We want every learner in our care to be able to say
I can use appropriate tools strategically.
(CCSS.MATH.PRACTICE.MP5)
But…What if I think I can’t? What if I have no idea what are appropriate tools in the context of what we are learning, much less how to use them strategically? How might we offer a pathway for success?
Level 4:
I can communicate details of how the chosen tools added to the solution pathway strategy using descriptive notes, words, pictures, screen shots, etc.
Level 3:
I can use appropriate tools strategically.
Level 2:
I can use tools to make my thinking visible, and I can experiment with enough tools to display confidence when explaining how I am using the selected tools appropriately and effectively.
Level 1:
I can recognize when a tool such as a protractor, ruler, tiles, patty paper, spreadsheet, computer algebra system, dynamic geometry software, calculator, graph, table, external resources, etc., will be helpful in making sense of a problem.
We still might need some conversation about what it means to use appropriate tools strategically. Is it not enough to use appropriate tools? Would it help to find a common definition of strategically to use as we learn? And, is use appropriate tools strategically a personal choice or a predefined one?
How might we expand our toolkit and experiment with enough tools to display confidence when explaining why the selected tools are appropriate and effective for the solution pathway used? What if we practice with enough tools that we make strategic – highly important and essential to the solution pathway – choices?
What if apply we 5 Practices for Orchestrating Productive Mathematics Discussions to learn with and from the learners in our community?
- Anticipate what learners will do and why strategies chosen will be useful in solving a task
- Monitor work and discuss a variety of approaches to the task
- Select students to highlight effective strategies and describe a why behind the choice
- Sequence presentations to maximize potential to increase learning
- Connect strategies and ideas in a way that helps improve understanding
What if we extend the idea of interacting with numbers flexibly to interacting with appropriate tools flexibly? How many ways and with how many tools can we learn and visualize the following essential learning?
I can understand solving equations as a process of reasoning and explain the reasoning. CCSS.MATH.CONTENT.HSA.REI.A.1
What tools might be used to learn and master the above standard?
- How might learners use algebra tiles strategically?
- When might paper and pencil be a good or best choice?
- What if a learner used graphing as the tool?
- What might we learn from using a table?
- When is a computer algebra system (CAS) the go-to strategic choice?
Then, what are the conditions which make the use of each one of these tools appropriate and strategic?
[Cross posted on Easing the Hurry Syndrome]
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“The American Heritage Dictionary Entry: Strategically.” American Heritage Dictionary Entry: Strategically. N.p., n.d. Web. 08 Sept. 2014.
Experiments in Learning by Doing 
OK. I have a totally different take on what the levels should be for this math practice. First, students need to learn how to use the tools (some are easy-to-learn and some are hard-to-learn). Then, they need to figure out when in the problem solving process they can employ these tools. Then, I think of level 3 as using them strategically (or wisely). Just because you can use a tool doesn’t mean you should. And, I think of a level 4 as writing a program on a calculator that will solve the problem for you. In other words, using the tool to do all the work. I am having a hard time organizing my levels into “I can” statements.
1. I can learn to use basic tools in the math classroom like a protractor, ruler, patty paper, and basic calculator skills
2. I can learn to use tools that are more complex to learn like graphing & table skills on a calculator, geometry software, etc.
3. I can use appropriate skills strategically.
4. I can program a calculator or computer to do the work of solving the problem for me.
I’m not sure I am pleased with my levels either. Maybe there needs to be more one level 1 and level 2 skills?
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Great, great comment, Jeff! Thank you! I appreciate your feedback. I wonder what strategically means to a young learner, and I wonder if my strategy has to be the same as my partner’s strategy. I also wonder what is basic in 2014. I don’t think a calculator is basic and computer software is advanced.
I’d also like to hear more about Just because you can use a tool doesn’t mean you should. I’m not sure I agree with you about using the tool to do all the work. I suppose it depends on the problem and the tool. For example, I don’t think it is Level 4 to use CAS to solve a system of equations if the learning objective is to solve a system of equations. I do think it is Level 3 to use CAS to solve a system of equations if I’m solving a complex physics problem.
Thanks again…We’ll keep thinking.
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