Category Archives: Grading

I know something!

A motley band of brothers traveling as a pack ambled in at 7:58 for Pre-Cal. Just in time. From a distance they are handsome and well dressed in coats and ties. Up close, they are a little disheveled, like they stepped out of their clothes last night and into them again this morning.  My favorite part is the peacock-ness of their hair.  They slept hard, and it shows. It helps me remember how young they are when they look so grown up. I wonder how many of them brushed their teeth and decided not to go there.

They live together, play together, and learn together. Boarding school builds family and familiarity and deepens connectedness.  Yesterday’s test results require a preface. I prep them by explaining what I learned about them and what we need to do now.  Learning is our focus, and this moment in time tells us that we need to do more, go deeper, and practice harder. This milestone marker says that we need to back up and try again.

I made a 42!” he exclaimed with genuine jubilation. It’s what he said next that confirmed his glee.  “I know something!

“I know something!”

I am in awe of what happens next.  Every man, child, boy learner, in their coats and ties, stands and high-fives him as if he as won a gold medal, sunk the winning shot, made the field goal in the final 30 seconds.

And then, just as quickly as it started, they were all seated as he said “Bring it, Ms. Gough. What do we do now?”

Group culture is one of the most powerful forces on the planet. We sense its presence inside successful businesses, championship teams, and thriving families, and we sense when it’s absent or toxic. (Coyle, xvii pag.)

Culture is a set of living relationships working toward a shared goal. It’s not something you are. It’s something you do. (Coyle, xx pag.)

Live, learn, work, and serve in a community that highlights what is going well. Focus on learning. Build living relationships. Work toward shared goals.

CULTURE: from the Latin cultus, which means care.

Coyle, Daniel. The Culture Code: The Secrets of Highly Successful Groups. Random House Publishing Group. Kindle Edition.

Could it be as simple as adding rather than subtracting? (TBT Remix)

I prefer to think of myself as their coach.  “I coach kids to learn algebra” says that I am dedicated to my kids.  “I teach 8th grade algebra” indicates that my dedication may be to the content.  Being their coach does not make me less of an evaluator.  Their athletic coaches evaluate them all the time.  The coach decides which kids make the team and which kids are cut.  The coach decides who starts and who rides the bench.  The coach decides how much playing time, if any, each player has.

There are some things I just have to do as their teacher.  Yes, I mean grading.  (Remember, our grade books are sparse; we have very few grades.  We assess quite often; we grade little.)  We’ve just finished our semester exams.  My team grades together in the same room using the same scoring guide.  Prior to our exam day, we agreed on the questions as well as the solutions, predicted student errors, and completed the exercise of negotiating partial credit.  Some say that is good enough; there is no reason to grade in the same room when everyone understands the scoring guide.  Really?  Would we say that there is no reason to play on the same court or field since everyone knows and agrees upon the plays?  Don’t we expect the other team to have a plan of their own?

Are our learners the opponents in the exam process?
Are we trying to keep them from scoring?
Do they feel that we are? 

Are we still considered their coach?
Are we trying to help them compete?
Do they feel that we are?

How are we thinking about scoring items on the summative assessment?  Do our scoring guides assign points for good work or do they document how we will subtract points for errors?  Are we grading in team?  Do we take our issues to our teammates or our table-leader when we have a question about work that is out of the norm or unexpected?  (Or, is the amount of partial credit awarded based on how nice, sweet, cooperative, participative -or not – a child is? YIKES!)

Could we alter everyone’s mindset about this stressful event by changing our approach and attitude about how we mark, score, and grade each item?  What if we add points for what is done well instead of subtracting points when an error occurs?  Could our scoring guides be more about assigning credit and less about docking points?  What if we chose to add points for bright spots in the work instead of appearing to play “gotcha” by subtracting points?  Would our grades be closer to representing a true score of what has been learned?

How would a learner respond if we handed them a paper that was filled with +4, +2, +3 and so on rather than -2, -4, -3?

Let’s try adding up the good things we find
rather than playing “gotcha”
by subtracting when an error is found.

Could the self-reflection prompts during the exam analysis process, similar to the post-game film analysis, ask the learner to identify why they earned the points that were scored?  Could we get them to write about what they did well?  Could they work in team to identify what others did well that they wish they had done too?  Could they work in team to identify what others did that they find different or unusual and explain why it worked?  Would this process motivate them to improve their understanding and help each other learn?

Would this help us all learn to blend the 4C’s (critical thinking and problem solving; communication, collaboration; and creativity and innovation) with the 3R’s?

