# 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!)

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?

CL:

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.

# Deep Practice in practice

Let’s think more about the idea of deep practice for homework and what it might look like.  The children that I am coaching to learn Algebra I are encouraged to complete the homework the idea of deep practice.

We are trying to move learners from “If at first you don’t succeed, hide all evidence that you tried!” an attitude of “If at first you don’t succeed, try, try again.”

When homework is assigned, part of the homework is to complete the assignment in deep practice.  All complete solutions are posted my webpage and the answers only are posted on the Algebra I team’s MOODLE course (password protected).

Students are to work a problem, check the answer, and try again if necessary.  To keep them from getting stuck, if they are not successful after three attempts they should move on to another problem, question, or task.  So that we can diagnose their error in class, the student should simply x out incorrect work and try again.

When students come to class, they should know that their answers are correct or know where they have questions.  As our class is getting settled, students should be asking and answer each other’s questions.  I wander around and document how many answers are correct and how many they had to do in deep practice.  Here’s an example of a student’s work on a traditional Algebra I homework assignment.  (I just asked for a random homework page that showed deep practice from the students my last class on Friday.)

The diagnosis for the student above is really simple since there is evidence of her work and thinking. In problem number 4, there was a simple division error; she reduced 12/15 incorrectly the first time.  In questions 5 and 16 (and other problems on the page) we can identify a pattern in her work.  Her fundamental misunderstanding is about Integers.  Subtracting is the same as adding a negative.  The negative is missing in step two for this child every time the variable term is subtracted from a constant.  A simple-to-fix error IF it can be diagnosed.  (The correction for number 5 is also not correct…sigh…there is still so much work to do.)  We should make the time to coach our students to value proof-reading their work and analyzing their mistakes for learning.

As fate would have it, I ran into the mother of the child whose work is displayed above the same day that I collected this example.  Mom stopped me to tell me a story about her child, M.  According to M and her mother, M has not felt successful in previous math classes.  M’s mom says math is now M’s “favorite class”.  Her confidence has increased significantly and is still increasing. M also feels comfortable asking you questions and knowing you will willingly answer them.  Mom also says the biggest change in M is her willingness to make a mistake.   She quoted her child “Mom, Ms. Gough has taught me that it is okay to make a mistake.  We learn from them.  It’s how we learn.”

Worth repeating

“…it is okay to make a mistake.  We learn from them.  It’s how we learn.”

Let me pause here and say that I do not grade homework; I do not give credit for homework; I do not count homework in any way.  We do, however, document homework; we also document attendance in Office Hours.  My students help me with this documentation.  If and when a student is disappointed or frustrated with their progress, we can look at their rate of homework completion and how much deep practice is attempted compared to the number of times they come for addition coaching during Office Hours.  Often the data is very revealing to a student.  I struggle with my homework, and I have questions, but I never come to work on these questions.  Hmm… what steps could be taken to begin to improve?

One more thing about the above work…We have had to work really hard to correct a misunderstanding with kids that you can see in the above work.  She has documented that she had 6 correct answers and 6 deep practice. From my point of view, she has 11 correct, and 1 that still needs work.  It has taken about 3 months to get kids to the understanding that their homework is “correct” if they arrived at answer with good work no matter how many times they had to try.

We are trying to move learners from “If at first you don’t succeed, hide all evidence that you tried!” to M’s attitude of “…it is okay to make a mistake.  We learn from them.  It’s how we learn.”

# Is time a variable? Is learning a constant?

I think that I need some counseling – a reality check, if you will – about the meaning of:

Time is the variable and learning is the constant.

Is it true all of the time, some of the time, regularly with some exceptions, or only applicable to small children learning to walk and talk?

There are deadlines – we have an exam coming up that signifies the end of first semester.  So let’s take the idea of unlimited time off the table.  What, then, does “Time is the variable and learning is the constant” look like in practice, realistic on-the-ground, in-the-trenches, day-to-day practice?

A child performs poorly on a relatively high-stakes assessment; an assessment that carries a grade that some use to “define” this child.  Do we offer this child a mulligan?  Do we offer every child the same opportunity for said mulligan?  Do we require the “do-over” of this child?  Do we require the “do-over” of every child?

Let’s break these questions down with some details and more questions.  If we embrace “Time is the variable and learning is the constant”, then YES to the 2nd chance… or…are there more questions to be asked?

• AG was sick the entire week prior to the assessment…mulligan?
• DP is so nice, sweet and tries so hard…mulligan?
• SM was irresponsible having no homework showing no effort…mulligan?
• JH is disrespectful and disagreeable…mulligan?
• RT is misplaced in this course (shh, she just can’t cut it here)…mulligan?

If yes is the answer to any (or all) of the above, is the do-over optional or required?

What about an assessment?  Is time a variable?  Should AG, DD, SM, JH, and RT be able to (have to) express their learning, understanding, and growth in the same 55 minute time frame?

• AG is a visual leaner; she needs to draw and outline her thinking before documenting it formally.
• DP is a memorizer; as long as there are no curve-balls on the assessment, she is great.
• SM is unprepared but SMART; he can pull the information back, but it is slow going due to lack of practice.
• JH checks his work on every question; he is determined not to make a mistake.
• RT is carrying a heavy personal load at home and can’t concentrate; everything is a struggle.

Do we provide these students additional time to show and document their current level of ability, work, and understanding, or at the end of the period, is time up?  Does it matter which child you are? Does knowing more about why the additional time is needed change your feelings about providing additional time?  (What if you can’t know every child’s story?)

The two latest arguments being discussed within my team are that we were not preparing our students to take the SAT if we give them additional time and that something is wrong if you can’t do the work in the given time-frame.  I don’t wake up every morning planning to improve the future SAT scores of my 8th grade students; should I?  How will I know what is wrong if I can’t see this child’s work?  How will this child know what is wrong if they are not given the opportunity to “fall down”? What am I unintentionally teaching by providing or denying additional time?