Saturday, August 29, 2015

Using Twitter for Awesome

For many years, Twitter just didn't make any sense to me.  I understood how it worked at a technical level, but I didn't understand why anyone in the right mind would want to use it.  Over the years, I had a few levels of epiphanies, so I thought I would share for anyone who is still on the fence.

Twitter for learning who's out there and what ideas are taking off:
Back in college, I took a leave of absence with five friends to start an EdTech company.  One of the things that we really nailed that year was connecting to the pulse of the network of innovative teachers.  If you wanted to hear the latest applications of EdTech tools and see how new ideas about learning were being tried daily in classrooms, you needed to follow a handful of teachers on blogs and on Twitter.  We never mastered meaningful online engagement with the group, but we know what they were doing, thinking, and frustrated with.  We also were able to find them in person at a handful of awesome conferences.  As a lurker, it was important.

Twitter for local connections
In 2011, I graduated college and decided to become a teacher.  My school's innovation and tech director, @jenhegna, was really into Twitter.  She connected with all kinds of people in meaningful ways, but to me, the conversations felt too abstract and disconnected from the kind of work I was doing.  Within our district, she started using Twitter to share resources between our digital learning coaches, modeling community amongst a small group.  This helped a lot, and I started to use Twitter for this purpose, but it still seemed like an extra medium when I knew everyone's email addresses.

Twitter for connecting to teachers in your content area
Later that year, she brought us up to the TIES tech conference in Minneapolis and introduced me to @rutherfordcasey.  He welcomed me to a magical place I had never heard of: the MathTwitterBlogoSphere, or #MTBoS.  He showed me both a set of hashtags and introduced me (digitally) to the people that I needed to follow.  It was neat to have somebody tweet at me that I didn't know.  However, since I didn't have time to watch what everyone was saying on Twitter, and my timeline was so full, I never really know what to say or to whom to say it.  Occasionally when I did something that I thought was cool with my Stats class, I would tweet out at the hashtags, but nobody ever seemed to notice.  The biggest thing I got out of my connection to the #MTBoS world was awareness of a conference called "Twitter Math Camp" (TMC).

Twitter for following up with people you met once at a conference
Look back on some old posts to see my thoughts on TMC14 in Oklahoma.  I met some amazing people and made sure that the TMC15 dates for California were quickly in my calendar.  However, I had 12 months before I would be able to meet with these people again, and in the meantime, there were blogs and Twitter that I could use to connect.  For the rest of last summer, I was fairly active and kept up with a few discussions.  I found myself tweeting directly at people more often.  I implemented a number of ideas from other #MTBoS teachers during the following school year.

A few insights that made Twitter a lot more useful
After last school year started, I disappeared from the internet.  I hardly blogged until Christmas break and only occasionally tweeted.  During this summer at TMC15, I finally figured out that the #MTBoS community utilized their timeline far more than they followed hashtags.  I went through and cleared out the noise -- anyone that I followed that talked too much in vague, non-helpful ways was un-followed.  I also added many new friends who had great insights and ideas to share.  This simple process meant that I could open my general timeline anytime and find a great conversation to watch or engage.  Given the lack of great multi-hashtag-following apps (my opinion) like Tweetdeck in the browser, this also made Twitter on my phone a lot more useful.

Another insight was Twitter etiquette: it is not rude to jump into someone else's conversation.  In fact, it almost seems encouraged!  I became more comfortable jumping in when I had something to share, leading to a few great chats with both people that I knew face to face and those whom I have never met.

My biggest insight: Twitter is a lot more useful when you need something that others have.  This summer, I was excited for our new Algebra 1 class.  As a result, all of my energy at TMC15 was focused here.  It turns out that there are a LOT of people who have taught Algebra 1, far more than non-AP, PBL Stats (where I previously tried to engage online), and there is no shortage of resources, ideas, and opinions out there.  After the conference, it was really easy to start conversations directed at some of the people I was working with to seek further advice.  These people either responded themselves or amplified the conversation so others could more easily jump in.

A victory story
One of the people who jumped into a discussion was @kathrynfreed.  Eventually, we were going back and forth for a few days with all kinds of awesome questions that significantly evolved my class and my thinking.  She was even nice enough to offer a lot of detailed feedback on a 8 page Google Doc with the basic course plan.  This is the epitome of Twitter facilitating what I consider a meaningful, awesome connection.

