Part 8 of 8, Strategies for Integrating the Mathematical Practices into Instruction

By Dr. Michele Douglass

Last but definitely not least in this series on Integrating the Mathematical Practices into Instruction is MP#6: Attend to Precision, which often impacts a solution more than any other practice. This practice is generally understood to be about accuracy of solutions and good estimations. While these ideas are certainly part of the practice, it includes so much more.

“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.” —Common Core State Standards (CCSS), MP#6: Attend to Precision

When students are attending to precision, they do the following:

• Talk with other students using correct math vocabulary
• Keep vocabulary journals that allow them to interact with the vocabulary word through pictures, drawings, and their own words
• Use correct symbols and terminology and are able to give examples and nonexamples
• Give explanations for solutions using accurate vocabulary
• Use correct labels (both context and math) with word problems
• Measure using the appropriate unit of measurement and label the measurements, including those displayed on a graph
• Use appropriate vocabulary words in explanations that help clarify their thinking
• Focus on clarity and accuracy of process of problem solving
• Calculate with accuracy and efficiency

Example 1: Rebecca goes to the store to buy a present for her friend’s birthday party. She buys a book for $7, a CD for $18, a gift bag for 75 cents, and a card for 99 cents. How much money does she spend?

Example 2: How much carpeting will you need for a room that is 11 feet by 3 yards?

In both of these problems students must recognize that they need to have common units before they can begin the calculation. If they just add the given numbers in Example 1 or if they multiply in Example 2, they are not attending to precision. Additionally, attending to precision is used a second time in the second example when students have to use square units to label the total amount of carpeting. I also realize that if I allow my students to only put numbers without labels as solutions, I am not asking them to attend to precision. Attending to precision is certainly a practice that requires me to pay attention as I create tasks but also as I grade and provide feedback.

As I think about assignments and tasks that ask students to attend to precision, I catch myself thinking of questions such as these:

• Does the assignment require students to use precise vocabulary (written and/or verbal) when communicating the mathematical ideas?
• How does the task expect students to use symbols appropriately?
• Does it embed an expectation of how precise the answer must be, or is an estimate appropriate?
• Does it ask students to explain if the solution was found using an efficient method?

Vocabulary development is what I find the hardest part of this mathematical practice. It is hard because it requires that I use precise language as I instruct lessons. It also means that I am working with students to develop their own precise language, which takes time.

One thing that is different in teaching math vocabulary is that it occurs within teaching the content and through experiences with the concept. It builds over time. When students haven’t had exposure to a word, it doesn’t usually pay off to preteach the word.

Providing students with multiple opportunities and exposures to these new words is critical. A great way to start is with games such as “I Have, Who Has” or “Pictionary.” Other ways to develop vocabulary are having students build a word wall throughout the year and using an interactive dictionary. Have them label pictures, diagrams, and equations in their notes with the terminology, including the meaning and names of the symbols. As with all the mathematical practices, facilitate discussions and use probing questions.

Here is a list of some great questions to consider when you are working on building students’ attention to precision. Use these to further students’ abilities to attend to precision as they are building their content in mathematics this year.

• What does the word ____ mean?
• Explain what you did to solve the problem.
• What mathematical terms apply in this situation?
• What labels could you use?
• How do you know your answer is accurate?
• What mathematical words might we use to describe this process?
• Did you use the most efficient way to solve the problem?
• What mathematical language …, definitions…, and properties can you use to explain…?

Thank you for reading about ways to help your students develop important processes and proficiencies that will help them succeed in mathematics. We'd love to hear your feedback and ideas from your classroom in the comments below.

We have compiled all strategies from this 8-part series into a complimentary white paper that can act as a guide for teachers.

References and Additional Resources: 

Common Core State Standards Initiative Website: http://www.corestandards.org/Math/Practice/

Implementing the Mathematical Practice Standards Website: http://mathpractices.edc.org/

Inside Mathematics Website: http://www.insidemathematics.org/index.php/mathematical-practice-standards

Mathematics Assessment Resource Service Website: http://map.mathshell.org/materials/stds.php

 

Michele Douglass, Ph.D., is the president of MD School Solutions, Inc., a company that contracts with school districts on content and pedagogy with teachers and leaders. Her experience ranges from math instructor to director of curriculum and instruction at Educational Testing Services. She has authored several math curricula, as well as technology programs and professional development, including NUMBERS® with John Woodward, Ph.D., and Mary Stroh, M.S.

 

 

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