Tag Archives: Grant Lichtman

Focus on Learning: Establish Mathematics Goals to Focus Learning

Worry in her beautiful, tired, sad eyes communicates so much. Strain across her face makes my heart ache. As we sit down for coffee with our children playing nearby, she blurts, “I don’t know how to make myself clearer, Jill. They just don’t, won’t, can’t – I don’t know – get it!” I sigh into my coffee which causes steam to fog up my glasses, and she laughs through her tears.  

Knowing that I am an evidence-interested educator, she pulls out her unit plans for me to see and offer feedback. “You were in our class yesterday. What I can I do better…? How do I help them learn?” Love and concern for her students is evident in her thoughtfulness, craftsmanship, and design.

I was in this class yesterday and had been for many days of the unit. I go again and again, because I am learning from her and with her students. This strong, organized, empathetic teacher is, in fact, a very good teacher.  

“What if we take your teaching up a level to a stronger focus on learning? Let’s look at the output that is causing you this worry and stress. Together, can we look at their work and identify what they, in your words, ‘just don’t, won’t, can’t’ do?’ And then, what if we establish mathematics goals to focus learning for you and your students?”

Sitting there on the bank of the Chattahoochee, occasionally interrupted, joyfully, by a toddler that needed to show us a valuable rock or other important discovery, we combed through student work. Outpouring concern and frustration, she talked about each learner, their strengths, and what surprised her about what they did not understand. I listened in awe of what she knew about her students in granular detail, and what she thought they knew but didn’t really. My notes highlighted every success she saw and the joy and pride she felt with every success.

How might we shift her work to increase the amount of success for her and her students? How might we empower learners to take action, self-assess, and ask questions early and often to improve their understanding and communication? What if we take what we just learned about her class and level it out to make her expectations and her thinking visible?

We found four categories or groupings:

  1. As soon I as finish explaining the task, they are all over me, Jill. They have no idea what to do or are too scared to get started. They want me to hold their hand. They are not empowered or safe enough to try.” They are splashing around in the shallow end, maybe even thrashing.
  2. They started, but cannot think flexibly when their first attempt gets them nowhere. They will not hear feedback or collaborate to think differently. They just shut down.
  3. “They are happily working along and find success.” They are willing to work in the pool, but need support build around them to know this is a safe, brave space to draft and redraft to think and learn. Mistakes are opportunities to learn; they do not define you.
  4. “They are first and fast and successful. They want and need more. I want to deepen and connect their learning, not broaden it.” They are willing to dive into the deep end confidently to explore new connections and representations.

This hard, important work helped us gain clarity about what is essential to learn in her classroom. Articulating frustration points as well as success points during her analysis of learning in her classroom revealed and organized a path for communication of learning intentions.

How might we empower and embolden our learners to ask the questions they need to ask by improving the ways we communicate and assess?

What if we make our thinking visible to our learners? What if we display learning progressions in our learning space to show a pathway for learners?

Great teachers lead us just far enough down a path so we can challenge for ourselves.  They provide just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out to the world, makes me want to step to the next higher level. Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)

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

I can make sense of problems and persevere in solving them.  (CCSS.MATH.PRACTICE.MP1)

But, as a learner…What if I think I can’t? What if I’m stuck? What if I feel lost, confused, or discouraged? How might we offer a pathway for success? What if we provide cues to guide learners and inspire interrogative self-talk?

NCTM’s recent publication, Principles to Actions: Ensuring Mathematical Success for All, calls us to support productive struggle in learning mathematics. How do we encourage our students to keep struggling when they encounter a challenging task? They are accustomed to giving up when they can’t solve a problem immediately and quickly. How do we change the practice of how our students learn mathematics?

How might we coach our learners in to asking more questions? Not just any questions – targeted questions. What if we coach and develop the skill of questioning self-talk?

Interrogative self-talk, the researchers say, “may inspire thoughts about autonomous or intrinsically motivated reasons to pursue a goal.” As ample research has demonstrated, people are more likely to act, and to perform well, when the motivations come from intrinsic choices rather than from extrinsic pressures.  Declarative self-talk risks bypassing one’s motivations. Questioning self-talk elicits the reasons for doing something and reminds people that many of those reasons come from within.” (Pink, 103 pag.)

Our coffee is cold and our children have lost interest in playing together. As we wrap up our reflection, feedback, and planning session, we agree to experiment the next week with her students. How might the work and learning change if we make a pathway for self-assessment and self-talk visible to the learners?

We plan to post #LL2LU SMP-1:  I can make sense of problems and persevere in solving them in the classroom and on the tables for easy reference.  Our immediate learning goal for the students is to make sense and persevere, to ask clarifying questions and try again, to show thinking for clarity and questioning, and to find multiple ways to solutions and find connections.

Excellent teachers think hard about when they will present the learning intention. They don’t just set the learning intentions early in the lesson and then forget about them. They refer to these intentions throughout instruction, keeping students focused on what it is they’re supposed to learn. (Hattie, 55-56 pag.)


Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L.. Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series). SAGE Publications. Kindle Edition.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

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

Pink, Daniel H. (2012-12-31). To Sell Is Human: The Surprising Truth About Moving Others. Penguin Group US. Kindle Edition.

 

Summer PD: Day 1 Make Sense; Persevere

Summer Literacy and Mathematics Professional Learning
June 5-9, 2017
Day 1 – Make Sense and Persevere
Jill Gough and Becky Holden

Today’s focus and essential learning:

We want all mathematicians to be able to say:

I can make sense of tasks
and persevere in solving them.

(but… what if I can’t?)

Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level.  Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)

… designed to help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems.  (Flynn, 19 pag.)

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Agenda and Tasks:

Slide deck:

Resources:

Thinking from different angles. Facing challenges. (TBT Remix)

Thinking from different angles. Facing challenges. Making thinking more visible.

The modern world demands that we all think a bit more productively, more creatively, more rationally; that we think from a different angle, with a different set of muscles, with a different set of expectations; that we think with neither fear nor favor, with neither blind optimism nor sour skepticism. (Levitt and Dubner)

This means that facing challenges, both problems and opportunities, is vital to personal success. This is the arena in which we can grow, excel, create, and expand. Without these challenges, we wither. Because of this importance, it is equally vital that we examine the way in which we meet the challenges by questioning our path from the outset. (Lichtman)

So, if we really believe that good communication is core to intelligent strategy, to seamless teamwork, to the pursuit of excellence, we must take seriously the limitation of being literally blinded to larger realities. We don’t know what we don’t know until we ask others to add their perspectives and until we start drawing it out for everyone to see. (Brown)

The costs of changing nothing are stagnation and resignation to the status quo. But the benefits of changing your reality— and sharing that positive reality with others— are the kinds of successes, discoveries, and breakthroughs that can transform not only your own life but the world. (Achor)

What if we examine the way we meet challenges, think from different angles,  share perspectives, and share successes? How might we change our part of the world?


Thinking from different angles. Facing challenges. was originally published on December 22, 2014.


Achor, Shawn (2013-09-10). Before Happiness: The 5 Hidden Keys to Achieving Success, Spreading Happiness, and Sustaining Positive Change (p. 232). Crown Publishing Group. Kindle Edition.

Levitt, Steven D.; Dubner, Stephen J. (2014-05-12). Think Like a Freak: The Authors of Freakonomics Offer to Retrain Your Brain (p. 8). HarperCollins. Kindle Edition.

Lichtman, Grant (2010-05-25). The Falconer (Kindle Locations 1330-1332). iUniverse. Kindle Edition.

Silos Suck: How to Doodle Everyone Onto the Same Page.” Sunni Brown. Sunni Brown, 21 Nov. 2014. Web. 22 Dec. 2014.

Differentiation and mathematical flexibility – #LL2LU

How is flexibility encouraged and practiced? Is it expected? Is it anticipated?  What if we collect evidence of mastery of flexibility along side mastery of skill?

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.

This past week Rhonda Mitchell (@rgmteach), Early Elementary Division Head, and I collaborated to reword the learning progression for mathematical flexibility so that it is appropriate for Kindergarten and 1st Grade learners.

How might we differentiate to deepen learning?

If we want to support students in learning, and we believe that learning is a product of thinking, then we need to be clear about what we are trying to support. (Ritchhart, Church, and Morrison, 5 pag.)

How might we collect evidence to inform and guide next steps?

Monitoring students’ mastery of a learning progression leads to evidence collection for each building block in a progression. (Popham, Kindle location 2673)

How might we prepare for mid-course corrections to intervene, enrich, and personalize learning for every learner?

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.)

What if we consider pairing a skill learning progression with a process learning progression? How might we differentiate to deepen learning?

Students love to give their different strategies and are usually completely engaged and fascinated by the different methods that emerge. Students learn mental math, they have opportunities to memorize math facts and they also develop conceptual understanding of numbers and of the arithmetic properties that are critical to success in algebra and beyond. (Boaler and Williams)


Boaler, Jo, and Cathy Williams. “Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts.” Youcubed at Stanford University. Stanford University, 14 Jan. 2015. Web. 22 Feb. 2015.

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

Popham, W. James (2011-03-07). Transformative Assessment in Action: An Inside Look at Applying the Process. Association for Supervision & Curriculum Development. Kindle Edition.

Ritchhart, Ron, Mark Church, and Karin Morrison. Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. San Francisco, CA: Jossey-Bass, 2011. Print.

Drafts and the power of descriptive feedback

Math, writing, art, language, life… How might we grow and learn through descriptive feedback?

How many rough drafts to we expect from and offer to our learners?

Austin’s Butterfly: Building Excellence in Student Work – Models, Critique, and Descriptive Feedback

What if we allow, nay, insist on drafts and mulligans? Can we unlearn the “one-and-done” assessment mentality?

“Unlearning is required when the world or your circumstances in that world have changed so completely that your old habits now hold you back.”  (Davidson, 19 pag.)

