Category Archives: Questions

Lyrics and Improv – creating a flexible base

How many songs do we sing without reading and confirming the lyrics? How often have our lyrics been a source of enjoyment for others?

Be sure to make your instructional goals clear to your students.(Lehman and Roberts, 17 pag.)

Learning targets increase students’ independence by bringing the standards to life, shifting ownership of meeting them from just the teacher to both the teacher and the student. (Berger, 23 pag.)

It is not enough that the teacher knows where students are headed; the students must also know where they are headed, and both the teacher and the students must be moving in the same direction.  (Conzemius and O’Neill,  66 pag.)

Is it that, sometimes, what we hear isn’t really what is being said?

How often do we embrace improvisation?

While this may be a lesson introducing the steps of reading closely for text evidence, show [learners] how it can help them develop new ideas, like understanding their characters in deeper ways.  (Lehman and Roberts, 17 pag.)

Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices. (CCSS SMP)

How might we create a flexible base where we are moving in the same direction, singing the same tune, and confident enough to improvise?


Berger, Ron, Leah Rugen, and Libby Woodfin. Leaders of Their Own Learning: Transforming Schools through Student-engaged Assessment. N.p.: n.p., n.d. Print.

Conzemius, Anne; O’Neill, Jan. The Power of SMART Goals: Using Goals to Improve Student Learning. Bloomington, IN: Solution Tree, 2006. Print.

Lehman, Christopher, and Kate Roberts. Falling in Love with Close Reading: Lessons for Analyzing Texts and Life. N.p.: n.p., n.d. Print.

Standards for Mathematical Practice.” Standards for Mathematical Practice. N.p., n.d. Web. 15 Dec. 2014.

 

#HLTA: High-Leverage Team Actions

I’m reading Beyond the Common Core: A Handbook for Mathematics in a PLC at Work  written by Juli K. DixonThomasenia Lott AdamsEdward C. Nolan and edited by Timothy D. Kanold.

In their handbook, they offer tools that scaffold collaborative pursuit.   They identify 10 high-leverage team actions (HLTAs) to  impact learning and improve team work, instruction, and assessment.

What if we use this to set goals for our team and guide our actions in one team meeting per month/week/quarter? If we are not there yet, could we pick 1-3 and take concentrated action?


Dixon, Juli K; Adams, Thomasina Lott (2014-10-13). Beyond the Common Core: A Handbook for Mathematics in a PLC at Work™, Grades K-5 (Kindle Locations 3-5, 241-243, 273-279, 286-289, 300-302). Solution Tree Press. Kindle Edition.

Labeled…Mislabeled…Relabeled (TBT Remix)

There are few things sadder to a teacher or parent than being faced with capable children who, as a result of previous demoralizing experiences, or even self-imposed mind-sets, have come to believe that they cannot learn when all objective indicators show that they can. Often, much time and patience are required to break the mental habits of perceived incompetence that have come to imprison young minds.
~ Frank Pajares, Schooling in America: Myths, Mixed Messages, and Good Intentions

Watch and read about labels from The Power of Dyslexia:

Do you carry a label?
Was it of your own choosing, or were you labeled by others?

Do we listen to others or collect evidence ourselves when confronted with labels?

Knowledge is power.  Knowing where you are today, right now, affords the opportunity to take action and next steps.  Fear of the unknown…well, that’s a problem.

How might we uncover what is not known while celebrating what is known?

New perspective. Mindset shift. Remix.

Ask. Act. Learn.


Labeled…Mislabeled…Relabeled was originally posted March 12, 2012

Common denominators – “Let’s see why”

Everybody knows that you must have common denominators to add fractions, right?  Do we know why? If asked to construct a viable argument, could we? Can we draw it (i.e., communicate why visually)?  How mathematically flexible are we when it comes to fractions? 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.

Today’s Building Concepts lesson: Adding and Subtracting of Fractions with Unlike Denominators, had our young learners working to show their understanding of adding and subtracting fractions in multiple ways.

