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Visible Thinking in Math- Part 1

The conversation about visible thinking in Math started with one of our teachers at Graded, The American School of São Paulo, Adam Hancock, wanting to know how he could incorporate having students’ use their blogfolios in Math class. It seemed natural to have students write for Humanities (Language Arts and Social Studies), but writing did not seem part of what Middle School Math was about.

How could “blogging” go beyond taking a digital image of a Math problem on paper or a quiz and writing about  ”how the student felt about solving the problem or passing the test?”or ask themselves what they could have done better?

One of the first steps was to bring more “language” into the Math classroom. In a Skype call with Heidi Hayes Jacobs, she said that Math should be taught more like a foreign language.

photo 2

Students need to know vocabulary words and become fluent in “speaking Math”, in order to be able to communicate their thoughts and ideas.

photo 1

Videos and screencasts are great tools to articulate, visualize and then share ones’ thinking when working to solve a Math problem. Below is a video of Adam, modeling solving a mathematical equation.

Google Glass- Math Equation from langwitches on Vimeo.

Making Mathematical Thinking visible had the following purpose for Adam in his classes:

1. give students a truly differentiated math experience and expose them to a wide variety of math concepts.

2. encourage self directed learning and allow them to demonstrate their understanding in a way of their choosing.

3. make their learning process visible and allow students to reflect on their growth and learning in the process of solving the problem, by using the KWHL routine (What do I know? What do I want to know? How will I find out? What have I learned?)

KWHLAQ2

KWHL-Mary

KWHL by Mary

Prezi by Isabella

More student blog posts:

The process of making mathematical thinking visible, as well as the artifacts’ quality, was hopeful, awkward, “messy” and challenging…

Adam and my observations:

  • Students were working in different areas of math, and most of them had to learn something new, and tie it to what they already know in order to explain their problem.
  • It is not a natural skill for students to be able to “speak” Math. There is a need to expose and encourage students to use mathematical language to communicate.
  • The ability of being able to articulate and make a thinking process visible is a skill we need to support our students in becoming fluent in. It was challenging for students to think about and articulate their learning value instead the production value of their artifact.
  • Some students focused in their reflection on documenting the steps of what they did as they were solving the problem, not on the necessary thinking that was involved. Some students don’t/didn’t see the reason why they should be reflecting on their learning in Math.
  • It seemed unnatural to ask students to write a reflective blog post tagged on the end. It seems artificial and one more thing to do as an add-on, versus reflection as part of the learning process. Option of breaking the reflection process into different blog posts along the way, which later on can be linked to each other to demonstrate the process path.
  • When students are given a lot of freedom to demonstrate their understanding, a lot of them need structure and some clear guidelines or else the product does not turn out very well. This may improve with practice and more opportunities for them to work independently.
  •  Many students didn’t fully follow the KWHL routine, and only posted an explanation to their problem.  In some cases the explanations were wrong. In many cases, they didn’t actually post the KWHL page, and so they lost sight of “the point”.  Maybe because this was a new process, a lot of students produced “the bare minimum “. Generally speaking, students who are conscientious and engaged did well and produced meaningful blog posts. If they did the KWHL process correctly, they documented what they didn’t know before they began researching their problem, and then demonstrated what they learned in the process.
  • There is a sense among many students that this is actually ‘more work’ than just taking a test, and therefore it is harder.

These observations are helping us continue to strive for meaningful activities and strategies that support student learning. I am often reminded of Vicki Davis’ blog post, Fail Foward, Move Foward. The word “fail” has a connotation in education, that has to change, along the paradigm shift of how we learn best and differently. In the spirit of Failure is Mandatory in the Culture of Innovation, we are celebrating these “failures” and seeing them as challenges to continue to talk, think, rethink, repeat, throw out, tweak and re-imagine…

fail

Quote seen in Tweet during #asbunplugged

I am excited to see how we will continue to make thinking visible in Math and help students write /blog about their thinking strategies in order to become fluent in the language of Math. A big thank you goes out to Adam for  learning along side!
Stay tuned for Part 2 in Visible Thinking in Math…

Redefining My Learning

Silvana Meneghini and I  work as Academic Technology Coordinators at Graded, the American School of São Paulo. ” A flashlight in the fog of technology integration“, initially the title of a conference workshop proposal, quickly developed into the desire of creating a framework to guide and coach teachers based on Ruben Puentedura‘s SAMR model. The framework does not place emphasis on technology devices (or technology integration) in itself, but on the process of upward movement from substitution to redefinition of tasks and learning activities.

