Tag Archives: construct viable arguments and critique reasoning of others

Growth mindset = effort + new strategies and feedback

What if we press forward in the face of resistance?

For me, the most frustrating moments happen when a learner says to me I already know how do this, and I can’t learn another way.
Me:  Can’t or don’t want to? Can’t yet?

A growth mindset isn’t just about effort. Perhaps the most common misconception is simply equating the growth mindset with effort. Certainly, effort is key for students’ achievement, but it’s not the only thing. Students need to try new strategies and seek input from others when they’re stuck. They need this repertoire of approaches—not just sheer effort—to learn and improve. (Dweck, n. pag.)

What if we offer a pathway for learners to help others learn, and at the same time, learn new strategies?

What if we deem the following as essential to learn?

I can demonstrate flexibility by showing what I know more than one way.

I can construct a viable argument, and I can critique the reasoning of other.

The trick is to choose a goal just beyond your present abilities; to target the struggle. Thrashing blindly doesn’t help. Reaching does. (Coyle, 19 pag.)

How might we provide pathways to target the struggles to learn new strategies, to construct a viable argument, and to critique the reasoning of others?

MathFlexibility #LL2LU

ConstructViableArgument

What if we press forward in the face of resistance and offer our learners who already know how to do this pathways to grow and learn?

How might we lead learners to level up?


Coyle, Daniel (2009-04-16). The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. Random House, Inc. Kindle Edition.

Dweck, Carol. “Carol Dweck Revisits the ‘Growth Mindset’” Education Week. Education Week, 22 Sept. 2015. Web. 02 Oct. 2015.

Common denominators – “Let’s see why”

Everybody knows that you must have common denominators to add fractions, right?  Do we know why? If asked to construct a viable argument, could we? Can we draw it (i.e., communicate why visually)?  How mathematically flexible are we when it comes to fractions? From Jo Boaler’s How to Learn Math: for Students:

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.

Today’s Building Concepts lesson: Adding and Subtracting of Fractions with Unlike Denominators, had our young learners working to show their understanding of adding and subtracting fractions in multiple ways.

Kristi Story (@kstorysquared) used a phrase today that has really stuck with me is “Let’s see why…”  It immediately reminded me of Simon Sinek’s How great leaders inspire action.

And it’s those who start with “why” that have the ability to inspire those around them or find others who inspire them.

I wonder if, when young learners struggle with numeracy, it is because they do not see why.  Have they been so concerned with “getting the right answer” that they have missed the theory, reasoning, and geometry? photo[1]

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What if we  leverage appropriate tools and use them strategically? What if we use technology to personalize learning and offer every learner the opportunity to see why?


#LL2LU draft for use equivalent fractions as a strategy to add and subtract fractions.

Level 4:
I can solve real-world and mathematical problems involving the four operations with rational numbers.

Level 3:
I can solve word problems involving addition and subtraction of fractions by using visual fraction models or equations to represent the problem.

Level 2:
I can add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions.

Level 1:
I can understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

I can recognize and generate simple equivalent fractions, and I can explain why the fractions are equivalent using a visual fraction model.


#LL2LU for I can apply mathematical flexibility.

  Level 4: I can analyze different pathways to success, find connections between pathways and add new strategies to my thinking.

Level 3: I can apply mathematical flexibility to show what I know using more than one method.

Level 2: I can show my work to document one successful  method.

Level 1: I can find and state a correct solution.


#LL2LU for I can construct a viable argument and critique the reasoning of others.

Level 4: I can build on the viable arguments of others and use their critique and feedback to improve my understanding of the solutions to a task. 

Level 3: I can construct viable arguments and critique the reasoning of others.

Level 2: I can communicate my thinking for why a conjecture must be true to others, and I can listen to and read the work of others and offer actionable, growth-oriented feedback using I like…, I wonder…, and What if… to help clarify or improve the work. 

Level 1: I can recognize given information, definitions, and established results that will contribute to a sound argument for a conjecture.

SMP3: Construct Viable Arguments and Critique the Reasoning of Others #LL2LU

Screen Shot 2014-09-01 at 5.14.27 PMWe want every learner in our care to be able to say

I can construct viable arguments and critique the reasoning of others. CCSS.MATH.PRACTICE.MP3

But…what if I can’t? What if I’m afraid that I will hurt someone’s feelings or ask a “stupid” question? How may we create a pathway for students to learn how to construct viable arguments and critique the reasoning of others?

Level 4:
I can build on the viable arguments of others and take their critique and feedback to improve my understanding of the solutions to a task.

Level 3:
I can construct viable arguments and critique the reasoning of others.

Level 2:
I can communicate my thinking for why a conjecture must be true to others, and I can listen to and read the work of others and offer actionable, growth-oriented feedback using I like…, I wonder…, and What if… to help clarify or improve the work.

Level 1:
I can recognize given information, definitions, and established results that will contribute to a sound argument for a conjecture.

Our student reflections on using the Math Practices while they are learning show that they recognize the importance of construct viable arguments and critique the reasoning of others.

Jordan says “If you can really understand something you can teach it. Every person relates to and thinks about problems in a different way, so understanding different ways to get to an answer can help to broaden your knowledge of the subject. Arguments are all about having good, logical facts. If you can be confident enough to argue for your reasoning you have learned the material well.jordan quote

And Franky says that construct viable arguments and critique the reasoning of others is “probably our most used mathematical practice. If someone has a question about a problem, Mrs. Wilson is always looking for a student that understands the problem to explain it. And once he or she is finished, Mrs. Wilson will ask if anyone got the correct answer, but worked it a different way. By seeing multiple ways to work the problem, it is easier for me to fully understand.”

franky quote

What if we intentionally teach feedback and critique through the power of positivity? Starting with I like indicates that there is value in what is observed. Using because adds detail to describe/indicate what is valuable.  I wonder can be used to indicate an area of growth demonstrated or an area of growth that is needed.  Both are positive; taking the time to write what you wonder indicates care, concern, and support.  Wrapping up with What if is invitational and builds relationships.

Move the fulcrum so that all the advantage goes to a negative mindset, and we never rise off the ground. Move the fulcrum to a positive mindset, and the lever’s power is magnified— ready to move everything up. (Achor, 65 pag.)

The Mathy Murk has recently written a blog post called “Where do I Put P?” An Introduction to Peer Feedback, sharing a template for offering students a structure for both providing and receiving feedback.

Could Jessica’s template, coupled with this learning progression, give our students a better idea of what we mean when we say construct viable arguments and critique the reasoning of others?

[Cross-posted at Easing the Hurry Syndrome]

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Achor, Shawn (2010-09-14). The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work (Kindle Locations 947-948). Crown Publishing Group. Kindle Edition.