[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.

MathMistakes

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: mathmistakes.org. 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.

Conclusion

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!).

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

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.

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 wordpress.com doesn’t allow iframes…)

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).

Precalculus

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.

Chemistry

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.

I 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.

Physics

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.  🙂

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).

View this document on Scribd

View this document on Scribd

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.

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.

My SBG Adventure

I’m going to try SBG next year, I *think* in all my classes (Precalculus, Chemistry, and Physics), and I want to start thinking critically about it now so that I have as few regrets as possible for the following year.

The Setup

First, I’m blessed in that my principal doesn’t mind whatever grading system and/or computer program I use to record grades, as long as it is easy for parents and students to see where they are.  I hope that mine makes it even easier than before.

I didn’t want to fork over the money to pay for Active Grade (even though it looks awesome), and the school I teach for is currently poorer than I am, so they sure aren’t going to pay for it.  So I turned to Google Spreadsheets.

Google Spreadsheets has a function called “importRange”, which pulls cells from one spreadsheet into a separate spreadsheet.  The function can be finicky (which is one of my only major hesitations), but besides that, it’s great because it allows me to share one spreadsheet with each student (a good job for a TA at the beginning of the year) and then students can see their own progress on each assessment.

“But that would take forever to setup and get just how you want it!”

Too late, I already spent the time making it.  Here it is.

So below I’m going to show you an overview of what it is.  If you want to play around with it, you’ll have to make a copy of it, fix a small handful of keys (really just the “teacher key” in the “gears” sheet of all the student spreadsheets), and then you can tinker to your heart’s desire. go for it cause I don’t need it anymore (just try to keep it similar for those who also might be interested in it after you).

But First…

Before I get too into it, I really have to thank Jim Pai, with whom I started having some great conversations about SBG and who helped me think about what I really wanted.  I’m still wrestling with many of these issues, and hope to have many more great conversations with Jim and others, so I’m as ready as possible to start SBG next year.

What the Student Sees

All of my students will be required to have Google accounts next year (not sure how much I’ll do with it, but it looks very promising–just go over to Julie’s blog and you’ll see!)

I will share a separate spreadsheet with each student.  When they open it up, they’ll see something like this (after they’ve had some assessments)

Notice that I’m starting simple: 1, 2, 3, and 4. (I was going to stay away from numbers with B, D, P, and M, but numbers are easier to do things with in spreadsheets, as I found out).  The numbers are also nicely color-coded along with an explanation on the right.  Each standard could have a comment, along with a generic comment just under the student’s name (“Alice” is an example–right now I have not students with that name).  All of these fields, including the name, are pulled from different areas of the teacher spreadsheet, so once the class is setup, I’ll never have to open up a student’s spreadsheet again! [1]

You’ll also notice the “Details” and “Gears” sheets at the bottom.  The “Gears” are the formulas that go on in the background… which is why I make these sheets un-editable by students because they could really screw things up in there.  If the student were to click on “Details”, they’d see something like so:

Notice that I now have every assessment listed here, along with every reassessment and even certain “assignments” like “Talked to student”.  I’m starting to feel the SBG buzz.  This gradebook is infinitely better than my previous one, where if a student reassessed, I’d have to replace the old grade with the new one.  Now I can just enter it right afterwards and we everyone (the student, parents, and myself) can see how the student progressed.  How do I calculate the “summary” grade?  I’ll talk about that down below.

Also notice how the spreadsheet opens with the “Summary” rather than the “Details” because I want students to focus more on the standards than the specific assignments.  Hoping to foster that discussion of “what do I need to understand” rather than “where can I get these points?”

What the Teacher Sees

Now, one of my goals was to make it as easy as possible for me, as the teacher, to enter grades, comments, new assignments, AND new standards, and sure enough, I believe that Google Spreadsheets delivers, thanks to the “importRange” function.

Here’s what the teacher sees when he/she opens their (separate from the students) spreadsheet.

Disclaimer: all the student names are examples, (no my class does not incredibly have one student with every single letter of the alphabet in it, though that would be awesome!).

So teachers enter “grades”, one for each assessment (running across the top) for all the students (running down the left side).  The standards are placed above the assessments, grouped so that all the subsequent assessments for a standard are to the right of the first assessment, and these can even be further grouped into units.

To add a unit, standard, or assessment, the teacher simply inserts a new column (there are at least 3 ways to do this in Google Spreadsheets) and fills out the appropriate names at the top.

