All posts by Jill Gough

Learner, Love Questions, Problem-finding, Math w/technology. Interests: Collaborating, PLC, Formative Assessment

Assessment Goals Inspired by The College Board

Around here there has been some conversation about AP.  If you’d like to read some of the thoughts, check out the following blog posts. 

While I agree that many are “over the top” about AP, I believe that there are many good things to be learned from The College Board’s AP program and assessment process.  I think we have to ask ourselves if it is the AP program or how we use it that causes problems.  A hammer can be a tool for constructing new things, repairing damage, or a weapon that causes destruction.  How the hammer is used is what is critically important.

So here is a list of my top goals about assessment, learning, and teaching inspired from The College Board.

Goal 1:  Agree upon a common curriculum for our students.
Think about it…How easy is it to reach consensus from everyone in your building about what is essential to learn about a course they have in common?  Imagine getting the majority of the calculus teachers in our country to teach from a common curriculum.  Wow!  Now, there are too many learning targets in AP Calculus AB to teach and learn in the given time frame.  We have to pick the ones that have longevity and leverage.  We’ve seen The College Board do this too.  No longer do we find epsilon-delta proofs and trig-substitution in the essential learnings of AP Calculus AB.  Does this mean I shouldn’t teach them?  No, but I should think about it rather than teaching it out of habit or because I had to learn it in college in 1980. 

Goal number one is to continue finding common ground and agreement among all teachers of our course in our school.  It isn’t about me and what I love to teach; it is about what is important for every child to learn from our course.  It is about a guaranteed curriculum for each child in our care.

Goal 2:  Make learning targets and assessments as transparent as possible
Why should there be such mystery and stress about what is going to be on the test or assessment?  Shouldn’t students have access to multiple representations of the learning targets that are going to be tested or assessed?  If we have learned nothing else, we know that our learners need more than a list of learning targets written in words.  They are young and tend to over-estimate what they know and can do.  The College Board releases their free response questions publically the day after the assessment is given.  Periodically, they release their multiple choice questions too.  Let’s be clear; The College Board writes a new set of free response questions each year.  They do not give the same test and just change the numbers.  Releasing the test questions gives information about the test style and level of difficulty.  How often do we offer our students examples of our assessment style?  Remember, telling them that there are X multiple choice questions, Y short answer questions, and Z matching questions might not indicate the style or level of depth these questions might have.

Goal number two is to help our students perform better on our assessments by publishing our previous assessments in hopes of offering them multiple representations of our learning targets.  Are we brave enough to publish the scoring guide too?

Goal 3:  Expect retention, application, and synthesis of the essentials
Don’t my colleagues teaching 9th grade geometry and physics expect my students to be able to solve an equation, compute slope, and write the equation of a line when they enter the next level of coursework?  Yep.  The College Board’s assessment expects all students to retain, apply, and synthesize algebra, pre-calculus, and calculus topics as indicated in the assessment items of the exam.

Goal number three is to find ways to spiral our curriculum so that these essentials continue to occur on assessments and problem-solving opportunities.  We strive to find application of said essentials and connections with other essentials.  We are challenged to compare and contrast ideas in relevant ways.

Goal 4:  Find balance in our assessments
How often do we assess our assessments?  How balanced are they?  Do our assessments offer every child the opportunity to show what they know?  Is there a good balance of knowledge, comprehension, application, analysis, synthesis, and evaluation?  Do our assessments offer students the opportunity to leverage technology?  And is the point distribution balanced?  The AP Calculus AB free response questions are each weighted 9 points.  No one question counts 20% of an assessment. 

Goal number four is to assess our assessments to make sure that there is a balance of essentials tested, to know that we have asked some questions that every child can answer, and that there are questions that will promote higher-ordered thinking skills.  We need to make sure that the interesting (challenging) questions have point distribution balance.  No one question should take a learner’s grade down a level.

Goal 5:  Assign credit, as a team, for quality work rather than deducting points for errors
Have you listened to yourself when you are grading?  Have you listened to your teammates while they mark papers? Are points awarded for work shown, or are points docked for errors?  The College Board’s scoring guides are about awarding points for work shown.  I checked several scoring guides.  Have you seen The College Board’s scoring guide for last year’s AP Biology exam?  How about the AP Macroeconomics scoring guide?  All of these scoring guides state reasons to award credit and very rarely state when to deduct points.  Grade, mark, and score papers together, sitting at the same table.  Know that points are awarded across the board; know that credit is awarded for quality work. 

