Rethinking Grading: Ch. 5

Chapter 5: How to Reform Grading: Making Change Happen
Cathy Vatterott

Changes need not be grandiose to have a huge effect on student learning or to improve the accuracy and validity of student grades.

We must decide what we believe about the purpose of grading.

If they believe the purpose of grading is to accurately reflect achievement, then it becomes inconsistent to punish behaviors such as cheating, tardiness, or attendance with grades.

If an individual teacher believes the purpose of grading is to reflect academic achievement only, they could begin by removing nonacademic behaviors from the grade, by no longer grading practice work, and by giving more ungraded formative feedback.

When we agree on purpose, methods follow purpose.

Lesson learned:
One. Start small.
Two. Let it grow.
"Teachers need time to grieve the loss of what they thought was right."
Three. Include all stakeholders.
Four. Create a belief statement or guiding principles.
five. Have a comprehensive communication plan.
Six. Make students and teachers your allies.

When implementation is top-down with no teacher by-in, there's often a limited understanding of the changes and no commitment to the mission. Teachers notoriously find ways around policies they had nothing to do with creating.

Rethinking Grading: Ch. 4

Chapter 4: What, How, and When to Grade
Cathy Vatterott

Pre-tests set the stage, shave instruction for all, and guide individual learning. After the pre--testing process, formative assessment provides feedback to students while they are still learning; summative assessment shows the level of mastery at the end of the learning cycle.

Most teachers of you and formal feedback and formative assessment as two different things. It's easier to think of formative assessment as structured tasks designed by the teacher, results of which may be marked or documented in some fashion, so students and parents can have a record of the students progress toward the learning targets.

Feedback is a two-way recurring conversation between teacher and student.

For teachers to be able to give feedback to students, it is necessary to limit direct instruction enter create activity-based lessons.

All feedback does not have to come from the teacher; peer feedback can also be useful.

As we get targeted feedback to individual student and as they are empowered to learn in their own way, the differences in learners become smaller.

If, after repeated attempts, a student or group of students has failed to master a learning target we must take a fearless inventory of our instructional process and ask yourself these questions;
What's their level of learning properly diagnosed with pretesting?
What's the feedback about learning timely specific and helpful?
Did our differentiation move the student or group of students forward?

Using the result of a pre-test, feedback, or formative or summative assessment, teachers can identify patterns in the students work or clusters of student need. Students can then be organized into two or more groups for ungraded group learning the activities at each table are based on the errors that students made on the form of assessment.

In a purely standards-based grading system, only summative assessment counts in the final grade.

Typically formative assessments are evaluated and descriptive feedback is given to the learner, such as with practice tests.

Ungraded practice tests are especially beneficial to learn as they Activate "retrieval learning" and strengthen the connections in the brain.

One technique for practice test is called "find it and fix it." Rather than marking the answers that are incorrect, the teacher notes to the student, "five of these are incorrect; find them and fix them". This requires a student to reengage with the questions and precipitates a lot of learning.

Mastery checks: these assessments are written using three levels: green, yellow, and red. The green level questions are basic skill problems and didn't really require only one or two steps to solve. Yellow level questions require multiple steps and or multiple ideas to solve. The red level questions are generally questions of the students have never seen before, requiring them to go beyond knowledge they have obtained and\or apply the knowledge to a new situation. Students are expected to attend all three levels of questions. Their answers help the teacher to determine the students his level of mastery.

The current consensus is that homework should be formative assessment the checks for understanding or that helps prepare students for summative assessments. Therefore, and I truly standards-based system, homework should not be graded. Standards-based policies usually state that homework will be reviewed and feedback will be given, but not counted in the grade.

The final achievement of learning is more important than the steps it took to get there.

Formative assessment is assessment for learning and occurs when there is still time to improve. Summative assessments are assessment of learning that occur the end of a predetermined learning cycle, after learning has taken place.

How in assessment is used is what determines whether it is formative or summative.

Students who eventually achieve mastery should not be penalized for earlier struggles.

The most recent evidence of learning is the most accurate and grades should be replaced by the most recent evidence.

Student should never be allowed to retest without showing additional evidence that they have mastered the concept that caused him to do poorly on the original assessment.

Remember that our goal is to minimize the number of retakes a student needs to show mastery.

We want to hoops to result in additional learning, not just for students to complete missing work.

Feedback is free help-there is no grade or Mark associated with feedback.

Formative assessments give students multiple opportunities to improve, free from the threat of grades while they are still learning, and summative assessments verify and report their learning progress.

Rethinking Grading: Ch. 3

Chapter 3: What Grading Looks Like in the Standards-Based Classroom
Cathy Vatterott

The standard show us the results that we want students to achieve. We then work backwards from those results to create more specific learning targets. We synthesize or unpack the standards into learning targets, usually written as "I can" or "We can" statements.

But when we organize individual targets into lesson-sized tasks, keeps them separately, and assess them separately, students may fail to see the relevance and connection. A better method is to group targets together so that several targets may be addressed by the same activity.

Self assessment is formative assessment-it should always focus on improving the students progress toward the learning target, not I'm getting a better grade.