Our collaboration in developing said framework became a prime example it itself, demonstrating the power of a metacognitive approach to redefining the creation of a professional development framework. In an attempt to motivate educators to take another look around and evaluate the relevance in our modern world of traditionally taught lessons and activities, skills and curriculum, we encourage educators to continue learning how to learn.

This past week, Silvana  and I hosted our first Google Hangout on Air . The hangout was the next natural step in transforming our own growth as learners. We wanted to share our framework, solicit feedback, gain perspective from the various experiences from other professionals and be open to revisions to our thoughts and framework.

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The short story of our transformative learning experience is as follows. Silvana used to have her own office. Isolated from daily informal interaction with a colleague to spontaneously chat, talk, request feedback, question, challenge or agree with. We share an office since I moved to São Paulo  at the end of last July.

REACHING OUT- Local, face2face
We talked, we pushed each other’s thinking on our thoughts, points of view, practices and visions of educational technology and modern teaching and learning. There were some extremely good conversations going on in our little office. The big huge whiteboard which takes up one entire wall in the office, was being put to good use as we brainstormed, wrote, erased, doodled, starred, circled and started over again several times. Our essential question: How could we best support our teachers in going beyond adding technology to their existing lessons and units?

Silvana marveled at the relationship of the SAMR model, technology and pedagogy and reflected in her fascinating blog post titled Technology shoving Pedagogy to the center stage? TPACK Reviewed.

From our brainstorming thoughts and attempts in articulating our idea of helping teachers think deeply about the difference of using technology to substitute a traditionally taught lesson and what redefining relevant LEARNING means, we started reaching out.

REACHING OUT – Global, Small group

We enlisted the help of 3 trusted colleagues of our PLN, who we knew would support us in starting to create a depository of classroom activities that were put through the different stages of the SAMR model (developed by Ruben Puentedura.

Andrea Hernandez (USA), Allanah King (New Zealand) and Maggie Hos-McGrane (Mumbai) contributed the first three examples and in the process helped us see the value of creating the SAMR framework and exercise to support teachers in working through the relationship of technology, pedagogy and relevant teaching and learning.

REACHING OUT- Global, Crowodsouring, open group

In our belief that a myriad of examples of different grade levels, subject areas and activities would support and benefit our teachers and in turn other educators as well. We reached out further to ask members of our PLN to contribute to a Google Form, that guided them through the SAMR exercise. The feedback was positive, that going through the exercise proved to be “incredibly helpful” and “forced me to think about tech integration”.

SAMR-exercise-evidence

SAMR_Exercise_Template_-_Google_

REACHING OUT- Global, for feedback, amplification, deep discussion and conversation

Blogging is part of my reflection and learning process. It was natural to share and solicit feedback via Langwitches. My readers did not disappoint by leaving thought provoking comments. Dissemination via Twitter is another unconscious part of my learnflow. Monitoring responses, questions and RT (retweets) allows me to gauge the interest, feasibility and helpfulness of an idea, template or resource that I am sharing with my network.

SAMR-exercise-evidence4

twitter-speading

twitter-speading2

SAMR-exercise-evidence5

Challenging ourselves to take it beyond the comfort zone of our blogs and Twitter, we invited Cathy Beach (educator from Canada) and  Laurel Jankewitz (Math teacher at Graded, The American School of São Paulo) to be part of our first attempt in using Google Hangout on Air. We created an event and disseminated the day and time via our PLN.

