Precision in words and actions is an important skill. It helps communicate ideas and understanding. Without precise language and processes, miscommunication, misunderstanding, confusion, and chaos rule. Obviously, in the bigger scheme of things, lack of precision can be dangerous. For example, if a civil engineer designing a bridge is not precise in their measures and calculations, bridge collapse and death are possible. One of the things educators need to do is foster this skill of precision in our instructional practice. Which is why helping students “attend to precision”, is one of the 8 Mathematical Practices in the Common Core State Standards. Teachers should be cultivating precision in their classroom.
Math Practice #6: Attend to Precision
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
If you look at some of the words/phrases I have highlighted above, you will note that precision focuses on communication, using definitions and symbols accurately and appropriately, labeling and identifying quantities carefully, giving explanations based on facts and definitions. In short – understanding the words and symbols being used in mathematics in order to communicate with others. Being precise has to do with helping others understand what you are doing and saying. It is not enough for the student to understand a mathematical concept, they have to be able to help others understand. Why is this so important? Because, the Common Core Standards are designed to help students become “college and career ready”, and in college and in careers, people must communicate with others to accomplish tasks and solve problems. They must be able to precisely explain what they mean, what they have developed, what they want others to do – which requires common language and clear explanations. In other words, precision.
So, let’s go back to what this means in the context of the classroom. Teachers, no matter what grade – preK through college – should be using the correct language of mathematics and expecting their students to also use this language precisely and appropriately. They should expect students to explain their thinking using that language, whether verbally or in writing, as students progress through the grades. I know students always groan when they hear “show your work”, but it is important. And not just their work, but the why of their work. If students are working with measures, then their solutions and explanations should include units of measure. They should use vocabulary and definitions to explain their thinking. The more we have students talking and communicating with math, right from the beginning, the more confident and precise they will become. As teachers, we need to model this as well, by making an effort to use proper mathematical language and symbols, as appropriate for your students, and helping students do the same.
Below is a chart, based on work I did this summer with teachers exploring the Mathematical Practices, that gives some student outcomes aligned to teacher actions that may be helpful as you think about ways to help students “attend to precision” in your classroom.
Students should be able to…… Teachers support this by…. Use correct math vocabulary Teaching vocabulary, (with visuals, if appropriate), and using precise mathetical vocabulary consistently Know and use definitions appropriately Teaching definitions and modeling using these consistently and intentionally Communicate/explain their thinking using words and symbols, both written and verbally Encouraging classroom discourse; use think aloud strategies; establishing a culture of inquiry and communication Record and label their work Providing exemplar for what precision looks like; setting expectations, modeling expectations and providing consistency Choose and use appropriate mathematical symbols when solving problems or explaining Teaching appropriate symbols and their meanings and using/modeling these consistently