Learning is not so much instruction or a lesson to be taught, as an activity to be experienced.

I never heard of a student not doing *his* work; it's *our* work he's not doing.

If we want to encourage students to view mistakes as a necessary step in learning, we need to remove the threat of grading while they are learning.

Grades are not necessary for learning, but feedback is. In fact, feedback has been shown to be one of the most effective strategies to improve learning.

Rethinking Grading: Ch. 2

Chapter 2: Why We Need a New Grading Paradigm
Cathy Vatterott

Treating all students the same resulted in a certain percentage of students who failed.

Instead of teach, test, and MoveOn and one large group, learning is a series of mastery's for individual students-teach, check for understanding, apply learning, get feedback, revise learning, and get more feedback until mastery is achieved.

Unlike the old paradigm of one-shot learning, a feedback loop exist that makes learning dynamic-feedback to the students informed their learning and teachers change instruction as they see what individual students need.

Within the traditional grading paradigm, it's not safe to make mistakes. In a traditional paradigm, failure is a judgment and a validation of her students lack of ability.

Learning is hard and frustrating, but ultimately achievable and satisfying. Mistakes are a natural part of learning and mistakes or something you do, not something you are. Lack of understanding is a puzzle to be solved-not a validation of stupidity.

As grades are used to punish behaviors, they overshadow the grades students receive for learning.

In the traditional grading paradigm, when teachers grade everything, the grade means nothing.

When first attempts, including practice, are graded and went all grades are permanent, students are penalized while they are still learning. Mistakes are permanently recorded and there is no redemption.

If you have a bad week practicing, you don't show up on Friday night with -5 on the scoreboard. The only way to win the game is to get better at the learning.

Rethinking Grading: Ch. 1

Chapter 1: The Culture of Grading
Cathy Vatterott

But teachers intervene-they teach with the goal of having all students learn. "If the distribution of student learning after teaching resembles a normal bell-shaped curve, that, too, shows the degree to which our intervention failed. It made no difference."

Belief #1: Good Teachers Give Bad Grades
As teachers, we bought into the idea that a bell curve indicated rigor and misinterpreted it to be a rule to follow. We came to believe that of success were scarce and great spell into a bell curve then we were tough teachers.

Grade inflation is the arrive from the belief that rigor equals a scarcity of high grades and that the purpose of grading is to sort and rank.

Rigor and difficulty was often equated to the amount of work done by students rather than the complexity and challenge of the work.

Such practices reinforce the belief that some students could not learn and perpetuated a system that not only allowed four but actually expected failure. In many ways, sorting and ranking practices institutionalized failure and conveniently of dissolved teachers of the responsibility for student failure.

Belief #2: Not Everyone Deserves an A

Many people feel strongly that grades reflect more than learning. We review grades as a package deal; to succeed, seras must have it all-academic achievement and moral virtues.

Belief #3: Grades Motivate Learners

The first misconception is that learning is only a means to an end-to escape punishment or get a reward, the learning has no intrinsic value, and that students would not be interested in learning for its own sake.

The second misconception is that a single entity called motivation exists, the students either have it or don't have it, and it can be manipulated by external forces.

The third misconception is that the most effective method is the use of rewards and or punishment and that grades are in effect the reward and or punishment for all students.

Our believes have led to an abuse of grades.

Students have come to believe that effort however week, not learning, earns them the A.

And our relentless pursuit of the almighty A and the perfect GPA, something got lost-learning.

Reality Check #1: NCLB

This was a foreign concept to teachers-we had never been expected to ensure that all students were proficient. We didn't know how to do that. We were not even sure that it was possible.

NCL be exposed a dirty little secret-graves don't equate with performance on standardized test.

Accountability for learning demands grades that are reflective of learning.

Reality Check #2: Grades Are Misleading About Succeeding

A puzzling example is that good grades in high school and students cheaper car insurance. Why-because good students are safer drivers or because good grades mean you are an accomplished rule-follower who will follow the rules of the road?

We thought that we were rewarding the right thing-completion of tasks, compliance, promptness. But in that process if we devalued mastery of deep conceptual learning, we have hampered students his future success. Maybe the grading practices that we thought were preparing students for the future really weren't.

Reality Check #3: The Common Core State Standards Changed Everything

Although standards and standardized test has supposedly driven instruction for years, we now see that we have been focusing too much on low-level rote learning.

Too often, we have neither allowed nor expected students to think. We have filled her head with facts and formulas and reward them for restarting it. We have done the analyzing, synthesizing, and evaluating instead of expecting our students to do it. We have done too much of the work of learning, perhaps because we didn't trust him to want to do the work, or perhaps because we weren't sure they were able to do the work.

To successfully navigate the standards, student grades will need to reflect mastery of skills, not memory of content.

Today we must prepare them for a world in which they must know how to take initiative, self-advocate, solve problems, be creative, and accomplish tasks without minute-to-minute supervision.

Quiz Retakes Formerly Known as SBG

If you've read my blog at all I'm sure you've already read something I complained wrote about SBG before.

This is my best idea yet.

