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?
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?
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?
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?
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.
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?