Monthly Archives: May 2013

[SBG] Synthesis Assessments: How Do They Work?

This post is about Standards Based Grading (SBG).  Refer to this post if you want to know more about what I’m doing next year or can’t follow along what’s going on below.

Having read Mathy McMatherson recently, he convinced me to organize my standards into categories by types, not just units.  If you want more info on these categories, read here and here. He breaks standards in to 3 categories: Foundational (I think he calls them Procedural), Conceptual, and Synthesis.

Brief Outline: Foundational, Conceptual, and Synthesis Standards

I’m going to briefly explain my understanding/adoption of these categories, and if you want a much better analysis, go read the two posts I liked above.

Foundational standards are ones that are essential for students to have before moving on.  For example: before doing just about anything in Algebra I, a student must be able to do basic operations on integers: add, subtract, multiply, and divide. (That would probably be 4 different standards, at least, but moving on.)

I pictures Conceptual standards as ones that make up the majority of a course: being able to graph a line and understanding what that means, for example.

Synthesis standards are ones that combine two or more other standards, usually conceptual, but not necessarily, and are much more difficult for the average student. For example, two standards might be “S1: Basic operations (+, -, ×, ÷) with fractions” and “S2: Solving simple equations for a variable” and a sample synthesis standard might be “S3: Solving equations for a variable with fractions”.

(Whether or not S1 and S2 are conceptual or foundational might depend on the course.  I would consider those foundational for a Pre-Calculus course.)

I really like this distinction because it helps the teacher to know what to look for.  I decided that as I am assessing this upcoming year, I might not allow students to assess a synthesis standard unless they show at least “Proficient” in the standards that make up the synthesis standard.

When Grading

Furthermore, getting a “proficient” or “mastery” level (my highest two levels) in a Synthesis standard would be cause for me to add a “proficient” or “mastery” level to the standards that are combined to form that Synthesis standard. This does a few things: (1) it adds to the amount of evidence that a student knows a standard, which is good for me and for them; (2) it could help their grade (right now I’m planning on averaging the latest 2 assessments).

However, doing poorly on a synthesis standard is not necessarily grounds for lowering a standard, and there are a few reasons for this: (1) I cannot necessarily identify which standard they did not understand or apply correctly in the context of a combined problem, unless they showed their work very carefully; (2) it may be that they are perfectly fine at each individual standard, but they have trouble combining the standards in some way because it relies on some other knowledge/standard that I did not identify.


All this figuring out “where/why does a student get a problem wrong” reminds me of an excellent website, which is Michael Persham’s project: This website was only of cursory interest before I moved to SBG, but now this kind of understanding is essential for students’ grades.  Which is excellent because it should have been essential even before the move to SBG.  One of the things SBG requires (if implemented property) is that it forces teachers (and students) to focus on what a student does and does not understand, which is essential for effective teaching & learning. I hope to contribute (and get feedback) much more this upcoming year using that excellent website.


So understanding mistakes are important, and if ambiguous, I can “mark down” in a Synthesis standard easily from a Synthesis assessment, but not so easily from a non-Synthesis assessment.  That’s just one more step to helping me use SBG better.  The more of that I do now before the year starts, the better for me (and for my students!).


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SBG Grading Percentages

There are a few things I need to decide when implementing my SBG for next year. I’m definitely doing a 1-4 scale where 1 is “Beginning”, 2 is “Developing”, 3 is “Proficient”, and 4 is “Mastery”. Any fewer and I would feel that I’m not giving enough specific feedback, whether to motivate faster learners or encourage slower learners. Any more and I might as well just go back to a 100 point grading scale (at least that’s what it feels like for some reason).

However, I still have to report grades, at the end of the quarters and on report cards, on the A, B, C, D, F scale. Therefore, the one thing I have to decide is “what % should I assign each value”.

To decide this I created an Excel sheet (actually a Google Spreadsheet), and I looked at some scenarios, having decided what I would want the outcome of that scenario to be, and edited the percentages to meet my expectations. I’ll list just a few below.

One thing you should know is that our school uses a 10 point grading scale, but doesn’t have D’s. Therefore a 70 is passing (C-), while a 69 is failing.

Student is exactly Proficient in All the Standards

Expectation: I want to reward this student because this is what I would like every student to accomplish at a minimum.

Result: I adjusted the “Proficient” to be at 85%. Therefore, if a student gets all proficients, they earn a B in my class (whatever that means… wow this is all so very subjective even though for so long I pretended like it wasn’t.)

Student is Proficient in Half the Standards

Expectation: I really don’t think this student should pass.

Reasoning: I want to raise my expectations of the students and expect them to become proficient in over well over half of the standards. However, if I simply calculated percentages from the fractions: 1/4, 2/4, 3/4, and 4/4, then in order for a student to pass, they would need at least 4/5 of their standards to be at “Proficient” AND the remaining ones to be at “Developing”. As much as I hate to admit it, this may be a little unrealistic, especially as I will be reassessing my students for retaining of the content.