For our first test in each of my classes, I allowed them to use their INB. But of course I didn't tell them this until the test started.

Some of my older students were used to me offering test retakes in former years...even though most of them never actually did them. So when they asked about it this year, I kinda felt like a butthole to say no.

Here's what I decided. They can retake quizzes as many times as they want, but no notebook. No retakes on tests, but they can use their notebook.

This has been like magic for me. Quizzes are much easier to make multiple versions of and much easier to grade. Which eliminates a lot of hassle for me. It's almost like every quiz is a formative. It shows them what they know and then they make an informed decision about their satisfaction with their knowledge.

I do it right during class which eliminates the need for students to come in on their own time and makes me feel less guilty about not having time to work with them.

It motivates studying because once they get their original quiz back, they look back in their notebook to see what they missed and why. I could never get them to do that before.

What I've seen is students asking for retakes that NEVER have in the past. Students asking why they got something wrong and arguing their thinking. Students who want to retake more than once. Students who failed a quiz improving their score to passing.  I call that perseverance.

For tests, I think letting students use their INB is more of a comfort to them than they realize. I know exactly what is in the notebook so I can choose to make my tests in whatever way I want for them to show me their knowledge. It also increases ownership of the notebooks.

I feel like tests are more a show of retention and application while quizzes are more skill based.  By students repeatedly retaking the skill based quizzes, I think they are more prepared for the application on a test.

The best of both worlds.

I do have to say that I'm not grading with a rubric which I feel guilty about but...baby steps.

Test Corrections

I've been doing SBG for a few years now but for me it only makes a difference in my grade book. Each year I have less than a handful of students who come in to retake any part of their test. It's more of an organizational tool for me than it is for the students. I don't know how to change this.

In reference to my last post on interventions, I'm thinking test corrections may be a better way for students to earn credit. I was reading through some of my old posts and found this link from @crstn85's blog. I like what she does a lot and I plan to use her idea and template.

There are some questions I'd like to pose to you. I've read about two different methods.

1. Test corrections earn back half of the points missed. 
2. Test corrections raise their grade to a 70% which is passing but not proficient.
   

• What if corrections are not correct? It seems like it would be easier to determine a grade using method 1. Or should I not accept them until they are correct?

• Are test corrections a way to show student learning? I'm working off this paragraph from an earlier blog post from a conference with Randy and Sue Pippen:

 "Their policy on grading was to make it count. Don't punish them for practicing. If I collect,  then they should have the opportunity to correct. They pointed out that the United States culture has taught kids as long as it's done, I'm done. Work is not done until it's correctly done. They did mention that they thought homework was important (which I am agreeing with less and less) but that it should be recorded and reported, not graded. They hit upon the fact that we all have students in our class who cannot do math. How did they get there? They have been passed along on their inflated grades thanks to homework completion and participation points. These types of grades are not informative. "  Would test corrections inflate grades too?

•  Would more students participate in this method rather than retakes? I like the idea of correcting our tests together as a class the first time so they know how the process works. But maybe if I would have done that with retakes, I would have had more participation. I like that this method can be done outside of class without me but then again they could just copy someone's test that got the problems correct. I could avoid that by keeping all the tests but that requires more of my space and time.
  
  
• Would this method motivate students to do work correctly the first time? I'm thinking if I required test corrections from students who did not pass, it might help them try harder the first time since I'm sure they will hate writing explanations. On the other hand, they might try less because they know they have a second chance. But the second chance is for only half the points.
  

• How would test corrections increase learning? One way is being able to analyze your own work and identify errors. A second way is being able to communicate those errors in writing. A third way would be redoing the problem a second time. But if they still redo it incorrectly, will that have more of a negative impact?

 

SBG + Holistic Rubric

Update: Check out my Star Wars Holistic SBG Rubric.

Sbg is coming together more and more for me.

My latest hang up was on how to grade, how to label grades, and how to calculate a percentage.

After tweeting with @druinok and @bowmanimal, here is what I've come up with. I will have four levels that are simply defined. Students will receive a level rather than a number, along with specific feedback. No numbers. Yet.

When it comes time to calculate a grade in the grade book, each level will convert to a percentage. Then I will average them all together.

Here is a student/teacher/parent/admin friendly picture of my holistic rubric.

The red is what I would think about while grading. The black is what students would be thinking while learning. Master and Expert are kind of confusing and I don't love Practitioner. I really like novice though. But these just sit better with me than Advanced, Proficient, Developing, Below Mastery, etc. Do you have any other suggestions? @mathtastrophe suggested Padawan, Jedi Knight, Jedi Master, and Jedi Grand Master. Maybe I do need something more teenager appropriate... Ninjas and unicorns anyone?

I posted the numerical scores on this so that I wouldn't forget them. Not sure if I should post them for everyone to see right away.

Here is my question. How would I go about communicating this? I want to get away from numbers on assessments and focus more on feedback. Obviously more descriptive feedback that just a level but still. Do I give students a copy of this with numbers on it? Then, aren't they still working for a percentage rather than learning? Do I wait until midterms and the end of quarter to put actual numbers in the grade book? That might be a nightmare and ignores students who want to constantly know their grade. But if I immediately convert the level to a grade, what is the point of the levels? I might as well go ahead and just call them percentages.