Closing thoughts:
The key to making Twitter useful starts with finding the community you want to engage with.  In my case, it was other math teachers.  Then you need to understand how that community works -- are blogs the main hub?  Is there a set of hashtags that everyone is watching?  Is there a tight-nit group that all follows each other and @-tweets at each other?  You also need to figure out why you are there.  The best case is when you are looking to learn something.  When you take someone's idea, try it in your classroom, and engage back with that person, now you have a relationship.  Eventually you may have something cool to share and there will be others ready to try it.  Sometimes, it only takes finding on person who shares a passion for some idea, class, or topic, and that is enough to get very meaningful results out of your time on Twitter.  I have a lot yet to learn, but after 8 years of having a Twitter account, I'm finally starting to get it.

A better space for learning

In my last post about our new extended Algebra 1 class, I mentioned the possibility of a new room.  I have an amazing school and awesome colleagues because, one week later, I'm moved in and ready to roll.

My old room was a computer lab with heavy, unmovable desks.  When I first moved in, I unplugged everything and rearranged it into a large U-shape to make it easy to collaborate with peers, quickly turn for a lecture or discussion, and for me to see every screen.  I loved having a lab since many of my classes utilized the technology available, and since I moved in the year we went 1:1 iPads, pressure for lab space was way down.  That said, we could not sit in groups facing each other, there were no free walls (except the front) that could be used for whiteboards, and lecturing with every desk either behind or to the side of a student was just not very effective.

The room I'm moving into used to house 35 thin client computers sitting on wooden tables.  The computers barely had enough memory to handle Google Docs, making it mostly useless to students, especially since even the iPads were more powerful.  With the permission of the tech staff and help from one of my robotics students (and some passing soccer players), we were able to take down the entire tech infrastructure in 90 minutes.  We moved around the tables into four rows of three, leaving a handful of extra tables (that we quickly put to use in other math classrooms).

Each table has room for four students, but this makes things pretty crowded.  It also means that half of the class is turned halfway around if I am talking up front at the end of the rows.  To top it off, I think groups of four are far less functional than groups of three.  Thus, each table now has two chairs on the outside and one on the inside to help alleviate those issues.

A couple views of the bare-bones, v1.0 new classroom

Since we allow students to quiz at their own pace, there is a row of eight desks against one wall.  The other three walls are saved for whiteboards everywhere!  #NPVS (non-permanent vertical surfaces)

Whiteboards posed a challenge -- our district believes in having a world-class learning environment, so the idea of drilling a bunch of holes in the brick to hang the cheap tileboard from Home Depot was shot down, despite my pleading.  However, my principal was able to stand up to some whiteboard vendors and get three high quality porcelain 4'x6' whiteboards to go up on the walls for under $600, offering a great start to the dream of 270 degrees of writable surfaces.  I plan to pursue additional funds from, our Parent-Teacher Organization, and other sources to have enough board space for every group of three to have a half of a board.

It is easy to forget how much you take for granted with tech infrastructure in a classroom.  I had no desire to get a SMART board, especially with a touch screen laptop and the ability to use AirServer to stream an iPad to the computer (and thus be mobile).  However, having no ceiling mount for a projector means it is in the way of some kids' view.  Lacking a projection screen is fine, but not ideal.  Having no speaker system or microphone connection means finding our own system to broadcast the computer and our voices to those who are hard of hearing.  Long-term, these are things the school needs to get so it is like the other classrooms, but my sudden urge for a better classroom after being inspired by the awesome learning spaces everyone shared at TMC15 mostly crept up on those controlling the budget.

I'm excited to start the year in a more flexible space, even if I will only be in there about half of the day for now.  In late October, the old teacher laptops will be used to build a full computer lab, and then I can move all of my computer-based classes back into the room without disrupting the ability to use the tables collaboratively when we are offline.  We will see how it all goes starting Monday!

Wednesday, August 12, 2015

Extended Algebra 1

I am REALLY excited for our new year-long Algebra 1 block!  It is roughly 90 minutes/day, all year long, for students who have previously scored low in math.  I am co-teaching the course with Ashlee, a special ed teacher, who is also excited to see something different that can meet her students' needs better in the math classroom.

