Category Archives: Grading

Connecting Ideas, Grading, Reading, Reflection

I know something!

February 18, 2018 Jill Gough Leave a comment

A motley band of brothers traveling as a pack ambled in at 7:58 for Pre-Cal. Just in time. From a distance they are handsome and well dressed in coats and ties. Up close, they are a little disheveled, like they stepped out of their clothes last night and into them again this morning. My favorite part is the peacock-ness of their hair. They slept hard, and it shows. It helps me remember how young they are when they look so grown up. I wonder how many of them brushed their teeth and decided not to go there.

They live together, play together, and learn together. Boarding school builds family and familiarity and deepens connectedness. Yesterday’s test results require a preface. I prep them by explaining what I learned about them and what we need to do now. Learning is our focus, and this moment in time tells us that we need to do more, go deeper, and practice harder. This milestone marker says that we need to back up and try again.

“I made a 42!” he exclaimed with genuine jubilation. It’s what he said next that confirmed his glee. “I know something!”

“I know something!”

I am in awe of what happens next. Every ~~man~~, ~~child~~, ~~boy~~ learner, in their coats and ties, stands and high-fives him as if he as won a gold medal, sunk the winning shot, made the field goal in the final 30 seconds.

And then, just as quickly as it started, they were all seated as he said “Bring it, Ms. Gough. What do we do now?”

Group culture is one of the most powerful forces on the planet. We sense its presence inside successful businesses, championship teams, and thriving families, and we sense when it’s absent or toxic. (Coyle, xvii pag.)

Culture is a set of living relationships working toward a shared goal. It’s not something you are. It’s something you do. (Coyle, xx pag.)

Live, learn, work, and serve in a community that highlights what is going well. Focus on learning. Build living relationships. Work toward shared goals.

CULTURE: from the Latin cultus, which means care.

Coyle, Daniel. The Culture Code: The Secrets of Highly Successful Groups. Random House Publishing Group. Kindle Edition.

Assessment, Connecting Ideas, Creativity, Grading, Learning, Questions

Could it be as simple as adding rather than subtracting? (TBT Remix)

October 1, 2015 Jill Gough Leave a comment

I prefer to think of myself as their coach. “I coach kids to learn algebra” says that I am dedicated to my kids. “I teach 8th grade algebra” indicates that my dedication may be to the content. Being their coach does not make me less of an evaluator. Their athletic coaches evaluate them all the time. The coach decides which kids make the team and which kids are cut. The coach decides who starts and who rides the bench. The coach decides how much playing time, if any, each player has.

There are some things I just have to do as their teacher. Yes, I mean grading. (Remember, our grade books are sparse; we have very few grades. We assess quite often; we grade little.) We’ve just finished our semester exams. My team grades together in the same room using the same scoring guide. Prior to our exam day, we agreed on the questions as well as the solutions, predicted student errors, and completed the exercise of negotiating partial credit. Some say that is good enough; there is no reason to grade in the same room when everyone understands the scoring guide. Really? Would we say that there is no reason to play on the same court or field since everyone knows and agrees upon the plays? Don’t we expect the other team to have a plan of their own?

Are our learners the opponents in the exam process?
Are we trying to keep them from scoring?
Do they feel that we are?

Are we still considered their coach?
Are we trying to help them compete?
Do they feel that we are?

How are we thinking about scoring items on the summative assessment? Do our scoring guides assign points for good work or do they document how we will subtract points for errors? Are we grading in team? Do we take our issues to our teammates or our table-leader when we have a question about work that is out of the norm or unexpected? (Or, is the amount of partial credit awarded based on how nice, sweet, cooperative, participative -or not – a child is? YIKES!)

Could we alter everyone’s mindset about this stressful event by changing our approach and attitude about how we mark, score, and grade each item? What if we add points for what is done well instead of subtracting points when an error occurs? Could our scoring guides be more about assigning credit and less about docking points? What if we chose to add points for bright spots in the work instead of appearing to play “gotcha” by subtracting points? Would our grades be closer to representing a true score of what has been learned?

How would a learner respond if we handed them a paper that was filled with +4, +2, +3 and so on rather than -2, -4, -3?

Let’s try adding up the good things we find
rather than playing “gotcha”
by subtracting when an error is found.