This is the last thing that is really nagging at me.  I don't want to be deceptive about how I'm calculating a grade. But it seems like if you tell them then it just loses some of it's meaning...or something.

So my two questions: What can I name my levels? When/how do I convert words to numbers?

10 Steps to SBG

After a long and involved Twitter chat last night, I think I've come up with my skeleton outline for how I want to do stands-based grading. Here are my 10 steps.

1. Write your concept list/pacing guide (aligned to whatever) and determine your priorities.
2. Write assessments for each standard separately (3-5 questions per standard).
3. Write extra questions that can be used for reassessments.
4. Teach; give assessments and grade (give specific feedback!).
5. Mark students’ proficiency on each standard individually in the grade book.
6. Offer students the opportunity for reassessment.
7. Require students who want to reassess to fill out reassessment form.
8. Give students a specific day when they can reassess and require them to inform you ahead of time.
9. Give reassessment.
10. Grade by giving feedback; change old grade for that standard to the new grade from the reassessment.

Here is my thinking. I will give reassessments every Thursday and require the reassessment form to be turned in on the previous Tuesday. This gives me all day Tuesday and Wednesday to check the links and revisions as well as prepare the reassessment. I don't want students to think they can write crap down and I will let it fly. Also, I chose those days because we are rarely out of school or have an early dismissal on a Tuesday or Thursday.

As for the form, I'm aware that students might just find a link without actually watching the video or reading the example. I'm also aware that they might just copy someone's problems for their revisions. But I'm thinking this is a way to teach that you don't get something for nothing and that you have to put forth effort to attain success. Even if they put forth a lame effort, then that can be a teachable moment. Lame effort doesn't lead to success.

When I (poorly) attempted sbg before, I surveyed my students at the end of the year to ask why they didn't come in to reassess. The answers that stuck with me the most were that students didn't know when to come in, if they did come in they didn't know what they were expected to do, and they figured if they didn't know how to do it the first time then how would taking it again help?

I hope that this plan will help solve those problems.

What else? Oh, I figure I will put graph paper on the back of the paper for questions that pertain to graphing. Did the form seem clear and easy to understand? Of course I will explain it all but I hope to have a pile in the classroom that students can grab and fill out at any time. I think (hope) this form will hold me accountable for giving specific feedback. How can students make corrections without it?

I'm finishing up my Algebra II pacing guide and then I will start writing assessments. I have the Kuta software so I think that will help when it comes to reassessments. I can click a button and all the numbers change. Yay. But there are definitely things Kuta doesn't offer that I will have to write myself. That's my biggest challenge for the moment.

Let's talk about grading for a second, shall we? I really liked the idea @mwmathews mentioned about using words rather than numbers. He mentioned Novice, Apprentice, Practitioner, and Expert. I'm thinking I want to use novice, apprentice, expert, and master. The difference between expert and master to me is that the expert is successful with that specific content but that the master is successful with learning and applying that content. That along with specific feedback seems like it could be really helpful.

Here is where I have two ideas. One is to convert the words to percentages for the grade book. Novice = D, Practitioner = C, Expert = B, Master = A. But then we are still averaging and I don't know how I feel about that.

Two is to calculate the percentage by dividing the number of standards labeled master/expert by the number of standards taught. But then what about a student who gets practitioner every time? He/she would normally be a C student but I wouldn't be counting those at all. What then?

Can you help me think of pros and cons for these methods? I'm really leaning toward the second one because it just seems more fair. Although, I'm not sure how that would work with my online grade book. That may limit me to the first method. What do you think?

A few other teachers mentioned that they grade holistically. I'm not sure how that would work since my brain is soooo analytical. Can you make a generic holistic rubric that works for any content?

My homework was to take my chapter 1 test and cut it apart, sorting into piles by standard. I don't know if I will actually do that yet. I would rather just start over- I like a clean start. But maybe I will work on a holistic rubric instead.

;)

SBG Exemplar and Rubric

I hate the new Blogger interface. It deleted my post that was supposed to be a draft and then published it so that only a title showed up. Boo. Luckily I can still revert to the old Blogger interface. If you clicked through to this before and saw nothing, my apologies.

After my SBG brainstorm post, I really started to zero in on what kind of rubric I want to create. The main thing I want my rubric to do is to easily show anyone who looks at it (parent, student, teacher, administrator) exactly what the student has done right and exactly what the student has done wrong. I want my rubric to give clear feedback and possibly even cues or questions that instruct students on what to do next.

Is this even possible? I think the thing that has been holding me back is that I thought I could create a rubric that would work for everything (ala a writing rubric, a team work rubric, etc). But that is just not true. I'm looking for different skills for each concept I teach and so the rubric must be adjusted accordingly. Another hint that I must do backwards design: I have to clearly outline the outcomes I want students to achieve (a key concepts list), the method I will use to determine if they learned it (the performance event), and the method of communicating to students if they were successful (the rubric).

