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.
I can use appropriate tools strategically.
(CCSS.MATH.PRACTICE.MP5)
Level 4:
I can communicate details of how the chosen tools added to the solution pathway strategy using descriptive notes, words, pictures, screen shots, etc.
Level 3:
I can use appropriate tools strategically.
Level 2:
I can use tools to make my thinking visible, and I can experiment with enough tools to display confidence when explaining how I am using the selected tools appropriately and effectively.
Level 1:
I can recognize when a tool such as a protractor, ruler, tiles, patty paper, spreadsheet, computer algebra system, dynamic geometry software, calculator, graph, table, external resources, etc., will be helpful in making sense of a problem.
Suppose you are solving an equation.
Are you practicing use appropriate tools strategically if you use the numerical solve command on your graphing calculator?
Or what about using your calculator to substitute values of x until you find a value that makes a true statement?
Are you practicing use appropriate tools strategically if you use a computer algebra system to explain your steps?
Or what if you use the graphing capability of your handheld?
Consider each of the following learning goals:
I can explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution, and I can construct a viable argument to justify a solution method. CCSS-M A-REI.A.1.
I can solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. CCSS-M A-REI.B.3.
I can explain why the x-coordinates of the points where the graphs of the equations y=f (x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. CCSS-M A-REI.D.11.
Does use appropriate tools strategically depend on the learner? Or the learning goal? Or the teacher? Or the availability of tools?
[Cross posted on Easing the Hurry Syndrome]
We want every learner in our care to be able to say
I can use appropriate tools strategically.
(CCSS.MATH.PRACTICE.MP5)
But…What if I think I can’t? What if I have no idea what are appropriate tools in the context of what we are learning, much less how to use them strategically? How might we offer a pathway for success?
Level 4:
I can communicate details of how the chosen tools added to the solution pathway strategy using descriptive notes, words, pictures, screen shots, etc.
Level 3:
I can use appropriate tools strategically.
Level 2:
I can use tools to make my thinking visible, and I can experiment with enough tools to display confidence when explaining how I am using the selected tools appropriately and effectively.
Level 1:
I can recognize when a tool such as a protractor, ruler, tiles, patty paper, spreadsheet, computer algebra system, dynamic geometry software, calculator, graph, table, external resources, etc., will be helpful in making sense of a problem.
We still might need some conversation about what it means to use appropriate tools strategically. Is it not enough to use appropriate tools? Would it help to find a common definition of strategically to use as we learn? And, is use appropriate tools strategically a personal choice or a predefined one?
How might we expand our toolkit and experiment with enough tools to display confidence when explaining why the selected tools are appropriate and effective for the solution pathway used? What if we practice with enough tools that we make strategic – highly important and essential to the solution pathway – choices?
What if apply we 5 Practices for Orchestrating Productive Mathematics Discussions to learn with and from the learners in our community?
What if we extend the idea of interacting with numbers flexibly to interacting with appropriate tools flexibly? How many ways and with how many tools can we learn and visualize the following essential learning?
I can understand solving equations as a process of reasoning and explain the reasoning. CCSS.MATH.CONTENT.HSA.REI.A.1
What tools might be used to learn and master the above standard?
Then, what are the conditions which make the use of each one of these tools appropriate and strategic?
[Cross posted on Easing the Hurry Syndrome]
________________________
“The American Heritage Dictionary Entry: Strategically.” American Heritage Dictionary Entry: Strategically. N.p., n.d. Web. 08 Sept. 2014.
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.
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?
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]
________________________
Lichtman, Grant, and Sunzi. The Falconer: What We Wish We Had Learned in School. New York: IUniverse, 2008. Print.
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.”
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.”
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]
_________________________
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.
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.
Which of these product rules could be used to quickly expand (x+y+3)(x+y-3)? Now, try expanding the expression.
Jennifer Wilson, Easing the Hurry Syndrome, and I have been tinkering with and drafting #LL2LU learning progressions for the Standards of Mathematical Practice. I have really struggled to get my head wrapped around the meaning of I can look for and make use of structure, SMP-7. The current draft, to date, looks like this:
What if I tried to apply my understanding of I can look for and make use of structure to Jeff’s challenge?
What if we coach our learners to make their thinking visible? What if we use learning progressions for self-assessment, motivation, and connected thinking? I admit that I was quite happy with myself with all that pretty algebra, but then I read the SMP-7 learning progression. Could I integrate geometric and algebraic reasoning to confirm structure? How flexible am I as a mathematical thinker? I lack confidence with geometric representation using algebra tiles, so it is not my go to strategy. However, in the geometric representation, I found what Jeff was seeking for his learners. I needed to see x+y as a single object.
How might we model making thinking visible in conversation and in writing? How might we encourage productive peer-to-peer discourse around mathematics? How might we facilitate opportunities for in-the-moment self- and peer-assessment that is formative, constructive, and growth-oriented?
What if we focus on what is happening in classrooms in purposeful and focused ways? What if we model and embrace formative assessment of our practice?
What if we add additional feedback loops in our culture? How and when do adults in our schools receive formative feedback? If I have a question about my practice, how do I and from whom do I seek feedback? If, as a school, we are studying formative assessment, self-assessment, and peer feedback, how are we practicing? Do I blog, journal, or keep a portfolio of my learning? What might I want to learn? Are my students learning?
Reading, Research, and Questions
How might we learn more about our practice? What if we team to discuss questions, concerns, and strengths of our learning environment, classroom culture, and planned learning episodes? What might we learn if we observe each other and discuss what we see, experience, and design?
What if we reflect, self-assess, and coach peers using the following protocol:
As a result of this observation of practice and feedback loop, which aspects of my teaching do I feel are bright spots?
As a result of this observation of practice and feedback loop, what questions do I have about my own teaching?
As a result of this observation of practice and feedback loop, what new ideas do I have?
In other words, will I see myself in my colleagues? Will I recognize effective strategies that we both use? Will I observe strategies that I might like to try? Will I want to know more about the instructional design? Will we ask each other questions where we need support?
As we piloted this 1-PLU course last spring, I enjoyed the observations and writing the reflections. I liked the emphasis on bright spots and questions about my own practice. However, the most powerful part of this learning experience was the debrief after each lesson. I was wowed by the questions, the vulnerability, and the humanity of discussions.
What if we shift the focus of peer observations from observing our peers to observing the products of their work – the actions of students?
We want every learner in our care to be able to say
I can make look for and make use of structure. (CCSS.MATH.PRACTICE.MP7)
But…What if I think I can’t? What if I have no idea what “structure” means in the context of what we are learning?
One of the CCSS domains in the Algebra category is Seeing Structure in Expressions. Content-wise, we want learners to
How might we offer a pathway for success? What if we provide cues to guide learners and inspire noticing?
Level 4
I can integrate geometric and algebraic representations to confirm structure and patterning.
Level 3
I can look for and make use of structure.
Level 2
I can rewrite an expression into an equivalent form, draw an auxiliary line, or identify a pattern to make what isn’t pictured visible.
Level 1
I can compose and decompose numbers, expressions, and figures to make sense of the parts and of the whole.
Illustrative Mathematics has several tasks to allow students to look for and make use of structure. We look forward to trying these, along with a leveled learning progression, with our students.
A-SSE Seeing Structure in Expressions Tasks
[Cross posted on Easing the Hurry Syndrome]