Could the self-reflection prompts during the exam analysis process, similar to the post-game film analysis, ask the learner to identify why they earned the points that were scored? Could we get them to write about what they did well? Could they work in team to identify what others did well that they wish they had done too? Could they work in team to identify what others did that they find different or unusual and explain why it worked? Would this process motivate them to improve their understanding and help each other learn?

Would this help us all learn to blend the 4C’s (critical thinking and problem solving; communication, collaboration; and creativity and innovation) with the 3R’s?

Can we use this type of process to add to our learning? Could it be as simple as adding rather than subtracting? Are we willing to experiment?

Could it be as simple as adding rather than subtracting? was originally posted on December 23, 2010.

Assessment, Grading, Questions, Reflection

Grading and feedback: what we do matters

September 21, 2015 Jill Gough Leave a comment

Thinking about feedback and marking papers… How should we mark our learners’ work? Do we offer the opportunity to learn through mistakes and corrections?

And, I wonder if we are unintentionally incorrectly using ratios and proportional reasoning when we then put a score on the paper.

Consider the following student’s work from a recent assessment.

math2

Do you see the error? Is it a big error? Does this young learner understand the task and how to solve it? What feedback should this learner receive?

This child was told that there was a multiplication error in the work. Do you agree? Is it a matter of close reading on the teacher’s part? What feedback do we hope for to accompany the arrows shown below?

math1

What if we exercise the art of questioning in our feedback? Compare What if you think about what happened here? to You have a multiplication error here. Which feedback will cause more action?

The score for this question was marked as 3.5/4. Losing 1/2 point for this error seems reasonable. Would losing 12.5 points also seem reasonable?

If we scale this out of 100 rather than 4, that 1/2 point become 12.5 points. Is that what we intend to do, and is it the message that we want to send?

Now, as it happened, this was a 4 question assessment. This young learner’s questions were marked 4/4, 4/4, 3/4, and 3.5/4. In question 4, there was the addition error described above. In question 3, the learner multiplied in the first step when division should have been used. All of these points seem reasonable as long as the items each garner 4 points. However, proportionally scaled up to 100 points, the 1-point error is now a 25 point error.

How might we rethink grading and scaling? What does research tell us about translating scores between scales?

If learning is our focus and results guide our decisions, what steps do we take now?

And, how are these results guiding the decisions of our young learners?

Assessment, Grading, Learning, Questions

Being Slow…Mindset…2nd Chances…Learning (TBT Remix)

January 15, 2015 Jill Gough Leave a comment

Rule Three from The Talent Code by Daniel Coyle is SLOW IT DOWN.

“Why does slowing down work so well? The myelin model offers two reasons. First, going slow allows you to attend more closely to errors, creating a higher degree of precision with each firing – and when it comes to growing myelin, precision is everything. As football coach Tom Martinez likes to say ‘It’s not how fast you can do it. It’s how slowly you can do it correctly.’ Second, going slow helps the practitioner to develop something even more important: a working perception of the skill’s internal blueprint – the shape and rhythm of the interlocking skill circuits.” (p. 85)

We still take a lot of heat from our colleagues about 2nd chance tests. It makes many people, teachers and parents, uncomfortable.

About our version of 2^nd 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 specifications 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 2^nd 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 2^nd Chance test.
Yes, it is completely possible to bomb the first test and end up with a 100 in my grade book.

My assumption is that this discomfort comes from how non-traditional – radical – this concept comes across. Just because it is different does not make it a bad idea, does it? The discomfort comes from gut-reaction or theory rather than practice. Shouldn’t you try it? What do learners say?

Here’s what some of my learners say.

“If you give your best effort the first time around, you will have learned more in the process and the second time around will be less stressful therefore making the hard work the first time more rewarding. I think that the second chance test is a very valuable learning technique. Even after that unit is complete, it shows you where you need to improve before you start building on those concepts. So far this year, I have seen great improvement in my learning from my previous years in math. This year it has all started clicking, and I am excited about the new units to come.”
~CM

“Before we jump into a new chapter, our class usually takes a formative assessment to tell us where we are and what we know before we actually start learning from Mrs. Gough. I take these seriously because I think they really do help. If I can see where I am in the beginning and then where I am in the end, I can see how much I’ve learned and accomplished.”
~ MC

In Mindset, Dr. Carol Dweck writes

“When people believe their basic qualities can be developed, failures may still hurt, but failures don’t define them. And if abilities can be expanded – if change and growth are possible – then there are still many paths to success.” (p. 39)

Feedback a la positivity – examples

December 30, 2013 Jill Gough 5 Comments

A colleague messaged me privately concerning the “positivity trip” I’m on in my posts. While I don’t care for the word used, I’ll quote the question.

