

More important, I love hearing the kids! I had a third grade student tell me, “I love math. I eat math!” The students’ enthusiasm, the look on their faces, and those moments when a child figures out a problem they’ve been struggling with — they are happening more often now. Teachers live for these moments; they make our day … it’s food for our soul.

Lessons learned and recommendations

  • Building a level of trust is super-important and it takes time. When you’re a coach, it takes a while to establish a trusting relationship. It took the first few months for the teachers to figure me out and realize that I wasn’t going to judge them. And, many felt like they’re bothering me; it’s not 2nd nature for a teacher to reach out to a math coach. There are still a few who are reluctant to ask for help and there are always going to be those who don’t want to open up because they’re afraid it makes them vulnerable.
  • Using video is intimidating but necessary. We’ve only held one video session this year — it took awhile to get the right platform and equipment — but videotaping and watching yourself is super-valid. Teachers are their own worst critics. We want to be that inspirational person that our students remember. Videotaping is the right way and trust needs to be built up in its use; it’s hard, but it’s how we get better.
  • Debriefing after a lesson demonstration. I’ve learned that after each model lesson I give, reviewing the strategies and techniques used in the classroom with the teachers is important. It gives the teachers the opportunity to internalize the ideas into their own teaching practice.
  • Once-a-month model teaching and review is adequate. Each week I’m at a different school, so I rotate through each one monthly. This cadence gives the teachers an opportunity to talk to me or to see me, and then a month to implement those ideas or get better at the practices we discussed. The next month they’re ready for a new concept. Trying to do more than that isn’t productive: Teachers need to work on one or two teaching strategies each month, otherwise they will suffer from burnout.
  • Contagious enthusiasm is the best lever. The number one way to get more teachers involved in this teaching methodology is enthusiasm. The first thing I learned as a coach is to help the teachers that want it and to try not to dwell too much on the others that don’t. When the teachers who sought help get excited, the buzz starts to go through the school and others get swept up in the excitement.
  • The same cohort should continue beyond one year and scale the program. I recommend staying with this cohort for another year because our work has just started. However, we’re looking for sustainability and scalability so I would like to keep this cohort and run a second one concurrently. There is a math lead in every school plus there are one or two teachers at every school that are just as passionate and wonderful at teaching math as me. I would like to see a new cohort of math leaders. Then when this program is done in three years, you would have all the math leads trained to be coaches for the future.

This year has been a very positive experience for the teachers and me. I’m excited to continue building relationships with other teachers and the next cohort. The positives so outweigh any frustrations that the program should continue and scale.

About Barbara Corna
Barb has been at Northwood Elementary for 27 years. She has taught everything from 3rd to 6th grade. Early on she developed a passion for teaching math in a more meaningful way and part of that started when she was attending Sonoma State. Her professor, Rick Marks, introduced the use of manipulatives to deepen her understanding of math concepts. At that point she wondered, “Why didn’t anyone teach it to me this way?” Visualizing math helped her to see the connection between ideas and that is what she tries to do with her students and the teachers she coaches.