Another thought that has held me back is thinking that I should be able to look at a student's grade and immediately know where they went wrong without looking at the rubric. I know, I know that makes no sense. But it kinda does. If you create a rubric like I've seen elsewhere, such as

• 4- Performs skill with no errors. 
• 3- Perform skill with minimal errors
• 2- Performs skill with major errors
• 1- Cannot perform skill

then technically, you could know how much a student messed up, but not at what exact point. So my new idea is actually better than the idea I was trying to live up to! Twisted.

I really liked Lizzy's comment about giving students one point for different steps in the process like the AP world does on a regular basis, Kristin's comment about giving students a basic, proficient, and advanced problem, and Adam's comment about having students use rubrics to make test corrections.

I'm going to combine these ideas into a giant megamind idea!

My exemplar will continue to be on system of inequalities and will now be accompanied with pictures.

Here we go:

#1 Basic

#1 is the most basic problem. Students would be graded as follows:

• Graphing inequality 1 with correct slope and y-intercept (2 points)
• Graphing inequality 2 with correct slope and y-intercept (2 points)
• Determining if inequality 1 is solid or dotted (1 point)
• Determining if inequality 2 is solid or dotted (1 point)
• Plugging in test point for inequality 1 (1 point)
• Plugging in test point for inequality 2 (1 point)
• Shading in the correct direction for inequality 1 (1 point)
• Shading in the correct direction for inequality 2 (1 point)
• Stating an ordered pair from the solution set (1 point)

These are the most basic skills to solving systems of inequalities. #1 is worth a total of 11 points.

Moving on to problem #2:

#2 Proficient

The only difference in this proficient problem is that now the inequalities are in standard form and must be put into slope-intercept form. Grading as follows:

• Solving inequality 1 with correct slope and y-intercept (2 points)
• Solving inequality 2 with correct slope and y-intercept (2 points) 

#2 is worth a total of 4 points. Students will only be graded on the new part of the problem because they have already completed the basic skills on #1. Students won't know this and won't know that I'm only grading part of it. This prevents students from doing the bare minimum.

On to #3:

#3 Advanced

The new skill in the advanced problem is that the student must write the system of inequalities from a word problem. Grading:

• Writing inequality 1 with correct slope, y-intercept, and inequality sign (3 points)
• Writing inequality 2 with correct slope, y-intercept, and inequality sign (3 points) 

Students will then have to solve (like they already did on #2), then graph (like they already did on #1.) Problem #3 is worth a total of 6 points.

The entire performance event would be worth 21 points.

Students would receive a rubric at the beginning of the unit to monitor their progress along the way and to give feedback. They would check off skills as they learn them and write the date. I could use this rubric to grade quizzes along the way, using the bottom section for specific feedback. Then I would use the same rubric to grade their performance event at the end of the unit. 

Rubric:

Rubric

Does this seem clear and easy to understand?

Do the grade ranges seem fair? For example, a proficient student scoring 12 out of 21 points would receive a B on my rubric but normally a 12 out of 21 would be a 57%. That feels crazy. Am I totally missing the mark here?

I actually did grade this way, I just didn't give students a rubric. The assessment really was worth 21 points and I really did just give percentage grades like the aforementioned. The difference is that I would now be clearly communicating what I expect students to be able to do and clearly communicating how I am assessing those abilities. The grade is the only thing that is throwing me off. Am I out in left field here?

SBG Brainstorm

Next year is my last year of having an instructional coach so I really want to get all of my big ideas out there on the table by next year so that I have some kind of help and guidance when things go wrong.

I am always thinking about SBG and how I can make it work. I re-read my last post on SBG, which was almost a year ago. I think that might now be possible. My math teacher counterpart is leaving after this year and I'm thinking the administration might consider hiring the current student teacher. If so, it will be their first year and so far they seem really...'moldable'. And I think any first year teacher would love to have another teacher give them resources, ideas, and collaboration. If this is true, we might be on the same page with SBG and so on!

Anyway, my brainstorm is this. My number one struggle with SBG has been not assessing everything I teach. In my mind, I feel like if I'm teaching it, why wouldn't I assess it? Now I'm thinking that I just need to cluster. Concepts build on top of each other toward an ultimate goal. If I only assess that ultimate goal, then it requires knowing the concepts that build up to that goal without assessing every little thing individually. I would call this ultimate goal a performance event and use a rubric idea to grade it. A perfect score would be getting every skill correct. Otherwise, each skill would move you one step higher on the rubric.

Here's my example based on a mini-unit of solving systems of linear inequalities. The ultimate goal of the unit would be to graph a system of inequalities from a word problem.

Skill 1: Write a system of inequalities from a word problem.
Skill 2: Solve each inequality for slope-intercept form.
Skill 3: Graph both lines of the system (dotted or solid).
Skill 4: Plug in a test point and shade.
Skill 5. Choose an ordered pair from the solution set.

To earn a 5 for the ultimate goal, they would have to correctly complete skills 1-5. If they could only do 1 and 2, their score would be a 2. By comparing the rubric and the students grade, it should still be easy to remediate.