There you go again, Jill. I’m gonna ask one more time. Aren’t you concerned about positivity and wussification of our students?

That’s not what I’m writing, talking, and thinking about. I want to be better – intentional – about offering specific, actionable feedback. The more I use and practice with I like…because…, I wonder…, and What if… the more favorable the responses are.

I also wonder if we have a “no news is good news” attitude when marking papers. If we did a little data mining on the most recent set of graded papers or feedback comments, would we see descriptive positive comments? Or, it is habit to mark what is wrong or needs improvement? Do learners look at the whole of the assessment, or do they look for marks and comments? What is the positivity ratio of what they find?

Constantly scanning the world for the negative comes with a great cost. It undercuts our creativity, raises our stress levels, and lowers our motivation and ability to accomplish goals. (Achor, 91 pag.)

So, I’m curious… Is there anything wussifying <ick!> about the following feedback?

Example 1: Algebra I – I can evaluate an expression involving exponents that are integers.

CL,

I like that you showed your work and thinking, because I can see that you do understand negative exponents. Questions 9 and 12 show that you have a solid understanding when asked to evaluate a negative exponent.
I like that your work in Question 10 is clear enough to show that you correctly evaluated the negative exponent. I wondered if you had trouble with fractions until I read your work in Questions 11 and 12. Nice corrections, by the way. I like that you can see what you thought initially and what you now think, because it will help you when you review.
I wonder if you understand Question 11 even now. What if we meet for a few minutes to discuss your understanding of complex fractions and why a number raised to the zero power equals one?

Example 2: Leading Learners to Level Up formative assessment

DD,

I like that Level 4 challenges learners to convert between different forms of a linear equation, because this will help with symbolic manipulation that is so important in 9th grade physics.

I wonder if the language will confuse learners. As you can see from my work, I did not answer the question as you intended. I read intercept form and used the slope-intercept form. What if we ask for the equation written in two-intercept form? I wonder if the additional language will offer learners clarity.

Example 3: New Ask, Don’t Tell Art of Questioning document for Algebra II.

<Sam> What do you think?

<Jill>

I like it, because it is clear why each form has advantages, and that knowing all 3 forms is helpful. I like it, because it is easy, using the slider bar, to navigate between the three forms.
I like that it is easy to see that the value of a is constant no matter the form. I wonder how learners identify patterns in forms of hypotheses and then check. I wonder if they will struggle with writing their hypotheses in words.
I wonder why the manipulatable points are so large. I wonder why the user-added font is larger than the font of scale and values of the graphing window.
I like that the value of a changes in fraction increments and that the functions are displayed with fraction coefficients rather than
decimals. I wonder if learners will notice and document the pattern of the fractional coefficients when moving an x-intercept.
I like that a double root is possible. I wonder if learners will adjust the window to have the y-intercept in the graphing view. I wonder if learners will know to adjust and reset the viewing window.
What if the axis of symmetry is added to the graph? I wonder if it would help or distract.
What if the background of the graphing window is graph paper? Would it help the visual process to be able to count?

<Sam> Thanks for the feedback. Incorporated a few changes.. Font size is what it is.

<Jill>

I like the addition of the words: vertex form, factored form, standard form, because it provides clarity. I wonder – I think – that it will offer learners language to document patterns and hypotheses in words.

What if we practice taking the time to offer positive, descriptive, and growth-oriented feedback? How might we change outlook, efficacy, and attitude? How might we learn to spot patterns of possibility?

_________________________

Achor, Shawn (2010-09-14). The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work (Kindle Locations 1351-1353). Crown Publishing Group. Kindle Edition.

Algebra, Assessment, Connecting Ideas, Grading, Information Age Learning, Learning, Presentations

#MICON13: Leading Learners to Level Up – or Ask; Don’t Tell

June 12, 2013 Jill Gough 3 Comments

How might we design assessments that teach, support questioning, and motivate learning? How might we bright spot or highlight what learners know rather than what they do not know? What if we design and transform assessments, non-graded assessments, to offer learners a path to “level up” in their learning?

