Math

As a teacher for over 15 years, I recognize that the kinds of experiences that teachers offer their students play a major role in determining the extent and quality of students’ learning. For example, rich problem-solving activities help students build understanding by actively engaging in tasks and experiences designed to deepen and connect their knowledge. Playing math games affords students the opportunity to build understanding while encouraging strategic thinking as students will have different approaches for solving problems. Using classroom activities and games is also a great way to check in on their progress as well as to provide reinforcement of key concepts. I like problem-solving activities that are easy to put together, fun, and require all students to participate.

When I was working in the school district office, we spent significant time putting together a plan that would meet the needs of a range of learners. Where there were almost an endless number of resources from which to choose for Reading, there were very few for Math. We looked at many options but struggled to put together anything as comprehensive as what we could offer for Reading. It was during this struggle that I was introduced to the work of Kathy Richardson, who is one of the leading math educators in the country. As I studied Kathy’s work, I came to understand that the very foundational concepts of number—counting, for example—were much more complex than I had given them credit for. As I became familiar with the Critical Learning Phases that Kathy identified, I realized just how important it is for students to build their conceptual understanding of number relationships.

I taught an Algebra 1 or Algebra 2 class every year I was teaching, and I was always looking for ways to make the content engaging for the students. I firmly subscribe to John Van de Walle’s notion that drill and practice are two very different things, and sought opportunities for the students to have meaningful practice with the concepts they were learning. As a result, I avoided the lengthy problem sets and worksheets that are prolific in high school math classes, opting instead for problems, explorations, and games that encouraged thinking and discussion.

Every year around this time, my family is getting ready for back-to-school night. Now that I have children in high school, junior high, and elementary school, it’s always fun to see how this event is handled at the different levels. When I was teaching high school, we were very structured, with parents moving from class to class as though on a regular schedule; I think we had each group for ten minutes, just long enough to quickly review the syllabus and policies and send them off to the next class. Regardless of the structure of back-to-school night at your school, there are a few things you can do to make the evening more engaging for students and their parents. A good place to start is having some manipulatives you’ll be using during the year out for parents to handle. Things like Unifix Cubes, Pattern Blocks, Ten-Frame Floor Mats and Fraction Tiles are always good choices.

Traditional dominoes have a variety of uses in the classroom. A simple internet search for “math domino games” yields thousands of ideas for using these tools to build number concepts. But eventually, the novelty wears off and they become more of a toy than a learning tool. But the matching aspect of dominoes lets us expand this teaching tool to domains beyond number.

The first time I ever saw a teacher using Unifix cubes in the classroom, it was not in an elementary school. I was coaching a middle school teacher who was introducing the concepts of mean, median, and mode to her students. They were using the cubes to “graph” the data and then find these measures of central tendency. Since then, I’ve seen Unifix cubes in classrooms at every grade level, used in a variety of ways to teach number sense, data, measurement, patterns, and an array of topics. They were never as useful a tool for Geometry… until now.

One of the things I really enjoyed about my Geometry classes in college was that they were very hands-on. We used a variety of manipulatives to explore geometric concepts, and the lessons have stayed with me for a long time now. I carried many of these ideas into the classroom when I started teaching, using ideas as simple as nets and tools like marshmallows and toothpicks. While these models are adequate for teaching the general ideas, they lack the consistency and formality that Geofix shapes offer.

My Preschool-age son likes to read with us, and one of the books in his “favorites” rotation teaches shapes and colors. On the page with the rhombus, I always use the term “rhombus” rather than “diamond,” which is what is printed in the book. While reading with his mother last week, she read the term on the page rather than substituting “rhombus.” My son quickly corrected her; he shared what his preschool teacher taught him: “Diamonds are shiny things in jewelry. That is a rhombus.”

When I was teaching high school, place value was a concept that just seemed to exist; it was inherent in everything I taught, yet received little attention. I simply took it for granted. As I transitioned to working with students and teachers in the elementary grades, I realized that this was a mistake because place value was a concept that many of my students probably never fully understood. Place value is far more than just ones, tens, and hundreds. To really understand the concept of place value, we need to understand the relationship between the places.

While on hall duty during my first year of teaching, I was surprised to see our math department chair leading her Calculus students to a large common area in the school. Curious, I checked in on them a few minutes after the class had started and found that they were plotting “points” by standing on a large coordinate grid mat on the floor. After watching the teacher use those mats over and over with students in Algebra 1 all the way through Calculus, I realized the value of this kinesthetic learning experience. Her students understood the concepts better, and were more engaged, because they were out of their seats and actively creating a life-sized visual model.