Learning from Leveling, Self-Assessment, and Formative Assessment

We have been back at school for 4 days. The first day was dedicated to exam analysis, exam corrections, and peer editing.  The second day we talked briefly about graphing simple exponential function and negative exponents and then worked more on their exams.  After school the usual crew worked in my room to complete their homework.  I was really surprised to be asked “Ms. Gough, what level are these questions?”  In an earlier blog post, Deep Practice, Leveling, and Communication, I wrote about the formative assessment with levels that is my team’s current assessment experiment.  On day 3, we decided to go ahead with a formative assessment on computational fluency with negative exponents and then have students investigate exponential growth with an investigation using M&Ms.  We were hesitant to give this assessment so early, but we thought it might serve as a diagnostic assessment too.

Let me stop here and offer our current thinking about the scoring and levels on this type of formative assessment.  These assessments are not graded.  They are taken individually as if taking a test.  The assessments are self-scored, and then our learners complete a table of specifications to help us all determine their level of proficiency and where they need support.  They are to work together to correct any problems up through level 3 and are encouraged to work on level 4 if they are moderately successful with level 3. 

Level 1 – We try to target the most basic of the prerequisite skills necessary for this learning target.

Level 2 – We try to assess a prerequisite area that might cause our learners to stumble based on our history and experience with learners of this age.

Level 3 – This is the target level.  Can our learners function at the desired level?

Level 4 – This is an enrichment level.  If you are functioning on target, can we challenge you to learn more?  These questions generally come from either the Honors Algebra I or the Algebra II learning targets.

If formative assessment informs the teachers and learner and causes a change in practice or behavior, then this was definitely formative assessment.  The M&Ms were out on the table ready to be tossed and counted.  As I looked through their tables of specifications, I learned that hardly anyone was working confidently at level 3.  So, we took a poll.  Do we postpone the M&M lab to work more on negative exponents?  Rarely do I get 100% agreement, but today I did.  “Yes, please Ms. Gough.  We need to work more on negative exponents.  And, will you teach us about exponents that are fractions?” 

It was great!  DD, my friend and teammate, was there to observe the M&M experiment.  We agreed with our learners that the best decision was to stop and teach more about negative exponents; how often are we asked to teach something?

Here are three examples of my learners work and reflections from this formative assessment. 

Isn’t it interesting that VB still puts a score on her paper, but MC and CL do not?  We can quickly see that VB needs pay attention to a few details and needs to be challenged to move to level 4.  MC needs to read the directions more carefully as well as correct her work and complete the table of specifications correctly.  She understands whole number exponents, but needs a little coaching on how to write her answers.  She may not understand the term evaluate, or she may need to read the directions.  MC also needs help with fractions and arithmetic, but she understands negative exponents.  CL is unclear when the exponent is zero and might need a refresher with fractions.  She needs to pay attention to parentheses and should be encouraged to investigate fractional exponents.

One other thing to notice…CL reported 50% at level 3 and marked that this is the level where the work is most consistently correct.  I just had to ask. Her response “yeah, if you look at my work, I messed up multiplying fractions and the zero exponent.  I got negative exponents. You don’t have to worry about me.”  I spend about the same amount of time with these formative assessments as I did when I gave quizzes, but now my job is more interesting.  It is problem-solving, coaching, and having conversations with my learners.  They have the opportunity to critique their work and report back to me.  I feel like I’m coaching rather than judging.  My learners talk to me about what they can do and what they need.

Does the formative assessment and table of specifications help these learners identify where they are and where we want them to be by the end of the unit?  Will it help us know how to plan and teach?  Does it tell us all where gaps are that need to be filled?  Can we work together to close each gap?

Don’t you love CL’s reflection?  “I think I need more help with Integers and exponents with rational numbers.  With rational numbers, I feel like I had no idea what was going on, and like I hadn’t learned that stuff yet.” 

It is about learning.