Goal five is to pay attention to our language and our thoughts.  We should be striving to award credit.  We must coach our students to show quality work that will earn credit which means that we have to identify what we mean by quality work.  We must pay attention to our thinking about finding the bright spots and good work.  We must challenge ourselves and each other to take stock of and add up what is done well.

Goal 6: Collect and provide student exemplars of quality work
Have we provided our students with examples of quality work that they can analyze.  Yes, if you count the teacher’s work as an example of quality work.  But, have students been given the opportunity to see quality work completed by a peer, a learner in the same stage of learning?  How often do we have our students use the scoring guide to mark a paper, to analyze work to learn from another?  Have you seen the AP Biology samples with commentary or the AP Macroeconomics samples with commentary that accompany the online information? 

Goal six is to show our learners what others have done to demonstrate understanding, to communicate process, and to record thinking.   

 Well, the goals above are all worthy goals – perhaps too many for one lone algebra teacher to tackle.  I wonder how much could be accomplished with my team, my PLC, my PLN and/or my critical friends.  Hmm…If we had to pick one, just one, which would you choose?  Why?

The self-discipline to watch, wait, and coach

On our 4th day of cookie baking, AS taught me a couple of really great lessons about learning with my students.  Once again, by popular request, we were making Reese’s peanut butter cup cookies.  We make peanut butter cookie dough, roll it into balls, and cook them in mini muffin pans.  As they come out of the oven, we press mini Reese’s peanut butter cups into the center of the cookies.  Delicious.  My small extended family blazed through 8 dozen in two afternoons.

For the first 4 dozen, I made the batter and rolled the cookies.  Together we pressed the candy into the cookies as they came out of the oven.  No big deal. 

How often do our students watch us do the work to solve the problem or answer the question?   

Baking the second 4 dozen was a very different story.  My mother gave AS her very own measuring spoons, spatula, and mini muffin pan that bakes 1 dozen muffins.  Now she had her own pan; she was in charge.  It would have been so much faster for me to have rolled the cookies.  But, no…her pan; her cookies.  Her mantra: “I can do it myself!” 


So, I watched, waited, and coached.  Some of the balls were too small and would have been difficult to press candy into after baking in the oven.  Some were too big and would have blobbed out on the pan during baking.  She fixed most of these problems with a little explaining from me. 

Isn’t this happening sometimes in our classrooms?  It is so much faster and more efficient for the teacher to present the material.  We can get so much more done in the short amount of time we have.  But, how much do the children “get done” or learn?  When efficiency trumps learning, does anyone really have success?  How do we encourage “I can do it myself!”?  How do we find the self-discipline to watch, wait, and coach?

That was the story for the first 2 dozen cookies.  Can you believe that she would alter my recipe?  We cooked our second dozen cookies, and while I was busy pressing the peanut butter cups into my cookies, she decided that Hershey kisses would be just as good or better.  With no prompting (or permission) she created a new (to her) cookie.  Santa left kisses in her stocking and she wanted to use them. 

Does it really matter which method a child uses to solve a problem or answer a question?  Isn’t it okay if they use the lattice method to multiply?  Does it really matter which method is used to find the solution to a system of equations?  Shouldn’t they first find success?  Don’t we want our learners to understand more than one way?  Is our way always the best way? 

Was AS pleased with herself and her creativity?  You bet.  Were her cookies just as good as the original recipe?  Sure!  How can you go wrong combining chocolate and peanut butter?

Do we applaud the process that our learners use to solve a problem or respond to a question?  Do we praise them when they try something different?  Are we promoting and encouraging risk-taking, creativity, and problem-solving?

Can we find the self-discipline to be patient while learning is in progres, to watch, wait, and coach?  Can we promote and embrace the “I can do it myself!” attitude?

Could it be as simple as adding rather than subtracting?

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?


So, there is one more thing to think about….Can we frame this in terms of teacher evaluation too? 