Student didn’t take an assessment?  Just leave it blank for that student–doesn’t affect the calculation.

Need to add an assessment for a previous standard?  Just insert it in after the last assessment for that standard.  Right now I think I have it setup to take in up to 120 assessments.  That should be enough for a semester, right?

So you want to check on class trends rather than each details assessment?  Click on the “Summary” tab and this is what you’ll see.

First, notice that this is an example, so I’ve only got grades entered for a few students.  But here, you can see that you can enter comments right next to each standard, and students can see these on their spreadsheet!  There’s also the “Generic Comment” that goes right next to the student’s name on the left side.  I suppose that if there start to be too many comments, you could freeze the first 2 columns so that is always there.

Want to see it with the students’ names along the top, but standards on the left?  There’s a tab for that: “Summary Transposed”.  Would rather see the details like that?  “Details Transposed”.  I’ve also got another tab “StudentList” where you can enter student’s names, e-mails, and other important info (which I’m going to get at the beginning of the year next year with a Google Form, so it’s easy to copy).  All the other spreadsheets pull the names from the “StudentList” sheet so it’s all centralized.  There’s even a tab listing the “Standards” and the “Assignments” (along with about 7 “Gears” tabs for running all the necessary calculations in the background.) [2]

Now, about those calculations…

About the Calculations

I waffled back and forth between a few ideas for figuring a student’s standard, and although I could have a whole post on this debate, that’s not the intent of this post, so I’ll try to keep it brief.

I started thinking “students should only be allowed to improve their standard, because otherwise they won’t reassess”.  But then I read this post.

So I started thinking “okay, I should take the minimum of their last n assessments”, and I was going to go all jujitsu on the spreadsheets and make n changeable with a single cell, but then I realized that was way harder than I had thought.

Then I thought some more about how students would have to take several more assessments to make up for one “bad” assessment which doesn’t seem right, even if I’m using SBG to figure out what a student knows rather than how well they do on a given day.

So I settled on this plan: I’m going to take the average of the last two assessments taken by the student.  These could be teacher-initiated or student-initiated.

Furthermore, I’m probably not going to tell students that this is how the formula works [3], lest they become too focused on “just doing enough” or “just getting the right score” and less focused on the standards themselves.

The nice thing is that this formula works even with blanks: three scores of {3, null, 4} actually average out to 3.5, whereas {3,1,4} [4] would average out to a 2.5. [5]

Have 10 assessments of 1’s and two 4’s?  Well, then, in my book (quite literally, right now), the student has mastered the content (see [5] again).

Some Kinks & Cons

As I mentioned above, “importRange” is a bit buggy at times.  Initially I actually had the teacher’s “Summary” page pulled from each student’s spreadsheet because the calculations were way easier.  Then I noticed that nearly 100% of the time, at least one of the 3 mock students I had setup at the time didn’t have any grades.  Now the teacher’s spreadsheet is totally independent and each of the student spreadsheets really only pull twice: once for the details and once for the summary+comments.

Another issue is that I’m not paying for this service, so if my spreadsheets accidentally get deleted, I’m up that creek (“crick”?) without a paddle.  So lotsa backup often will be required, at least until I become more trusting of Google’s Drive service. (Haven’t had any concerns yet, but wouldn’t it be unfortunate if the first time was when it mattered most?)

Another Con is the limited control I have over my formula.  Sure, I can change it, but then it changes for everyone.  I think a student actually had a concept mastered, but they have two scores: a 1 and then a 4, then the gradebook will require that they take another assessment just to make sure.  Which perhaps is a good thing?

How do these translate into grades for the gradebook required by my school?  Well, I’m still working on that.  Tentatively, right now, I’ve got them pegged at about these ranges: 4=100%, 3=80%, 2=50%, 1=0%.  Maybe the 1 is a little harsh?  But I want them to show lots of “proficients” as a minimum, so perhaps not.

Oooh, one more thing: the comments are setup so that if you enter a standard “out of order” (add a standard before another standard), then all the comments get kicked over to the wrong standard.  Fortunately, if you know this ahead of time, it’s an easy thing to fix, but you may have some very confused students for a while.

Some Pros

This is completely free!  Yeah, it took some time to make, but now that it’s made, it takes very little time to upkeep (fingers crossed), and it will hopefully be just what I’m looking for as a first year attempting SBG.  Yes, I need to take it for some more test runs before I’m sure all the kinks are worked out, but I’m hopeful.

