Category Archives: Assessment

Empower learners to deepen their learning

How might we empower learners to deepen their understanding?

After creating and administering common assessments, the next question is perhaps the most challenging: “Are students learning what we think they are supposed to be learning?” (Ferriter and Parry, 75 pag.)

What if our learners are grasping the content, but they are struggling to communicate what they know and how they arrive at a conclusion?

How might we make our expectations clear? What if we empower our learners to take action on their own behalf?

What if our culture embraces the three big ideas of a PLC?

Learning is our focus.
Collaboration is our culture.
Results guide our decisions.

Our #TrinityLearns 2nd grade team sat down together last week to analyze the results of the most recent common assessment.  While our young learners are grasping the basic concepts, we want more for them. We want confident, flexible thinkers and problem solvers.  We want our learners to show what they know more than one way, and we want strong clear communication so that the reader can follow the work without to infer understanding.

Teams at this point in the process are typically performing at a high level, taking collective responsibility for the performance of their students rather than responding as individuals. (Ferriter and Parry, 77 pag.)

As a team, these teachers sorted their students’ work into four levels, shared artifacts of levels with each other, and planned a common lesson.

Laurel Martin (@laurel_martin) explained to our children that the artifacts they analyzed were not from their class and that they belonged to a class across the hall.

Here’s the pitch to the students from Sarah Mokotoff’s (@2ndMokotoff) class:

Don’t you just love the messages: Be like scientists. Make observations. Offer feedback on how to improve.

Here’s what it looked like as the children analyzed artifacts from another 2nd grade class:

Once the analysis was complete, our teachers facilitated a discussion where the children developed a learning progression for this work.

From Kerry Coote (@CooteMrs):

We created these together after looking at student work samples that were assigned at each level. Our kids were so engaged in the activity; they were able to compare and give reasons why work was at a level 3 versus a level 4. It was really good to see! I believe this will empower them to be deeper thinkers and gradually move away from giving an answer without showing their thinking and work.

Here’s what the students in Grace Granade’s (@2ndGranade) class developed:


More from Kerry Coote:

After we helped them develop the learning progression, we conferenced with each child looking at their math assessment. They  automatically self-assessed and assigned levels for their thinking. Many scored themselves lower at first, but the activity of crafting the learning progression helped in making sense of explaining their thinking! Today in math a boy asked me – “so Mrs. Coote, what are those levels again? I know the target is Level 3, but I want to use numbers, words, and pictures to get to level 4.”  It is all coming together and making sense more with these experiences!

In their morning meeting the next day, one of Kathy Bruyn’s (@KathyEE96) learners shared the poster she made the night before.

Don’t you love how she explained the near doubles fact and her precise language?  Wow!

Since we focus on learning and results, this team offered learners an opportunity to show growth.

From Samantha Steinberg (@spsteinberg):

This is an example of leveling up after looking at our assessment.  Initially, [he] used the learning progression to rate his work at level 3.  After reading my feedback, he added words to his next attempt to show his additional thinking.

Before the class developed the learning progression:

Screen Shot 2015-10-01 at 8.08.58 PM

After the class developed the learning progression:

Screen Shot 2015-10-01 at 8.09.13 PM

Can you see the difference in this child’s work, understanding, and communication?

A growth mindset isn’t just about effort. Perhaps the most common misconception is simply equating the growth mindset with effort. Certainly, effort is key for students’ achievement, but it’s not the only thing. Students need to try new strategies and seek input from others when they’re stuck. They need this repertoire of approaches—not just sheer effort—to learn and improve. (Dweck, n. pag.)

Kudos to our 2nd grade team for reaching for the top stages of  the seven stages of collaborative teams! Learning is our focus. Collaboration is our culture. Results guide our decisions.

How might we continue to empower learners to deepen their understanding?

Dweck, Carol. “Carol Dweck Revisits the ‘Growth Mindset’” Education Week. Education Week, 22 Sept. 2015. Web. 02 Oct. 2015.

Graham, Parry, and William Ferriter. Building a Professional Learning Community at Work: A Guide to the First Year. Bloomington, IN: Solution Tree, 2010. Print.

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?