Can we use this type of process to add to our learning?  Could it be as simple as adding rather than subtracting?  Are we willing to experiment?

Could it be as simple as adding rather than subtracting? was originally posted on December 23, 2010.

Grading and feedback: what we do matters

Thinking about feedback and marking papers… How should we mark our learners’ work? Do we offer the opportunity to learn through mistakes and corrections?

And, I wonder if we are unintentionally incorrectly using ratios and proportional reasoning when we then put a score on the paper.

Consider the following student’s work from a recent assessment.


Do you see the error?  Is it a big error? Does this young learner understand the task and how to solve it? What feedback should this learner receive?

This child was told that there was a multiplication error in the work. Do you agree?  Is it a matter of close reading on the teacher’s part? What feedback do we hope for to accompany the arrows shown below?


What if we exercise the art of questioning in our feedback? Compare What if you think about what happened here? to You have a multiplication error here. Which feedback will cause more action?

The score for this question was marked as 3.5/4.  Losing 1/2 point for this error seems reasonable.  Would losing 12.5 points also seem reasonable?

If we scale this out of 100 rather than 4,  that 1/2 point become 12.5 points.  Is that what we intend to do, and is it the message that we want to send?

Now, as it happened, this was a 4 question assessment.  This young learner’s questions were marked 4/4, 4/4, 3/4, and 3.5/4.  In question 4, there was the addition error described above. In question 3, the learner multiplied in the first step when division should have been used.  All of these points seem reasonable as long as the items each garner 4 points.  However, proportionally scaled up to 100 points, the 1-point error is now a 25 point error.

How might we rethink grading and scaling? What does research tell us about translating scores between scales?

If learning is our focus and results guide our decisions, what steps do we take now?

And, how are these results guiding the decisions of our young learners?

Being Slow…Mindset…2nd Chances…Learning (TBT Remix)

Rule Three from The Talent Code by Daniel Coyle is SLOW IT DOWN.

“Why does slowing down work so well? The myelin model offers two reasons.  First, going slow allows you to attend more closely to errors, creating a higher degree of precision with each firing – and when it comes to growing myelin, precision is everything.  As football coach Tom Martinez likes to say ‘It’s not how fast you can do it. It’s how slowly you can do it correctly.’ Second, going slow helps the practitioner to develop something even more important: a working perception of the skill’s internal blueprint – the shape and rhythm of the interlocking skill circuits.”  (p. 85)

We still take a lot of heat from our colleagues about 2nd chance tests.  It makes many people, teachers and parents, uncomfortable.

About our version of 2nd chance tests:

  • Our learners take the test; we mark (not grade) each problem as correct or incorrect, and return the paper to the child without a number-no grade yet.
  • Their job is to find, correct, and identify errors.  We ask them to categorize an error as either a “simple mistake” or “needs more study”.
  • We also ask them to complete a table of specifications and determine their proficiency on the assessed essential learnings.
  • After all problems are corrected, students write a reflection about their work.
  • Armed with the experiences of teamwork, feedback, and self-assessment, students are given a 2nd Chance test and are tested on only the problems missed during the first testing experience.
  • The final test grade combines the correct work from the first test with the work from the 2nd Chance test.
  • Yes, it is completely possible to bomb the first test and end up with a 100 in my grade book.

My assumption is that this discomfort comes from how non-traditional – radical – this concept comes across.  Just because it is different does not make it a bad idea, does it?  The discomfort comes from gut-reaction or theory rather than practice.  Shouldn’t you try it?  What do learners say?

Here’s what some of my learners say.

“If you give your best effort the first time around, you will have learned more in the process and the second time around will be less stressful therefore making the hard work the first time more rewarding. I think that the second chance test is a very valuable learning technique. Even after that unit is complete, it shows you where you need to improve before you start building on those concepts. So far this year, I have seen great improvement in my learning from my previous years in math. This year it has all started clicking, and I am excited about the new units to come.”

“Before we jump into a new chapter, our class usually takes a formative assessment to tell us where we are and what we know before we actually start learning from Mrs. Gough. I take these seriously because I think they really do help. If I can see where I am in the beginning and then where I am in the end, I can see how much I’ve learned and accomplished.”
~ MC

In Mindset, Dr. Carol Dweck writes

“When people believe their basic qualities can be developed, failures may still hurt, but failures don’t define them.   And if abilities can be expanded – if change and growth are possible – then there are still many paths to success.” (p. 39)

More from my learners:

“Taking formative assessments and tests is something that I think is very important. I give my best effort, and work to learn from my mistakes. The second chance test is something that I think helps us actually learn from taking tests and making mistakes, rather than just getting tested on the material. Math has become one of my favorite subjects this year, and I have worked to learn from all my mistakes.

