I want a culture or climate of revision and redemption for my learners.  The first step is second chance testing.  My learners have the opportunity to learn from their mistakes and redeem points from their struggle to learn.  I am comfortable and confident in this approach to testing even when my learners’ parents struggle to understand this break from tradition.  For many learners, we see immediate results in improved test scores.

I am now faced with a new struggle concerning my grading practices.  After reviewing a couple of examples, I am hoping that you will comment below to give me your opinions and thoughts to help me move forward.  Please?  Just press post comment.  It will be okay.

MC is a hard working Algebra I student.  She regularly attends Office Hours with her team to work on her homework and check her understanding.   She really struggled with exponential growth and decay, but she stuck with it and learned.  Let’s look at her test scores:

Exponential Functions:  88
Polynomial Functions:   92
Cumulative Midterm:     96

What grade or test average would you assign this learner?  Why?

FH is a great learner in class.  He makes great eye-contact; he listens and asks great questions.  His work outside of class is average.  He really struggled with the algebra of polynomials.  Let’s look at his test scores:

Exponential Functions:  72
Polynomial Functions:   52
Cumulative Midterm:     83

What grade or test average would you assign this learner? Why?

Is the average of these three grades an accurate reporting of what has been learned.  Didn’t the struggle to learn more about polynomials cause this learner to continue to improve?  Should he be held to that 52 when it may have helped him learn?  It the spirit of revision and redemption, how can we accurately represent – with one number – what he has learned. If time is the variable and learning is the constant, what do I do with this data?  How do I make an accurate report?

PK shows up and does the daily work.  She regularly attends Office Hours with MS’s team to work on her homework and check her understanding.   She really struggles to put it all together.  She is great when the learning is compartmentalized, but when given choices, she struggles to know what to do when.  Let’s look at her test scores:

Exponential Functions:  90
Polynomial Functions:   83
Cumulative Midterm:     80

What grade or test average would you assign this learner?  Why?

Is there only one algorithm for computing the summary grade?  Are the conditions where the algorithm could/should change to represent what is learned?

I want a culture or climate of revision and redemption for my learners.  But there are deadlines, right?  Should a learner be held accountable for work in January that caused them to struggle and learn?  How could/should these scores be weighted?

How can one number communicate and summarize to a learner, a parent, and a future teacher what these children know and are able to do?

# Learning as a Team – A Big PLC Bright Spot!

AS KU arrived for our meeting today, I asked her if she would show the video that she made as a result of a lesson in an earlier PLC meeting.  Last week KP showed everyone how to produce teacher-made videos to support student learning.  KP’s lesson sparked collaboration as GJ spontaneously helped with the lesson answering a question for KP.  Isn’t this how learning should be?

KU practically sparkled with excitement as she shared not one, but two of her videos.  She spoke with such pride about now having a YouTube channel and being able to share her learning with our team.

And then, a really interesting thing happened…Our team began to ask questions and find common ground between the chemistry and algebra.  Through the questions we found similarities and differences between representations.  We discussed why our learners might struggle. Subscripts in chemistry act like exponents in algebra.  While superscripts in chemistry look like exponents, they do not function as exponents.

When KU got to this example in the video, she talked about the trial and error method to balance the equation.  This prompted GJ to talk about setting up a system of equations to help learners balance the equation.  Now he really had all the math teacher’s attention too.

It was so great.  GJ went to the board and, with BC’s engaged participation, setup a system of equations to find a solution to balance this equation.  There are an infinite number of solutions that will balance this equation.

LB talked about balancing simple equations in 7th grade pre-algebra.  DH laughingly said she would stick with the guess and check method; KU nodded.  (This is important; keep reading.)  DD, BC, and I talked about spiraling back to systems of equations to reinforce the chemistry.  We talked about reasons to present multiple ways of balancing equations to support meeting different student needs.

We found unknown common ground.  We can blend our content and skills to support learning for students across our disciplines.