Learning from Green, Pink, and Yellow Post-it Notes

Our last professional development day was a joint PD day with our colleagues from Drew Charter School.  I am a fan of many of our colleagues at Drew because of my interactions and learning with them through the Center for Teaching, so I had a great day.  The big learning themes were formative assessment and project based learning.  As a precursor to our day, we were asked to read a two-page summary of Inside the Black Box: Raising Standards Through Classroom Assessment by Paul Black and Dylan Wiliam.

In Inside the Black Box: Raising Standards Through Classroom Assessment Black and Wiliam say

There is a body of firm evidence that formative assessment is an essential component of classroom work and that its development can raise standards of achievement. We know of no other way of raising standards for which such a strong prima facie case can be made.”

Some of our colleagues got caught up in the statistics and questioned if these data are pertinent to our work since we serve an academically enabled population.  Others tweeted that they needed examples of formative assessment and how to do this in their classrooms.  Some educators say their kids need grades; they want grades.

I think our learners will respond to feedback as well or better than they do to grades.  How many times have we handed graded papers back and a child says “Why did is miss this? Why did you count this wrong? What am I missing here?”  Aren’t they seeking feedback?  And, since they didn’t get it, they have to ask for it.

And what happens to that graded paper next?  How many students use that graded paper to seek understanding, to learn more, deeper, better?  How many students stick it in their notebook to, maybe, pull it back out to prepare for an exam?

To grade or not to grade, that is not the question, right now.  Black and Wiliam state

“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.”

My team tried an experiment last week with our learners and their graded exams.  Our goals were simple.  We wanted them to identify their strengths and find their needs and questions.  We wanted each learner to analyze their exam to determine where simple mistakes occurred and where they need additional support.  We wanted to give them the opportunity to seek advice, support, and learning.  We wanted to differentiate and individualize the feedback and instruction.

In addition to completing the table of specification to determine their proficiencies for each essential learning, we asked our learners to complete their exam corrections on color-coded post-it notes.

  • Use a green post-it note if it was a simple error.  We define a simple error as one that you can fix yourself.  It causes you to think “duh, what was I thinking? How could I have done that?” Green for it’s mostly good, I just made a simple mistake.
  • Use a red (pink) post-it note if you needed help and support to correct the problem. It may have been a simple error, but if you can’t find it yourself, then you need more help and support.  Could it be that the pre-requisite skill is the root of the problem?  Red (pink) for STOP, this needs more attention; we need to work on this more.
  • Use a yellow post-it note to describe your work and what improvements were needed.  Write yourself a note describing what you learned from this correction.  Yellow for caution, I need to consider this in my future work.

We expected for students to use 2 post-it notes for every question where they missed something.  The first, green or pink, would have the correction, and the second, yellow, would have a descriptive note.  The yellow post-it note is our attempt at increasing students’ metacognition.  Can they think and write about what they were and should be thinking?  Wouldn’t that be great?  To see and hear what they were thinking instead of having to guess.

Each learner had to analyze their work individually to determine if a simple mistake occurred.  We hope this is good reflection and self-assessment.  It is interesting to consider how much they wanted to use the green post-it notes rather than the pink ones.  “But, Ms. Gough, all I really did was drop a negative.  I just needed someone to help me find my careless error.”  Nope.  If someone had to help you find it, then it was not so simple.

Learners are encouraged work together to complete these corrections, thus their interaction opportunities and feedback increased.  Their questions are so much better crafted when they got to the level of needing the “teacher’s” help.  Their questions were refined during their self-analysis and by their peers.

What we did not expect was the number of yellow post-it notes on problems that were not missed on exam day, in other words, there was no accompanying green or pink post-it note.  When asked, they uniformly explained that they still did not feel confident about solving this type of problem and wanted/needed to write themselves a note about their work and check their understanding.  Now that’s some really good feedback.  If we want our learners to know and feel confident about their work, we should assess their confidence and disposition as well as their success.

Again, from Black and Wiliam,

Thus self-assessment by pupils, far from being a luxury, is in fact an essential component of formative assessment. When anyone is trying to learn, feedback about the effort has three elements: recognition of the desired goal, evidence about present position, and some understanding of a way to close the gap between the two.