Reflection, Attitude, and Efficacy (TBT Remix)

How can we promote success-oriented behaviors to foster learning and self-efficacy?

I dare you to read the following journal entries but replace the word math with assessment or whatever you are struggling to learn right now.  Out of the mouth of babes


I’ve been rereading journal entries from August to reflect on the growth of children I coach to learn algebra.  The point of this particular journal entry was to help assess disposition.

Can we effect their growth in algebra AND their growth as learners? Can changing our assessment practices and our approach to learning help them learn to embrace the struggle, to see that a “failure” is an opportunity to learn?  Does success breed success?  Does success change your confidence, efficacy, and disposition?

How can we help failure-avoidant students grow to become success-oriented learners?  Are most learners both success-oriented and failure-avoidant with a strong preference for one or the other?

Wait… I choose to revise my question.  How can we promote success-oriented behaviors to foster learning and self-efficacy?

What do you think?
Is QB success oriented, failure avoidant, or both?

The reason why I chose a picture of a person repelling or climbing a mountain is because math is a mountain for me. A mountain is an object that you cannot go through or around. The only way to get to the top of the mountain is by climbing. Math for me is a mountain. I can only climb my way to the top. There will be slips and falls along the way but, that is the only way to get to the top of the mountain. Every step I take teaches me something about that mountain. When you climb to the top of the mountain you can look back and say all those little slips and falls taught me something about that mountain, but now I can see all those tiny steps added up.”

Every step I take teaches me something about that mountain. When you climb to the top of the mountain you can look back and say all those little slips and falls taught me something about that mountain, but now I can see all those tiny steps added up.”

I love this child; he spends many hours with me learning and improving.  We have two classes together, and he chooses to work with me after school several days each week.  When I read his journal on the first day of class, I put him in the success-oriented category.  As I have worked with him this semester, I have seen him on a rollercoaster ride, struggling to not lapse into failure-avoidant behaviors.  I believe it is my job is to be his cheer-master, his coach, and his support.  I want to coach him to find his strenghts and successes.

The same day, CL wrote:

I think this picture best describes my experiences in math for a lot of reasons. If you look at the girl’s face, it seems like she doesn’t know what she is doing. But if you look at her body, she seems to be doing the right thing. This is like me in math in a way. A lot of times I am doing the right steps, but I still think I am wrong. Like the girl in the photo, I don’t believe I am doing the right steps (or moves in her case). My feelings toward math are basic. I don’t love math, but I don’t hate it. Math also doesn’t come naturally to me. I have to work hard at something until I really understand it. I am more interested in math that we use every day than just random lessons. I also like to know the why in things. Like “Why do we use this trick?”. The why and how are keys words for me in learning math. I think my job in math is to learn new things, listed to the students and other students and the teachers, and to help others learn. I believe math is very helpful in everyday situations. I also believe math is hard, but if you work hard enough you will understand it. I want to learn from my mistakes in math. I also need different techniques to learn from if one doesn’t work. Lastly, my goal this year in math is to maintain a high grade by fully understanding the material.


How often do we make curricular decisions based on what we think we see?  Are we looking at the face or the body?  How often do we assume that our students are learning?  Do we check for evidence of learning – not grade – really check for proof?   When we see the body doing the right things, do we ignore the face?  Do we check for confidence?  I fear that we may promote failure-avoidant behaviors if we are not careful.

CL wrote:

If you look at the girl’s face, it seems like she doesn’t know what she is doing. But if you look at her body, she seems to be doing the right thing.”  

How do we give our learners enough feedback so that they know that they are doing the right work?  How do we build up their confidence so that they will either feel successful or know that it is safe (and encouraged) to ask questions to learn and grow?  How do we reward effort and willingness to struggle to learn without giving students a false impression of their achievement?


I want to learn from my mistakes in math. I also need different techniques to learn from if one doesn’t work.

Me too!  If we don’t assess learning and offer feedback in the midst of the experience, how will we know if we are promoting learning for all?  How will we know if some (or all) need a different approach? Again, we must be careful to promote success-oriented behaviors.

I also think that my team and I spend a fair amount of time in CL’s shoes.

A lot of times I am doing the right steps, but I still think I am wrong. Like the girl in the photo, I don’t believe I am doing the right steps (or moves in her case).

