Category Archives: Thoughts on Learning

Mathematical Practices

Mathematical Practices

  1. Make sense of problems and persevere in solving them
  1. Reason abstractly and quantitatively
    • Decontextualize and contextualize situations
  1. Construct viable arguments and critique reasoning of others
  1. Model with mathematics
    • Mathematize the world
  1. Use appropriate tools strategically
  1. Attend to precision
  1. Look for and make use of structure
  1. Look for and express regularity in repeated reasoning

Thinking Math – Letter to Parents

Dear Parents,

It’s hard to believe that we are already more than two-thirds of the way through the school year. That leaves roughly 30% ahead in which time we can still accomplish a great deal. I wanted to take a moment and share with you a few things to think about as your child progresses in mathematics.

So much of what students learn through math is an ability to think critically, problem-solve, collaborate, and communicate. In a time when basic calculators can do what was once the entire scope of elementary mathematics, the task at hand looks towards higher-level skills. Students are expected to be effective speakers and writers (in math) and be able to access and analyze data and other information. They should utilize curiosity, practice flexibility in their thinking, and know how and when to take the initiative. These are the core competencies that students need by the time they graduate high school, and they need to be developing them at age appropriate levels all along the way.

Your partnership in this endeavor has never been more important. Children need to learn to think in these ways both in and outside of school. Besides working with your children on mathematical concepts, you can look for opportunities to engage them in problem solving, collaboration, and thoughtful communication. In this risk taking, remember that failure is an essential attribute of innovation. Children need to be provided with opportunities to fail and given support in developing persistence, resilience, and time to reflect and reattempt.

You have probably heard about the Common Core Standards. These are a sequence of concepts and skills that students should know and be able to do by the end of each grade level. You should take 20 minutes and familiarize yourself with the standards[1] at the grade levels around your child’s grade. The Common Core includes the “Standards for Mathematical Practice” that run from K all the way to 12th grade. At the beginning of the year, we glued these into the inside cover of our math spirals  as a reminder that these are the skills we are attempting to develop. Beyond the practices you will find the content standards, which are rooted in 5 domains but critically focus on operations with fractions, multi-digit division, and an understanding of volume. The new standards have a narrower focus, but provide a deeper exploration of the concepts taught at each level. The standards are research-based and, similar to the Washington State Standards in Math (which these standards are replacing), they were developed in conjunction with the National Council of Teachers of Mathematics (so they’re really, really good).

Lead your child in mathematics by being curious about how and why things work in math. Don’t always expect to be able to find answers quickly – mathematics is no more about finding answers than poetry is about complete sentences. Mathematics is about making sense of the world. Let it be an exploration, let there be questions, and whenever possible, be a partner in your child’s ongoing exploration of the science of pattern and order.


Spencer Olmsted