Thanks to the extended timeline, this course is going to be a neat merger of our mastery-based units/assessments and the #MTBoS's amazing resources and ideas.  We are starting with a week of building up our class culture: name games, forming class and small group norms, utilizing random seating each day, and reflecting on our life story around math (Justin Lanier's Automathography assignment).  Half of each lesson will be guided by Jo Boaler's lessons that help students think about math differently than they have in the past.

By week two, we will jump into the content units, but a significant amount of time will be spent in group activities and multiple-entry group problems.  We will start each class with something that is not necessarily unit-specific, but builds on the big themes of the course.  These include turning patterns into functions (think Fawn's and estimation problems (based on Stadel's Estimation180).

When teaching topics for the first time, we will use short lectures in class rather than flipped videos.  With two of us, we can split the class into separate rooms or separate parts of the room to do this in a smaller setting.  However, we will keep the existing video library available for students to get more help on demand if they need it and a teacher is not available.

For space, I have come to the conclusion that my current classroom is just not a good place to learn math.  It is a computer lab with huge, unmovable desks in a large U around the room.  I LOVE having the computers for Stats and for our online (ALEKS) credit-recovery course, which is a big fraction of my schedule, but for this Algebra class all year we need something different.  Ashlee's room only holds about 15 (we have 33 students), so we need to go somewhere.

The only room in the school not being actively used has a bunch of old computers that are on the way out.  With a little re-arranging, moving in an unused projector from another room, and *hopefully* whiteboards of either the cheap/portable or expensive/wall-mounted variety, we could have the ultimate collaboration zone.  Following the model of my teammate Rob, we could also put in a row of desks along one wall for students to use during mastery quizzes (usually about once every other day for this class).  Students quiz as they are ready during work time.  As a lecture space, the room isn't great, but we can have students rotate their chairs and face forward or do it elementary school-style and just sit on the carpet in the front-middle area.

A non-artist's rendering of the ideal state of the room.

The most important reason for this blog post to exist is to serve as some context for our planning doc <-- (click on that one please!).  We have a rough collection of ideas by unit and a detailed plan of the first couple weeks.  I would love to get feedback and ideas to come pouring into this doc in order to question us, suggest new ideas, or encourage us as we try a whole bunch of new things this year.  Thank you in advance!

Saturday, August 8, 2015

Reflecting on TMC 15

When I went to Twitter Math Camp the first time in 2014 in Jenks, OK, it was everything I hoped it would be and more.  A year later, getting to go to Claremont, CA for TMC15, I was not disappointed with how many new ideas I continued to find.  It is hard to imagine ever missing a year after going.

One of the most positive feelings was nothing new, but rather confirmation that I shared a lot of perspectives with the group of teachers I looked up to most.  Some of the more important confirmations include:
  • Relationships, especially teacher to student, were universally treated as the most important thing a teacher can focus on.  Creating a class culture where learners are loved, respected, and valued mattered more than any curricular ideas or mathematical practices.
  • Growth mindset was simply understood to be a necessary way of thinking that needed to be taught and encouraged in students.
  • Effectively working in groups was universally valued, but unlike the way I have heard some teachers discuss it, the TMC discussions had much more purpose and structure to group work.  The most talked about thing was getting STUDENTS talking MATH through open-ended and ambiguous problems, Socratic seminars, debates, games, or simple class openers.
  • The Common Core's 8 Mathematical Practices offer common language and a sense of balance to the nature of the tasks we plan for students.

If I wasn't impressed enough last year, the generosity and kindness of the #MTBoS community continued to blow me away.  I could confidently ask for anything and know there were over a hundred people who would be willing to help me, and I would be more than happy to do the same for the others.  Rarely can you feel so instantly welcomed and accepted.

One major change from last year to this year was finding a morning group with a common goal to my own curricular goals.  Last year, I came into the Stats group fairly happy with the overall course framework I was using, but looking to tweak and extend it.  Though I did come away with a handful of awesome activities that I incorporated into my classes, I didn't find anyone else looking to teach a project-based, non-AP, year-long stats who could co-plan with me.  This year, I was looking for help thinking through a 9th grade extended Algebra course and was looking to really shake things up.  The combination of teaching a very common course and being more open to new ideas helped me get a lot more out of the 6 morning hours.  Max @maxmathforum and Anna @Borschtwithanna did a fantastic job of putting the minds in the room to productively discussing and building out resources and lessons that we shared with each other.  Since returning home, I have filled a giant text doc with ideas broken down by unit and an overall framework to guide the course.  Though a bit rough yet, I am very excited to discuss and solidify these ideas with my co-teacher this week.