If we, as a team, believe that the big ideas on our exam are essential for our children to learn, then we must find a way to coach our learners to close the gap between where they are and where they need to be.  If I needed additional evidence of how important it is to close the gaps for my learners, I can read Final Exam postmortem by Quantum Progress.  He is working with my previous set of learners; they are struggling with concepts I was responsible for during the previous school year.  They are still my kids; they are our kids. We want them to be successful; they want to be successful.  I certainly want my current learners to be well prepared when they move to physics in August.

This assessment experiment, we hope, involves student self-assessment, formative assessment, and team-assessment.  We want our students to know where there gaps are and recognize what they need to do to hit the targets.  We want to know what each learner needs so that we can intervene individually and collectively.  We want to analyze where our team’s strengths are and where we need to improve.

The combination of the table of specifications results, a numerical representation of progress, and the color-coded post-it notes, a visual representation of needs, can help us differentiate to meet our learners’ needs.

Can we undo the long-standing habit of sticking graded papers away, rarely to be seen again?  Can we help our learners grow and increase their confidence by helping them use graded papers formatively?  Will our work be easier, and will we save time if we incorporate self-assessment and peer assessment into our daily habits?

Will the number of pink post-it notes decrease over time?  Will this color-coding method work for others?

Can we coach our learners to seek, find, and close the gaps in their learning?

Are we willing to experiment and learn by doing?

Leading by Following

There are few things sadder to a teacher or parent than being faced with capable children who, as a result of previous demoralizing experiences, or even self-imposed mind-sets, have come to believe that they cannot learn when all objective indicators show that they can. Often, much time and patience are required to break the mental habits of perceived incompetence that have come to imprison young minds.
~ Frank Pajares, Schooling in America: Myths, Mixed Messages, and Good Intentions

How often do we assess the mindset and the self-efficacy of our learners? Read what my learners said at the beginning of the year:

I believe that I can do well in math, but due to my previous experiences in math I, however, am not very confident about my mathematical abilities. I need a teacher who can help me personally understand and not leave me confused. ~RU

My attitude towards math is somewhat hesitant. I don’t believe that I will ever say that I am good at math, but when I understand the concept and am aware of foolish mistakes, I enjoy doing problem after problem. My work is slow, but steadily I work upwards. ~ES

I do not love math, because I am not that good at it. This year, I hope to grow as a math student, and to learn to love it. ~AW

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.  ~CM

I dislike math because sometimes I don’t understand it very well and I get frustrated and just quit. ~AJ

I really don’t like math just because I’ve never been good at it or understood everything. It’s especially discouraging when I feel prepared for a test in math and feel I really understand and then get a grade that doesn’t reflect that. ~AR

I observed my friend and colleague @occam98 masterfully assess both mindset and self-efficacy during his class Friday afternoon.  I assess this at the beginning of the year and after every unit.  I realized that I should be checking more formally during the unit.  I check informally, but do I know what each child is thinking and feeling?  Can we minimize the demoralizing experiences to help students break the mental habits that cause frustration, lack of self-efficacy, and the willingness to just quit by simply checking their disposition and their success?  If we are the lead learners, how are we leading? 

  • Are we so far down the path that they can no longer see us? 
  • Are we moving so fast that they are having trouble keeping up? 
  • Are we just ahead dropping breadcrumbs hoping that they will follow? 
  • Are we doubling back to see if they are confident in the direction we are going?
  • Are we leading by following their paths? 

All good questions to ask as we begin the second half of our time with our learners.

Now, I have very little sense of direction.  Whichever way my nose is pointing is north.  Scary, right?  When walking, I walk out in front even when I don’t know where I am going.  (Do you know anyone who does this?)  My walking partner will quietly say “you know you should turn left here” or guide me to the correct path with a slight press in the small of my back.  Sometimes the key is to just stop and wait to see if and when I am going to check myself.  It is interesting to be led by someone following you. 

