Category Archives: Connecting Ideas

Visual: SMP-8: look for and express regularity in repeated reasoning #LL2LU

Many students would struggle much less in school if, before we presented new material for them to learn, we took the time to help them acquire background knowledge and skills that will help them learn. (Jackson, 18 pag.)

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

I can look for and express regularity in repeated reasoning.
(CCSS.MATH.PRACTICE.MP8)

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But…what if I can’t? What if I have no idea what to look for, notice, take note of, or attempt to generalize?

Investing time in teaching students how to learn is never wasted; in doing so, you deepen their understanding of the upcoming content and better equip them for future success. (Jackson, 19 pag.)

Are we teaching for a solution, or are we teaching strategy to express patterns? What if we facilitate experiences where both are considered essential to learn?

We want more students to experience the burst of energy that comes from asking questions that lead to making new connections, feel a greater sense of urgency to seek answers to questions on their own, and reap the satisfaction of actually understanding more deeply the subject matter as a result of the questions they asked.  (Rothstein and Santana, 151 pag.)

What if we collaboratively plan questions that guide learners to think, notice, and question for themselves?

What do you notice? What changes? What stays the same?

Indeed, sharing high-quality questions may be the most significant thing we can do to improve the quality of student learning. (Wiliam, 104 pag.)

How might we design for, expect, and offer feedback on procedural fluency and conceptual understanding?

Level 4
I can attend to precision as I construct a viable argument to express regularity in repeated reasoning.

Level 3
I can look for and express regularity in repeated reasoning.

Level 2
I can identify and describe patterns and regularities, and I can begin to develop generalizations.

Level 1
I can notice and note what changes and what stays the same when performing calculations or interacting with geometric figures.

If we are to harness the power of feedback to increase student learning, then we need to ensure that feedback causes a cognitive rather than an emotional reaction—in other words, feedback should cause thinking. It should be focused; it should relate to the learning goals that have been shared with the students; and it should be more work for the recipient than the donor. (Wiliam, 130 pag.)

[Cross posted on Easing the Hurry Syndrome]


Jackson, Robyn R. (2010-07-27). How to Support Struggling Students (Mastering the Principles of Great Teaching series) (Pages 18-19). Association for Supervision & Curriculum Development. Kindle Edition.

Rothstein, Dan, and Luz Santana. Make Just One Change: Teach Students to Ask Their Own Questions. Cambridge, MA: Harvard Education, 2011. Print.

Wiliam, Dylan (2011-05-01). Embedded Formative Assessment (Kindle Locations 2679-2681). Ingram Distribution. Kindle Edition.

SMP-8: look for and express regularity in repeated reasoning #LL2LU

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

I can look for and express regularity in repeated reasoning. (CCSS.MATH.PRACTICE.MP8)

But what if I can’t look for and express regularity in repeated reasoning yet? What if I need help? How might we make a pathway for success?

Level 4
I can attend to precision as I construct a viable argument to express regularity in repeated reasoning.

Level 3
I can look for and express regularity in repeated reasoning.

Level 2
I can identify and describe patterns and regularities, and I can begin to develop generalizations.

Level 1
I can notice and note what changes and what stays the same when performing calculations or interacting with geometric figures.

What do you notice? What changes? What stays the same?

Can we use CAS (computer algebra system) to help our students practice look for and express regularity in repeated reasoning?

What do we need to factor for the result to be (x-4)(x+4)?
What do we need to factor for the result to be (x-9)(x+9)?
What will the result be if we factor x²-121?
What will the result be if we factor x²-a2?

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We can also explore over what set of numbers we are factoring using the syntax we have been using. And what happens if we factor x²+1. (And then connect the result to the graph of y=x²+1.)

What happens if we factor over the set of real numbers?

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Or over the set of complex numbers? 

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What about expanding the square of a binomial? 

What changes? What stays the same? What will the result be if we expand (x+5)²?  Or (x+a)²?  Or (x-a)²? 

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What about expanding the cube of a binomial?  Or expanding (x+1)^n, or (x+y)^n?

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What if we are looking at powers of i?

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We can look for and express regularity in repeated reasoning when factoring the sum or difference of cubes. Or simplifying radicals. Or solving equations.

Through reflection and conversation, students make connections and begin to generalize results. What opportunities are you giving your students to look for and express regularity in repeated reasoning? What content are you teaching this week that you can #AskDontTell?

[Cross-posted on Easing the Hurry Syndrome]

 

 

How to be a boring, bad writer…and other ideas (TBT Remix)

I hadn’t thought about it this way:

So, if you want to be a boring, bad writer:

  1. Never ever learn new words.
  2. Be afraid to say interesting things.
  3. Read as little as possible.
  4. Always play on your laptops.
  5. Never touch a dictionary.
  6. Copyright.
  7. Never make [the reader] see the action.
  8. Never revise your writing.
  9. Definitely take the easy way.

Since I want to be a better writer, I should practice 1) using new words, 2) saying interesting things, 3) reading as much as possible, 4) leveraging technology to enhance learning, 5) using available resources, 6) striving to be unique and citing my sources, 7) presenting a good story, 8) repeating a revision cycle several times, and 9) understanding to “embrace the struggle.”

