Tag Archives: leveled assessment

Formative Assessment – Leading Learners to Level Up (#LL2LU) – A Definition of Derivative

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.)

Do we offer learners a way to decode their understanding and ask targeted questions to improve their work? Have we, as a team, identified what is essential to learn and at least one path to success? How do we communicate and collaborate with our learners and our colleagues to build paths to success for all learners?

What if we offered non-graded self-assessment that helped everyone calibrate what they know with what is essential to learn?

What does it take for a calculus learner to show they understand how to use a definition of the derivative? What might the essential learning look like?

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What must one be able to do to show understanding of this topic in calculus? Can the teaching team break it down into components that are necessary to use this definition of a derivative?

In our brainstorming session, Sam and I decided that the following was needed when finding a derivative analytically using this definition:

You have to understand function notation. You have to be able to use function notation when x is a constant and when x is a variable. You have to be able to simplify polynomial and rational expressions.

Do our young learners understand what the words in the previous paragraph mean? Do they need to see it too?  Are we communicating clearly? Is there a difference between saying I understand it and actually understanding?

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What if we asked our learners to show what they know by working through a document to “level” where they are based on our expectations?

Would young learners of calculus be empowered and emboldened to ask specific questions about their understanding? In other words, will learners begin to differentiate for themselves? I assure you it is much more rewarding and fun to be asked specific questions instead of fielding “I don’t know nothing” statements.

Would this type of ungraded self-assessment build confidence and relationship? From experience, I know the answer is yes IF the message is that it does not matter where you are as long as you are working to get to Level 3.  As a community, we must all get to Level 3, the essential learning.

How might we change the conversation in our classes?  How might we use assessment for learning? How might we provide enough insight to compel learners down a path?

The excitement of learning, the compelling personal drive to take one more step on the path towards wisdom, comes when we try to solve a problem we want to solve, when we want to solve, when we see a challenge and say yes, I can meet it.  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.)

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

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

Listen to Learn: Practicing & learning with @HollyChesser

More and more, I’m motivated and convicted about leveled assessment.  I’ve been reading and blending ideas from our #TrinityLearns summer reading list along with several other books.  The Foundational Ideas of the post #MICON13: Leading Learners to Level Up – or Ask; Don’t Tell motivated a morning coffee and think do tank learning episode with Holly Chesser (@HollyChesser).

Holly is an “English teacher” while I am a “math” teacher.  This, in fact, narrowly defines each of us. We are each actually much more diverse in skill, leadership, and learning.  After a quick Ignite talk (poor Holly) to provide an overview, we attempted to design a leveled assessment rubric to coach 9th grader learners.

We discussed how much easier leveled assessment was in math.  It is the common conversation that has to be processed before rolling-up-sleeves work begins.  Many never get past the math-is-so-much-easier phase.  I think math seems easier, because the assumption is that math is skill based.  Humanities seem to have more grey areas.  However, the “I’ll know it when I see it” comment does not help illuminate a path to success.  If we are content experts, shouldn’t we be able to articulate one or more ways to show, demonstrate, and accomplish success?

We discussed how important it is to communicate expectations and a path (or two) to success.  We talked about how to convey the levels to learners.

Level 1:  I’m getting my feet wet.
Level 2:  I’m comfortable with support.
Level 3:  I’m confident with the process. (The target for everyone!)
Level 4:  I’m ready for the deep end.

And then, the magic happened…Holly began to tell me a story of teaching 9th graders to construct an argument.  I did not understand.  So, she backed up.  She said in order to help the students understand process, she eliminated the difficulty of content by employing children’s picture books.  She discussed using the board book The Carrot Seed by Ruth Krauss.  (If you’ve not read the story – I had not – it is read to you in this YouTube video.)

Holly told me the story of The Carrot Seed and why it was an effective teaching tool.  As she talked, I wrote.  I listened to her tell a story and tried to gleaned what was important to be learned.  I scribbled a leveled assessment as she talked.

Imagine having this learning target:

I can find the learning lesson that rises from conflict and describe the hero’s journey.

What if I, as a learner, know that I am not there yet? Would I know how to proceed? Would I know what questions to ask? What if a path (and there are many correct paths) was clearly communicated in our learning community?

Level 1: I can read and summarize the story from the book I’ve read.