Am I doing the right things for my students?  My assessment plan is so different from what they will probably experience next year.  When I listen to others who are uncomfortable with this “radical” change, I question if I’m doing the right steps.  From what I read and study, I believe that I am doing the right things to help them learn and grow.

CL’s words where I have replaced math with assessment:

I don’t love assessment, but I don’t hate it. Assessment also doesn’t come naturally to me. I have to work hard at something until I really understand it.

My team experiments with me. Are we failure-avoidant teachers or success-oriented learners?  We collect data and ask questions; We refine our hypothesis and try again. We are learning by doing; we are making assessment and grading decisions based on what the data indicates.  Are we confident about our assessment work 100% of the time?  No…Does it cause us to ask questions, think deeply, risk, learn?  Yes…

It is certainly a work in progress.

Reflection, Attitude, and Efficacy was originally published on December 16, 2010.

Listeners: evaluative, interpretive, generative

What type of listener are am I right now? Do I know what modes of listening I use? How might I improve as a listener? What if I actively choose to practice?

Listening informs questioning. Paul Bennett says that one of the keys to being a good questioner is to stop reflexively asking so many thoughtless questions and pay attention— eventually, a truly interesting question may come to mind. (Berger, 98 pag.)

I’ve been studying a paper Gail Burrill (@GailBurrill) shared with us a couple of weekends ago.  The paper, Mathematicians’ Mathematical Thinking for Teaching: Responding to Students’ Conjectures by Estrella Johnson, Sean Larsen, Faith Rutherford of Portland State University, discusses three types of listening: evaluative, interpretive, and generative.

The term evaluative listening is characterized by Davis (1997) as one that “is used to suggest that the primary reason for listening in such mathematical classrooms tends to be rather limited and limiting” (p. 359). When a teacher engages in evaluative listening the goal of the listening is to compare student responses to the “correct” answer that the teacher already has in mind. Furthermore, in this case, the student responses are largely ignored and have “virtually no effect on the pre-specified trajectory of the lesson” (p. 360).

When a teacher engages in interpretive listening, the teacher is no longer “trying simply to assess the correctness of student responses” instead they are “now interested in ‘making sense of the sense they are making’” (Davis, 1997, p. 365). However, while the teacher is now actively trying to understand student contribution, the teacher is unlikely to change the lesson in response.

Finally, generative listening can “generate or transform one’s own mathematical understanding and it can generate a new space of instructional activities” (Yackel et al., 2003, p. 117) and is “intended to reflect the negotiated and participatory nature of listening to students mathematics” (p. 117). So, when a teacher is generatively listening to their students, the student contributions guide the direction of the lesson. Rasmussen’s notion of generative listening draws on Davis’ (1997) description of hermeneutic listening, which is consistent with instruction that is “more a matter of flexible response to ever-changing circumstances than of unyielding progress towards imposed goals” (p. 369).

If you’d like to read about these three types of listening the authors continue their paper with a case study.

Evaluative listeners seek correct answers, and all answers are compared to the one deemed correct from a single point of view.

Interpretive listeners seek sense making.  How are learners processing to produce solutions to tasks? What does the explanation show us about understanding?

Generative listeners seek next steps and questions themselves. In light of what was just heard, what should we do next? And, then they act.

For assessment to function formatively, the results have to be used to adjust teaching and learning; thus a significant aspect of any program will be the ways in which teachers make these adjustments. (William and Black, n. pag)

“Great teachers focus on what the student is saying or doing,” he says, “and are able, by being so focused and by their deep knowledge of the subject matter, to see and recognize the inarticulate stumbling, fumbling effort of the student who’s reaching toward mastery, and then connect to them with a targeted message.” (Coyle, 177 pag.)

What if we empower and embolden learners to ask the questions they need to ask by improving the way we listen and question?

Unless you ask questions, nobody knows what you are thinking or what you want to know.” (Rothstein and Santana, 135 pag.)

How might we practice generative listening to level up in the art of questioning? What is we listen to inform our questioning?

How might we collaborate to learn and grow as listeners and questioners?