#MICON13: Leading Learners to Level Up – or Ask; Don’t Tell

“Questions are the way points on the path of wisdom.” ~ Grant Lichtman. This session will focus on the art of questioning as a formative assessment tool. Work on becoming a falconer…leading your learners to level up through questions rather than lectures. Come prepared to develop formative assessment strategies and documents to share with learners to help them calibrate their understanding and decode their struggles. Be prepared to share your assessments with others for feedback and suggestions.

Foundational ideas:

By learning to insert feedback loops into our thought, questioning, and decision-making process, we increase the chance of staying on our desired path. Or, if the path needs to be modified, our midcourse corrections become less dramatic and disruptive. (Lichtman, 49 pag.)

But there are many more subtle barriers to communication as well, and if we cannot, or do not chose to overcome these barriers, we will encounter life decisions and try to solve problems and do a lot of falconing all by ourselves with little, if any, success. Even in the briefest of communications, people develop and share common models that allow them to communicate effectively. If you don’t share the model, you can’t communicate. If you can’t communicate, you can’t teach, learn, lead, or follow. (Lichtman, 32 pag.)

If we want to support students in learning, and we believe that learning is a product of thinking, then we need to be clear about what we are trying to support. (Ritchhart, Church, and Morrison, 5 pag.)

In order to engage in high-quality assessment, teachers need to first identify specific learning targets and then to know whether the targets are asking students to demonstrate their knowledge, reasoning skills, performance skills, or ability to create a quality product. The teacher must also understand what it will take for students to become masters of the learning targets. It is not enough that the teacher knows where students are headed; the students must also know where they are headed, and both the teacher and the students must be moving in the same direction. (Conzemius and O’Neill, 66 pag.)

If you are a teacher in a district with conventional report cards, you can still use the two grading principles that honor the commitment to learning: (1) assign grades that reflect student achievement of intended learning outcomes, and (2) adopt grading policies that support and motivate student effort and learning. You can do this by clearly communicating your ‘standards’ (in the sense of expectations for work quality) to students and grading on that basis. (Brookhart, 23 pag.)

The idea of using formative assessment for practice work and not taking a summative grade until students have had the opportunity to learn the knowledge and skills for which you are holding them accountable can be applied directly to your classroom assessments in a traditional grading context. (Brookhart, 24 pag.)

We want more students to experience the burst of energy that comes from asking questions that lead to making new connections, feel a greater sense of urgency to seek answers to questions on their own, and reap the satisfaction of actually understanding more deeply the subject matter as a result of the questions they asked. (Rothstein and Santana, 151 pag.)

The excitement of learning, the compelling personal drive to take one more step on the path towards wisdom, comes when we try to solve a problem we want to solve, when we want to solve, when we see a challenge and say yes, I can meet it. Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level. Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)

Session structure (120 minutes):

15 mins Introductions – who we are, what if we explore and prototype
15 mins Ignite (ish) and challenge
30 mins Ideation and prototype 1
15 mins Small group feedback with Q&A
20 mins Prototype 2 refined from feedback
20 mins Share session
05 mins Wrap up and conclusions

Examples of works in progress:

Computational fluency: Negative Exponents (Algebra I)
SMART GOAL rubric
PLC rubrics
Injustice Project Reflection from Philip Cummings (rubric)

_________________________

Resources cited:

Brookhart, Susan M. Grading and Learning: Practices That Support Student Achievement. Bloomington, IN: Solution Tree, 2011. Print

Conzemius, Anne; O’Neill, Jan. The Power of SMART Goals: Using Goals to Improve Student Learning. Bloomington, IN: Solution Tree, 2006. Print.

Lichtman, Grant, and Sunzi. The Falconer: What We Wish We Had Learned in School. New York: IUniverse, 2008. Print.

Ritchhart, Ron, Mark Church, and Karin Morrison. Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. San Francisco, CA: Jossey-Bass, 2011. Print.

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

Conferences, Grading, Information Age Learning, Math-Science Connections, Social Media

PBL Field Guide: Who forms your learning team?