In the category of MUCH MORE IMPORTANT, we found common ground as learners.  If we can learn together, if we can blend our content by finding common ground, and if we can integrate our curriculum, aren’t we furthering the four critical PLC questions?  We also found appreciation for each other.

Thursday, April 14, 2011 1:08 PM
To:  KU
Cc:  DD, MI, BA, JA, KP

Great job today, KU!  I so appreciate your willingness to learn and then share your learning with others.  I loved that you referenced learning from KP and GJ multiple times.

BA caught just a snapshot video at the beginning of your sharing session and posted on one of his blogs.

I loved that you inspired GJ to show us an algebraic way to present as an alternative to the guess and revise method.  I am inspired to learn a little more chemistry and help my Algebra I learners see the connection between algebra and chemistry.  You asked really great questions today, and you prompted others to ask questions as share as well.

Thanks again!  JG

Thursday, April 14, 2011 3:18 PM
To:  JG
Cc:  DD, MI, BA, JA, KP

You’re welcome, and I really can’t thank KP enough for showing me how to record and GJ for the editing software and another way to balance equations.  I tried his method and showed my classes today.  KU

This is very important!  After stating in the team meeting that she would stick with the guess and check method and after asking lots of questions, KU used GJ’s system of equations method in class THE SAME DAY!  Wow.  Learning that caused risk-taking and willingness to try a new method.

To give the full story, there is more to consider.  It takes a team to create this culture of collaborative learning.  Here is more of the story:

Thursday, April 14, 2011 4:16 PM
To:  KP
Cc:  DD, BA,  RLC

KP…

Thank you so much for your work and leadership with our 4th period team. KU’s presentation this morning is an outstanding artifact of your work, success, and collaboration. And just look at the learning that has been promoted by your effort and teaching!  GJ contributed, again, to the team’s learning.  I’m pretty sure that everyone asked a question or added to the discussion about the chemistry and the connections to math.  And, if that wasn’t enough, KU applied what she learned from GJ TODAY in her class.

Your leadership to help the team learn caused many ripples in our pond. Excellent work!  Brava!

I’m so proud of you, and I so appreciate you.

JG

Thursday, April 14, 2011 4:45 PM
To: DD
Cc:  BA, RLC

DD…

I want to make sure that you recognize your HUGE contribution to this BRIGHT SPOT for our team. You facilitated this learning. It was your plan. You selected the topic, and found the right person to lead the learning.  You are the team member that made the learning possible. You contacted PD; you gathered the necessary equipment. You led the event. The facilitator’s job is to make the work easier for the team. You certainly accomplished making the work easier. It is often easy to overlook the “behind the scenes” leg work required to make things happen. Thank you for being the leader, the facilitator, and the detail-oriented person that made this good work possible.

This good work would not be happening without your initiative, actions, and follow through.

JG

Often I see the struggle and overlook the bright spots.  This is a habit I hope to unlearn.  I strive to see the bright spots and appreciate the struggles.  The struggles, after all, are part of the learning process, right?

Today we learned as a team; it was a BIG BRIGHT SPOT.

# Informing Assessment: Need to Check for Acquisition of Skills over Memorization

Integrated studies and a spiraling curriculum…Not only do we need to help our learners make connections between our discipline and other disciplines we need to help them make connections between topics in our own discipline, even when it is about skill building rather than application.

Wow! We’ve learned a lot about our learners this week. Our latest leveled formative assessment has highlighted an additional need for our learners and impacts our curriculum. I’d love for you to see it; I think it’s a really good one. DD and I created it together in her kitchen on our unexpected day off. (Terrible weather here in Georgia knocked the power out all over; no school on Tuesday.)

We are studying quadratic functions. This leveled formative assessment asked our learners to identify x- and y-intercepts graphically in Level 1 and algebraically in Level 2. Virtually no learner got out of Level 2 unscathed. It is illuminating to say the least. Over 50% of my learners did not know how to state the locations of the intercepts in a way that would communicate to a reader an understanding of the intercept location. Often they just plunked down a number. We would see x-intercept: __1__. This might be right (??), but how do I know if they meant (0, 1), (1, 0), x=1, or y=1? Did they know? Talk about an opportunity to discuss conventions and symbol choice!

