In previous blog posts, we have discussed the Common Core State Standards. Before we have focused on the content that these standards recommend students learn. But in addition to content standards, the Common Core also consists of math practice standards. Instead of articulating recommended content, these standards showcase particular skills and habits that students should learn while practicing math. Over the next two weeks, we’ll give you a brief introduction to each of the eight math practice standards. This week we’ll focus on the first four:
Make sense of problems and persevere in solving them
This standard provides a background for conceptual understanding. If students are not able to deeply understand the problems they solve, they wont be gaining important mathematical skills. To encourage deep understanding, have your child talk about the problems he solves and explain his reasoning. Have your child get in the habit of checking his work by both monitoring his calculations and checking for understanding. The other part of this standard has to do with perseverance. It’s important for students to solve problems that they don’t automatically understand, so that they gain experience grappling with problems and persevering through complex mathematical situations. Help your child to see difficult problems as opportunities to learn, rather than causes of frustration.
Reason abstractly and quantitatively
To be successful in math, students need to be able to both contextualize and decontextualize. To contextualize means to understand the meanings of all parts of a mathematical problem and to be able to see how the parts relate to each other. For example, when looking at a bar graph, students should be able to interpret the graph and contextualize the information it presents (thinking about what exactly the data presented means). To decontextualize means to abstract math problems from given situations, using symbols to represent the situation and thinking about the symbols as separate from the situation. For example, when reasoning about buying eggs that cost $2 each, students could represent this situation by the equation 2x = y.
Construct viable arguments and critique the reasoning of others
This practice standard also encourages deep conceptual understanding. Students need to be able to use their knowledge of math to make conjectures and investigate whether their conjectures are correct or not. Similarly, students need to be able to investigate others’ mathematical reasoning. By explaining, experimenting, and questioning, students gain real-life experience grappling with difficult mathematical concepts. They will begin to see that there may often be one correct answer to math problems, but there are usually many ways to arrive at this answer.
Model with mathematics
Throughout the grades, students should be recognizing how mathematics can be used to represent real-life situations. This will not only improve their math skills, but also help students to make math meaningful. Modeling mathematics can come in many forms, from writing equations to fit real-world situations to coming up with ratios to describe a proportional relationship.