The challenge is to spend this semester leading our students by following their work and checking their understanding.  Can we quietly say “I’ve been watching; have you tried ____ or thought about _____?” To minimize or elimnate demoralizing experiences, we should not grade until they are prepared and ready to be formally assessed.  We should check for understanding along the way and know when they are ready.  They should know that we care enough to know what they need and that we are willing to coach them to success.

RU said “I need a teacher who can help me personally understand and not leave me confused.”  Doesn’t RU want us to be the guide to learning by knowing RU’s current location and starting there?

ES said “I don’t believe that I will ever say that I am good at math, but when I understand the concept and am aware of foolish mistakes, I enjoy doing problem after problem.”   Look at this child’s language.  “I don’t believe that I will ever…” and “…foolish mistakes…”.  Isn’t it sad that SE has learned to see mistakes as foolish when, in fact, they are an opportunities to learn.

CM said “…I need a little bit of encouraging to reach my full potential. I often need help…” How can we encourage and help CM reach full potential? 

How can we help AW, AJ, and AR grow as learners, keep going, and feel encouraged?  I want to make a case for formative assessment, both formal and informal.  We all use informal assessment regularly by asking questions in class and walking among our students watching them work.  But do we change what we are doing based on what we see?  Do we show our students how important their understanding is to us by changing course when we see them struggle?   If we ask one question and take one answer, do we know what the other 16-36 students are thinking, feeling, and learning? 

This is where we need to leverage technology.  In Algebra I, we have been using the TI-Nspire Navigator system to ask a question and collect an answer from every child.  What decisions are to be made when faced with the results below?


 Do we go forward?  Do we try again?  Here’s what we know:  16/24 students agree, though a couple of them need help with their notation or their technology,  6 students have made a error somewhere, and 3 students did not have enough time or the confidence to answer the question. 

I ask my students what to do next.  Do we go forward with the next level of question or application?  Do we try this level again to improve our class score because right now we are at 67%.  Before we go forward, what action needs to be taken?   In our community, to quote the kids, “we leave no man behind, Ms. Gough!”  There is a 2:1 ratio of teachers to learners at this point.  The search-and-find teams go into action.  There are 2 students actively working to decode the error and explain a different method for every one child that had an error.  Talk about formative assessment.  “Oh look, Ms. Gough, she just dropped a negative.”  “Wow, I should have been able to do that myself.”  “Dude, you need to go to Office Hours; you need major help!” 

Lead the learning by following their work; watch them go down the path; provide them with feedback and coaching. 

In Synergy 8, we use TodaysMeet to see what learners are thinking and questioning.  We want to hear every voice.

Can we use this method of backchanneling to check for understanding?  We asked our learners to summarize the big idea from the Steve Johnson’s TED talk Where Good Ideas Come From

Here’s a string from the backchannel:

innovative ideas happen when you collaborate with other people
BM at 13:49 PM, 27 Sep 2010 via web
Ummm I think the main idea was that through long periods of time ideas can be born and then perfected through collaboration with others.
RU at 13:49 PM, 27 Sep 2010 via web
Main idea was that peoples ideas make other people start to think about it in their own way, when they are in the same room.
AW at 13:49 PM, 27 Sep 2010 via web
the main idea of the talk was how people’s ideas will SPARK other’s ideas to add on to your idea, making our universe more innovative
CP at 13:49 PM, 27 Sep 2010 via web
The main idea from the TED talk was how do ideas and theories grow and where do they come from, and what do they do when they are not quite
QB at 13:49 PM, 27 Sep 2010 via web
It’s better to synergize because, then you add on to each other’s thoughts to have something better than any of them could have had alone.
AS at 13:50 PM, 27 Sep 2010 via web
Hacking allows us to launch ballistic missiles. Progress comes from people building off others ideas, and when there is collaboration
JG at 13:50 PM, 27 Sep 2010 via web
A network that shares ideas will create and improve those ideas, giving a greater chance of success.
CS at 13:50 PM, 27 Sep 2010 via web
when you collaborate with others and share your ideas, you can create a great new idea “chance favors the connected mind”
SZ at 13:50 PM, 27 Sep 2010 via web 

We share our understanding with each other and record these thoughts to review later.  Do we have a better idea whether our learners found the main message?  Do we know who may need intervention or additional support?  We know more than we did before.

