Use Appropriate Tools Strategically
Part 4 of 8, Strategies for Integrating the Mathematical Practices into Instruction
By Dr. Michele Douglass
There are few times that students in math classes or on assessments are asked which tool they should use to complete a problem. Think about the test questions that ask students to measure something. If it’s a length, the ruler is aligned to the object within the test question. If it’s a temperature, a thermometer appears in the question. We even provide the manipulative that students should use to solve a given problem.
Although the mathematical practice of Using Appropriate Tools Strategically is one that should be easy for most of us to implement, our testing world has never required us to use this practice as it is intended.
Fast-forward to classrooms teaching this practice or, better yet, classrooms where students are using this practice independently. They know how to use the tools and when to use them appropriately. Tools can be anything from mental math; pencil and paper; physical tools such as rulers, protractors, compasses, etc.; to calculators and computers. Mathematical tools also include graphic organizers, charts, tables, and manipulatives. What is critical in the development of this practice is that students are given opportunities to use each tool and to learn when its use is appropriate.
For example, is it better to use a tape measure or a ruler to measure the length of a room? Why? In what situation would you use a protractor? Why would pattern blocks be a tool for helping students understand the need for a common denominator when adding or subtracting fractions? Is this the only tool students should experience with this specific content?
“Mathematically proficient students consider the available tools when solving a mathematical problem. …. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.” —Common Core State Standards, MP5: Use Appropriate Tools Strategically
With this practice clearly defined, you might have already thought of a wide variety of lessons that would incorporate it. It is important to plan tasks that will require tools to solve. Consider problems that can be solved using multiple learning tools. I want to show a progression of learning of a single concept that builds across grade levels.
Example 1: Using a tool, show how 3 x 4 and 4 x 3 will always equal 12.
Example 2: What model or models can you use to show all the multiplication steps that occur when you are multiplying 65 x 24?
Example 3: What tool(s) could you use to help you mulitply (y + s – 5) (q – 2)? How does your choice of a tool connect to the algorithm for multiplying multidigit numbers as well as polynomials?
Other ways to involve students in tasks and lessons using tools could involve the following:
- NCTM Illuminations (http://illuminations.nctm.org/): There are many lessons here that embed tools and will allow students opportunities to use tools in specific ways that can transfer to new problems.
- National Library of Manipulatives (http://nlvm.usu.edu/en/nav/vlibrary.html): There are too many types of online manipulatives on this site to name. They are grouped by grade levels and many include activities and lessons.
- Have containers with different measuring tools in places for students to easily access.
- Have containers with various types of manipulatives that students can choose to use when they are solving problems.
As you plan for these types of lessons, remember that students won’t just pick up these tools to use them appropriately without first seeing them demonstrated and modeled. For example, think about how you might model fractions with pattern blocks as students are learning to write these values. I have learned how important it is to be consistent with the models as well as how important it is to ask students to explain their thinking.
I don’t want to end this mathematical practice before I address questioning strategies. If you have been following these blogs, you have noticed a pattern. Students learn through the questions we pose in lessons to help them think and sort through the ideas that are forming. We can’t just ask, “Who understands?” or “Got it?” After carefully designing a lesson specific to using tools appropriately, I find that learning is accelerated when I am also asking these types of questions:
- How could you use manipulatives or a drawing to show your thinking?
- How is this tool/strategy helping you to solve the problem? What else might you try?
- Which tool/manipulative would be best for this problem?
- What other resources could help you solve this problem?
- Why was it useful to use _______?
- What can a ___________ show us that a _________ may not?
References:
Common Core State Standards Initiative Website: http://www.corestandards.org/Math/Practice/#CCSS.Math.Practice.MP2
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#standard1162
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.