“I think that first chance tests and formative assessments are amazing because I can first understand my level and see what to work on and then really learn the material on the test to do better on the second chance. I do well in groups (except for the occasional random moments), and I love working in groups instead of taking notes the whole time. By helping others, it also helps me understand what I am doing wrong or just what I am supposed to do.”
~ HA

I feel the same as Daniel Coyle in the epilogue of The Talent Code when he writes

“Mostly though, I feel it in a changed attitude toward failure, which doesn’t feel like a setback or the writing on the wall anymore, but like a path forward.”

One more quote from our learners

“Overall, I feel as though I have done a pretty good job so far, but there is no one who can stop me from really stepping it up to an unbelievable level. The rest of the year I am going to fix any flaws I have, and show everyone what I can do when I REALLY put my mind to something.”
~ LM

In case this has been too broad for you, let’s go deep.  Here is one learner’s story from three perspectives.

From my perspective…

“GW came to me feeling that she is not very good at math and that she hasn’t been encouraged to like math.  She seeks an advocate and coach.  I strive to support GW as she becomes empowered to take control of her learning.  She is learning that it is great to struggle to learn; it is worth it to struggle to learn; and through the struggle she finds success.  Success leads to more confidence and more success.”   

From GW’s perspective…

“When I started out in math I had a really hard time and math was a definite challenge for me and my first test grade didn’t make it any easier. I was “in a hole” as my parents would tell me and I had to dig myself out. I started to go to extra help a lot more often and made solid B’s on my midterm and exam grades. What helped me through this process was the support. Support from not only my family but from Mrs. Gough and the faculty that really encouraged me to do my best.”

 From GW’s parents’ perspective…

“GW quietly got way behind in math first semester.  Partly due to an inner voice telling her she did not do well in math and partly a lack of commitment and time management. GW had given up.  Mrs. Gough communicated to us that GW needed to demonstrate the deep practice method on all homework. With our support and encouragement (not hands on help) GW began to do the deep practice on homework and began to “review and preview” every night. Our emphasis was ‘the process’ not the letter grade.

Her great success is directly attributed to the teacher/student relationship that Jill forged. Through encouragement (emails), support (office hours), an emphasis on deep practice and patience, Jill taught GW to try and try again, make the mistake, work through it, and get to the answer. Through perseverance, determination and resilience GW moved from failure and “not being good at math” to more than just passing. For us the 80 on her final exam was an A+ in effort, team work, student/teacher relationship, and determination.”

There are many take-a-ways for me…

  • If I can see where I am in the beginning and then where I am in the end, I can see how much I’ve learned and accomplished
  •  It’s not how fast you can do it. It’s how slowly you can do it correctly.
  • I have worked to learn from all my mistakes.
  • There are still many paths to success.
  • This year it has all started clicking.
  • I am excited about the new units to come.
  • There is no one who can stop me from really stepping it up to an unbelievable level.
  • Try and try again, make the mistake, work through it, and get to the answer. 

So here’s to being slow, making mistakes, and trying again.  It’s about learning content and skills.  It’s about learning perseverance and determination.  It’s about learning.  Period!

Time is a variable.

Learning is the constant.

Being Slow…Mindset…2nd Chances…Learning was originally posted on February 12, 2011.

Coyle, Daniel. The Talent Code: Greatness Isn’t Born : It’s Grown, Here’s How. New York: Bantam, 2009. 217.  Print.

Dweck, Carol S. Mindset: the New Psychology of Success. New York: Random House, 2006. 39. Print.

Feedback a la positivity – examples

A colleague messaged me privately concerning the “positivity trip” I’m on in my posts.  While I don’t care for the word used, I’ll quote the question.

There you go again, Jill.  I’m gonna ask one more time. Aren’t you concerned about positivity and wussification of our students?

That’s not what I’m writing, talking, and thinking about.  I want to be better – intentional – about offering specific, actionable feedback.  The more I use and practice with I like…because…I wonder…, and What if… the more favorable the responses are.

I also wonder if we have a “no news is good news” attitude when marking papers. If we did a little data mining on the most recent set of graded papers or feedback comments, would we see descriptive positive comments? Or, it is habit to mark what is wrong or needs improvement? Do learners look at the whole of the assessment, or do they look for marks and comments? What is the positivity ratio of what they find?