Have our circumstances at school changed so completely that old habits are holding back progress?  Am I holding on to my old habits so hard that I am holding back my learners? Every learner has access to amazing amounts of information at their fingertips via their smart phone, iPad, and computer. YIKES!  Circumstances have changed.

“It means becoming a student again because your training doesn’t comprehend the task before you.  You have to, first, see your present patterns, then, second, you have to learn how to break them.  Only then do you have a chance of seeing what you are missing? (Davidson, 19 pag.)

What habits have I tried to break or change to see what I’m missing?  What have I been willing unlearn and relearn?

How are we making learning pathways more visible to learners so that they are empowered to help monitor learning and offer descriptive feedback?

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.)


Davidson, Cathy N.  Now You See It: How the Brain Science of Attention Will Transform the Way We Live, Work, and Learn. New York: Viking, 2011. Print.

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

Thinking from different angles. Facing challenges.

Thinking from different angles. Facing challenges. Making thinking more visible.

The modern world demands that we all think a bit more productively, more creatively, more rationally; that we think from a different angle, with a different set of muscles, with a different set of expectations; that we think with neither fear nor favor, with neither blind optimism nor sour skepticism. (Levitt and Dubner)

This means that facing challenges, both problems and opportunities, is vital to personal success. This is the arena in which we can grow, excel, create, and expand. Without these challenges, we wither. Because of this importance, it is equally vital that we examine the way in which we meet the challenges by questioning our path from the outset. (Lichtman)

So, if we really believe that good communication is core to intelligent strategy, to seamless teamwork, to the pursuit of excellence, we must take seriously the limitation of being literally blinded to larger realities. We don’t know what we don’t know until we ask others to add their perspectives and until we start drawing it out for everyone to see. (Brown)

The costs of changing nothing are stagnation and resignation to the status quo. But the benefits of changing your reality— and sharing that positive reality with others— are the kinds of successes, discoveries, and breakthroughs that can transform not only your own life but the world. (Achor)

How might we change our part of the world?


Achor, Shawn (2013-09-10). Before Happiness: The 5 Hidden Keys to Achieving Success, Spreading Happiness, and Sustaining Positive Change (p. 232). Crown Publishing Group. Kindle Edition.

Levitt, Steven D.; Dubner, Stephen J. (2014-05-12). Think Like a Freak: The Authors of Freakonomics Offer to Retrain Your Brain (p. 8). HarperCollins. Kindle Edition.

Lichtman, Grant (2010-05-25). The Falconer (Kindle Locations 1330-1332). iUniverse. Kindle Edition.

Silos Suck: How to Doodle Everyone Onto the Same Page.” Sunni Brown. Sunni Brown, 21 Nov. 2014. Web. 22 Dec. 2014.

Making #LL2LU Learning Progressions Visible

From Chapter 3: Grading Strategies that Support and Motivate Student Effort and Learning of Grading and Learning: Practices That Support Student Achievement, Susan Brookhart writes:

First, these teachers settled on the most important learning targets for grading. By learning targets, they meant standards phrased in student-friendly language so that students could use them in monitoring their own learning and, ultimately, understanding their grade.

One of these learning targets was ‘I can use decimals, fractions, and percent to solve a problem.’ The teachers listed statements for each proficiency level under that target and steps students might use to reach proficiency.

The [lowest] level was not failure but rather signified ‘I don’t get it yet, but I’m still working.’ (Brookhart, 30 pag.)

How are we making learning progressions visible to learners so that they monitor their own learning and understand how they are making progress?

Yet is such a powerful word. I love using yet to communicate support and issue subtle challenges.  Yet, used correctly, sends the message that I (you) will learn this.  I believe in you, and you believe in me. Sending the message “you can do it; we can help” says you are important.  You, not the class.  You.  You can do it; we can help.

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Self-assessment, self-directed learning, appropriate level of work that is challenging with support, and the opportunity to try again if you struggle are all reasons to have learning progressions visible to learners.

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Making the learning clear, communicating expectations, and charting a path for success are all reasons to try this method.Screen Shot 2014-11-09 at 6.32.15 PM

In addition to reading the research of Tom Guskey, Doug Reeves, Rick Stiggins, Jan Chappius, Bob Marzano and many others, we’ve been watching and learning from TED talks.  My favorite for thinking about leveling formative assessments is Tom Chatfield: 7 ways games reward the brain.

As a community, we continue the challenging work of writing commonly agreed upon essential learnings for our student-learners.  Now that we are on a path of shared models of communication, we are able to develop feedback loops and formative assessments for student-learners to use to monitor their learning as well as empower learners to ask more questions.

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.)

Are learning progressions visible and available for every learner?

  • If yes, will you share them with us using #LL2LU on Twitter ?
  • If no, can they be? What is holding you back from making them visible?

Brookhart, Susan M. Grading and Learning: Practices That Support Student Achievement. Bloomington, IN: Solution Tree, 2011. Print.

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