November 13, 2011 Jill Gough 1 Comment

The Professional Learning Communities reflection in Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age challenges the reader to model collaborative learning, learn and share, and develop learning teams. This is right in line with our Learning for Life vision statement, NET•S, and NET•T.

Three of the essential actions called for in our Learning for Life vision statement are

Problems that require critical thinking, creativity, and collaboration
(Problem-based/Project-based learning)
Teachers in teams supporting learning and innovation
(PLC/Critical Friends Circles)
Content and Relationships that connect us to the larger world and the world to us (Global Citizenship)

Bo Adams (@boadams1, It’s About Learning) and I co-direct our Professional Learning Communities (PLCs). Our school makes a commitment to adult learning and collaboration by affording teachers job-embedded time to work and learn together. For a glimpse into our PLCs, see Pull Together, Part II from It’s About Learning and Learning as a Team – A Big PLC Brightspot from my blog.

From Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age:

Professional learning can certainly support your shift to project-based instruction, but the fundamental program changes you make will require frequent and intentional collaboration with your colleagues. [p. 31]

In Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age, Carmel Crane describes her process when getting ready to launch a project with her students.

Before [introducing] the project to students, I presented it to about 10 teachers. I laid out all the planning details, and they gave me critical feedback. It was a great opportunity to see things I may have overlooked.

Other teachers could see how we might work together on future projects to reach our shared goals. [p. 31]

On Friday, the 4^th Period Math-Science PLC took another step toward PBL and Lesson Study by participating in the Eggs Over Easy project that our Science 8 team is planning for the Monday-Tuesday prior to our Thanksgiving break.

In the 55-minute period, we assembled our carriers, did the drops, and debriefed the lesson. There is more video coming about the debriefing session. Our plan for Monday is to “do the math” and the reflection questions concerning potential and kinetic energy. But, the lead teacher for Algebra I has already asked how we can support this lesson in our Algebra classes – another step in integrated studies. Woohoo!

Again from Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age:

A project-based learning collaboration among students is a lot like a professional learning community among teachers. For both, the learning is relevant and rigorous, and the “students” learn to learn together. [p. 32]

Bo and I co-facilitate Synergy 8, a non-departmentalized, non-graded, transdisciplinary, community-issues-problem-solving course for 8^th graders. A new school policy about student images on faculty blogs prevents me from showing you how closely the work of our Synergy team matches up with our PLC teacher teams. [If you want to know more about #Synergy, then you can search that category/tag on either of our blogs.]

Paraphrasing Professional Learning Communities at Work: Best practices for enhancing student achievement: PBL delivered by a high-functioning PLC of teachers can be the “engine of improvement” that drives a school forward.

Once again from Reinventing Project-Based Learning: Your Field Guide to Real-World Projects in the Digital Age:

Anne Davis, an advocate for blogging with elementary students, suggests using your personal blog as a tool for making connections with like-minded colleagues. A team of two is better than no team at all, but image the compounding effect of a large team, an entire faculty, or an international community of colleagues. [p. 33]

If you could assemble your “dream-team,” with whom would you collaborate for PBL? How and with whom do you learn, reflect, and share? How do you create opportunities for your learners to build their “dream-team” to learn, reflect, and share? How do we leverage technology to engage with our learning teams?

Assessment, Grading, Learning, Questions

Translating Rubric Scores When You Have To…

October 16, 2011 Jill Gough 4 Comments

I work and learn with several teams using rubrics to promote learning and growth. We have been working to translate our 4-point rubric scores to the 100-point scale required by our school.

It is that time of year. We want to report our learners’ progress to their parents, Grade Chairs, and other important members of their learning teams. While we understand the 4-point rubric score and what it means in terms of a child’s learning and growth, we feel that it is necessary to report their progress in more traditional terms.

We know that a single number can never represent the unique progress and learning of a child. We include a written comment with this number to provide additional information and evidence of learning. See the following blog posts for more information about these comments.

Why I Do What I Do…
Quantum Progress, October 15, 2011
Testing out some verbiage on quarter grades
Quantum Progress, October 15, 2011
Grade Reporting: To comment or not to comment…that is the question!
Experiments in Learning by Doing, December 31, 2010

But, for now…We must have that single number.

We have worked together to develop a plan. We started by studying Classroom Assessment & Grading that Work and Transforming Classroom Grading by Robert J. Marzano. As a team, we have analyzed student work to calibrate our understanding of the rubric and how we score student work.