One difference I found from last year to this year was the kinds of discussions I found myself in at night.  Last year, I played a lot of games and joined in larger-group discussions down in the lobby of the Jenks, OK Holiday Inn Express.  This year, with the large outdoor patio and many non-TMC folks at the hotel, there wasn't the same kind of "cozy" space to hang out.  Alcohol was also treated differently this year than last since so much was available.  I loved the conversations I was able to have this year, but I missed last-year's overall night culture.  I hope the dorms at TMC16 will bring back that kind of environment.

The most surprising and amazing thing I got out of TMC15 was some magical comfort with Twitter for the first time.  I have been tweeting, with teachers, since I was working on a startup in college (2009), I heard of TMC via Twitter in 2013, and I went to TMC14, and despite all of that I just didn't really "get" it.  I could understand how blogs were useful for deeper reflection, but why Twitter was a useful medium still escaped me.  My ahas include:

  • comfort with jumping into conversations when I have questions
  • tweeting out thoughts and ideas at specific people rather than hashtags (and knowing who is interested/an expert in what)

Once again, TMC blew me away with respect for these educators and left me with inspiration and tools to move in the right direction.  Most importantly, I feel like I am confident engaging in the year-round discussion that makes TMC more of a reconnecting with friends than a catch-up of what I missed in the past 12 months on Twitter.  We will see how this all works once the reality of the school year sets in, but my #1tmcthing is to engage in a meaningful way in the #MTBoS community to support my lesson and classroom culture design during the school year.

Friday, July 24, 2015

Our take on the mastery workflow

After some great conversations at #TMC15 about formative assessment, mindset, and flipped instruction, I wanted to put to words what we're currently doing and why.

A school year ago, all of our classes assessed with a one-try final, one-try unit tests, and one-try quizzes.  We did our best to build formative feedback into our daily lessons and homework, but avoided retake assessments in fear of students entering a death-spiral of retakes and falling behind.  Our classes were all fully-flipped, and I started moving away from guided notes into only making example videos for the homework packet.

This past year, with our resources allowing us to make classes self-paced, we made the leap into self-paced quizzing (only when students were ready to try).  Each quiz was hyper-focused on a narrow concept and thus grading was very binary -- either you essentially "got it" or you didn't.  We also offered a B and C quiz to retry mastery of a concept if they did not pass the first time.  To qualify for a requiz, students needed to show us evidence of new learning, ranging from a set of problems to a productive conversation.

Since the assessments were short and the grading was simple, we started grading the quizzes immediately upon completion.  Students loved the instant feedback.  I loved being able to immediately jump into a feedback conversation while the material was fresh in the students' minds.  Near the end of class, it was impossible to keep up and still circulate / help with questions, so those quizzes were returned the next day.

We found with our grading scale that many students were passing all of their quizzes, but still doing poorly on tests.  My colleague Rob realized that the pass/not-yet scoring was sending the message that "mostly right" on a quiz would lead to a successful test.  To correct for this, he implemented a 0-4 rubric score (0=didn't try, 1=getting started, 2=conceptual errors, 3=minor errors, 4=perfect or very close).  Students didn't like it at first, but then their test scores started going up, and thus their course grades, so they came around.

Efficiency was a growing challenge in class.  Even when dedicating 80% of class time to self-paced practice (in groups) and quizzing, it was hard to offer mini-lectures to groups, answer questions, check-in with everyone, grade quizzes, and go over quiz errors all during class.  In some classes, we were able to get a student assistant to help with real-time grading, but it wasn't always as helpful as needed.  Rob made another leap by setting his keys out for students to self-correct.  They did it in another color with pencils away so they would not change answers.  Once self-checked, they brought him the quizzes to him, discussed the errors and reasons behind them, and agreed on a 0-4 score for the quiz.  After holding out for a couple weeks, I tried it too and immediately loved the extra time and student empowerment that quickly followed.  The follow-up conversation after quizzes saw an improvement as well as students often figured out their errors and the root causes on their own.  They did most of the talking and I just nodded and handed out high fives.