Constantly scanning the world for the negative comes with a great cost. It undercuts our creativity, raises our stress levels, and lowers our motivation and ability to accomplish goals. (Achor, 91 pag.)

So, I’m curious… Is there anything wussifying <ick!> about the following feedback?

Example 1: Algebra I – I can evaluate an expression involving exponents that are integers.

Screen Shot 2013-12-29 at 4.29.52 PM


  • I like that you showed your work and thinking, because I can see that you do understand negative exponents. Questions 9 and 12 show that you have a solid understanding when asked to evaluate a negative exponent.
  • I like that your work in Question 10 is clear enough to show that you correctly evaluated the negative exponent. I wondered if you had trouble with fractions until I read your work in Questions 11 and 12.  Nice corrections, by the way. I like that you can see what you thought initially and what you now think, because it will help you when you review.
  • I wonder if you understand Question 11 even now. What if we meet for a few minutes to discuss your understanding of complex fractions and why a number raised to the zero power equals one?

Example 2: Leading Learners to Level Up formative assessment

Screen Shot 2013-12-28 at 11.22.12 AM


I like that Level 4 challenges learners to convert between different forms of a linear equation, because this will help with symbolic manipulation that is so important in 9th grade physics.

I wonder if the language will confuse learners.  As you can see from my work, I did not answer the question as you intended.  I read intercept form and used the slope-intercept form.  What if we ask for the equation written in two-intercept form? I wonder if the additional language will offer learners clarity.

Example 3: New Ask, Don’t Tell Art of Questioning document for Algebra II.

<Sam> What do you think?


  • I like it, because it is clear why each form has advantages, and that knowing all 3 forms is helpful.  I like it, because it is easy, using the slider bar, to navigate between the three forms.
  • I like that it is easy to see that the value of a is constant no matter the form.  I wonder how learners identify patterns in forms of hypotheses and then check.  I wonder if they will struggle with writing their hypotheses in words.
  • I wonder why the manipulatable points are so large.  I wonder why the user-added font is larger than the font of scale and values of the graphing window.
  •  I like that the value of a changes in fraction increments and that the functions are displayed with fraction coefficients rather than
  • decimals.  I wonder if learners will notice and document the pattern of the fractional coefficients when moving an x-intercept.
  •  I like that a double root is possible.  I wonder if learners will adjust the window to have the y-intercept in the graphing view. I wonder if learners will know to adjust and reset the viewing window.
  • What if the axis of symmetry is added to the graph?  I wonder if it would help or distract.
  • What if the background of the graphing window is graph paper? Would it help the visual process to be able to count?

<Sam> Thanks for the feedback.  Incorporated a few changes..  Font size is what it is.


  • I like the addition of the words: vertex form, factored form, standard form, because it provides clarity.  I wonder – I think – that it will offer learners language to document patterns and hypotheses in words.

What if we practice taking the time to offer positive, descriptive, and growth-oriented feedback? How might we change outlook, efficacy, and attitude? How might we learn to spot patterns of possibility?


Achor, Shawn (2010-09-14). The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work (Kindle Locations 1351-1353). Crown Publishing Group. Kindle Edition.

#MICON13: Leading Learners to Level Up – or Ask; Don’t Tell

How might we design assessments that teach, support questioning, and motivate learning?  How might we bright spot or highlight what learners know rather than what they do not know? What if we design and transform assessments, non-graded assessments, to offer learners a path to “level up” in their learning?

#MICON13: Leading Learners to Level Up – or Ask; Don’t Tell

“Questions are the way points on the path of wisdom.” ~ Grant Lichtman. This session will focus on the art of questioning as a formative assessment tool. Work on becoming a falconer…leading your learners to level up through questions rather than lectures. Come prepared to develop formative assessment strategies and documents to share with learners to help them calibrate their understanding and decode their struggles. Be prepared to share your assessments with others for feedback and suggestions.

Foundational ideas:

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.)

But there are many more subtle barriers to communication as well, and if we cannot, or do not chose to overcome these barriers, we will encounter life decisions and try to solve problems and do a lot of falconing all by ourselves with little, if any, success. Even in the briefest of communications, people develop and share common models that allow them to communicate effectively.  If you don’t share the model, you can’t communicate. If you can’t communicate, you can’t teach, learn, lead, or follow.  (Lichtman, 32 pag.)

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.)