Level 2: I can recognize/articulate/identify the conflict in the story.

Level 3: I can find the learning lesson that rises from conflict and describe the hero’s journey.

Level 4: I can apply the hero’s journey to the human condition.

As a student-learner, this can help me talk with my teacher about what I can do and what I want to be able to do.  As a teacher-learner, this can help me convey expectations and a path to success.

Holly and I ran out of time just as we began to dive deeper into the learning progression outlined above.  What if I am at Level 1? What actions do I take to level up?  Level 1 might have targets too.  For example, I can read and summarize the story from the book I’ve read might have a supporting statement such as I can circle words I don’t know, define them, and understand them in the context of the story which might coach the learner to action.

What if we used this type of rubric with learners? Will learners be able to say what they can do and what they want to do? Will learners be able to self-diagnose and self-advocate? Will we improve communication and collaboration around learning?

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.)

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.)

What if we try? What might we learn?

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

Leading Learners to Level Up – #LevelUpMath #LearnFwd12

At Learning Forward 2012 Conference in Boston, Jeff McCalla and I offer a session as described below:

Learn to model practical classroom formative assessments that naturally offer differentiation. Hear stories and gain artifacts from National T3 instructors as they share their struggles and successes as well as their students’ struggles and successes in middle school and high school math. Develop processes and tools for creating formative assessments that integrate technology and motivate student collaboration.

Our “lesson plan”

  • Quick introduction using Dan Heath: How to Find Bright Spots
  • Ignite talk, shown below, to overview the why of learning to create leveled formative assessments
  • Formative assessment using TI-Nspire Navigator for Networked Computers to get to know our audience
  • Enter workshop mode – our challenge is to let the participants choose the path that we take.

In our description we say “Hear stories and gain artifacts from National T3 instructors as they share their struggles and successes as well as their students’ struggles and successes in middle school and high school math.”  Here are some of the stories and artifacts that we plan to use:

  • Learning from Leveling, Self-Assessment, and Formative Assessment
    I spend about the same amount of time with these formative assessments as I did when I gave quizzes, but now my job is more interesting.  It is problem-solving, coaching, and having conversations with my learners.  They have the opportunity to critique their work and report back to me.  I feel like I’m coaching rather than judging.  My learners talk to me about what they can do and what they need.”
  • Helping Students Level Up
    The change in response from our students is remarkable.  The improvement in our communication is incredible.  Students now come in after school, sit down with me, and say “Ms. Gough, I can write the equation of a line if you give me a slope and a point, but I’m having trouble when you give me two points. Can you help me?”  Look at the language!  We are developing a common language.  Our learners can articulate what they need.  Regularly in class a child will ask “Is this level 3?”  They are trying to calibrate our expectations.
  • How do we use the December Exam as Formative Assessment
    In Algebra I, we aim to get “in the weeds” about this reflection and intervention.  We want every child to reflect on what they could demonstrate well and where they need additional help.  We do not want them to move to high school and geometry next year with any doubt or weakness if we can help now.  But, how do we know who needs help?  We collect data, but we let our learners do the data collection.  We need to be informed; they need to be informed.  We are a team working toward the goal of mastery or proficiency for all learners.
  • Informing Assessment:  Need to Check for Acquisition of Skills over Memorization
    We used our leveled formative assessment to identify a need, a gap, in understanding.  Our learners and our colleagues are helping us find the path to teach and learn.  Isn’t this the way it should be?  We should struggle to learn, but shouldn’t we struggle to learn together?  Shouldn’t we learn what needs to be learned rather than what is in some book written x years ago?
  • Level Ups with Formative Assessment to Improve Communication and Skill
    An unexpected by-product of this type of formative assessment is the leveling up of their vocabulary.  Rarely does a student now say “I don’t get it.”  Much more often a child will come by after school and say ‘I need help writing the equation of a line when you give me a point and the slope.’

In our session, we model using technology to make these type of assessment easier and more manageable to deliver, implement, and process.  We share video evidence of increased peer-to-peer communication and collaboration. We also share teacher-made classroom ready assessments as a jumping off point to “develop processes and tools for creating formative assessments.” 

We have several documents to share. If interested in having copies of these leveled formative assessments, please email me using jplgough dot gmail dot com, and I’ll share the Dropbox folder with you.