Within a unit (typically 8-10 block periods long), there were 3-6 sections with their own A-B-C quizzes.  We expected all students to get a 4 on all sections.  Some students were able to reach this in the first half of the unit without taking work home, leaving them a lot of extra time.  We added the revised expectation that students with 4's do the retake quizzes again to confirm that they still have a mastery of the material before the test.  There was no risk of lowering the grade, but most students bought into the idea of a double-check before the test.

Despite our flexible approach to quizzing, we kept the unit test dates fixed.  Since the quarter had fixed dates, we needed to keep this structured so students would finish the course.  However, we offered a single retake for each unit test during the week of the quarter final, a perfect time to go back and study old content that was not mastered the first time.  This kept everyone on pace during the year but offered hard-working students one more chance to relearn the material and make major grade improvements before the end of the quarter.

The classroom layout played a major role in facilitating the mastery workflow.  My room, due to being a computer lab, did not work particularly well.  Rob cobbled together tables from across the building to replace most of his desks, creating collaborative work areas.  He kept 8 desks against the window for students to take quizzes individually.  The teacher desk is used for self-grading quizzes with the keys.  I think this is the ideal layout (see below):

The course grades for our Geometry and Algebra 1 courses (the ones using mastery) were composed fully of assessments: 30% mastery quizzes, 50% unit tests, 20% final test.  I thought this was a fair breakdown given that it all reflected what students could do, 30% could be infinitely repeated (before the unit test), and 80% could be repeated at least once if needed.

WINS: Looking back on the year, there were a lot of wins:

  • Student learning (as measured by unit test proficiencies) were the highest they had ever been in nearly all sections.
  • Student mindsets appeared to become more open to revision and relearning with effort.
  • Student engagement during work-time was up (likely due to nearly-daily quizzing and instant, actionable feedback on the quizzes)
  • Conversation quality between teacher and student went through the roof -- it was so focused on learning!  Complaints about points nearly disappeared, feedback was mostly student-generated with only teacher refinement, and the ability to measure real progress in learning eliminated the mystery in the process.
  • Anxiety was way down amongst students on quizzes and tests.  They loved being able to take a quiz when they were ready.  However, all of the practice with the quizzes and re-quizzes also made them more comfortable to take the scheduled unit tests.
  • I could predict test scores pretty well from the sum of the max quiz scores for each section, meaning that they were actually aligned and that relearning was as effective as someone who mastered it on the first try
UNCERTAINTY: I'm not sure how to think of the assessments:
  • Dylan Wiliam and other experts in the formative assessment are heavily opposed to attaching grades to formative assessments.  We grade ours 0-4, and even though a 3 is "proficient", it is a 75% (C) in the gradebook.  The up-side to this is that it is very motivating to work for a 4/4 through retakes (which most students choose to do).  The down-side is that we are calling a "C" proficient.
  • Quizzes are only 30% of the grade, but that can still have an impact.  The ideal case is to make it 0% of the grade and make it purely formative assessment.  However, that makes the grade 100% determined by 6 big tests.  That adds a lot more anxiety and reduces grade control for students without really shifting the grade (remember that quiz and test grades are highly correlated).  In addition, from talking to students about it, there is likely less motivation to shoot for 4's on each section, unraveling some of the wins we made this year through mastery.
  • Regardless of the grading situation, I think the quizzes are true formative assessments.  They inform students with exactly how they are doing in a test-like scenario, with test-level questions, and can be taken whenever they are ready.  If they self-correct and find they did many problems wrong, they have a conversation with a teacher.  They zero in on what went wrong and what they need to do to learn.  The grade is only applied at the end of that and students usually know what they are getting based on the conversation, so the teacher is just part of grading for calibration and integrity of the system.
INTENSE FEAR: Are we trapped in a local maximum?
  • With all of the great process work happening, I worry that our curriculum is simply bad math.  We have nearly no word problems and no contextualized situations -- just naked numbers, expressions, and equations.  The example videos have concept instruction embedded, but due to the way some units are divided up, it can be learned as procedures, not mathematics.
  • One fear is that embedding multiple-entry-point, contextualized discussion problems that groups can work on will not lend themselves to this assessment structure.  A greater use of whole-group time would reduce time for individual practice and quizzes.  It would also be harder for the class to be self-paced with more whole-group activities.  This fear may be unfounded.
  • A larger fear is the utility of the flipped videos -- if I stop telling them how to directly do everything to move to inquiry and discussion in more interesting problems, the videos are not only unhelpful but actually destructive to learning.  The practice problems would need to be fully re-written and the videos would need to be isolated to vocabulary or the rare procedure that just needs to be memorized.  Part of this fear may be unfounded as there are a decent number of "just memorize it" terms and procedures, but I think a long road is ahead of me here.
  • A huge fear is getting trapped by student success.  If we start teaching real mathematical thinking everywhere, grades will drop.  We got really good at teaching procedures efficiently and effectively in a way that the vast majority of students could learn and repeat.  Students (claim to) hate word problems, contextualized situations, and ambiguity because they are difficult and unfamiliar in their math courses.  If we upped the rigor and taught through discussion, analysis, and inquiry, students (and parents) would get upset, preferring to go back to "what worked".  I'm still committed to moving in this direction, but I'm terrified.
If you made it all the way to the end, you rock.  I would love to hear your thoughts on any or all of this -- there is a lot here.  Special thanks to Lisa @lmhenry9 for pushing me to get this all down in writing and to Princess @MathPrincessC for talking through parts of this with me tonight after her TMC session.  Huge thanks to Rob W. for trying out and then teaching me most of the ideas I'm talking about in our mastery workflow, to our student teacher Rob N for serving as the core of my reflecting all semester and cross pollinating ideas between Rob W and I, and to our entire PLC for reflecting with us and pushing us forward.