Can we lead by following?  Will we lead by following?

Embrace Dr. Pajares’s thought:    

The human brain is far too complex an organ to determine that x can’t be taught.
~ Frank Pajares during a discussion in EDS 771

Lead by following.

Social Media Experiment: Brain & Learning; Formative Assessment

As an experiment in Learning by Doing, I sent the following email to my tweeps (and then others) to help me practice primacy-recency.

I’m hoping you’ll be willing to experiment with me, experiment with something that we are learning in the Faculty Cohort.  This year we are using How the Brain Learns by David A. Sousa as the foundation reading for our work.  We been working on a practitioner’s corner about primacy-recency.  (An excerpt from the chapter is linked at http://bit.ly/PrimacyRecency.)

Will you consider taking a quick break at approximately 20 minutes after class begins to take 2 minutes to tweet what is being learned in your class?  

“This research indicates that there is a higher probability of effective learning taking place if we can keep the learning episodes short and, of course, meaningful. Thus, teaching two 20-minute lessons provides 20 percent more prime-time (approximately 36 minutes) than one 40-minute lesson (approximately 30 minutes). Note, however, that a time period shorter than 20 minutes usually does not give the learner’s brain sufficient time to determine the pattern and organization of the new learning, and is thus of little benefit.”
How the Brain Learns, David A. Sousa

If you are willing to participate, could we try this next week.  Could we try the following?

  1. Pause at approximately 18-20 minutes and ask our students to do a quick write about what they are learning or doing in class.  (a form of self-assessment; do I know what I’m supposed to be learning?)
  2. Let them quickly share what they wrote.  (a form of formative assessment, are they learning what I intend?)
  3. At Twitter.com from your computer (displayed for Ss to see) tweet a summary of what is being learned or done using the hashtag #20minwms. (this models using social media for learning)
  4. Follow the tweets from this hashtag to be more informed about each other and what we are learning/doing in class to possibly find curricular connections and common ground.

If you lead learning for students older than 18, will you tweet too? 

We have found that asking the kids to help us pause for this break works really well.

 Will you forward this to other WMS colleagues that tweet?

 What do you think?


use #20minwms as the hashtag.  I might practice tomorrow.

The results of the practice day have been fun as well as interesting.  The tweets, of course, can be seen if you search with our hashtag.  The conversations have been great!

  • Three colleagues created a Twitter account.
  • Four other colleages tweeted for the first time.
  • Four colleages have read the research and discussed it with others.
  • Approximately 35 tweets by 9 faculty members. (Some are still learning about hashtags, isn’t that great?)
  • The Director of Teaching and Learning at one of our feeder schools was intrigued enough to tweet in and ask a question.  Her first tweet said “Hey WMS folks, I’m super intrigued by – connected 2 @, I know, but pls explain.”
  • Quantum Progress not only participated but documented his method and results in his 20 minute pulse checks! blog post.
  • Two different PLCs briefly discussed the big ideas of Dr. Sousa’s research.
  • Colleagues report how amazed, impressed, wowed they are by their learners’ summaries of what is being learned.
  • Colleagues discuss the difference in affect and engagement after the short break.  Students are ready to learn; they will concentrate again.
  • Some teachers tweeted with their phones; others tweeted from the computer displayed on their SmartBoard.  Students could see first hand how to use social media for learning.  We modeled what we want them to learn.

Teachers tackled the request in different ways.  I observed, first hand, @occam98 have his students do a quick write about what they were learning on a scratch piece of paper.  He collected the papers, shuffled them, and handed them back.  Each student read one aloud, but it was not their own sentence.  Then the class summarized the learning of the class.  From my perspective, this gave students confidence to share their thoughts even if they said “I have learned that I lack confidence in what we are doing.”  He was kind enough to document some individual responses on his blog.