Berger, Warren (2014-03-04). A More Beautiful Question: The Power of Inquiry to Spark Breakthrough Ideas . BLOOMSBURY PUBLISHING. Kindle Edition.

Coyle, Daniel (2009-04-16). The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. Random House, Inc.. Kindle Edition.

Davis, B. (1997). Listening for difference: An evolving conception of mathematics teaching. Journal for Research in Mathematics Education. 28(3). 355–376.

Johnson, E., Larsen, S., Rutherford (2010). Mathematicians’ Mathematicians’ Mathematical Thinking for Teaching: Responding to Students’ Conjectures. Thirteenth Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education Conference on Research in 
Undergraduate Mathematics Education. Raleigh, NC. Retrieved from on September 12, 2015.

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

Wiliam, Dylan, and Paul Black. “Inside the Black Box: Raising Standards Through Classroom Assessment.” The College Cost Disease (2011): n. pag. WEA Education Blog. Web. 13 Sept. 2015.

Yackel, E., Stephan, M., Rasmussen, C., Underwood, D. (2003). Didactising: Continuing the work of Leen Streefland. Educational Studies in Mathematics. 54. 101–126.

Focus on Learning: Observation of Practice (TBT Remix)

What if we add additional feedback loops in our culture?

How and when do adults in our schools receive formative feedback? If I have a question about my practice, how do I and from whom do I seek feedback?

If, as a school, we are studying formative assessment, self-assessment, and peer assessment, how are we practicing? Do I blog, journal, or keep a portfolio of my learning?  What might I want to learn? Are my students learning?

What if we focus on what is happening in classrooms in purposeful and focused ways? What if we model and embrace formative assessment of our practice?

What if we lend another our perspective?

We are going to pilot Observation of Practice this week in 4th Grade.  After reading my reflection of the class we taught together, Arleen and Laura both commented on how helpful it was to see their class from another perspective. We want to know if Observation of Practice will integrate formative assessment and reflection with peer observation.

What if we shift the focus of peer observations from observing our peers to observing the products of their work – the actions of students?

What if we focus on learning?

Job-embedded PD: Observation of Practice – Focus on Learning was originally published on November 18, 2013.


Try on a new lens – (TBT Remix)

We perceive only the sensations we are programmed to receive, and our awareness is further restricted by the fact that we recognize only those for which we have mental maps or categories. (Zander, 10 pag.)

The following was posted on the last day of Pre-Planning my first year at Trinity.  While no longer a stranger, I continue to need and learn from  the stories of our children and colleagues.

From August 14, 2012:

I am new to my community – a stranger, if you will.  As a fledgling member of the community, I need and want to hear the stories of the children and my colleagues, the history of the people and the place. One spectacular opportunity afforded me is to hear the same story from multiple perspectives.  I value the luxury of learning and seeing through multiple lenses.

Through which lens do I choose to look at my surroundings?  On what do I choose to focus?  How do I practice seeing bright spots?  How often do I focus on success rather than struggle?  How do I make the practice of bright-spot-seeking a habit?  Do I teach this habit to others?

For our children, school begins tomorrow. What will they want and need from us, their teachers?  How will we offer feedback as they learn and grow?  Is it our habit to highlight their success or their struggle?  When we mark student papers, do we “award credit” or do we “take points off?” Literally, what do we mark?  What is our habit? What are we teaching through our habit?

How do our actions impact the lens through which our learners see themselves? How does our habit impact the way we see our learners? I am learning to make a point to change my lens to see with different clarity.  What does the story say if I change my view? What do we learn as we try on a new lens?

The frames our minds create define – and confine – what we perceive to be possible.  (Zander, 14 pag.)

Draw a different frame around the same set of circumstances and new pathways come into view. (Zander, 1 pag.)

How do our actions impact the lens through which our learners see themselves? How does our habit impact the way we see our learners? I am learning to make a point to change my lens to see with different clarity.

What does the story say if I change my view? What do we learn as we try on a new lens?

[This post was originally cross published as Try on a new lens – edu180atl: jill gough 8.14.12 and “edu180atl: jill gough 8.14.12“]

Zander, Rosamund Stone, and Benjamin Zander. The Art of Possibility: Transforming Professional and Personal Life. Camberwell, Vic.: Penguin, 2002. Print.