Here's where my idea breaks down. What if they complete every skill but they screwed up on skill 2? If they complete the subsequent skills based on their answer for skill 2, they may have done the process correctly but still ended up with a wrong answer. Would they then get a 2 because that is the level where they screwed up? Or would they get something like a 4.5 because they did the process correctly? Translating to the gradebook, if each skills was worth 20%, would the student get a 40% (2) or a 90%(4.5)? That's a huge difference.

Another option would be to count each skill as one point (20%) so that they get credit for every skill they performed correctly but then their score would tell me nothing about where they messed up. :(

Other than that, I am liking this idea. The individual skills will be assessed throughout the unit through class work and homework quizzes but the unit test would now be replaced with this performance event idea.

I also want to try math portfolios next year. I'm thinking (hoping) that this idea would naturally tie into the portfolio. After completing the performance event, the student would then write a structured reflection/explanation of the process. Throughout the year, these performance events and reflections would be collected as a demonstration of mastery.

One last thing we are working on are End-of-Course tests. This is not a state mandate but a district suggestion. We want it. We have currently finished our Algebra I EOC minus a few edits. We will give this four times a year to show growth over time. This will also help students be prepared for long, standardized tests as opposed to the short performance event quizzes covering only one concept.

Please tell me where you see potential downfalls and advise me on how to grade!

I want to make this workkkkk.

SBG + PLC = I Finally Get It

This one article assigned in our PLC class has finally cemented how SBG should work FOR ME.

*from Revisiting Professional Learning Communities at Work pg 190-193
Dufour, Dufour, & Eaker, 2008

Diana, Se, Marie, and Amy, the second-grade team at Westlawn Elementary, began their collaborative process for improving  math proficiency for their students by engaging in collective inquiry regarding the current results and practices in second-grade math. Their math achievement data from the previous year's summative district assessment indicated 78% of second graders met or exceeded the district's proficiency target in math. They agree to establish a team SMART goal to improve upon last year's results by at least 10% on that same summative district assessment. The goal was strategic in that it was aligned with the school's goal to increase the percentage of students meeting or exceeding proficiency in math as measured on local, county, state, and national indicators. The team goal was measurable because it asked for a 10% increase over the previous year. The team believed the goal was attainable because improved results (higher levels of student learning) were required to achieve the goal. It was time-bound because the goal was to be accomplished within the course of the school year.

Prior to developing strategies to achieve their goal, Diana, Se, Marie, and Amy had a candid conversation about how they had approached the math curriculum in the previous year. They acknowledged they had followed the same 4-step pattern for each unit:

• Step 1. Administer the pre-assessment from the textbook.
• Step 2. Teach the unit.
• Step 3. Administer the post-assessment from the textbook.
• Step 4. Move on to the next unit, repeating steps 1 through 3.

They recognized they would only improve student performance in math across second grade by seeking out and implementing new and better practices. They committed to each other to use the team learning process of a PLC to guide their teamwork throughout that year.

What Did They Do?
1. They clarified the 8 to 10 most essential student learning outcomes (skills, concepts, dispositions) in math for each semester by doing the following:

• Talking with the third-grade team to determine the skills and concepts most essential to student success in math for entering third graders
• Analyzing and clarifying their state and division second-grade math standards
• Consulting with school and division math specialists to clarify multiple interpretations of the same standards
• Analyzing the district assessment, and identifying where their students had struggled in the previous year.
• Developing a math curriculum map and common pacing guide they all agreed to follow

2. They created a series of common formative assessments aligned to the essential math outcomes by doing the following:

• Studying the language and format of the district's summative assessment of second-grade math
• Selecting appropriate items aligned to the essential math skills from math textbooks, individual teacher assessments, and state and national websites providing released math items
• Creating new items deemed by the members of the team to be valid ways of assessing the essential skills
• Including at least five items per skill on each common assessment to provide students an adequate opportunity to demonstrate their proficient
• Increasing the number and frequency of assessments so that only two or three skills were considered on each assessment

3. They established a proficiency target of 80% for each skill on each assessment. For example, if they used five terms to assess a particular skill, students needed to solve four of the five problems correctly to be deemed proficient.

4. They collectively analyzed the results from each common formative assessment, identifying, skill by skill, the individual students throughout second grade whose scores exceeded, met, or fell below the team's proficiency target.

Through this collaborative analysis of common formative assessment data, the team was quickly able to do the following:

• Identify individual students who were experiencing difficulty on any skill.
• Identify individual students who were already highly proficient
• Create flexible groups of students across the grade level for the intervention/enrichment period each day based on skill-by-skill proficiency.
• Establish a protected block of time each day for the team, resource specialists, and instructional assistants to provide students with coordinated and precise intervention and enrichment based on students' personal needs.
• Identify the teachers whose students were experiencing the greatest success on each skill.
• Assign students who were struggling with a particular skill to work with the teachers experiencing the best results in that skill on the common assessments during their intervention/enrichment period.
• Explore and discuss the strategies being used in individual classrooms

The team also engaged students in the process of monitoring their own learning by requiring each student to maintain simple bar graphs indicating his or her proficiency on each essential math skill. Items on the assessment were arranged by skill, and each item was assigned its own box on the graph. After every common assessment, students would color in the box for each item they answered correctly. As individual students discovered they had not not met the proficiency target on a particular math skill or concept, they knew to report to the corresponding small-group tutorial during the intervention/enrichment period to receive additional support for their learning.