During the Writing Workshop team meeting, @epdobbs planned to have each student write their sentence, share, and then one quote was selected to represent the class.  A student could see their sentence published.  One example:

 learned 2 use diction in a poem; poems can be difficult when comparing two things; diction adds layer; wc=theme; FUN; verse! -D7

In drama, @galanesmcmillan reported 

“Kids learning to “read people….made us a better audience and actor…follow hunches…talking not always all that acting is” .  

And in 6th grade math, @kplomgren broadcast

 Fractions & Mixed #’s & how to convert; in division, numerator is always the remainder, how to find the mystery # – 5th per s’s.”

Isn’t this what learning should look and feel like?  We are learning together, choosing to learn, teaching and supporting each other.  While we generally teach in isolation, we can leverage social media to find connections and common interests.  We are, in a sense, celebrating our work and the learning of all involved no matter their age.

We are modeling learning, examining and sharing our practices, and having fun!

Learning Challenge – Take a Small Step in Their Shoes

How many times have you “practiced” your password to your email? 
When was the last time you changed this password?

Will you consider an experiment about learning and practice?
Will you add one number or letter to the end of your password?

Will you pay attention to the ease (or not) of this change?
Will you come back to this post and record data by answering the following poll questions after 1 day?  2 days? a week?  The poll will be open for your return to enter new data.

We chose our password; we chose the additional learning.  How long does it take us to “learn” this new choice?  How easy is it?  How frustrating can it be?  What if it was not your choice?

How much time and practice is needed to add to current learning?

Believe – One Word 2011

I teach; I learn.  I strive to believe.

  • Believe that all things are possible.
  • Believe that together we can learn and do.
  • Believe in seeing the bright spots of others.
  • Believe that we are better together than alone.
  • Believe that change is necessary as well as possible.
  • Believe that we can and will contribute to making a difference.

There are many words on the walls of our classroom.


Believe greets us; it is the first word we see every day.



Grade Reporting: To comment or not to comment…that is the question!

Grades – A Measure or a Rank from It’s About Learning along with an impromptu tweetup with @occam98 have prompted me to question the value of the comments I have written to accompany my grades this semester. 

For a little background, I am required to write a comment for every student in October and March. Additional comments are required in September, November, January, February, and April for any student failing or having a significant drop in their grade. 

I have chosen to write a comment for every learner every time I have reported their grade.  My goal was to add context to the single number that is supposed to convey a summary of a child’s learning (achievement?, mastery?) up to the given date.

Only one parent has given me feedback on these comments.  On October 28, 2010 she wrote

“Dear Ms. Gough, Thank you for providing the detailed comments regarding [my child] as a student in your Algebra 1_J course this past grading period. The information shared was insightful.”

The tweet (after my tweetup with @occam98) shown below spurs me to seek feedback.  Am doing the right thing or wasting my time?

I am to report grades again next week.  I’ve been wondering if I should write another comment for each learner, and asking does my comment tell the learner, the learner’s parents, and other interested parties anything?  Is there added value by having the accompanying comment? 

What follows is a case study, the series of grades and comments, for one of my learners.  If you are willing, would you please read through the series and give me feedback?

 September 20 – Grade reported:  P     
(P for passing; we were not ready for a number.)

In Algebra I, we identified eight essential learnings for first semester. As we continue to learn new material during the semester, we will revisit all identified essential learnings to help all students retain and improve these skills and concepts. Details concerning the essential learnings can be found at http://www2.westminster.net/faculty/jgough/AlgI/First_Semester_EL.html.

Our first unit focused on students learning to solve linear equations, linear inequalities, and graphing on the Cartesian coordinate plane. As is our practice, the first test is scored with no partial credit awarded. The student’s job is to find and correct any errors on this test as well as learn from their mistakes. Each student is then offered a second-chance test opportunity to demonstrate that they have learned from the error-correction process as well as to improve their grade. Please remember that our focus is on learning; it is okay for students to struggle with the material on the first test if it helps to focus their effort and improve their understanding.