Over 75% of my learners did not know how to find the x- and y-intercepts algebraically. Over 75%! Many said that they were looking for b in y = mx + b. In the Quadratic Functions unit??? YIKES! Let me say that we have been working on the Zero Product Property and the Quadratic Formula for weeks.

The most illuminating example is from, in my opinion, my very best, most motivated learner. She correctly substituted 0 in for y in y = 3x + 2 to find the x-intercept. So now she needed to solve 0 = 3x – 2. She was stuck, really stuck. She said “I don’t know what to do. I can only use the quadratic formula, and it is not working for me.” Double YIKES!

The assessment changed the course of the content and the instruction as well as the methodology. Today’s lesson, delivered via the TI-Nspire, was still about the vertex form of a parabola, but we also had to decide of the graph or table was linear, quadratic, exponential, absolute value or none of these.

We could check for understanding with a quick poll.  We could check for participation with screen captures.  The learners’ questions were awesome. “I don’t know how to tell the difference between exponential and quadratic. They are both curves.” I rarely said anything. I took lots of notes on the board and asked questions to help them get unstuck. “How do you know if it is quadratic or an absolute value?”

It was a great discussion with real questions being asked and answered by the learners.  The results after the discussion were much better.

The challenge became to document our work.  How am I supposed to take notes when the entire lesson is on my calculator?  Am I supposed to take notes?  What will I use to study later if I don’t take notes?

The graphic organizer was developed through our learners questions.  We first just put L-Linear, E-Exponential, A-Absolute Value, and N-None of these on the board.  As they started sharing their questions and what they did not know, we added notes to the side as a graphic organizer.

We used the technology to deliver the content.  We used the technology to check for understanding and consensus.  We used the technology to guess-test-and-revise.  We used the technology to make sure everyone was taking a swing at each problem.  While your identity could be hidden, our learners requested that we start showing names so that they could help each other and identify resources in the room.

We have no book to lead us down this path.  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?

# Stopping Distance Reflection – Where did it take us?

We are studying quadratic functions.  We started with the Stopping Distances data to look at quadratic data visually.  Our hypothesis was that the distance required to stop while braking is proportional to the square of speed, d=k·v².  Many of our learners had trouble fitting the curve; they were hesitant to take a swing.

What if we read Peter Reynold’s The Dot in class?  What if we encouraged our learners to just try to find an equation, to see where it takes them?  What if we used the TI-Nspire Navigator to “frame” their first marks, to celebrate that they took a swing?

Here’s what @fencersz, a learner in DD’s 3rd period, said in a couple of tweets to me about the class:

@jgough I thought it was really interesting to look at math in a way that involved creative problem solving as opposed to just applying a set model to the problem, was surprised b/c I’ve never though about math like that b4 and would like 2 get better at this.

What if we did this for each other too?  DD just happened to come for part of my class while I was teaching Stopping Distances.  She liked it, but said she thought she could never teach it.  We agreed to team-teach the lesson in one of her classes.  The following is her reflection on teaching it alone for her other class.

I had the best time teaching my 5th period today.  I know it was not as smooth as yours, but I think it was pretty good for my first go-round.  I remembered things to say that you said; there were even things I sort of got lost in, yesterday, that I wasn’t planning to do, but understood what you did when I got to it and was able to show the kids.  I don’t think they had any clue that I was just learning what I was talking about when I gave my spiel on velocity being speed with direction to explain one reason it would be quadratic rather than exp.  The kids were asking great questions and making good connections.  They were also engaged.  Thank you for teaching this to my third period so I could learn it.  I know you felt horrible yesterday, but you trooped on over anyway.  What about you and me team teaching this lesson in 4th period PLC as our first lesson study (so we can improve it for next year) with the new TI-Nspire software?

Model learning.  Encourage others.  Try new things.  Collaborate.  See where it takes you.

# The Dot: “Just Make A Mark And See Where It Takes You”

Have you read The Dot by Peter Reynolds?