At one point there were 20+ viewers of the live stream. We truly learned as a group across timezones and continents. Canada, USA, Mexico, Brazil, UK, India, and Australia were viewers who identified themselves during the event.  The active participation of the following educators truly lifted our understanding and learning to new levels. Thank you for staying / getting up at all hours of the night/ morning to be part of the learning. Thank you Dana Watts, Karin Hallett, Josh Mika, Joe Dale, Becky Fisher, and Chrissy Hellyer!

redefine-learning-3

TweetDeck-2

Below are some of my notes as I was going over the questions submitted during the Hangout. At one point the question was raised, if the Google Hangout in itself

SAMR Exercise Feedback P1

SAMR Exercise Feedback P2 SAMR Exercise Feedback P3 SAMR Exercise Feedback P4 SAMR Exercise Feedback P5

Karin Hallett, a friend and former colleague (we happen to speak German/English with each other) gave me feedback via email after reading my blog posts about the framework. She questions the last step of the process being revision and suggests the addition to evaluation/reflection as an integral part of the PROCESS subfocus area.

SAMR-exercise-evidence2

 

Of course! How could we forget the reflection as part of the process. Back to the drawing board.

consume-produce-feedback-revise-reflect

 

credit for the “reflection icon”that is part of the one above goes to Kevin S. (a Graded student)

Next week, Silvana and I are on our way to ASB Unplugged to present in person our framework and ask our workshop participants to put their activities through the exercise, pick it apart, judge it for usability to think deeper about pedagogy and modern teaching and learning.

Looking back on the process of my learning that I have described above, I truly believe it has been redefined. My LEARNING has been redefined, not because I was able to have a Hangout or blog or tweet, but because of the ability to receive feedback, talk to colleagues and learn with people who believe just as passionately about the value in sharing and contributing to other people’s learning than I do. The biggest take away for me is Becky Fisher’s comment about the IMPACT, not the ACTION that defines the redefinition stage. So… how do we translate that into our schools to give our students the IMPACT, not just the ACTION?

Reflection in the Learning Process, Not As An Add On

Is it personality? Are some people born with it? Can it be learned?

I am talking about REFLECTION.

At the beginning of the week, I had the opportunity to be part of a workshop during our pre-service ( we just returned from our summer break here in the Southern Hemisphere) with our ES Principal, MS Principal and HS Assistant Principal. The topic was  student reflection.

The following ESSENTIAL QUESTIONS emerged out of the planning for this workshop

  • How does student reflection impact student learning?
  • How can we embed reflection into assessment practices so that it is not seen as an add-on?
  • How can we make the reflection visible and sustainable?

According to Carol Rodgers in  Defining Reflection :Another Look at John Dewey and Reflective Thinking, four criteria emerge from Dewey’s work that characterize reflection.

  1. Reflection is a meaning making process that moves a learner from one experience into the next with deeper understanding of its relationships with and its connections to other experiences and ideas.

  2. Reflection is a systematic, rigorous way of thinking, with its roots in scientific inquiry.

  3. Reflection needs to happen in community, in interaction with others

  4. Reflection requires attitudes that value the personal and intellectual growth of oneself and others.

I know that most teachers acknowledge the role of reflection in learning. I see reflective practice when I visit classrooms, but I also acknowledge that most of that reflection seems to be in oral form. A form that allows the reflection to disappear, to evaporate after the moment has passed.  We wanted to make teachers aware of platforms and experiences that supported reflection in teaching and learning. After orally reflecting with students during a classroom conversation or possible silent ( intrapersonal ) reflection taking place by individual students, the next most used media and platform seemed to be text. Since we have a 1:1 laptop in High School and Middle School, most these types of reflective texts are written on Google Docs, Blogs or digital online sites. I wanted to move teachers’ focus beyond using text as the medium for reflection.

Reflection

We notice when working with students that simply asking them to go ahead and write a reflection, might not be the best approach to be able to expect quality work. We initially introduced our workshop attendees to four frameworks for reflection.