Can we model a strength-based peer observation process? Let’s try adding up the good things we find.  What if we chose to document bright spots in each other’s work?  Could we write about what is done well?  Could we work in team to identify what others do well that we wish we would do too? 

If any of this is interesting to you, then I dare you to give it a try.  Experiment.  Learn by doing.  Form a team of friends, critically important friends, to learn together.  Let’s add to our toolkit by sharing our practices and asking each other questions.

What we see isn’t always what we’ve got…

Can we identify what do these two learners have in common?

Academically, they are both new learners.  AS is new to reading while ES is new to abstract reasoning and variable representation.

AS’s reading hit a plateau in late October.  She began to struggle with short vowels.   We practice with AS daily to improve her word recognition, her reading, and her confidence.  We applaud her work and praise her improvements.

ES’s use of variables to mathematically model a problem hit a plateau in early November with systems of equations. We offer ES the opportunity to practice every day, but does he?  There are so many more variables for ES than for AS.  ES has to choose to come after school to work with us one-on-one, or we have to require it.  Would he come for extra help if he knew that we were going to work from his strengths?  Would his confidence and self-efficacy improve if he knew that we would find his bright spots and work there?  He is very good at solving single-variable equations, and his written work is well organized.  If he knew that he would be praised for what he does well and encouraged for his attempts, would he be more receptive to additional practice and attempts?

AS is shy about reading in front of her peers.  Will they laugh at her; will they think she is not smart; what will happen if she makes a mistake?  Is this true for ES too?

How do we react to these two learners?  Some say “I taught this; they need to come for extra help if they don’t get it.”  Others say “We will do whatever it takes to help get this child over the plateau.”

Does the age/size/attitude/behavior of the child contribute to our response?  Should it?  When I look at the children that work daily with me, I see big kids, kids that look grown-up.  They are the oldest in our building, the leaders.  But, what should I see?  What if I could change my view?  What if I could imagine them as young learners seeking praise and bright spots?

We have started project to help us visualize where we are as learners.  An example:

We should see young learners working to understand math with variables; we should see learners that need praise and support.  When AS has some success and gets applause, she smiles and tries again; do our big kids?   When Annie is offered encouragement, she tries again.  This is her first day without her training wheels.

What if we offered mathematically-young students, no matter their age or size, the same level of support as we naturally offer AS?

How do we find ways to celebrate those initial steps in learning?  How do we offer authentic feedback and coaching that will promote success-oriented behaviors and a desire to improve?  How do we build confidence and motivation to attempt more challenging topics and ideas?  How do we remember what we see – a 6’4″ basketball giant – is not always what we’ve got – a young learner in need of support, confidence, and success?

Hiding in Plain Sight or Walking the Path Together?

It just breaks my heart when I think about one of my classes.  Their behavior is awful.  I have been counseled over and over again – it’s not your fault Jill; it is the combination of personalities.  Well, it may not be my fault but it is my responsibility. 

Their behavior is bad (relatively speaking of course, remember I teach in Camelot); they are rude to each other and to me.  Individually, they are great kids.  I love each of them as individuals – collectively, not so much.  This statement – “collectively, not so much” – is not true.  If I did not love them, would I worry about this so much? 

What is most discouraging is that they are hiding their lack of understanding.  They are using their behavior to mask deficiencies and to distract me and others from the real problems they face.  It is like they are jumping up and down, waving, screaming “look at me, look at me” so that we won’t notice they are struggling to learn.  It is too risky to ask a question and reveal publically that you just don’t know something or anything. 

In contrast, in my other classes, they regularly say “is it okay that I’m at Level 0? I don’t know any of this and need help.” It will be blurted out “Help! I’m at Level 1 and want to be at Level 3.  Who understands this and will help me?”  Literally, two or three other kids will get up and begin to coach.  There is no snickering; no mocking looks are exchanged.  The culture of our community says we all learn together; if one struggles, we all struggle.  We are walking this path together.    

I feel like Dr. Jekyll and Mr. Hyde.  I have an hour of let’s hide in plain sight, tear each other down, if I can’t learn this no one will, followed immediately by an hour of let’s learn together, build each other up, leave no man behind. 

Which classroom would be your pick if you were a student?

Let’s apply this question and the situation to our own work.  What if the teacher described above was a school administrator and the classes were two different schools?  Which school would be your pick if you could choose?