Do you know any learner’s that are stuck?  Are they convinced that they can’t?  Read this book.  Listen to the messages.  The first strong message is about getting started.  “Just make a mark and see where it takes you.”  I bet you’ll end up repeating Vashti’s sentiment of “Hmmph! I can make a better dot than that.”  The second message is about leadership, encouragement, and support of others.  “Show me.”  “Please…sign it.”

I serve and learn in several teams.  Often we leap to what can’t be done.  “This won’t work because…”  “We can’t do this because…”  Creativity and brainstorming come﻿ to a halt more often than not.

Two weeks ago, we challenged ourselves to engage in a discussion of what we can do.  We would not use any of the typical phrases that shut down thinking or distract us from what we can do.  No idea would be shot down.  All ideas were welcomed.  We lasted 21 minutes before the word “can’t” was launched.  And, in that 21 minutes, we made progress.  We came to a consensus about the what and how of building a lesson together.

Last week at the same team meeting, we started with The Dot.  Here I was reading to our team of seasoned professionals.  The story is so powerful; one of our team finished the story before I could turn to and read the last page.  The thought that we don’t know how to build a lesson or series of lessons seemed okay and less daunting because we could just make a mark.  We could see where it might take us.  This idea coupled with Theo Jensen‘s reflection that the walls between our disciplines exist only in our minds has challenged us to find common ground.

What is it that you want to do?…that you’ve been asked to do?  If you are stuck, what is causing you to be stuck?  What can you do?  What can we do?

Just make a mark…see where it takes you.  Frame it for others to see.  Encourage others to make their mark.

________________________________________________
Reynolds, Peter. The Dot. Cambridge, MA: Candlewick, 2003. Print.

# Connections: Questions, Photographs, Algebra Graphs, Perspective, Environment

Several of my tribe are participating in the 3six5 project (365 days, 365 points of view) which has caused us to wonder about this experience for education.  Here’s the invitation I received:

Dear Ms. Gough, Tara, Sarah, and Whit:

There are many stories to tell in the world of education and many voices that need to be heard.  We have started a new project, edu180atl, designed to share stories of learning and highlight voices from the Atlanta community.  During the 2011-2012 school year, we hope to have 180 different learners (students, parents, educators, etc.) participate in this project.  The purpose of edu180atl is to nurture and encourage the spirits of those who love to learn, to connect learners across disciplines and settings, and to deepen the national conversation about education by enabling parents, students, and educators to share stories of what they are learning every day.  In order to test the feasibility of such a project, we will be piloting a similar experience (edu180atlbeta) during the month of April.

We would like to invite you to be one of the founding writers for this project.

If you are interested in participating, please complete our beta signup form (link: http://bit.ly/edu180altsignup) and select two Monday-Friday dates (your first and second choice) during the moth of April when you will be able to submit a reflection based on the prompt:  what did you learn today? We will respond with a confirmation of the date and further instructions for submitting your reflection.  We ask that your reflection be no more than 250 words (1 typewritten page), and if you choose, you may also submit a photograph or a short video (no more than 90 seconds) to go along with your submission.

We look forward to this project and how you will consider participating.

**  Due to a limited number of days in April, we may not be able to accomodate every learner who wishes to participate.

One of our Synergy 8 team, Whit Weinmann (aka @runningwitty), started us off on April 1 with a challenge to realize connections.  In Synergy 8 we believe in the value of prototyping and the power of feedback.

I spent the weekend working with my writing team in Dallas planning a professional development experience for teacher-learners.  I thought I might practice answering the question: what did you learn today?  I also want to ask for your feedback while I practice and prepare for my edu180atlbeta day on April 11.

____________________________________________

The theme of the day has been the art of questioning. My learning revolves around trying to ask better questions, questions that are open-ended enough to promote risk-taking, differentiation, and finding connections.

How can we leverage the technology in our hands help learners apply what we are teaching and see the beauty of the world through their learning?

