The Connection Between Real Life and “New Math”

I teach high school math, and I know the public has a love-hate relationship with it. This relationship is long overdue for therapy: integrated math model therapy, to be specific. Here’s a specific example from my school district and my classroom.

When it comes to math, I can imagine cold fear running down the center of many parents’ spines. I get it. I teach high school math, and I know the public has a love-hate relationship with it. (Minus the love.)

But I think this relationship is long overdue for some therapy. As a teacher, I hear parents’ frustration all the time: “They’ve changed math so much that now I can’t help my third grader with his homework!” “Aren’t our kids supposed to be memorizing times tables?” “Where did all those graphs, figures, and extra words come from, anyway?” Enter the resident boogeyman fueling these concerns: the Common Core State Standards (CCSS).

I won’t try to convince you that the CCSS is without its challenges. Any initiative is bound to have opportunities for improvement. In fact, many of the complaints about Common Core are part of the normal growing pains with any systemic change. Since these changes include how we teach and assess our children, this only makes the debates and discussions more heated.

A current high school student in North Carolina will take Integrated Math 1 (ninth grade), Integrated Math 2 (tenth grade), and Integrated Math 3 (eleventh grade) before senior year. Each of these math courses focuses on some of the portions of traditional classes. For example, my Math 2 class started the semester talking about geometry topics. Later on, we will do a unit on trigonometry, followed by several algebra units. Before the end of the year, students will also be introduced to new topics in probability.

At its best, the integrated math model encourages students, teachers, and parents to understand the big picture in math. It’s not about algebra or discrete math or calculus. Instead, it’s about logical ways to view, measure, and even describe the world in which we live.

Ideally, a student who has been taught using CCSS could explain how to model real-life phenomena such as gentrification of a local community, while also recognizing the significance of each factor and variable from the created model. In other words, math takes on real-life meaning for our students. My colleagues and I hope the new standards will give us the freedom to perform more real-world analyses in the classroom and fewer tasks focused on rote memorization.

I see the positive impact of the new standards when I review my sons’ homework. My third-grade son is working to understand the reasoning behind the math facts he learns. He is still memorizing the multiplication tables, but he is also learning that multiplication is repeated addition. This means that when he gets to high school, he will understand that math is not just about plugging in formulas or solving random equations. This understanding and willingness to use critical thinking and writing in the math classroom allows us to explore, do projects, and truly understand math—as opposed to memorizing more math facts.

Ideally, the CCSS point teachers towards student-centered learning and more hands-on assessments, as opposed to traditional pencil-and-paper tests. Although we still have traditional tests in math, the standards are written to encourage educators to incorporate guided explorations, portfolios, discussions, and projects in the curriculum.

For example, as my colleagues and I collaborated at the beginning of the year on how to teach students the new standards, we actively sought out opportunities for students to explore and find key formulas—as opposed to just handing them formulas to memorize. Our discussion led me to design a lesson where students observed the similarities and differences between geometry shapes. They had to categorize those similarities and differences and then translate them into the language of math, using symbols and variables. This type of exploration and group discussion was designed to increase students’ understanding and analysis of those shapes—not just memorize their similarities and differences.

Next week, my students will begin their introduction to trigonometry. I won’t be starting the discussion with the fabled SOHCAHTOA, the mnemonic device used for years to help students remember trigonometry facts. Instead, my students will begin discussions in small groups by finding patterns and (hopefully) making their own mnemonic devices to remember the trig ratios. They will still be asked to memorize formulas, just like Civics students would be asked to memorize the branches and roles of government. However, our discovery and discussion will also provide students the tools to “re-find” the formulas and describe the rules in their own words.

Still not convinced? Here are a few more examples of positive changes because of the new standards. A month ago, my students traversed all three floors of my school in a scavenger hunt centered on geometry transformations. My learning team (teachers who teach the same subject) and I used the scavenger hunt as a review and informal assessment tool. Last semester, I asked students to come up with their own word problems for quadratic equations. Students got very creative, with one response referencing a flying squirrel and the X Games.

The standards challenge teachers to bring the curriculum to life for students. Attitude shifts in education allow for more discovery, which in turn encourages student creativity. I hope that as we move towards the true spirit of the standards—critical thinking and real-world problem solving—and away from an obsession over testing, real-world examples and thought-provoking activities based on students’ interests will become the norm in classrooms–not the exception. More and more in my classes I find myself taking on the role of facilitator instead of lecturer. I pose a problem and ask questions to guide students in their thinking. Near the end of this semester (18 weeks), students have started asking one another probing questions and thinking through problems together.

