Tag Archives: reflection

Enhancing Growth Mindset in Math – Learning together

We asked:

How might we, as a community of learners, grow in our knowledge and understanding to enhance the growth mindset of each of our young learners?

As a team, we have completed Jo Boaler’s How to Learn Math: For Students and have shared our thinking, understanding, and learning.

Blending online and face-to-face learning, we worked through the Stanford units outside of school so that we could explore and learn more when together.

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Here are some of the reflections shared by our team.

As a teacher my goal is to help children approach math and all subject areas with a growth mindset. It is of utmost importance that my students truly know that I believe in them and their ability to succeed!

Everyone my age should know that you should never equate being good at math with speed. Just because someone is a slower problem solver does not mean that they are a weak math student. Rather, sometimes the slower math thinkers are the strongest math thinkers because they are thinking about the problem on a deeper level. Being good at math is about being able to think deeply about the problem and making connections with it.

When talking to yourself about your work and learning new things, reminding yourself that you can try harder and improve is critical to potential success.  People are more willing to persevere through difficult tasks (and moments in life) when they engage in positive self talk.  

Mistakes and struggling, in life and in math, are the keys to learning, brain growth, and success.

Thinking slowly and deeply about math and new ideas is good and advantageous to your learning and growth.

Taking the time to think deeply about math problems is much more important than solving problems quickly.  The best mathematicians are the ones who embrace challenges and maintain a determined attitude when they do not arrive at quick and easy solutions.  

Number flexibility is so powerful for [students]. I love discussing how different students can arrive at the same answer but with multiple strategies. 

Working with others, hearing different strategies, and working strategically through problems with a group helps to look at problems in many different ways.

“I am giving you this feedback because I believe in you.”  As teachers, we always try to convey implicitly that we believe in our students, and that they are valued and loved in our class.  However, that explicit message is extraordinary.  It changes the entire perception of corrections or modifications to an essay–from “This is wrong, you need to make it right” to “I want to help you make this the best it can be,” a message we always intended to convey, but may not have been perceived.  

Good math thinkers think deeply and ask questions rather than speeding through for an answer.

Math is a topic that is filled with connections between big ideas.  Numbers are meant to be manipulated, and answers can be obtained through numerous pathways.  People who practice reasoning, discuss ideas with others, have a growth-mindset, and use positive mathematical strategies (as opposed to memorization) are the most successful.

We learn and share.

#ILoveMySchool

MyLearningEdu 1.5 (week 5) – Learning Together

How might we learn, reflect, and share?  What if we take a moment of learning and share it with others?

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  1. Read one (or more) of the following blog posts:
  2. Add a Share button to you blog posts to make it easy for others to share your blog posts.
  3. Reflect, write, and post. Read and comment on posts from at least two others in ourMyLearning 1.5 cadre.  You might consider using the following protocol for your comments:
    • I like…
    • I wish…
    • I wonder…
    • I want to know more about…


 

MyLearningEdu 1.5 (week 4) – Learning Together

How might we learn, reflect, and share?  What if we take a moment of learning and share it with others?

  1. Screen Shot 2014-09-01 at 8.36.43 PMRead Reflecting on My Learning 1.0.
  2. Watch The Future of Publishing (shown below).  How might we reframe or reverse the way we are seeing, learning, thinking, and acting?
  3. Reflect, write, and post. Read and comment on posts from at least two others inourMyLearning 1.5 cadre.  You might consider using the following protocol for your comments:
    • I like…
    • I wish…
    • I wonder…
    • I want to know more about…

BONUS: If you have written and published for other websites or magazines, cross post your work on your blog as artifacts of your writing and contributions to the learning of others.  (Examples:  Falconry: I believe in you is posted on Experiments in Learning by Doing and on Flourish.


 

MyLearningEdu 1.5 (week 3) – Learning Together

How might we learn, reflect, and share?  What if we take a moment of learning and share it with others?

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  1. Read Categories vs Tags and Silvia Tolisano’s (@langwitchesAnatomy, Grammar, Syntax & Taxonomy of a Hyperlink. Return to your previous post(s) and add both categories and tags and improve any hyperlinks  if you have not already done so.
  2. Watch Matt Cutts: Try something new for 30 days (shown below). What habits should we practice? What habits are we modeling and teaching? What habits do our student-learners want to acquire? How can we make reflection part of the habit of schooling?
  3. Reflect, write, and post. Read and comment on posts from at least two others in ourMyLearning 1.5 cadre.  You might consider using the following protocol for your comments:
    1. I like…
    2. I wish…
    3. I wonder…
    4. I want to know more about…

 


 This course is designed to build teacher experience, confidence, and understanding of reflection, digital portfolios, and feedback.  Strategies employed in this course will be hands-on and digital development practices for reflection, self-assessment, learning, feedback, and growth.