Imagine learning about linear functions, perspective, design, and environment simultaneously.  Do we think helping our learners see that the patterns we teach actually model things they see will help them find relevance and pique their interest?  For our artists, would it be fun to insert their art into our technology and model the shapes and structures that exist in our community?

Can we take a photograph of the bridge to the Summer Camp and find the algebra in the photo?  What can we learn?  Do we need a lesson on perspective to gain an understanding of why these lines are not parallel in the photo but are in reality?

Can there be an entire theme for integrated learning around our bridge and the environment where it sits?  Who comprises the team that would spend just even one day using this bridge as the catalyst for learning?

Where are our resources to integrate and blend curriculum to support learning? How can we model lifelong learning side-by-side with the young learners in our care?  Will we?

I learned I am willing to try. It is worth the risk.  Will you join me?

____________________________________________

It is interesting to me that I could write about what I learned today in 250 words, but I’m having trouble describing myself in 140 characters.  I think it is good to know this today while I have time to think and revise.

I’d love your thoughts and feedback.

# Swing Even If You Miss; Stepping Up To The Plate Is Not Enough

Is a swing and a miss better than no swing at all?  I used to coach my learners to step up to the plate, just step up.  You can do it.  But now I realize that just stepping up is not what it takes to learn.  It is a great first step, but it is just a first step.  Will you ever hit it out of the park if you don’t swing?

Today I got to co-teach Algebra I with D. Dietrich with her learners.  It was day two of Stopping Distances.  After reviewing what we accomplished during the last class, we stopped to ask them to write a complete sentence about what the graph of reaction distance vs. velocity represented.

When I asked for volunteers, no one responded.  Yikes!  Now, they all had written something.  Finally, one sweet, brave learner volunteered.  It was a sentence that needed some coaching.  We talked about the structure of the sentence as well as the need to be more specific about units.  Since the distance is in feet, what are the units of velocity?

We collected this sentence with our TI-Nspire Navigator system.  The screenshot above allowed the entire class to have multiple representations of the sentence.  They could see it as it was being read.  The screenshot is evidence of a swing.

I asked for another volunteer…  …  …  …  So, I finally asked the one child that was making eye-contact with me why he didn’t want to read.  “Because I know it is not perfect.” Isn’t this what learning should be about?  Can’t we have a culture where it is okay to not be perfect?  How will I ever learn if I am not brave enough to share my thoughts with others?  Being in school should be about drafting and making revisions, shouldn’t it?  Have we built a culture where we are afraid to try because the only correction I get is criticism?  (double-Yikes!!)

We edited and coached and then tried again for the second graph, braking distance traveled vs. velocity.

We got, without question, the best sentences of the day for the second writing. The power of feedback and revision was demonstrated.  Unknown to me, the learner that volunteered for the second writing rarely speaks in class and never volunteers.  Isn’t that great?  She found the confidence to write and share.

But, as the facilitator of the learning, do I know how many of these learners actually took a swing?  Not really.  I love that one student wrote his sentence on the screen of his calculator.  But it is the only one I could monitor.

Which makes me wonder…how many times are my learners telling me they understand when they have not actually taken a swing?  Are they so conditioned to tell us that they understand that they are not testing their understanding and seeking feedback?  WOW!  That is a problem!

We stopped and talked about trust.  We talked about risking being wrong to grow and learn.  But, again, were they just agreeing with us because they know it is what we want to hear?  Would they take action…to swing and possibly miss?  Would we celebrate the swings and give quality, safe feedback for a miss?  Risky for everyone, right?  Trust is the key.

Yesterday we wrote the equations for both of the graphs above.  y = 1.1x and y = 0.05x², where x is velocity in miles per hour and y is the distance traveled in feet.

New learning for today…How do we find the model, the equation for the data, of total distance traveled in feet based on velocity in miles per hour.  Important questions must be asked.

1. How will we calcuate the total distance traveled based on the given data?
2. What pattern does this data follow?
3. Is the pattern exponential or quadratic?Okay, so let me stop here and say that the question exponential or quadratic is an important question.  If you can’t answer it, how will you know what type of model to write?  This is Algebra I; we are not using regressions.  We are hand fitting data.Aren’t the results interesting?  Q for quadratic, E for exponential.