  1. KWHLAQ chart
  2. See- Think- Wonder
  3. Think-Puzzle-Explore
  4. 3-2-1 Bridge

KWHLAQ2

See a 5th grade sample of using the KWHLAQ reflection routine on a blog. The student’s teacher Paul Solarz is doing fantastic work on reflective eportfolios.

KWHLAQ-reflection- http:::psolarz.weebly.com:150:post:2013:10:how-was-the-universe-created-by-ethan-k.html-2

Leika Prokopiak’s 6th grade Science students,  here are Graded, are also experimenting with the KWHLAQ reflection routine on their student portfolios.

KWHLAQ-science \

KWHLAQ-science2

see-think-wonder

After a visit from Libby Stephens, a speaker about the Third Culture Kid experiences, Ms Arcenas, had her 7th grade advisory students reflect, in writing on index cards. They used the See- Think- Wonder routine about their take away from the session with the speaker.

Think-see-wonder-analog

3-2-1-Bridge

Claire Arcenas reflection on using 3-2-1- Bridge in her 10th grade PE class

321-Bridge

321-Bridge-2

think-puzzle-explore

After introducing the four above mentioned frameworks, we asked teachers to choose one article from five pre-selected ones and use one of the four thinking routine methods to guide their reflection of their chosen article.

  1. 35 Questions for Student Reflection by Mark Clements
  2. Creating a Culture of Student Reflection by Clyde Yoshida
  3. Four Levels of Student Reflection by Maryellen Weimer
  4. Reflect, Reflective, Reflection by Silvia Tolisano
  5. High Tech Reflection Strategies Making Learning Stick by Suzie Boss

We briefly shared further visible thinking routines with the attendees and made the application visible by sharing examples from the classroom with them.

Blog commenting as reflection.

blog-commenting0

blogcomment-1

Video as a media for capturing reflection

Around the World With 80 Schools- Helsinki from langwitches on Vimeo.

Kindergarten using Explain Everything app to explain Math Scenarios from langwitches on Vimeo.

Reflection via Infographics.

overpopulation-by-ivanna

Collaborative reflection via Twitter Hashtag (Teacher Reflection)

 

Twitter-Reflection

 

 

Twitter-Reflection2

Mindmapping as a platform for reflection (organization, grouping, color coding…)
mindmapping

mindmapping2

Maps as a platform for raising awareness through visualization. Start tracking a the geographic setting of books read to see patterns and gaps emerge that were previously not noticed.

google-maps

How do you reflect with your students? What are your thoughts on using visible thinking routines to give students a strategy? What platforms are you exploring? What types of reflective experiences are you facilitating for your students?

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TPCK

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Redefining My Learning

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Silvana Meneghini and I  work as Academic Technology Coordinators at Graded, the American School of São Paulo. ” A flashlight in the fog of technology integration“, initially the title of a conference workshop proposal, quickly developed into the desire of creating a framework to guide and coach teachers based on …

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Visible Thinking in Math- Part 1

fail

The conversation about visible thinking in Math started with one of our teachers at Graded, The American School of São Paulo, Adam Hancock, wanting to know how he could incorporate having students’ use their blogfolios in Math class. It seemed natural to have students write for Humanities (Language Arts and …

(2 Comments)

Redefining My Learning

story

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Reflection in the Learning Process, Not As An Add On

Reflection

Is it personality? Are some people born with it? Can it be learned? I am talking about REFLECTION. At the beginning of the week, I had the opportunity to be part of a workshop during our pre-service ( we just returned from our summer break here in the Southern Hemisphere) …

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selfies

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eduplanet

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SLC

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Visible Thinking in Math- Part 1

fail

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Visible Thinking in Math- Part 1

fail

The conversation about visible thinking in Math started with one of our teachers at Graded, The American School of São Paulo, Adam Hancock, wanting to know how he could incorporate having students’ use their blogfolios in Math class. It seemed natural to have students write for Humanities (Language Arts and …

(2 Comments)

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image2-lens-of-pedagogy

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pedro

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storytelling-app

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