Strategies and models and tools…oh my!

[kaustin]

Hi Bill,

I’ve had the opportunity to work with elementary educators around the country as they adopt/adapt curricula to meet the CCSS-M. Educators are using the terms “strategy,” “tool,” and “model” differently and sometimes interchangeably. My goal is to provide some clarification based on the intent of the standards and your own interpretation.

The progressions documents have provided clarification and created new questions.

1. What is the difference between a strategy and a method?

In response to an earlier question (http://commoncoretools.me/forums/topic/algorithms-grades-2-5), you point out that strategies are tied to written methods in many standards (e.g., 1.NBT.4).
Can “written methods” be used interchangeably with “notation?”

In the OA progression at the top of page 6 where Level 1, 2, and 3 , “method” seems to take on a slightly different meaning, perhaps tied to strategy, “Methods used for solving single-digit addition and subtraction problems.”
Can “method” and “strategy” be used interchangeably?

2. Typically, the word “model” is used in the elementary progressions along with “visual” (e.g., “visual model,” “visual fraction model”). Is it fair to say that a model could be concrete objects, drawings, diagrams, charts, simulations, equations? I’m beginning to define model (n) as a visual representation that helps to conceptualize, solve, or explain a mathematical situation or relationship.

3. Would you consider the number line as a model or a tool?

Thanks for your insight!

Kate

[Cathy Kessel]

I don’t know if this is part of your concern but note that the front matter for the Progressions says: “Terms used in the Standards and Progressions are not intended as prescriptions for terms that teachers must use in the classroom.”

Generally in the Progressions, a method is more specific than a strategy, e.g., two different methods might use a make-a-ten strategy.

“Notation” vs “written method”: Generally, in mathematics, “notation” is used to mean “any series of signs or symbols used to represent quantities or elements in a specialized system” (the first meaning here: https://www.thefreedictionary.com/notation). A written method might use such notation, or not.

Generally in the Progressions, various things are identified as models in discussions of how they act as models, e.g., in examples of MP4. (See pp. 1–6 of the Modeling Progression.) Some of the same things might be identified as tools in discussions of using appropriate tools strategically (MP5).

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