At the end of this course, participants should be able to say:

  • I can use reflection as a formative assessment and self-assessment tool.
    • I can develop and utilize journaling and e-portfolios.
    • I can use authentic peer-to-peer and self-assessment practices to inform professional growth and learning.
  • I can design processes that can be used in a classroom to promote and celebrate self-reflection for learning.
    • I can integrate technologies that enhance self-reflection and asynchronous communication.
    • I can facilitate authentic peer-to-peer and self-assessment practices to motivate growth and learning.
This class will meet asynchronously throughout the semester from August 1 through January 1.  Participants will document their learning on their professional blog.  Participants will collaborate, learn, and share by commenting on the blogs of others participating in this course.

To earn 2 PLU credits (Georgia Department of Education), participants will

  • establish a professional portfolio to document the journey of becoming a more reflective teacher.
  • demonstrate fulfillment of required activities by posting completed work and reflections to individual blogs.
  • model connectedness by reading and commenting on the reflections of others in this course.
  • practice offering warm and cool feedback in constructive, kind, and purposeful ways using suggested protocols.

MyLearningEdu 1.5 (week 2) – Learning Together

How might we learn, reflect, and share?  What if we take a moment of learning and share it with others?

  1. Screen Shot 2014-09-01 at 8.36.43 PMRead What Do You Know About Creative Commons by Bill Ferriter and/or How to Attribute Creative Commons images in your blog properly?
  2. Peak Learning Exercise – “Think about your own life and the times when you were really learning, so much and so deeply, that you would call these the “peak learning experiences” of your life. Write a rough draft: Tell a story (you may include pictures, symbols, or other icons, too) about this peak learning experience, and respond to the question, “What were the conditions that made your high-level experience so powerful and engaging?”(adapted from 21st Century Skills: Learning for Life in Our Times, Trilling and Fadel, 2009; used as choice in Writing-Is-Thinking CFT Pre-Institute Assignment with Bo Adams in 2012.)
  3. Post one of your Peak Learning Experiences on your blog.


 At the end of this course, participants should be able to say:

  • I can use reflection as a formative assessment and self-assessment tool.
    • I can develop and utilize journaling and e-portfolios.
    • I can use authentic peer-to-peer and self-assessment practices to inform professional growth and learning.
  • I can design processes that can be used in a classroom to promote and celebrate self-reflection for learning.
    • I can integrate technologies that enhance self-reflection and asynchronous communication.
    • I can facilitate authentic peer-to-peer and self-assessment practices to motivate growth and learning.

 

Visual: SMP-3 Construct Viable Arguments and Critique the Reasoning of Others #LL2LU

We 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 might we facilitate learning and grow our culture where critique is sought and embraced?

From Step 1: The Art of Questioning in The Falconer: What We Wish We Had Learned in School.

By learning to insert feedback loops into our thought, questioning, and decision-making process, we increase the chance of staying on our desired path. Or, if the path needs to be modified, our midcourse corrections become less dramatic and disruptive. (Lichtman, 49 pag.)

This paragraph connects to a Mr. Sun quote from Step 0: Preparation.

But there are many more subtle barriers to communication as well, and if we cannot, or do not choose to overcome these barriers, we will encounter life decisions and try to solve problems and do a lot of falconing all by ourselves with little, if any, success. Even in the briefest of communications, people develop and share common models that allow them to communicate effectively.  If you don’t share the model, you can’t communicate. If you can’t communicate, you can’t teach, learn, lead, or follow.  (Lichtman, 32 pag.)

How might we offer a pathway for success? What if we provide practice in the art of questioning and the action of seeking feedback? What if we facilitate safe harbors to share  thinking, reasoning, and perspective?

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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.

How might we design opportunities for intentional, focused peer-to-peer discourse? What if we share a common model to improve communication, thinking, and reasoning?

[Cross-posted on Easing the Hurry Syndrome]

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Lichtman, Grant, and Sunzi. The Falconer: What We Wish We Had Learned in School. New York: IUniverse, 2008. Print.

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.