Monday, July 13, 2015

Using the mastery quiz work-flow to eliminate project grading


When my colleague Rob and I discussed Stats projects and reflections, we were reviewing the value of each and time we need to invest in them.  On a parallel track, we have both been using mastery quizzes in our other classes and are moving them now into Stats.

The projects in Stats class (Infographic, Prove-it video, Minute to Win It paper, Ultimate Frisbee spreadsheet) are fun to do, and students seem to learn a lot, but the grading process is tedious and doesn't seem to correlate with individual learning (reflecting only the effort of the hardest worker on the team).  The reflections, which are individual, are a great opportunity to see what each person really learned, but students rarely take them seriously.  Since they always come at the end after I went through multiple revision cycles of the project with students, they either get no direct response from me or only something small.

My thought was to stop grading projects altogether.  I would keep the rubrics up as the ideal to work towards, but I would remove the points.  Instead, I would create mastery "quizzes", let's call them "check-ins", that ask students to explain (in writing) specifically how the project taught them the skill in question.  When finished writing, they would bring that check-in sheet and their project (on computer/iPad) and show it to me.  If I think they understand it AND their project is an artifact of that understanding, that individual is checked off with that skill.  Each person in the group needs to do this.  They can all share the project itself, even if they divided and conquered some of the work, but everyone needs to defend their understanding of the core components individually.  That is part I would track.

Since this check requires that the work gets completed (except any busywork that didn't lead to any objectives of mine), I don't have to directly grade the project.  Since the check-in involves self-reflection on the desired outcome, I can also skip a separate reflection assignment.  Most importantly, the time I spend assessing would be mostly in direct dialogue with students.  This is the change we saw in our department when we transitioned into mastery quizzes elsewhere, and class becomes very productive.

I think the hardest part will be properly sizing the assessments so there are not too many to handle each class, but being comprehensive enough to ensure that the key learning is taking place.

If you think this makes sense, please let me know.  Also please tell me if this is a terrible idea so I don't invest too many hours in it, or at least tweak it as soon as possible.  Thanks!

A more interesting way to learn experimental design

My colleague Rob and I were talking last week about how he used to introduce the big ideas of stats.  He told the story about the farmer (whom I suppose has a name, this is a true story) a few centuries back who wanted to understand cause and effect with his crops.  Since the problem was mixing together all the input variables, he broke his land into plots and tested each variable separately.  This was (as far as I know) the start of modern experimental design.  I loved the story but didn't think most students would buy-in.  They had to feel the experience of the farmer somehow.

