MeTA musings

In my statistics class, I didn't grade homework during the last chapter of the semester.  I had a few critical conversations with students about my philosophy on points, learning and homework.  Most of them knew it was coming. 

Later on, I asked them to journal about it.   The responses were generally in support of not grading homework.  I was delighted to read that so many of them "got it."  The picture below is one of the many responses that reassured me the message was being communicated clearly.

Many said that they were still going to do the homework so that they would later be successful on a quiz or test.  I incorporated a few mini formative assessments (quizzes) to provide written feedback and ensure that students were not all falling behind.

Yet another student said,

"I thought that it was OK.  I did all my homework but I think that if you understand it fine then you should only have to do 1 or 2 problems especially when its this long of problems.  I will still do my homework but it would be nice to get some credit for doing it."

For additional commentary and background on this subject, you may want to consider reading a few of my previous posts:

• "I just don't get it..."(why grading formative assessments doesn't make sense)
• "Getting past grading homework" (it's easier than you think)

I'm in the process of moving to standards-based grading in this course now, too.  More on that later. 

Kate Nowak blogged about it first.  Evan Abbey asked for this post.  Here goes nothing.

I teach Geometry therefore I also teach proofs, specifically two-column proofs about congruent triangles.  It's a Geometry student's nightmare.  Ask a Geometry alumnus what they didn't like about Geometry, chances are it's proofs.

Aside from showing the "girls are evil" proof, it used to be one of my least favorite topics to teach.  Honestly, who cares if two triangles are congruent?  Furthermore, who cares to prove two triangles are congruent "given" some sort of figure marked up with congruent sides and overlapping angles?  Yeah, yeah, we need to expose our students to this type of recipe-like logical reasoning.  Yeah, yeah, we should be exposing our students to mathematical proof in the unlikely event one or two go on to become math majors.  For the super-majority of my students, Geometry is the first and last time they'll see congruent triangles as well as two-column proofs.  It's up to me to make it a little bit interesting.

Here's how it all shook down a few months ago:
Me: Let's say I tell Tommy to go home and cut out a triangle with three sides: 3 cm, 4 cm and 5 cm.  He's really good with his protractor, ruler and scissors and won't mess up the triangle.  I give the same instructions to Sandy - go home and cut out a triangle with three sides: 3 cm, 4 cm and 5 cm.  Sandy is also really good with her protractor, ruler and scissors.  Would they come back tomorrow with the exact same triangle?

Student A: No way!  They will definitely be different.  Just because they have the same sides doesn't mean the two triangles will be exactly the same. 


Student B: Yes!  The same three sides means it will be the same exact triangle.

Me: Interesting thoughts.  Who thinks Student A is right?  Who thinks Student B is right?  How about this scenario:  If I tell Randy to cut out a triangle with three angles...40 degrees, 45 degrees and 95 degrees and Leslie to do so as well, will both of these students come back tomorrow with the same triangle?


Student A: No way!  They will be different, just like Tommy and Sandy's triangles.

Student B: Yes!  There's only one way to draw a triangle with those angle measures.

Student C: Yes!  I've done it before, Mr. Townsley.

Me: Wow.  Who thinks Randy's triangle will be the same as Leslie's triangle?  Of those of you that voted yes, how many of you also think Tommy and Sandy's triangles will be the same?  How many of you think that there's a difference between these two pairs of triangles?

...and the conversation continues until a student finally says, "let's try it out!!"
-----------------------------------------------
Over the next class period, pairs of students cut out 12-15 triangles and test some conjectures I propose.  Are two triangles with congruent and corresponding angles always going to be congruent?  What about two triangles with congruent and corresponding sides?  What about a combination of angles and sides?

Will many of my students (and yours) ever think about triangle congruence theorems and/or two-column proofs again outside the math classroom?  Probably not.  In my earlier years of teaching, I used to motivate this kind of lesson with some sort of artificial "real-world" problem.  I'm starting to learn that its often more engaging and meaningful to address the math for what it is rather than pretending it is immediately applicable to adolescents' lives.   Pure mathematicians:  can/should a high school math teacher get away with this type of rationale or am I providing a disservice to my students?

I'm amazed at the number of edu-bloggers who are giving standards-based grading a try in their classrooms.  I talked with a colleague in the parking lot one day and now he's blogging about it, too. 

I get emails and comments from readers asking for advice as I'm sure many of you do, too.

Newsflash:  I did not invent standards-based grading or a common sense approach to feedback.  I read about it somewhere else just like some of you have read about it here on MeTA Musings.  

I'm also amazed at the amount of credibility I apparently have built up locally here in Iowa regarding the Iowa Core's "assessment for learning" characteristic of effective instruction.  I've been asked to speak at several neighboring school district's professional development days, a state conference and at a local workshop following UCLA's Margaret Heritage.  I'm not trying to brag here, I promise. 