Kristi Story (@kstorysquared) used a phrase today that has really stuck with me is “Let’s see why…”  It immediately reminded me of Simon Sinek’s How great leaders inspire action.

And it’s those who start with “why” that have the ability to inspire those around them or find others who inspire them.

I wonder if, when young learners struggle with numeracy, it is because they do not see why.  Have they been so concerned with “getting the right answer” that they have missed the theory, reasoning, and geometry? photo[1]

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What if we  leverage appropriate tools and use them strategically? What if we use technology to personalize learning and offer every learner the opportunity to see why?


#LL2LU draft for use equivalent fractions as a strategy to add and subtract fractions.

Level 4:
I can solve real-world and mathematical problems involving the four operations with rational numbers.

Level 3:
I can solve word problems involving addition and subtraction of fractions by using visual fraction models or equations to represent the problem.

Level 2:
I can add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions.

Level 1:
I can understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

I can recognize and generate simple equivalent fractions, and I can explain why the fractions are equivalent using a visual fraction model.


#LL2LU for I can apply mathematical flexibility.

  Level 4: I can analyze different pathways to success, find connections between pathways and add new strategies to my thinking.

Level 3: I can apply mathematical flexibility to show what I know using more than one method.

Level 2: I can show my work to document one successful  method.

Level 1: I can find and state a correct solution.


#LL2LU for I can construct a viable argument and critique the reasoning of others.

Level 4: I can build on the viable arguments of others and use 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.

#TEDTalkTuesday: 2 Stories behind creating a movement

Nancy Frates: Meet the mom who started the Ice Bucket Challenge

The first thing is, every morning when you wake up, you can choose to live your day in positivity.

 Be passionate. Be genuine. Be hardworking. And don’t forget to be great.

Adam Garone: Healthier men, one moustache at a time

It’s about each person coming to this platform, embracing it in their own way, and being significant in their own life.

Learning Progressions – Zooming out and in

Do we take the time to zoom out as well as zoom in? Are we aware of what is essential to learn in the course that precedes ours or the course after?

Zooming out:

From Common Core State Standards: Numbers and Operations__Fractions:

Grade 6

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Apply and extend previous understandings of numbers to the system of rational numbers.

Grade 5

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and division

Grade 4 

Extend understanding of fraction equivalence and ordering.

Build fractions from unit fractions

Understand decimal notation for fractions and compare decimal fractions

Grade 3 

Develop understanding of fractions as numbers

Zooming in:

#LL2LU draft for Develop understanding of fractions as numbers.

Grade 6 – Level 4:
I can understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q).

Grade 6 – Level 3:
I can interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem.

Grade 6 – Level 2:
I can understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

Grade 6 – Level 1:
I can extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.


Grade 5 – Level 4:
I can interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem.

Grade 5 – Level 3:
I can add and subtract fractions with unlike denominators, including mixed numbers by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Grade 5 – Level 2:
I can apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Grade 5 – Level 1:
I can interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).


Grade 4 – Level 4:
I can add and subtract fractions with unlike denominators, including mixed numbers by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Grade 4 – Level 3:
I can decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation, and I can justify decompositions by using a visual fraction model.

Grade 4 – Level 2:
I can add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction.

Grade 4 – Level 1:
I can understand a multiple of a/b as a multiple of 1/b, and I can use this understanding to multiply a fraction by a whole number.


Grade 3 – Level 4:
I can decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation, and I can justify decompositions by using a visual fraction model.

Grade 3 – Level 3:
I can explain equivalence of fractions in special cases, and I can compare fractions by reasoning about their size using a visual fraction model.

Grade 3 – Level 2:
I can compare two fractions with the same numerator or the same denominator by reasoning about their size.

Grade 3 – Level 1:
I can express whole numbers as fractions, and I can explain why fractions that are equivalent to whole numbers.

What if we vertically align and share learning progressions based on both the zoomed out view and the zoomed in view?

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.