Strategies for Counting

This summer I was fortunate to attend the 5-day workshop Investigations in the Classroom workshop, hosted by my school. The training focused on how children develop number sense and mathematical reasoning skills.  We were able to explore some of the games and activities that are part of the Investigations curriculum and consider how we might adapt or extend these learning experiences to meet the needs our students.  

One of my biggest take-away from the sessions was the difference between strategies and tools.  As a math teacher, especially of young mathematicians, my hope is that my kiddos develop many strategies for solving math problems. I want them to be able to approach a problem in different ways so that, eventually, they can find the most efficient and practical way to solve it. 

However, too often, we end up teaching students to use the same strategy with a variety of tools.  For instance, students may learn to add using their fingers, cubes or counters, and by drawing pictures, but they may only use the simplistic strategy of "counting all" (starting at 1 and counting up).  Similarly, students can learn the "counting on" strategy (starting at the larger number and counting up) using their fingers, a number line, and a 100-chart.  

While tools, such as the 100-chart, are necessary and valuable for young learners; it is important to emphasize the strategies that students choose, rather than just the tool, so that the students can become critical of their choices.  I often see kiddos, especially when I'm tutoring struggling older students, who are reliant on tools, like pictures or number lines, and can not analyze a problem to choose a creative, logical, or more effective strategy to find a solution.

This year, I am trying to be very explicit with my kiddos about strategies.  I made a chart to remind us of the strategies we already know; as the year goes on, I'll add to it.  When a kiddo volunteers to share how he solved a math problem, I encourage him to name the strategy he used and then explain his tool (if any). We are currently playing a lot of games where the kiddos are combining numbers (more on these games later) so they are getting lots of practice explaining their strategies with partners as well.