## 2.20.2012

### 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.

I want to make this workkkkk.

1. I like the idea of a performance event...I would like to try that, too! Would they be able to reassess?

Currently I base my assessments on the California standards, a separate assessent for each of the 25 standards. They usually consist of a basic question, proficient question, and advanced question. If they get one answer right, I give them a 3, 2 correct answers earns a 3.5, and all correct is a 4. I constantly reassess, since the assessments are so short and sometimes I give more than one at a time. I really want them to retain what they have learned. And their newest grade overrides the older grade. They can also reassess before/after school when I am around.

I would definitely give them credit if they get skill 1 or 2 wrong, but other skills correct, based on that error. One reason is because I think you example skill 1, writing the inequalities from a word problem, is a more advanced skill then some of the following skills. For my students, your skill 1 would be the most advanced. I think plugging in would be more basic.

I am now wondering how I can incorporate your performance idea into my assessments...or maybe in addition? hmmm...

2. I attended an A.P. Calculus conference this past summer and the teacher showed us how the A.P. Calc test graders grade the free response problems. They give one point for each step in the process. If a student makes a mistake in one step (like a sign error) they lose a point for messing up that step, but then the tester follows their logic through the rest of the process and as long as their logic is sound and the follow through the next steps correctly (although with incorrect information) then they get the points for knowing the process. I think that this is a really fair way to grade and it fits in with what you're trying to do. I also really like your idea. I've been toying with the idea of having tests- but having those tests with just one mega problem that uses all the skills the students learned in that unit. I still have reservations about it though. Students are intimidated easily and even if they have the knowledge, sometimes if they see something as scary (i.e. it's a really long word problem) they won't even attempt it.

3. I agree with Lizzy-Sensei, the AP method of grading may benefit you better than any other. If they can do the process correctly, then they deserve the points. One careless error early should not completely destroy their score.

I have done things similar to this for the last few years. All of my test questions I formulate a rubric similar to that of the AP rubrics, meaning the students don't just get points for the correct answer but also get points for knowing how to set up or explain the mathematics involved. Also, with a rubric, it allows me to set up for one of my most successful methods: Test-Correct-Recall. I will be happy to share a writeup of this method with you, if you are interested.

Great idea!!! Keep them coming.

4. Kristin,
Yes they would be able to reassess. Our admin is talking about changing our advisory period to a rotating schedule so that all students would have a math day during the week which seems like the perfect time to remediate and reassess. I like the idea of grading on a basic, proficient, advanced rubric as well. My instructional coach is always talking about a 'balanced' assessment and I also think this could be a way to differentiate assessments. Maybe your idea would work better. If they answered the basic question it would be a 70 or so, basic would be an 80, and proficient would be 90 or above, based on errors. Thanks for sharing that, I may go that route.

Lizzy,
I know next to nothign about AP and I don't currently grade with a rubric per se, but I do grade similarly. I will give different steps so many point and then just take off for whichever step they messed up on. Maybe you could also take into account Kristin's idea of basic, proficient, and advanced so that students who are easily intimidated still have a chance. I really like how this could give several entry points for students on different levels.

I think you hit on an important point for all of us- formulating our own rubric. I think I will have to do this for each performance event because each will have it's own unique important process. I can't just make one generic rubric that will serve every topic. I would love to hear more about your Test-Correct-Recall methods.

5. Ok, Test-Correct-Recall.

The first part is very clear, the test. Students take the test and it is graded based off of rubrics created for each question. The hardest part about the test is actually creating it, as it involves very thorough questions with strong rubrics.

The corrections come from the test. Any points the students miss they have to rework or explain their error. Also, for each question they miss any points on there is a conceptual, short answer question they must complete. Since they have to do a large amount of work, I do give some points back on the test.

About a week after corrections are completed, I give a short recall quiz. This quiz is usually multiple choice and is based on the same material from the test. The questions are focused on any common mistakes that were made on the test. These quizzes are a great way to include EOC practice questions on a regular basis.

By the way, sorry it took me so long to get back to you.

6. I just finished reading _Mastery Learning in the Science Classroom_, and I found it very applicable to the way I teach math. You might consider reading it for ideas on assessment, since that seems to be my difficult part as well. A fantastic colleague of mine is doing something very similar to what's in the book for her class of struggling math students, and they have taken it on like you would not believe. It's a short book and a quick read, from NSTA press, so not too pricey. If you have access to a college library you might be able to get it (that's what I did).

7. Thanks for the suggestion Patti, I'll look into it. What was your favorite part of the book?

8. I've been reading about sbg and debating whether or not to include it in my classroom for my first official year of being a teacher (I've been part time and subbing). I am impressed, intrigued, and eager, however I would be the only teacher that I know of following this format and it would be tough.

Your concern lies in how to grade this problem since the skill that you're testing them on isn't the only skill they need to solve the problem. We all get to decide how we want to grade within the spectrum of standards based grading, however your students should have already received a score for the objectives A:solving for slope intercept form and B: graphing inequalities prior to C:systems of inequalities from word problems. Why not let this question give them the opportunity to improve their score on the prior knowledge skills, but only introduce a new score for C:systems of inequalities?

For example:

Sandy has a 3.0 for graphing inequalities, a 2.0 for solving for y = mx + b and a 3.5 for writing equations. When she attempts this inequality you anticipate that she may struggle with isolating y, but will most likely get the rest of the problem correctly. If she demonstrates proficiency with the idea of solving systems of inequalities graphically give her a 3.0 or a 3.5 to indicate that she can solve with minimal errors. On the other hand, if she solves the problem perfectly this could be an opportunity for her to achieve a 4.0 on systems of inequalities as well as raise her score on solving for y = mx + b form since she had to demonstrate it on two separate equations.

I hope this makes some sense to you as it is slowly starting to make some sense to me.

9. I understand exactly what you're saying. It just keeps getting more and more messy. There are so many gray areas and different interpretations that sometimes I feel like I've read everything and other times I feel like I know nothing! Frustrating. I don't think I would advise trying it in your first year.