In Transforming Classroom Grading we read and studied Chapter 5. Assigning Final Topic Scores and Computing Grades and Appendix D: The Power Law Formula.

We investigated the following conversions by scoring student work and then analyzing the following scales to determine which scale most closely aligns with the team’s thinking about a score out of 100 points.

We looked at this data graphically. We wanted to see how a power function looked on the data.

Looking at Scale 1…
4 translates to 100, 3 translates to 90, 2 translates to 75, and 1 translates to 60.

It appears that a power function would fit the data.

It appears that this power function would over estimate the team’s rubric score of 2 when converted to the 100-point scale. Would there be another function that might fit better? Should we adjust the translations? We tried another type of function.

This is the same data – no adjustment in the translation – but we used a logistic model rather than a power function. Interesting, huh?

Looking at Scale 2…
4 translates to 100, 3 translates to 90, 2 translates to 75, and 1 translates to 65.

Power Function:
Logistic Function:

Looking at Scale 3…
4 translates to 100, 3 translates to 88, 2 translates to 73, and 1 translates to 65.

Power Function:

Logistic Function:

Numerically, the logistic function more closely converts our 4-point rubric scores to our agreed upon 100-point scale translation than the power function.

You are welcome to make a copy of our 4-Point Conversion E-PLC or 4-Point Conversion S-PLT Google spreadsheet and investigate for yourself.

This is where we are today. We have decided which of these scales works for our teams. We have calibrated our understanding and use of our rubrics. We have investigated these conversion tables numerically, graphically, and analytically. We have agreed to use the same conversion table to represent our learners’ work and progress.

This is a work in progress. We would love to know how you translate your rubric scores to the 100-point scale.

Assessment, Grading, Learning, Questions

Being Slow…Mindset…2nd Chances…Learning

February 12, 2011 Jill Gough 9 Comments

On the drive to school yesterday morning AS (age 6) explained to me that she was the slowest in her class. It was very matter of fact. “I am the slowest in class, Momma. I finish last every time. It takes me longer than everyone else.” With a very heavy heart, I explained that I thought it was okay to be last. Learning is not a race. Everyone learns in their own time. AS persisted “But, Momma, I am always last. I am slow.” I asked her why; why did she think she was slow? “I like to read what I write. It is fun, but it takes a long time. I like to look at it to figure out the words.”

Rule Three from The Talent Code by Daniel Coyle is SLOW IT DOWN.

“Why does slowing down work so well? The myelin model offers two reasons. First, going slow allows you to attend more closely to errors, creating a higher degree of precision with each firing – and when it comes to growing myelin, precision is everything. As football coach Tom Martinez likes to say ‘It’s not how fast you can do it. It’s how slowly you can do it correctly.’ Second, going slow helps the practitioner to develop something even more important: a working perception of the skill’s internal blueprint – the shape and rhythm of the interlocking skill circuits.” (p. 85)

We still take a lot of heat from our colleagues about 2^nd chance tests. It makes many people, teachers and parents, uncomfortable.

About our version of 2^nd 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 2^nd 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 2^nd Chance test.
Yes, it is completely possible to bomb the first test and end up with a 100 in my grade book.

Here’s what some of my learners say.

“If you give your best effort the first time around, you will have learned more in the process and the second time around will be less stressful therefore making the hard work the first time more rewarding. I think that the second chance test is a very valuable learning technique. Even after that unit is complete, it shows you where you need to improve before you start building on those concepts. So far this year, I have seen great improvement in my learning from my previous years in math. This year it has all started clicking, and I am excited about the new units to come.”
~CM

“Before we jump into a new chapter, our class usually takes a formative assessment to tell us where we are and what we know before we actually start learning from Mrs. Gough. I take these seriously because I think they really do help. If I can see where I am in the beginning and then where I am in the end, I can see how much I’ve learned and accomplished.”
~ MC

In Mindset, Dr. Carol Dweck writes

“When people believe their basic qualities can be developed, failures may still hurt, but failures don’t define them. And if abilities can be expanded – if change and growth are possible – then there are still many paths to success.” (p. 39)

Learning from Leveling, Self-Assessment, and Formative Assessment

January 13, 2011 Jill Gough 11 Comments

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.

View this document on Scribd

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.

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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.