You, too, can become an "expert."  Here's a simple three-step process to gaining credibility from your local and virtual peers.

1. Put theory into practice using a common sense approach and a bit of risk taking in your classroom.
2. Write about it in an electronic medium.  Let your audience decide if its worth anything.  If it is, they'll share it with their virtual and face-to-face colleagues.  
3. Repeat cycle.

When readers come-a-commenting, respond in an honest and transparent fashion.

Along the way, you're bound to do plenty of self-reflection.  That's a good thing.  Your students will surely benefit.

That's it. You're up.

You probably already caught it on Dan's blog, but if not the first 40 seconds are worth repeating:

"Can I ask you to please recall a time when you really loved something...a movie, an album, a song or a book and you recommended it whole heartedly to someone you really also really liked and you anticipate the reaction and you waited for it and it came back and the person hated it...so by way of introduction, that is the exact same state in which I spend every working day for the last six years.  I teach high school math.  I sell a product to a market that doesn't want it, but is forced by law to buy it.  It is just a losing proposition."  - Dan Meyer

 Check out the TEDxNYED video for the rest of the twelve minute talk on math education.



Maybe there's a reason why teaching secondary math is considered a shortage area in Iowa? (pdf)

Karl Fisch recently wrote about his proposed assessment scheme for next year's Algebra class.  He plans to weight his grades:

• 10% - Preparation
• 70% - Formative Assessment
• 20% - Summative Assessment

Karl admits that a Dan Meyer-esque system is the ideal, but he's just not ready to take it to the next level in his own classroom yet.  Karl's proposed system is much better, in my opinion, that the majority of the grading schemes in your typical secondary classroom, so this post is in no way intended to downplay his current effort, but instead it has helped me examine my own practice as you'll see at the end of this post.  His writing brings up a question that I'm often asked in my conversations with colleagues and speaking engagements:

"Should a formative assessment ever be entered into the gradebook?"

I've written about the classic "grading practice" question once before, but it's worth revisiting.

Karl says he is going to report out learning by skill.  Standards-based grading, I like it.  Are these assessments still considered formative though, if they don't inform future instruction?

"One distinction is to think of formative assessment as "practice." We do not hold students accountable in "grade book fashion" for skills and concepts they have just been introduced to or are learning." - National Middle School Association

 I don't know how much feedback Karl will be giving his students before he administers the "formative" assessments he's referring to in his post.  He will giving repeated assessments until a student understands/masters the skills.  Is this an example of a repeated summative assessment or a formative assessment in action?  I might be getting hung up on the fact that it is entered into the grade book each time.  Two more questions come to mind:

1. Are these types of assessments truly formative if we're entering them into the grade book...or is this just semantics?  Or are we kidding ourselves into thinking they're formative just because there's a second chance down the road?
2. Assuming the types of assessments Karl refers to his post are not "formative," what types of assessments should we be doing in our classroom that are formative?  More ungraded quizzes?  Exit slips?  A closer look at daily homework/practice?

Sometimes I think my assessment system is on the right track.  Other times, I question if it needs revamped.  Since I critiqued Karl's system, I am also going to provide a brief overview of my current Geometry assessment scheme:

1. Teach the big ideas using direct instruction, inquiry activities or some combination of the two.
2. Students complete some "homework" problems I assign.  Answers are posted on the board immediately for students to check at anytime and to encourage asking questions of each other or me.
3. The next day, students finish checking their answers, write the troublesome problem numbers on the board.  Either I go over a few of the requested problems or students work in groups to get their questions answered.  Students turn in their homework assignments and record the number of assignments they've completed without regard to their level of content mastery.
4. Every two to four days, I give the students a quiz covering the big ideas they've learned since the last assessment.  The next day I hand back the quizzes with marks on a lykert scale indicated how each student is doing in relation to mastery of each of the assessed learning targets.  Students with relative strengths and weaknesses are paired together for 5-10 minutes to ask questions of each other or me for the sake of learning from their mistakes.  These quizzes are not entered into the grade book.
5. At the end of every chapter, students are given a test.  The tests are not reported as a single score.  Instead, a score of 0-4 is recorded for each learning target.  More information about the grade book can be found here.
6. Students who would like to improve their learning target scores come in outside of class and are given opportunities to replace their learning target scores based on new evidence of understanding. 

I hope to write more about this assessment system in detail sometime in the near future as I've recently realized that I have never put it all together in one place, but I think the outline above will give at least the avid reader enough of a refresher to engage in a meaningful conversation.  