Result: Because “Proficient” is at 85%, I moved “Developing” down to only 40%. This requires that at least 2/3 of the standards be “Proficient” AND the rest be at “Developing”.

Student gets Several Standards at “Mastery” but Completely (or Mostly) Ignores Other Content

Expectation: I don’t want students to earn an A and then give up on other content.

Reasoning: First of all, I’m going to try to make getting “Mastery” fairly difficult for the average student, depending on the standard. However, I would feel guilty making

Result: I moved “Beginning” down to 20% and “Mastery” down to 96%. Another thing you should know about our school is that we use the +/- scale, so some of our students are constantly chasing down A’s, instead of A-‘s.  These percentages would essentially require that a student who wants an A would have to get “Mastery” in nearly all of the standards, and get “Proficient” in the rest: a difficult task, but not impossible.[1]

Results Continue reading


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An SBG Finals Idea

How about this for an idea for finals within a Standards Based Grading context:

Instead of giving a separate test or final, students may request to take certain standard.  Let’s say Alice is okay with “Fractions”, but needs to work on “Decimals” and “Linear Equations” (grossly oversimplified standards, but just for the sake of example, bear with me).  Alice can choose which ones she wants to retake so she doesn’t have to “worry” about Fractions. It’s basically a student-initiated assessment which is compulsory for students who are too low on their standards.

Some notes:

  • This would be in the context of a class that has already “spiraled”, meaning, Alice has already repeatedly shown that she’s fine with Fractions–the teacher isn’t relying on a single quiz or test she took 4 months ago.  By “repeatedly” I mean for that to include that the class has spiraled back on that standard within the last month.
  • The grade-book is one that takes into consideration more than just the most recent standard. Right now my plan is to average the most recent two, which rewards students who have studied and repeatedly shown that they’ve met standards.  This would prevent students from jumping from 0% to 100% on any standard.
  • Students grades can go down!  This is so a student doesn’t request to take all the standards and just pick and choose the one he/she remembers so that they might (shot in the dark) increase their grade.  They have to be confident of what they’re doing.
  • Perhaps I’ll include that students must attempt a certain # of standards.  However, if the spiraling has been successful, “not having a final” would be a nice reward for students who have worked hard and already demonstrated mastery on all the standards (how often does this occur?).

I think I like this better than my last idea for SBG finals. Even though Hedge (@approx_normal) favorited my tweet, getting favorited by “Captain Bad Idea” is a little like being applauded by Captain Obvious for an observation…

As always, please leave critical feedback, especially if you’ve tried this before.

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SBG Introduction to Students

I’m so excited about starting SBG next year, that I went ahead and made a Prezi to introduce the idea to them.

Disclaimer/Confession/Copyright Warning: All of the ideas (even down to making a Prezi on it!) were stolen from Bowman Dickson (@bowmanimal) and can be found at his blog right here. He was even kind enough to share his Prezi, but his grading system was different enough that I decided to start the Prezi from scratch and just steal his ideas.  That and I don’t look enough like him to fool my students.

Please check out the Prezi here and leave critical feedback so I can improve it before I get the critical feedback from students!

(I was gonna embed it, but doesn’t allow iframes…)


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All My Lessons

(and assessments).

Yeah, it’s the end of my 2nd year of teaching Precalculus, Physics, and Chemistry, and I figure I should be able to post my lessons without too much shame.

Actually, I am embarrassed of some things, because I’d like to think I’m a better teacher than I have been, but I think I’m growing.

I’ll do one better than just posting all my lessons: I’ll link my Dropbox for the three classes, so they’ll update as I change them throughout the year.

I’ll also critique each class a little below so you know what’s coming (and so I can reflect, briefly, on where I want to go with my lesson planning).


All my files for Precalculus

Precal changed the most this year, thanks to the mathtwitterblogosphere.  I used to lecture way more, and now I’m actually doing activities where students are learning as they work.  I still hope to get to the level of Fawn Nguyen, but she’s way more creative than me (and more experienced, and just awesomer (<– is totally a word even though Chrome spell-check says “nope”)).

In the future, I hope to have more activities and I want to make the whole subject more cohesive.  Right now it is totally a fragmented mess where students learn isolated units.  Something for me to work on over the summer.


All my files for Chemistry

Chemistry changed the least, but I spent the most time on it my first year around.  Of course, that’s when I thought that lecturing was still the way to go, so it has plenty of good notes (for me, at least) and (now) many decent tiered assessments.

want to change Chemistry and make it more like a modeling class, where students discover properties on their own.  At our school, since math is leveled/tracked early on, it is probably therefore the hardest class that every student is required to take (their Jr. year).  I appreciate that I have students all over the map, but it does get hard in terms of the math sometimes, when you’ve got students in Precal and students in Geometry working together on the same algebra equations.  I think SBG will significantly change the way I teach this, hopefully for the better.