Today, I watched the class after I posed a problem. At first there was confusion: “What am I supposed to do?” they asked. Then I posed one simple question to guide their thinking: “Does this graph go on infinitely?”. Next, one student saw where the answer to that question led him. He told three people nearby, and he practically ran across the classroom to tell the next person how to start the problem. This new person took on the torch and asked his small group, “What if you look at the problem like this?” Within a matter of five minutes, 90% of the class had correctly solved a warm-up problem that, at the start of the period, no one knew how to even begin.

This all started because of a question about how high a cell phone bill could get. The excitement of students who finally feel like they understand math is unbelievable. It gives me hope that we’re not all doomed to a deep-seated feud between math and the general public. Maybe we can even convince some folks that math isn’t so bad after all.

Nicole Smith is high school math teacher in North Carolina. She is a supporter of meaningful standards and student-centered learning. Nicole is a proud veteran of the United States Marine Corps, a wife and mother of two sons who attend local public schools. She is a member of the Center for Teaching Quality Collaboratory and believes in the power of good educators to change lives.

  • Rod Powell

    Authenticity!

    Great post Nicole!

    Great description of how the standards go beyond rote and make math real for students.  I wish you could have been my math teacher in middle school.  I think that's where we lose many in the drill and kill of testing standardization.

     

  • Anonymous

    “…My third-grade son is

    "…My third-grade son is working to understand the reasoning behind the math facts he learns. He is still memorizing the multiplication tables, but he is also learning that multiplication is repeated addition. This means that when he gets to high school, he will understand that math is not just about plugging in formulas or solving random equations."

    I thought this issue had been settled, after the exchanges following Keith Devlin's interchange with teachers:

    https://www.maa.org/external_archive/devlin/devlin_06_08.html

    • nicolesmith

      I think part of the problem

      I think part of the problem comes from a great many teachers in the past being told that multiplication was not repeated addition but then having no tangible way to describe multiplication to elementary kids. It is repeated addition and at the same time it is more than repeated addition.

  • Dean Yap

    Worrying Parents should read this

    Parents who are worried about "new math" should read this and not be intimidated by the new standard and teaching methods. In fact, parents can learn together with children (not teach), they will have a new tool to see real world problem in another perspective, a quantitative perspective.

     

  • Stephanie

    3 Cheers for the Integrated Approach!

    It's refreshing to read about a teacher's success with non-traditional course programming. 

    I tried to get the arts-integrated public charter school I work for to use the integrated model for math when we expended to include high school, but concerns about transcripts and college acceptance get in the way.

    How can we convince colleges that the Integrated model is as rigorous and worthy as the traditional course sequence?

  • David Mazur

    Is Common Core Really the Hero?

    The teaching methods being described as benefits of common core, are really good teaching practices that have been encouraged by former BEST CT Teacher Certification practices for years.  Teaching for understanding and real life context should not be seen as a "discovery" of Common Core, but rather a re-inforcement of good teaching practices by Common Core.  The problem was the establishment and "established" teacher communities did not adequately support and promote these good teaching practices in the past because they require more creativity on the teacher's part.  What state adoption of Common Core does is prevent the more established teachers from telling new teachers, "Don't worry about doing it that "new fangle" way, do it the "old-fashioned way" instead."  Connecticut has actually developed a common core based Algebra 1 curriculum available to all Connecticut teachers.  Now that's "Good Teaching Practices Support".

    • nicolesmith

      No Contest

      I think we agree on the methods and ideas highlighted being best practices, as opposed to completely new ideas. That’s one of the main points of the article. Common Core isn’t something to fear, as if it’s composed of new, untried principles. On the contrary, whereas our old standards may have implied that such thinking should be used when planning lessons, CCSS explicitly lists the ideas highlighted here and more. 

  • Kim C.

    Teaching the parents

    "As a teacher, I hear parents’ frustration all the time: 'They’ve changed math so much that now I can’t help my third grader with his homework!'" I was one of those parents. I suggested to the school that they hold a tutoring session for parents so that we could learn the math they way they were teaching it so that we could help our kids at home. I got no response, which was unfortunate, because homework should not result in both kids and parents being frustrated. I have no problem with a new and improved way to teaching math, but please help the parents understand it as well!

     

    • nicolesmith

      So True

      I couldn’t agree more, Kim. Parents should be given the tools to help their children understand work. What isn’t explicitly stated in that line is part of the standards include a productive struggle. Perseverance in students is a goal and we as teachers constantly walk the line between giving just enough information to allow students to think critically and giving so much information that the hard work is already done for them.