I critiqued Karl.  Now I'm leaving myself open to criticism, too.  Have I gone far enough with 'formative" assessments or do I have room for improvement, too?  
(Update: see Jason's post for more reaction to this conversation) 

Last week, I had an afternoon Iowa Core district leadership team meeting on Monday and had a sub again all day Wednesday to attend the Iowa 1:1 Institute.  I will be gone again for a full day to start the week to co-present with Kathy Kaldenberg, Shannon Miller, and Deron Derflinger at the IASL Spring Conference.

I typically try to schedule written assessments for days I'm out of the classroom.  It is pretty easy for a substitute teacher to hand out a test or quiz and have students hand them into the basket when they're done.  Once students work on some review problems after the assessment, it pretty much fills up an 84-minute block. 

Well, being out of the classroom this often doesn't lend itself to easy planning.  There just aren't enough written assessments I can give to my students right now.  So, I decided to try yet another experiment in virtual education, this time in my Statistics & Discrete Math course. 

First, students will be asked to watch this video explaining the day's activities- a late night clip created by me with my MacBook and its build-in iSight camera.
Second, after reading a few pages from the textbook, students will watch this video from the textbook's website to see an example of a hypothesis test being worked out. 
Last, students will complete several problems from the textbook to practice the hypothesis test algorithm.

The last day we met together, we did several activities explaining the concept behind hypothesis testing, so they should be vaguely familiar with much of the terminology presented in the examples.  This virtual setup is far from ideal, but aside from assigning more busy work, it is the only way I could think of to push forward knowing that not many substitute teachers have a deep understanding of hypothesis tests. :)

What other great ideas are out there for keeping students busy (as sad as it sounds) AND learning while you're out of the classroom?

Today is a sad day for me and (maybe?) my students, too.  I announced to them that I will not be teaching math next year.  Pending school board approval next week, I will be Director of Instructional Services beginning July 1 in the same school district. "Director of Instructional Services" is a nice title that really says,

Matt - you're now in charge of professional development, the technology budget, curriculum budget, and going to many more meetings. 

I'm sad to leave the classroom and the daily interaction with high school students.  I'm excited to have even more time to help teachers improve their assessment practices and use technology in a more meaningful way.  Sadness, nervousness, excitement are all running through my mind.  From a two dimensional, math nerd sort of perspective, it's like a crazy sine or cosine curve of emotions. 

I don't know yet how the focus of this blog will change.  I hope it will still continue to focus on technology and assessment, but probably with a more of a cross-disciplinary/grade-level focus. 

I had hoped to go back to school someday to finish a Ph.D (Punya Mishra's program looks awfully appealing!), but I don't think I can afford to take administrative classes beginning this fall AND pursue an ed. tech doctorate at the same time. 

To all of my avid subscribers - this is your invitation to remind me in the future what it's like to be in the classroom.  It's a difficult job. You know it.  I know it.  I don't want to ever lose sight of it. 

My colleague next door has laid out a bit of a standards-based grading manifesto.  Read it here.  You'll be hooting and hollering or extremely furious, depending on where you stand.  Either way, it will get you thinking.  A few snippets to wet your reading appetite:

On the problem with traditional grading schemes...

Prob­lem: Kids want to play games to get points in order to get an ‘A’. This is a prob­lem because it puts empha­sis on accu­mu­lat­ing points and not on what the points are sup­posed rep­re­sent: learn­ing. You must migrate your sys­tem of grad­ing away from grad­ing every sin­gle assign­ment sum­ma­tively (that is assign­ing a sta­tic grade for every­thing a kid does), and towards grades that are indexed by content.
Stu­dents could not care less about their score on “Quiz 5″ from last month; they don’t even know what was on that quiz. Don’t put that in your grade­book. Put the indi­vid­ual ideas that that quiz assessed in your grade­book, so that the stu­dents know what it is you care about. I do this, and my grade­book has bal­looned to about three times its pre­vi­ous size. Oh well.

 and some thoughts on implementing standards-based grading so students understand it...

Major Hur­dle: Kids don’t lis­ten on the day you present the syllabus/explain expec­ta­tions, so they won’t under­stand your new grad­ing sys­tem. You can bela­bor the point for the entire first day (why are you spend­ing a whole day on the syl­labus? Get going; they can read), but the stu­dents are so dead to class­room logis­tics that you’re going to have to teach about SBG as they go along.
I have many moments through­out the semes­ter where kids show me how trained they are by the pre­vi­ous sys­tem. Kids will ask me if they can do extra home­work to raise their grade. Why the hockey sticks would some­one ask that? It’s absurd. I don’t even grade home­work!! I say, “No, but you can study and show me that you under­stand this topic from a pre­vi­ous chap­ter that you’ve pre­vi­ously demon­strated a low under­stand­ing of.” They usu­ally snap back into our real­ity. This is the behav­ior I’ve wanted all along, and I’m happy to say I have it now.

Tweet about it.  Send it to your colleagues.  Post it to your listserv.  It just makes sense.