SO easy to enter grades.  I always wondered why grade-book programs didn’t just use a simple spreadsheet to enter grades: if you make a mistake, “undo” is right there!  And moving between cells with arrow keys and/or tab is so much easier! And it just feels more comfortable (perhaps because I’ve used spreadsheets way longer than grade-book programs?)

Feedback

Here is where I need your feedback on this.  Tell me what’s stupid (I won’t feel insulted) or crazy, or what you like.  And if you’d like to know more about it and/or try it for yourself, I’ll gladly share, so please let me know that, too!  I actually am getting excited about grading for the first time in my life, and can’t wait to start SBG next year!

[1] Except that I forsee myself opening these up to explain to students & parents exactly what we’re doing here.

[2] I was actually worried about reaching the Google Spreadsheet complexity limit of 40,000 cells with formulas.  Oops…

[3] Some will inevitably figure it out.

[4] The resemblance to pi was totally unintentional, but yes, I suppose I did spot it…

[5] Whether you think that is a good result or not is a philosophical education debate, but the spreadsheet math works, darn it!

What Precal Students Can’t Do

I am the fortunate (perhaps?) position of teaching Chemistry simultaneously with Precalculus, and so often times I will come across an equation and wonder “can my Precalculus students do this?”  Today’s equation I “simplified” (read: took away the decimals and made into integers [1]) into this:

At first it depressed me that my students didn’t intuitively know what to do and where to go, in addition to the fact that they were not at all confident in their answer.  Soon after, I became more depressed by the fact that some couldn’t solve it on their own.

Our Alg II teacher told me that they were done a little early with their curriculum, and asked if there was anything that he wanted me for the upcoming Precal students to work on.  I told him that I wanted them to be able to solve the above problem.

I wonder if my frustration is increased because of the fact that there are about half a dozen different ways to do this problem.  Of course, about half of those involve stupid little tricks, which I don’t like because they don’t increase understanding, but there are more than a few legitimate ways of solving this without resorting to “cross multiplication” and “cancelling” (ugh, bad words).

After school, I had a few Chemistry students who were talking about solving that kind of equation (well, I brought it up), some of whom are Alg II students and others whom are Precal students. Some of the Alg II students could do the problem and others couldn’t, and likewise some of the Precal students could do the problem and others couldn’t.  I used to think that students forgot how to do this kind of thing because they had a whole summer to forget how to do it, but now I’m realizing that students forget how to do this kind of thing because they have an entire school year to forget how to do it.

[1] As another teacher pointed out, it is really sad that making an equation have decimals rather than integers increases the complexity for students.

Polar Coordinate Kickball

Here’s another way to build intuition for Polar Coordinates.  Great of lower-level students.  Brief explanation: one student calls out a polar coordinate (e.g. “five comma fifty four degrees!”) and other students flick a “ball” to try to get as close as possible to that point.

Setup

Students break into groups of 4 or 5.  Each group gets a big (2′ x 3′) whiteboard.  They sketch an x-axis and y-axis, and can sketch more if they want to (they know a little about polar coordinates at this point).

One student is designated the “Caller/Referee” and all the others in the group are players.  The players set up whatever they are going to “kick” (flick) on the corners of the board–we used small wooden blocks.  The Caller says a polar coordinate (e.g. “five comma fifty four degrees!”), and then starts counting down from 10. (10… 9… 8…)

The players have until the caller reaches “0” to flick their object to that point.  From here you can make up whatever scoring system feels fair.  I told them “2 points for the closest person and 1 point for the next closest”.  If you want them to be more accurate, you could make it more like golf: lower score is better and you get a point for every cm away from the point your block is.  This would take longer to figure out, but would require students to be much more precise with their measurements.  Since my goal was building intuition, I passed on this approach.

Fun Video

Here are a few videos of the students having fun with the game:

Analysis

Students had a blast and learned a little.  We spent only part of a period on it, so that’s reassuring, but it’s just not conceptually difficult.  I didn’t do this for my advanced class, because though they would have fun, they’d probably get very little out of it.

One good thing was they were required to figure out the polar coordinate often and quickly.  A few times I yelled “only negative r’s for a round!” so students had to quickly figure out what that meant.  I suppose we could bring in functions and other things into the game, but the students need to learn about those first.

Oh yeah, and the next day they came into class asking “can we play Polar Coordinate Kickball?”.  I said no and instaed we played the Polar Coordinate Battleship, after which they asked “can we play Polar Coordinate Battleship tomorrow?”  Wow, I found something that HS Seniors want to do.