SMP5: Use Appropriate Tools Strategically #LL2LU

14 Sep

We want every learner in our care to be able to say

I can use appropriate tools strategically.


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 Experiments in Learning by Doing]


“The American Heritage Dictionary Entry: Strategically.” American Heritage Dictionary Entry: Strategically. N.p., n.d. Web. 08 Sept. 2014.


Posted by on September 14, 2014 in Standards for Mathematical Practice


Tags: , ,

6 responses to “SMP5: Use Appropriate Tools Strategically #LL2LU

  1. Jeff McCalla

    September 14, 2014 at 4:57 pm

    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?

    • jwilson828

      September 15, 2014 at 5:41 am

      I wonder whether the teaching of the tool comes as part of the content standard and that the practice standard is about using the tool. For example, there is a content standard in grade 4 about using protractors to measure to the nearest whole number. There is a high school geometry congruence standard about using compasses and dynamic geometry software to make geometric constructions. While writing a program for the calculator or computer to solve a problem for you will work for many algorithms, it might not work for many open-ended tasks. Thanks for sharing your progression. It definitely gives us something to think about, and it will make me observe my students more closely as they use this practice.

    • jplgough

      September 18, 2014 at 3:53 am

      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.

  2. howardat58

    September 14, 2014 at 5:38 pm

    Firstly, where does the desire to start each bit with “I can” ?
    Isn’t it enough that the students do stuff using common sense, knowledge and understanding ?

    Secondly the mathematical practice document keeps on and on about “Mathematically proficient students”, and ” at the grade level”. Would this be referring to the 30% (hopefully, that will achieve “College and Career Readiness”, or the 5% who will end up actually using the math they understood, or only the 0.2% who will go on to be professional mathematicians. There is a lot of wishful thinking going on in this document, particularly when thinking about the “Mathematically less proficient students”. (No mention of these!!!!!)
    An educational target should be reachable by the majority of the students, or it becomes selective and divisive.

    Thirdly, if you get this far, the word “strategically” is not only redundant but also makes me think of tactical and strategic nuclear weapons.

    Fourthly, if a tool is not appropriate for a job then it will turn out to be useless. The student has to figure this out, otherwise he ain’t learned nuffin.

    • jplgough

      September 18, 2014 at 4:04 am

      I can… comes from many sources. I implemented the use I can… instead of The student will… after hearing John Hattie speak and reading Rick and Becky DuFour’s Whatever It Takes: How Professional Learning Communities Respond When Kids Don’t Learn and The Power of SMART Goals: Using Goals to Improve Student Learning by Anne Conzemius and Jan O’Neill.

      Using I can… altered the conversations in my classroom and empowered the learners to self advocate in new ways. So my answer to your first question is no, it isn’t enough that students are doing stuff using common sense, knowledge, and understanding. We want them to be reflective and intentional about their choices.

  3. jwilson828

    September 15, 2014 at 5:57 am

    The “I can” language comes from reading the work of John Hattie (Visible Learning) and James Popham (Transformative Assessment, Transformative Assessment in Action). I’m sure Jill could list others – these are the two authors that have had the most impact on my own classroom. Their research on student achievement shows that students need action-oriented goals. I have been using them with my students for about two years now, and I can tell that it helps students not only focus on the learning targets for the unit but also gives them the language to say what they can do and what they still need help doing.

    The goal for leveled learning progressions is that all students reach Level 3. We want all of our students to be mathematically proficient. Not just the “smart ones” or the “fast ones”. Having all students mathematically proficient will not happen overnight; nor will it happen if we continue teaching as we have been. I have seen a difference in what students at my school can do mathematically as a result of our focus on the Math Practices.


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