Before you boo, a bunch of learners came without their technology or had login issues.

But notice, even when anonymous, one learner did not take a swing. It was a 50-50 shot at being right and this learner would not take a swing.

New and MUCH more interesting questions are now possible.

1. Is the majority always right?
2. Can we listen to an opposing view and try to understand their reasoning?
(Shouldn’t Democrats and Republicans try this occasionally?)
3. Can each side make a reasonable argument for why they made their choice?
4. Are you willing to consider that the other side might be right?

The minority view, quadratic functions, explained first.  Then a member of the majority party raised her hand and said “I voted exponential, but I can now give another reason why it is, in fact, quadratic.  Is that okay?”  WOW!  We stopped and voted again.

Progress!  But, what do we do about the 2 remaining e’s?  Remember, the majority is not always right.  More discussion ensued.  The two e’s identified themselves, AB and SS, and explained why they were now in the quadratic function camp.  Also notice, they everyone took a swing this time around.

Let me stop here and say that this is where and why I prefer using my TI-Nspire Navigator over Poll Everywhere and the SMARTBoard clickers.  While it appears to be anonymous, I can click on Poll Details and see which learners need intervention if they don’t self-identify during the lesson.  I can also see what is on every learner’s graph which I will show if you keep reading.

Now that we established that we are pretty sure the function to write is quadratic, we again returned to the data.

How was the data in the total column computed?  “Everyone knows, Ms. Gough, that you just add the reaction distance to the braking distance, duh!” Eyes rolling as only 14 year-olds can do.

So, if that is true, write the equation that fits the total distance traveled in feet based on the velocity in miles per hour.  You have all that you need.  You can do it.  Take a swing.

No one got it right the first time. Some took a swing and missed; some got close; some just stood at the plate.  At least two students were still in the dugout – maybe the parking lot; Caswell and St. Cloud were absent the day before.  They did not ask for the file.  St. Cloud was working to catch up; Caswell was just observing.  And we absolutely would not have known if we didn’t see their calculator screens.

Vuckovic looks like he took a swing, but no.  He connected his scatter plot; he had not attempted to construct a function.  Gibson has tested a function that is close, but does not fit very well; he took a great swing which we celebrated.

So we asked again, how was the data in the total column calculated?  Can you use this information to write an equation that will fit the data?

Before class was over, everyone took a swing and got a hit.  It was very collaborative.  We then took the model and began to interpolate and extrapolate.  If I was in a car going 65 miles per hour, how much distance would I need to not crash?  Easy, but we needed to talk about how to document our work and thinking so that future physics teacher would know how we arrived at our answer WITH units.

If I am a stunt car driver and know that I have a football field’s length to stop my car, what should my top speed be when I hit the brakes?  This question was not so easy.  Learners fell in to three camps.

• Camp 1:  I substitute 100 in for y.  They got feedback quickly from their peers that 100 was in yards and the units were feet!
• Camp 2:  I substitute 300 in for x because that is where I substituted 65 before.  They also got quick peer feedback that x was in mile per hour and to pay attention to your units!!
• Camp 3:  I substitute 300 in for y, but what do I do now?  Unfortunately, in this class, they got no peer feedback.  We facilitators were informed to say the least!  Not one child connected this to using the quadratic formula to solve.  (triple YIKES!) Good formative assessment that they are not connecting the skill to the application.

Once they realized that they could use the quadratic formula to solve, they were successful.  We could monitor the swings, and lack of swings, using our Navigator.  By now, everyone was swinging because they knew we were supporting their effort and learning.

The big take-away for me:  Formative assessment that offers feedback and support in the moments of learning are critical for success and confidence.

The big take-away for my learners:  You can do this; we will help!

You will not hit it out of the ballpark if you do not swing.  A swing and a miss is so much better than no swing.  Step up to the plate; dare to swing.  Miss; swing again.  You can do this; we will help!