Would you choose to teach in a school where the culture is “it is too risky to ask questions and reveal that I am struggling with an area of my teaching?” 

Or, would you choose the school where the culture says “we all learn together; if one struggles, we all struggle; we are walking this path together?”

Aren’t there both schools here in Camelot today?  Which school are you in now?  Are you walking the path with others or hiding in plain sight?  Where do you want to be? No move needed; great!  What can be done to help you move if you want to move?

Reflection, Attitude, and Efficacy

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?  And, is it really that black and white?  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 than 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. 


I dare you to go back and read both journal articles on this page replacing the word math with assessment or whatever you are struggling to learn right now.  Out of the mouth of babes…

2nd Chance Tests, Effort, and Assessment

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?

Listen to what my learners are telling me. 

 I chose this picture because this is me after a few hours of trying to figure out a math problem. I get frustrated when I don’t understand the concept or material. This picture shows you that I hate math because it is obviously not my best subject. Math obviously doesn’t come easy to me, but what this picture shows is only after a little while of focusing. What this picture doesn’t show is that sometimes certain material comes easy to me and I do well on that certain section. This picture is mostly for the harder concepts that I do not understand and wish I didn’t have to do. My goal : My goal is to do the best I can, meaning studying more than usual and not racing through homework, but really taking my time so I make sure to understand everything. I expect to accomplish this goal by pushing myself to study and take longer on homework and not turning on the computer, TV or phone.  

KW wrote

I get frustrated when I don’t understand the concept or material. This picture shows you that I hate math because it is obviously not my best subject.” 

I want to say that there is nothing in this writing that gives evidence that math is not her best subject, however, I infer that she hates math because she has not experienced success from struggle.  Could it be that she has never been given the opportunity?  Would a different testing philosophy change her attitude and efficacy?

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 specification 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. 

To answer the most frequently asked question… Yes, it is completely possible to bomb the first test and end up with a 100 in my grade book.  

 CM wrote:

Math can be a challenge for me because sometimes I feel that I give the effort and it just doesn’t reach the results that I wanted. Like this picture it seems as though I climb towards a better way to understand it and achieve my goals but never reach there. Sometimes I feel that others make it to the top before I do. That can be discouraging, when I am ready and prepared to climb the mountain I feel better about the outcome, whatever it may be. I think that I am good at math just sometimes I need a little bit of encouraging to reach my full potential. I often need help from peers and my teacher to show me easier ways to reach my goals.My job in this class is to participate in class and offer my ideas to help me and my peers to better understand a math problem. My obligation in class is to learn math in new ways to that I can better understand math in a whole and be able to apply it to life. I believe that every day is a learning experience and every day even if I don’t succeed that I am trying towards my goals and get one step closer every time I make a mistake. I think that math is a real challenge for me but if I work hard I can do well this year. I feel that this class is going to beneficial to my learning this year. For my year to be even more successful I need in a class, projects, communication, opportunities to make up grades so that I can learn from my mistakes. What I want is a way to make math more fun and enjoyable.

Goals for Math
My goals in math are to really understand the problems and not only memorize them but to learn from my mistakes and apply them at the next chance. I hope to get a good grade in this class and learn new things I didn’t know about math.

 CM wrote

My goals in math are to really understand the problems and not only memorize them but to learn from my mistakes and apply them at the next chance.” 

How often do we provide the opportunity for students to learn from their mistakes and apply them?  When do they get a next chance?  We, the Algebra I team, take a lot of flak from our colleagues and parents about our 2nd Chance Test commitment.  This flak comes in many forms, some subtle, some not so subtle. And, most arguments fall apart when we point out that you can take the SAT multiple times and bank your scores.  Hmm….

The bottom line is that we have seen positive learning results on our semester exam that we contribute to allowing children to learn from their mulligans.

CM also said

Math can be a challenge for me because sometimes I feel that I give the effort and it just doesn’t reach the results that I wanted.”

Our grade books are sparse; we have very few grades.  We assess quite often; we grade little.  We are rewarding effort, but not because you are sweet, try really hard, and/or are compliant.  We expect proof that the effort yields results.

In January, we will ask our students for feedback our course and assessment strategies to get a feel for their perception of their learning.