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

**I can use appropriate tools strategically.**

**(**CCSS.MATH.PRACTICE.MP5**)**

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.

Suppose you are solving an equation.

Are you practicing **use appropriate tools strategically** if you use the numerical solve command on your graphing calculator?

Or what about using your calculator to substitute values of x until you find a value that makes a true statement?

Are you practicing **use appropriate tools strategically** if you use a computer algebra system to explain your steps?

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Or what if you use the graphing capability of your handheld?

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Consider each of the following learning goals:

I can explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution, and I can construct a viable argument to justify a solution method. CCSS-M A-REI.A.1.

I can solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. CCSS-M A-REI.B.3.

I can explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. CCSS-M A-REI.D.11.

Does **use appropriate tools strategically** depend on the learner? Or the learning goal? Or the teacher? Or the availability of tools?

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[Cross posted on Experiments in Learning by Doing]

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howardat58

September 15, 2014 at 8:47 am

I can use tools (math dictionary: tools = appropriate tools strategically) to get the answer to a problem/ to save me from doing arithmetic/ doing algebraic manipulation/ plotting graphs by hand/ using my memory/ etcetera. (Learner’s own goal)

Or, I can use tools to check my results/get a picture of what is going on/gain some insight into some aspect of math/ etcetera. (Teacher’s goal)

But using tools is not going to help me explain the steps in what I have done. ( apart from pencil and paper) – No tool is going to help in CCSS learning goal 1 in your post.

I like the computer algebra example

“Are you practicing use appropriate tools strategically if you use a computer algebra system to explain your steps?”

The computer output explains nothing, it just goes through the steps. My view is that if you do this simple algebra yourself then you must have had a reason for each step, and that constitutes the explanation, and if you are unable to do it on your own then you will not have a clue about what the computer is showing.

So the answer to the question is “No, you are just trying to cut corners/impress others/display your talent with computers.”.

jplgough

September 18, 2014 at 3:52 am

Howard, I appreciate your comments; they help me think about my practice and goals. Your comment above has me considering point of view. We are looking at this from very different perspectives. My goal as the “teacher” or facilitator is to guide and coach students to use tools strategically –

to gain insight, to find patterns, to visualize. When learners “short cut” to just an answer, they are working in the shallow end. The learning progression shared above offers “lost” learners a pathway to think differently about their methods and ask questions. AND, it helps us stay true toappropriatetools being usedstrategically. We are making our thinking visible to ourselves and the other learners in the room.We use technology to deliver the content. We use technology to check for understanding and consensus. We use technology to guess-test-and-revise. We use technology to make sure everyone was taking a swing at each problem. We highlight multiple pathways to success.

We also use paper and pencil to do all of the above too. We highlight multiple pathways to success.

I’m sorry that you can’t see through the lens of my point of view. I see learners growing in understanding and confidence because of the availability of many tools: graphs, algebra tiles, calculators, paper, pencils, pens, iPads.

There is more than one route…