I hear it from adults. "I'm not a math person" or "I don't like math" or more likely, "I hated math when I was in school." That concerns me, especially when these adults say it in front of children. What message are they sending when they say that?
When I was in school, math was a subject I enjoyed. Memorizing procedures came easily to me, and I got good grades as a result. But I realized years later that I remembered very little of what I had learned in high school, and today, I would struggle to do even the most basic algebra, geometry, or trigonometry problems without assistance. So did I really "learn" that math? I don't think so.
As an early childhood teacher, our students learned math through hands-on exploration activities - counting objects, matching pictures, making patterns, and learning about number concepts like more and less, one-to-one correspondence, and ordering objects by size. At that age, math was fun.
When I began teaching second graders, I admit that I followed the grade level curriculum and students completed assigned work in their workbooks. Those who were finished early were able to "play" in the math center which had a variety of games and activities, and I provided extra assistance to the struggling students. My teaching changed dramatically after I had the opportunity to attend a series of sessions throughout the year on math problem-solving. We met with same-grade teachers from other schools, created a common assessment task, examined student work, and had deep discussions about what we observed about student understanding. We learned with and from each other, and I was so grateful to have had the opportunity to collaborate with teachers from other schools. More importantly, I no longer viewed math as a series of problems to be answered in a workbook; I saw it as an opportunity to talk about numbers and to have discussions with students to understand their thinking.
I transferred to another school, and the expectation from administration was that teachers would collaborate, create common assessments and rubrics, and share our student work. Math was integrated into our interdisciplinary units, and I found many opportunities to extend and expand students' mathematical thinking. It was an exciting time for me, as a teacher, to have a principal and colleagues who understood the value of going beyond the surface level, and math was an important part of our school day.
When I became a principal, I observed that students were primarily using grade level math textbooks and workbooks. One of my goals was to help our teachers to transition to a different way of teaching math. We had two wonderful instructional coaches who worked with grade level teams to make their lessons more relevant and engaging and to listen to students to check for understanding. It was evident through our observations and conversations that many of our teachers were challenged with using concrete objects to solve math problems so we learned about the Concrete Representational Abstract Approach Teachers had the opportunity to explore different manipulatives to discover and discuss how to use them with their students for deeper understanding. We had other professional learning opportunities focused on math such as Lesson Study, Math Misconceptions, and Math Problem-Solving. It was challenging; teachers struggled to have conversations about math with their students. They were so used to following the textbook and looking for correct answers, but to their credit, they realized the importance of changing how they had always taught math. In fact, many teachers chose to have me observe a math lesson for their required educator evaluation, and we had rich discussions during our post-observation discussion. That, to me, was validation that we were on the right track. Schools are often so focused on "covering" the curriculum and raising test scores; our teachers were having conversations about math. I knew this was not the norm, and even in my retirement, I continued to explore how we could change math instruction in our schools, which is like a staircase, going in one direction, one step at a time. Learn a concept, do some practice worksheets, take an assessment, move on to the next chapter. Math instruction needs to change.
I recently listened to a podcast "Why a New Teaching Approach is Going Viral on Social Media." The introduction states, "When a professor's research showed that standard methods of teaching problem-solving weren't working, he set out to figure out what led to more student thinking." What was this new teaching approach? I was intrigued and listened to the podcast, and it was an 'aha!' moment for me. How do we get students to do the thinking where math is concerned? The word that shouted to me in the podcast was "mimic.". Instead of having students work in teams to grapple with a problem, we adults teach them how to solve it, and students follow the example to work on similar problems. They aren't thinking; they are mimicking the process.
That is a problem. No wonder we don't see the beauty in mathematics. No wonder kids hate the monotony of math class. Rather than thinking and being challenged, our students are just mimicking. Often, teachers spend valuable time reviewing math concepts after a break or before high-stakes tests. If students forget what they learned, have they really learned it?
Students need to be exposed to real-world math experiences with opportunities to struggle, to think, to ask questions, to research, and to problem-solve. This article, Understanding the World through Math shares how important it is for students to explore math in a real-world context. Our high school grandsons take advanced math, but our math conversations focus on NFTs, baseball cards, and more recently, Fantasy Football. They patiently and confidently explain about their investments and are learning about buying and selling. They make mistakes, but they are thinking and learning in the process. They are learning to look at statistics to determine if they should switch out a member of their team. As this year is an election year, we will have discussions about the presidential race, looking at polls in different parts of the country and discussing how candidates decide where to focus their campaigns to get the 270 Electoral College votes to be elected. Politics is an important topic of conversation in our family, and there is so much math involved.
So back to my opening statement about adults who say, "I'm not a math person" or "I don't like math" or "I hated math when I was in school." I am positive that math plays an important role in their everyday lives. It might not be analytical geometry or calculus or trigonometry, but they are adjusting recipes for their families, looking for the best deals at the supermarket, determining how many buckets they'll need to paint the exterior of their home, tracking their daily exercise, deciding where to go for a loan to pay their child's college tuition; the list is endless!
I've posted this poster before in my previous blogs, but I am reposting it because I think it most accurately depicts what math education looks like in many schools and districts and what it can and should look like.
I am hopeful that maybe enough teachers will change the way students learn math to be less mimicking and more thinking.. Our students deserve it.
The following are a few of the blogs I wrote about math education:
Textbooks or Professional Development?
Opportunity to Model Math Problem-Solving
Math Literacy
Thoughts about Math Fluency and Homework
I Wish I'd Learned Math This Way
Playing with Math
Playing with Math - Part II
A New Generation of Learners
