Human beings are pattern-seeking & natural problem solvers.
We strive to make sense of our surroundings. When given the opportunity, we will use our prior knowledge and experiences and apply them to new contexts. These innate skills should be transferrable to the math classroom. Spaces that allow for authentic mathematical thinking give students room to problem solve, provide reasoning for their thinking, communicate ideas, make connections, and represent mathematics in appropriate ways.
Indicators of Mathematical Thinking in the Classroom
Authentic problem solving allows students to choose and analyze their strategies. There are multiple entry points and viable strategies for working towards a solution. Students are given the opportunity to execute conceptually sound mathematical procedures.
Students understand the relationship between mathematical concepts, procedures, and strategies. They see mathematical ideas not as discrete parts, but as pieces of a coherent whole. This allows students to apply mathematical concepts to new contexts.
Reasoning & Proof
Students are making valid mathematical arguments and providing justification. They are encouraged to verify their solutions and think about if an answer makes sense, as well as critique others students' arguments.
The classroom should encourage students to create accurate mathematical representations to solve problems and portray solutions. Students should be able to use multiple representations within a given context.
The classroom should support students in using appropriate mathematical language and notations to communicate their thinking to a variety of audiences. Students should be given the opportunity to communicate understanding using multiple formats.