SMP2: Reason Abstractly and Quantitatively #LL2LU (Take 1)

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

I can reason abstractly and quantitatively.

I wonder what happens along the learning journey and in schooling. Very young learners of mathematics can answer verbal story problems with ease and struggle to translate these stories into symbols. They use images and pictures to demonstrate understanding, and they answer the questions in complete sentences.

If I have 4 toy cars and you have 5 toy cars, how many cars do we have together?

If I have 17 quarters and give you 10 of them, how many quarters will I have left?

Somewhere, word problems become difficult, stressful, and challenging, but should they? Are we so concerned with the mechanics and the symbols that we’ve lost meaning and purpose? What if every unit/week/day started with a problem or story – math in context? If learners need a mini-lesson on a skill, could we offer it when they have a need-to-know?

Suppose we work on a couple of Standards of Mathematical Practice at the same time.  What if we offer our learners a task, Running Laps (4.NF) or Laptop Battery Charge 2 (S-ID, F-IF) from Illustrative Math, before teaching fractions or linear functions, respectively? What if we make two learning progressions visible? What if we work on making sense of problems and persevering in solving them as we work on reasoning abstractly and quantitatively.  (Hat tip to Kato Nims (@katonims129) for this idea and its implementation for Running Laps.)

Level 4:
I can connect abstract and quantitative reasoning using graphs, tables, and equations, and I can explain their connectedness within the context of the task.

Level 3:
I can reason abstractly and quantitatively.

Level 2:
I can represent the problem situation mathematically, and I can attend to the meaning, including units, of the quantities, in addition to how to compute them.

Level 1:
I can define variables and constants in a problem situation and connect the appropriate units to each.

You could see how we might need to focus on making sense of the problem and persevering in solving it. Do we have faith in our learners to persevere? We know they are learning to reason abstractly and quantitatively.  Are we willing to use learning progressions as formative assessment early and see if, when, where, and why our learners struggle?

Daily we are awed by the questions our learners pose when they have a learning progression to offer guidance through a learning pathway.  How might we level up ourselves? What if we ask first?

Send the message: you can do it; we can help.

[Cross-posted on Easing the Hurry Syndrome]


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