At the completion of this skill-driven cycle, the team administered another form of the common assessment to students who had experienced difficulty on any of the essential skills. At that point, new student learning groups were formed. Students who demonstrated proficiency were moved to enrichment groups, while students who continued to struggle were moved to smaller, more intensive group interventions.

This intervention/enrichment process ensured that any student in second grade who was having difficulty understanding a skill would receive intensive, small-group instruction from the most effective teacher on the team for that particular skill. The process allowed the team to continue with new direct instruction during the regular math period each day, so the difficulties of a few did not adversely impact the opportunity for all students to learn new material. Meanwhile, the team continued to build shared knowledge of the best way to help young students acquire math  skills through  a collective study of the research on the topic. At the same tine, however, members were conducting their own action research on effective math instruction and learning from one another.

Real SBG

Can sbg be sbg without choice?

Is the power in sbg the fact that students are self-motivated to practice and re-test?

What would happen if I turned choice into a requirement?

Say, anytime you score less than an 80%, you a required to do a practice sheet and retest.

Is that not real sbg?

Is it motivating the students to make sure that they get an 80% the first time so they don't have to do more work?

Is it handicapping them because they know if they do bad, they have a freebie?

I self-diagnosed my biggest sbg  failure as not getting students to come in and retest. This is an option I thought of to try next year. Especially if I introduce it as a brand new system created specifically for their class in order to make sure that they cannot fail.

Forget Common Core, I'm going back to my ACT College Readiness Skills. If I can have a practice sheet tied to each of those skills, then as soon as someone scores less than 80%, BAM, I whip my practice sheet back and forth. And if I make two versions of every quiz ahead of time, then BAM, they satisfactorily complete the practice,  and I hand out the new quiz. Is this how it is supposed to work people?

I am in the brainstorming process of this so go ahead...hit me with your best shot.

Fire awaaaaaayyyyyy.

SBG #Fail

Today I gave up on SBG.

SBG: How To Grade

I think my issue with sbg is how to grade.

I know my main problem with sbg is getting students to come in and reassess, but hopefully the conversations I had with 16 parents this week at Parent Teacher Conference will start to move that into motion.

So for me personally it's the issue with grading. I started out doing two questions per skill per assessment. I created my own rubric with a mixture of C's, P's, and I's with the second question weighted more heavily than the first. But sometimes the rubric didn't serve my students well and I couldn't, in good conscience, always stick to it. Which probably implies I need a new rubric.

But as I began to work with my instructional coach and discover second-year-teaching wisdom, I realized you all were right and I was assessing way  too many skills. I started to broaden my skills so that one skill contained baby ones. I suppose you understand what I mean. We also started to look at the ACT and the Work Keys and pulling questions from there so that I could backwards plan my lessons to lead up to hard problems I normally would have avoided asking my students. We've already established that I should plan backwards, I've just started it, moving right along...

So my past couple assessment have only been assessing one skill but I've asked about 8 questions. How do I grade that with a rubric?

Give each question a score 0-4 and then average them together? I thought averaging was the devil...

Grade as usual, giving a certain amount of points for each problem, counting off, and then giving a percentage of points correct out of points possible? My twitter peeps said this puts me back into points instead of levels of understanding. But what if I assigned a range of percents to a rubric, say:

100% =4
90-99% = 3.5
80-89% = 3
70-79%= 2.5
60-69%= 2
50-59%= 1.5 
40-49%= 1
30-39% = .5


But I guess that still isn't providing accurate information to the student because a 73% doesn't tell them what they messed up on.


I previously tried @druinok's idea of asking 3 questions per skill on different levels but that rubric was still confusing to me too.


Am I asking too many questions per skill? How often do you assess and how long are the assessments?


We've been working on developing assessments that come naturally at the end of a small unit. My coach has talked to me about balanced assessments: including some more basic, straightforward questions as well as application, word problem, synthesis type of problems. And I like that. I like the assessments we've been creating but I don't know how to give an overall score when I'm asking so many questions. 


What happens with multiple choice? If they get it right a 4? If they get it wrong is it a 1, 2, or 3?


@dcox gave the advice:  Say you have one basic, one "proficient" and one application/synthesis problem. Students who can do all three =5, 2/3 =4, 1/3 =3. But what if they do 1.5 out of 3, or 2.5 or 3.5? What then? What if they make small mechanical errors that throw off the whole problem? What if they start off well and then nose dive?

It's like no matter what rubric I find or create, when I'm grading, I always find a loophole that leaves me staring blankly at a paper trying to estimate how much they know based on the test and what I see in class.

What am I missing?

SBG: Error Analysis

It's the end of the first quarter. I don't want to give up on sbg just yet. I've got to figure out what's going wrong so I can make this thing work.

I've separated grades in the gradebook according to skill.

I've been giving shorter,weekly assessments addressing specific skills.