I wonder if the same set of ideas can be applied to PBL.  How to avoid PBL, Design Thinking, and makery:

  1. Never ever learn new applications and strategies.
  2. Be afraid to try interesting, complex problems.  It might take too long.
  3. Read and research as little as possible. Don’t read and watch Edutopia, Deep Design Thinking, or It’s About Learning resources or ideas from 12k12.
  4. Always use technology for one-way communication.  Just tell them what to do.  Don’t offer students the opportunity to have voice and choice in learning.
  5. If you try PBL, and it doesn’t work; just give up.  Never seek additional support and resources.
  6. Never collaborate with others on projects and problems that integrate ideas and/or concentrate on community-issues.
  7. Avoid applications and real-world experiences.  Never offer the opportunity to present to an authentic audience.
  8. Never say “I don’t know,” or “let’s find out together.” Answer every question asked in class, or better yet, don’t allow questions.
  9. Definitely do the very same thing you did this time last year.  It’s easy.  Take the easy way. Remember…the E-Z-way!

How about applying these ideas to balanced assessment?  How to be single-minded about assessment:

  1. Never ever try new techniques, methods, and strategies.
  2. Be afraid to try alternate forms of assessment: performance based assessment, portfolios, etc.
  3. Read and research as little as possible. Don’t read anything by Tom Guskey, Jan Chapuis, Bob Marzanno, Dylan Wiliam etc.
  4. Always use assessment to generate grades.  Never try non-graded assessment to make adjustments to learning that improve achievement.
  5. If you use rubrics or standards-based grading, and students don’t respond; just give up.  Don’t allow students to revise their understanding and assess again.  Let them learn it next year or in summer school.
  6. Rely on results from standardized tests to compare students.  Just follow the model set by adults that have not met you and your learners.
  7. Never assess for learning and reteach prior to a summative assessment.  Think that you are teaching a lesson if failure occurs with no chance to revise.
  8. Never offer 2nd chance test or other opportunities to demonstrate learning has occurred.
  9. Definitely use the very same assessment you did this time last year.  It’s easy.  Take the easy way. Remember… E-Z-way!

I find this approach connected the anti-innovation ideas from Kelly Green in her 2/21/2012 ForbesWoman article I found by reading Bob Ryshke’s post, What schools can do to encourage innovation.  It also reminds me of Heidi Hayes Jacob’s style in her TEDxNYED talk I found by reading Bo Adam’s What year are you preparing your students for?” Heidi Hayes Jacobs #TEDxNYED post.

I like the provocation of the video and the anti-ideas.  I appreciate the challenge of rephrasing these ideas as statements of what I could do to get better.  I wonder how we should practice to become better at PBL, balanced assessment, innovation and creativity, etc.  In the comment field below, will you share how would you answer this prompt?

Since I want to be a better ___________, I should practice 1)  _____, 2)  _____, 3)  _____, 4)  _____, 5)  _____, 6)  _____, 7)  _____, 8)  _____, and 9)  _____.


How to be a boring, bad writer…and other ideas was originally published on February 26, 2012.

 

#TEDTalkTuesday: problems, inventions, school

Alanna Shaikh:  How I’m preparing to get Alzheimer’s

There’s about 35 million people globally living with some kind of dementia, and by 2030 they’re expecting that to double to 70 million. That’s a lot of people.

Kenneth Shinozuka:  My simple invention, designed to keep my grandfather safe

… I was looking after my grandfather and I saw him stepping out of the bed. The moment his foot landed on the floor, I thought, why don’t I put a pressure sensor on the heel of his foot? Once he stepped onto the floor and out of the bed, the pressure sensor would detect an increase in pressure caused by body weight and then wirelessly send an audible alert to the caregiver’s smartphone.

Geoff Mulgan: A short intro to the Studio School

What kind of school would have the teenagers fighting to get in, not fighting to stay out? And after hundreds of conversations with teenagers and teachers and parents and employers and schools from Paraguay to Australia, and looking at some of the academic research, which showed the importance of what’s now called non-cognitive skills — the skills of motivation, resilience — and that these are as important as the cognitive skills — formal academic skills — we came up with an answer, a very simple answer in a way, which we called the Studio School. And we called it a studio school to go back to the original idea of a studio in the Renaissance where work and learning are integrated. You work by learning, and you learn by working. 

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.

#TEDTalkTuesday: Math in an Information Age

Conrad Wolfram: Teaching kids real math with computers
We can engage so many more students with this, and they can have a better time doing it. And let’s understand: this is not an incremental sort of change. We’re trying to cross the chasm here between school math and the real-world math. 
Dan Meyer: Math class needs a makeover
 Math makes sense of the world. Math is the vocabulary for your own intuition.

#TEDTalkTuesday: Wicked problem: share ideas; don’t be afraid

Tom Wujec: Got a wicked problem? First, tell me how you make toast
First, drawing helps us understand the situations as systems with nodes and their relationships. Movable cards produce better systems models, because we iterate much more fluidly. And then the group notes produce the most comprehensive models because we synthesize several points of view. So that’s interesting. When people work together under the right circumstances, group models are much better than individual models.

Tim Brown: Tales of creativity and play

We’re embarrassed about showing our ideas to people we think of as our peers, to those around us. And this fear is what causes us to be conservative in our thinking. So we might have a wild idea, but we’re afraid to share it with anybody else.

Elizabeth Gilbert: Your elusive creative genius

And what I have to, sort of keep telling myself when I get really psyched out about that,is, don’t be afraid. Don’t be daunted. Just do your job. Continue to show up for your piece of it, whatever that might be.