All my files for Physics

Physics was the one I taught worst last year (my 1st year teaching it, and I’m definitely under-qualified).  However, it still is a really fun class, and we get to do awesome projects that (if I have time) I’ll set to a music video.

I tried to go modeling and got there partway.  I was learning a ton as I went, and yet, it still felt like I was putting this class on the back-burner, and for that I apologize to my students.  Everything was brand new this year, and definitely better, though it wasn’t that hard to get better from last year because (in my opinion) it was so awful.

All My Classes

So that’s that.  And I apologize if the links don’t work because I change some folder name further down the line.  If that happens, please shoot me an e-mail, comment below, or tweet @newmjh3.

Oh, and also let me know if you can edit those Dropbox files–I’d rather my assessments not change under me.  🙂

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LaTeX for Assessments

Long story short:

  • I wanted more ram but didn’t want to shell out $$$ for Windows 8. (Had 32-bit Windows 7.)
  • Switched to Ubuntu (12.10 at the time) once I bought a 4GB ram stick (they’re cheap these days!!)
  • Need to edit documents so used LibreOffice.  However, it doesn’t play super-nice with graphics and some other things so…
  • Found WPS (Chinese-made MS Word rip-off).  Works nice with .doc files, even looks and feels like Word 2010.  Except it’s not at all compatible with .docx files.
  • WPS also doesn’t use equations, but I (being a Math + Science teacher) need to write equations on assessments.
  • I also am moving to SBG, so I’d like to be able to clearly mark what students earned.

I was watching participating in this Global Math meeting where this guy (also has 1st name Jonathan) was sharing and he mentioned that he uses LaTeX for all of his assessments. I thought “awesome, but I haven’t used that since Grad School”.  But decided to go to his blog anyway and he has this page dealing with how to use LaTeX as a math teacher.

I guess the page isn’t super-friendly if you’ve never used LaTeX before, but he (Jonathan Claydon) points that out on the page.  And for someone like me, who used LaTeX long ago and dabbles in computer science (by “dabble”, I mean it in the “I-put-a-tiny-fraction-of-my-small-toenail-in-the-pool” sense of the word), it’s just perfect.  So now I’m making assessments for next year and adding a header for students to really understand what SBG is all about.

Check out my first assessment below (Yes, I’m giving these to Jr’s and Sr’s in Precalculus, and no, I’m not confident that they will all ace them…) and please give feedback.

Edit: now that I published this, the pdfs don’t look nearly as nice on Scribd as they do “in person” (when you download them).

Note that these standards are much broader than the ones that I’ll actually be teaching: this is just to make sure that they have the “basics” before we really get into Precalculus–otherwise they’ll be “up that creek”. I hope to be much more specific in my assessments and standards when we get to Precalculus topics.  I’ll also be incorporating some ideas from this year’s tiered assessments–more on that to come.

I’ll be using these Google Spreadsheets to keep track of their progress, and I hope that they will catch on pretty quickly what the heck SBG is.

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SBG Idea: Final Exam Exchange

The Setting

It’s the middle of exam week and mentally I’ve already moved on to next year.  I am so ready to start SBG (Stanards Based Grading) that I’m actually a little sick and embarrassed of my finals this year.

But I started to wonder “what’s the role of final exams in SBG?”  As soon as I started looking, I realized how silly it is of me to think that I’m the first to have thought of that.  There are great posts dedicated to this topic from Shawn Cornally, from Jason Buell, from Frank Noschese, and from Daniel Schneider.

As I was reading these posts, I had an idea.

An Idea

What if we (the mathtwitterblogosphere) had an exchange of finals, and made it sorta a competition between students (for the students’ sake, not for the teacher’s egos and definitely not for administrators to wield as a “we’re better than you” tool weapon).  I think my students would be way more motivated by me saying “hey, here’s another teacher’s final–show me how well you can do on it because you know each of these skills!”

The other thing this would do, which would interest me as a teacher, is it would remove the “specifics” of my assessments which might inadvertently help students out, and I could really see how well they know the standards.

Must Be Careful Of…

I guess we need to be careful with other’s finals that they don’t fly out into the greater community (read: students cheating).

Another thing is that I (and whoever would try this with me) would have to be careful not to give assessments that rely on knowledge that is so specific to the course that it is not immediately transferable to the same course at a different school or taught by a different teacher. I think that in the long run this is a good thing because it forces us to focus on what’s important. (I mean, that’s the goal of SBG, right?)  And by “focus” I mean focus our teaching, HW, prior assessments, explanations: the whole shebang. (Is that how you spell “shebang”?)

Different schools provide different amounts of time for finals… consider the problems that go with that.

Last Thoughts

Often times I’ll blog about something that came to me and I thought was an awesome idea.  Then I’ll look back on it a few days later and think “meh”.  This idea is already starting to look “meh” in my mind, but feel free to run with it as you like.

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