Since I love simulations for everything, especially in stats, I thought a simple farm simulation with a few plots and different parameters you could set would be a good starting point.  The idea was to build a simulator with too many variables (inputs) and a poor understanding of detailed cause and effect.  Students would work in groups of 2 or 3 and have 10 "growing seasons" to learn all they could about how the simulation worked.  Then each group would have one shot to try their inputs on my screen and advance in a tournament bracket (everyone loves a good bracket) to the final farming round.  The most profitable team wins.

With only 10 rounds to learn from, only teams with a disciplined approach would be able to learn enough to give them a strong shot at winning.  Haphazard clicking would leave a lot up to luck.

The first time through, I would introduce the game before I taught them anything, using the simulation as an intro event.  After playing and finding the winners, we would talk through their approaches during the 10 practice rounds and what they were able to learn.  We would discuss the challenges they found in trying to learn things.  THEN, I would introduce some of the core concepts of experimental design.  After some teaching, I would throw them back into the simulator (with a different crop / parameters) to see if they are able to better learn the ideal conditions and everyone can be more profitable.  I would assess them on how they approached the second game (they could write a summary of what they did, how it compared to the first time through, and why they made changes).

Here is an ugly but functional prototype to get the idea across.  I would love it if you can play around with the farm simulator and my description above on the lesson intent and offer feedback / ideas / links / anything to help me make this better.  Both the lesson and the simulator are very rough at the moment, but I think they could be awesome if it became a community-designed lesson.  Of course all of it will be shared freely if you want to use it.  Thanks in advance!

Monday, May 25, 2015

Even Retake Quizzes Predict Test Success

If I had to summarize this academic year in one word, it would be mastery.  Following the lead of my PLC teammate, and with the support of our department's intern teacher, I learned a ton about mastery learning and assessment.  It would take a few dozen blog entries to tell the whole story, but I'll start with something interesting: the strong correlation between cumulative quiz results and test results in the mastery setting.  These results held true in both a 5th grade classroom where I provided some assessment support and my high school Geometry class.

Generally speaking, quizzes SHOULD predict test scores if they are in proper alignment.  However, in our mastery classrooms, students have a lot more control over their quiz scores.  First, they are self-graded.  There are not a lot of opportunities to be dishonest the way the classroom is setup, but I am continually impressed at how accurately most students self-check their work.  Second, students can take unlimited retakes.  This means that they can nearly guarantee a score of 4/4 (meaning no mistakes) if they are willing to keep working and seek help to make improvements between quizzes.

5th grade: multiple choice mastery quizzes (by standard) predict MCA (state NCLB assessment) test scores, r=0.91.  Reaching 60% proficient in the Mastery Connect quizzes that we created nearly guaranteed MCA proficiency with only a few exceptions in the 60-70% range.  Every student below 55% on the Mastery Connect quizzes was not proficient on the MCA.  This means that there is no longer guesswork needed for interventions -- students can be reliably identified by January as unlikely to pass the state assessment and can receive necessary remediation.

Geometry: quiz totals by unit (mastery) predict test scores.  Over 4 units, correlation ranges from r=0.66 to r=0.81, with most on the higher end (see graphs below).  When talking about proficiency, I made the cut-line of an average quiz score of half 3's and half 4's (3.5 average).  See the table immediately below for number of students who were proficient on the test (above 80%) when they were above or below the cut-line.  In the earlier units, this did not prove to be as predictive or critical.  By the last unit, the quiz scores essentially told you if you would be proficient or not.

Below 3.5 quiz avgAbove 3.5 quiz avg
Alg Expressions7/197/7
Alg Equations4/177/9


I like mastery-based quizzing because it gives students a sense of self-control over the course outcomes.  If they want a high quiz grade, they can adjust their effort level and actually achieve it.  More importantly, the high correlation with tests means that, by proxy, effort is highly correlated with test scores and thus overall course grade.  Students have the ability to control their outcomes more than ever.  Next step: communicate these results to students and continue to help them overcome the fixed mindset that leads many students to delay their first quiz or not even attempt re-quizzes.  Second step: rethink the context that motivates students to WANT to succeed, even if it takes extra effort, in order to encourage students to work harder than they ever have.