AS has consistently demonstrated her effort to learn algebra by engaging in the deep-practice method of working and learning from homework.  AS has begun the process of self-assessment of her algebra skills, and she can describe her strengths and her challenges.  In her latest report, she says “I need to work on equations in which the variable is on both sides.” I am very pleased that AS can express needs in mathematical language that focuses our work to help her improve.

October 18 – Grade reported:  81

To date, we have been investigating and working on six of the eight essential learnings for the first semester of Algebra I.  After the midterm exam at the end of October, we will begin our study of solving systems of linear equations and systems of linear inequalities and their applications.  The theme of this semester is solving equations, finding patterns, and using linear functions to solve application problems.  At the end of the semester we will work on pattern-finding and computational fluency as we move from linear functions to irrational numbers and the Pythagorean Theorem.  Details concerning the essential learnings can be found at http://www2.westminster.net/faculty/jgough/AlgI/First_Semester_EL.html.  Students’ self-assessment of where they are for each learning target has become a routine.  Throughout each unit, students assess and reassess their learning.  These assessments are strategically designed to help students identify their current level of understanding and know where to focus their efforts.  We continue to use error analysis and correction to build skills and knowledge. 

In her first journal, AS wrote “To understand Algebra better, I will need to pay more attention to small details and remember to write the formula for the equation each time.  I really enjoy having real-life examples, so keep doing that! I think that every week we should have a quick check in with you to make sure that we understand the material. This can vary from a checklist to a short assessment (not for a grade) with you.”  I hope that I am meeting AS’s needs with regard to real-life examples and assessments.  The formative assessments are one way that we communicate our expectations, and they are a way AS can prepare for our tests with confidence.  AS has done a good job with her self-assessments.  She says “A significant moment for me was when I actually understood how to do equations with negative numbers. I finally realized that a negative sign is the same as a subtraction sign. I also learned that negatives can’t go in the denominator, which cleared up many of my questions.”  As I look through both of AS’s tests, I can see that working with Integers causes many of her errors.  I am pleased that she has identified this problem and is working to improve her work.  AS has a good attitude, and she is willing to help others learn.  I applaud her good effort and work ethic.

November 11 – Grade reported:  81

In Algebra I we have covered five of the eight essential learnings of the semester:  solving equations, understanding slope, writing equations of lines, solving inequalities, and using linear functions to solve application problems. 

At http://www2.westminster.net/faculty/jgough/AlgI/A1_chap03.htm you will see several formative assessments.  Our team designs these formative assessments to offer remediation and enrichment for all students.  The goal is that every student self-assess using these assessments and determine the level at which their work is most consistent.  The target level for Algebra I is level 3.  The level 4 questions are offered to challenge and further the learning of students that work at a slightly accelerated pace.   The level 1 and level 2 questions are provided to help students when they are struggling with an essential learning.  These assessments also give students specific language to express where they need to focus their work.  They are great conversation starters.  Students not performing on target are expected to seek help and improvement with their team and an algebra teacher during Office Hours.  Students performing on target are encouraged, but not required, to challenge themselves to enrich their learning and problem-solving through the struggle to rise to level 4.

AS’s preparation for the initial testing for the second unit shows much better results than for the first unit.  Her original test score is much higher on the second unit test.  I want AS to push herself to do more independent practice to prepare for the second chance test.  I think this additional effort will add to her learning and her confidence.  I am pleased that AS has been coming to Office Hours to check in and work on her homework. 

January 4 – Grade to be reported 88

Do you want more information than the reported 88?

We all know that a single number cannot convey the accomplishments and learning of a child in a class.  It was my hope to provide everyone involved with additional context concerning the reported number.  

Quite frankly, it is time consuming work and if no one cares, if it does not provide additional, important information about learning to all interested parties, then I will use this time for other meaningful work. 

So, I would like to know what you think.  Do these comments provide needed context or just more stuff to read?  Should I write a comment to go with the grade I’m going to report in January, or is my time better spent elsewhere?  Would you take my survey and/or leave a comment?

Please tell me what you think.


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.

Seeking brightspots and dollups of feedback about learning and growth.

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