Our program promotes a deep conceptual understanding of mathematics, emphasizing the quality and quantity of connections children make with existing ideas. Our objective is to develop critical thinking and fluency in problem solving. To do so, we emphasize having an arsenal of different strategies to apply to a wide range of problems and being able to explain one’s thinking. We stress that there can be different paths towards the same answer and instill in children confidence in their own ability to problem solve in math.
Daily Number Routines. In each classroom, daily routines around numbers and mathematical thinking help children develop fluency and confidence. For example, children might be asked to share a “problem of the day” whose answer incorporates the day’s date. Younger children might say “6 plus 1 equals 7,” while older children might instead offer “49 divided by 7 equals 7.” Children benefit not only from creating their own equations, but also from hearing the equations other children create.
Problem Solving. Mathematics involves logic and common sense. Students learn best when they make sense out of math concepts rather than just being shown the steps to follow. We utilize open-ended problems to allow for multiple entry points and solutions. We also utilize real-world problems wherever possible, including problems drawn from the classroom itself. Students are encouraged to collaborate in problem solving, sharing ideas and strategies. For example, second and third grade students studying geometry recently began by learning about geometric shapes and angles, creating designs and exploring the topic using manipulatives. This study evolved into the creation of a quilt where the students worked together to identify the size of each finished square and then worked backward to calculate length, width, and perimeter of individual pieces. Working this way generated a deep understanding of geometry and geometric thinking, as well as a beautiful quilt that demonstrates the application of this knowledge.
Explaining your Strategy. We want students to explain their reasoning and share strategies. We create an environment where it is okay to make mistakes, as this is how we learn. Teachers respond to children’s articulation of math strategies in a non-evaluative manner, such as “how can we tell if your answer makes sense?” In this way children learn from each other and understand multiple strategies or perspectives in mathematical thinking.