In order to engage in high-quality assessment, teachers need to first identify specific learning targets and then to know whether the targets are asking students to demonstrate their knowledge, reasoning skills, performance skills, or ability to create a quality product.   The teacher must also understand what it will take for students to become masters of the learning targets.  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.)

If you are a teacher in a district with conventional report cards, you can still use the two grading principles that honor the commitment to learning: (1) assign grades that reflect student achievement of intended learning outcomes, and (2) adopt grading policies that support and motivate student effort and learning.  You can do this by clearly communicating your ‘standards’ (in the sense of expectations for work quality) to students and grading on that basis. (Brookhart, 23 pag.)

The idea of using formative assessment for practice work and not taking a summative grade until students have had the opportunity to learn the knowledge and skills for which you are holding them accountable can be applied directly to your classroom assessments in a traditional grading context. (Brookhart, 24 pag.)

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.)

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.)

Session structure (120 minutes):

15 mins      Introductions – who we are, what if we explore and prototype
15 mins      Ignite (ish) and challenge
30 mins     Ideation and prototype 1
15 mins      Small group feedback with Q&A
20 mins     Prototype 2 refined from feedback
20 mins     Share session
05 mins     Wrap up and conclusions

Examples of works in progress:


Resources cited:

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

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

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

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.

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

PBL Field Guide: Who forms your learning team?

The Professional Learning Communities reflection in Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age challenges the reader to model collaborative learning, learn and share, and develop learning teams. This is right in line with our Learning for Life vision statement, NET•S, and NET•T.

Three of the essential actions called for in our Learning for Life vision statement are

  • Problems that require critical thinking, creativity, and collaboration
    (Problem-based/Project-based learning)
  • Teachers in teams supporting learning and innovation
    (PLC/Critical Friends Circles)
  • Content and Relationships that connect us to the larger world and the world to us  (Global Citizenship)

Bo Adams (@boadams1, It’s About Learning) and I co-direct our Professional Learning Communities (PLCs).  Our school makes a commitment to adult learning and collaboration by affording teachers job-embedded time to work and learn together.  For a glimpse into our PLCs, see Pull Together, Part II from It’s About Learning and Learning as a Team – A Big PLC Brightspot from my blog.

From Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age:

Professional learning can certainly support your shift to project-based instruction, but the fundamental program changes you make will require frequent and intentional collaboration with your colleagues.  [p. 31] 

In Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital AgeCarmel Crane describes her process when getting ready to launch a project with her students.

Before [introducing] the project to students, I presented it to about 10 teachers.  I laid out all the planning details, and they gave me critical feedback.  It was a great opportunity to see things I may have overlooked.

Other teachers could see how we might work together on future projects to reach our shared goals.  [p. 31]

On Friday, the 4th Period Math-Science PLC took another step toward PBL and Lesson Study by participating in the Eggs Over Easy project that our Science 8 team is planning for the Monday-Tuesday prior to our Thanksgiving break.

In the 55-minute period, we assembled our carriers, did the drops, and debriefed the lesson.  There is more video coming about the debriefing session.  Our plan for Monday is to “do the math” and the reflection questions concerning potential and kinetic energy.  But, the lead teacher for Algebra I has already asked how we can support this lesson in our Algebra classes – another step in integrated studies.  Woohoo!

Again from Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age:

A project-based learning collaboration among students is a lot like a professional learning community among teachers.  For both, the learning is relevant and rigorous, and the “students” learn to learn together. [p. 32]

Bo and I co-facilitate Synergy 8, a non-departmentalized, non-graded, transdisciplinary, community-issues-problem-solving course for 8th graders.  A new school policy about student images on faculty blogs prevents me from showing you how closely the work of our Synergy team matches up with our PLC teacher teams.  [If you want to know more about #Synergy, then you can search that category/tag on either of our blogs.]

Paraphrasing Professional Learning Communities at Work: Best practices for enhancing student achievement:  PBL delivered by a high-functioning PLC of teachers can be the “engine of improvement” that drives a school forward.

Once again from Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age:

Anne Davis, an advocate for blogging with elementary students, suggests using your personal blog as a tool for making connections with like-minded colleagues.  A team of two is better than no team at all, but image the compounding effect of a large team, an entire faculty, or an international community of colleagues. [p. 33] 

If you could assemble your “dream-team,” with whom would you collaborate for PBL? How and with whom do you learn, reflect, and share?  How do you create opportunities for your learners to build their “dream-team” to learn, reflect, and share?  How do we leverage technology to engage with our learning teams?