Students have their own bubble sheets to fill in so that they can self-analyze what they know and don't know.

I've had 6 out of 68 students come in to reassess.

And 4 of those 6 were girls who had B's instead of their normal A's.

Overall, grades are lower than last year. But I have different students. I'd like to say that the grades are a truer picture of their abilities since I am only grading quizzes but with the rubric I was using, I can't necessarily agree with that.

Pitfall #1: I was forcing my instruction to fit in a quiz every Friday whether or not a skill logically ended that way. It didn't matter if we were in the middle of a skill or not, come Friday, we quiz.

Solution #1: By creating my assessment first, I can expect more out my students since I can plan better lessons. Creating the assessment first forces me to focus my instruction on the skills that are imperative to build up to the same level of ability that the assessment addresses. This way my teaching covers all the needed parts and class logically ends with an overall assessment.

Pitfall #2: It's possible that the students do not have enough independent practice to prepare them for taking an independent assessment. I've been trying new strategies to get away from direct instruction but 90% of what the students are doing is with a partner, in a group, or as a whole class. Maybe I am making it too easy for them to tune out and just write things down without holding them accountable for anything. Also, I don't give homework. If we don't finish something in class, I will tell them it's homework. They don't do it. We finish it in class the next day anyway. The whole idea of not grading homework is to give them guidance and correction through constructive feedback. I have morphed into giving no homework at all which translates into no written feedback until the actual assessment. So the only concrete evidence that they know what they are doing is the few minutes I walk around the room while they are working and give minor feedback.

Solution #2: My instructional coach is advising me to create a chart or some kind of system to check the work the students are doing, even if I'm not actually grading it. I started an Excel sheet where I catalog a C for Complete, I for Incomplete, or a 0 if they didn't turn anything in. This at least gives me a point of reference for discussion with a student/parent/administrator. Another idea I had is to hang up charts (like in Kindergarten or Sunday School) and let a student each day collect the assignments and go mark the C, I, or 0 for their class. That would give the students some involvement and maybe hold them a little more accountable since everyone could plainly see who is completing their work and who isn't. From there I could reward those that constantly complete their homework but I don't really want to start bribing them. Another idea she had is if maybe once a week I randomly checked a couple problems so that students would never know when I would be checking or for what. I really don't want to do that. I just hate grading. I don't want to grade all that and completion grades become fluff.

Pitfall #3: Students are not retaining information. I was doing my best to assess every skill twice in class to help those students who will never come in for reassessment as well as the retention issue. I don't know that it helped other than highlighting the fact that students are not retaining information.

Solution #3: Although I have created some thoughtful ideas on how to summarize my lessons, I have yet to do any. When faced with a time crunch, I tend to want to finish the notes or activity we're currently doing rather than stopping to start something new. I guess the truth is I haven't seen the value of summarizing as a tool for retention. Yet. Also, it seems like a waste for students to do the summary for me to glance at it and throw it away. On the other hand, most of the work we do in class gets less than a glance from me.  Touche. I wonder if my students would be more likely to do summaries if they had laptops to type them on? What I'd like to do is give two problems (preferably on index cards, which I heart!) of homework each day. Surely everyone could manage that. But, I still don't want to grade it. And is 2 problems really enough to aid in retention?

Pitfall #4: Students don't care about their grades. No one wants to reassess. A good portion don't even fill out the bubble chart (skill tracking form) because it's not for a 'grade'. I suppose as long as they are passing, it doesn't really bother them. Report cards come out next week, so I guess we'll see what happens then. We had progress reports at the halfway point of the quarter, but I guess no one was really upset by their grade.

Solution #4: If I knew how to make students care, I could be rich and famous by now.

SBG Common Core Geometry Pacing Chart

Geometry Pacing Chart

Common Core Standards

2010-2011

Priority Standards in Bold- Priorities are things we will keep coming back to over and over throughout the year and are assessed on ACT.

Note: In order to bridge gaps between Algebra I and Algebra II, the following Algebra I skills will be embedded as much as possible:

• Solving equations and systems of equations

• Factoring

• Analyzing and graphing linear, exponential, and quadratic functions

Quarter I

Foundational Geometry Terms

• G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

• G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

• G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. (Note: Include factoring and systems of equations.)

Parallel Lines

• G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

• G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Transformations

• G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

• G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Quarter 2

Parallelograms

• G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Triangle Congruency

• G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

• G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Include CPCTC.

Similarity

• G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

• G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

• G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

• G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.

o a. A dilation takes a line not passing through the center of the dila- tion to a parallel line, and leaves a line passing through the center unchanged.

o b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Quarter 3

Area and Volume (Focus on real-world applications not simple use of formula.)

• G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

• G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

• G.GMD.4 Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

• G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (Note: Informal arguments for area and volume formulas can make use of the way in which area and volume scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k2 times the area of the first. Similarly, volumes of solid figures scale by k3 under a similarity transformation with scale factor k.)

• G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

Probability and Statistics

• S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

• S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

• S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

• S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

Quarter 4

Right Triangles

• G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Circles

• G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle Include factoring.

• G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

• G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle

• G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

• G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

• G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*