I am terrible at leading classroom discussions.

I think that I do fairly well at engaging my students when I lecture.  And my assessments require students to demonstrate in various ways that they truly understand the concepts.  I have implemented some successful projects.  But I am JUST PLAIN HORRIBLE at facilitating meaningful and rich mathematical discourse in my classroom.  Inspired by wonderful blogs and websites, I have been trying to lecture less and get kids to think for themselves and engage in rich tasks and have meaningful discussion . . .with almost zero success so far.  On Monday I decided to begin my unit on Sequences and Series by using some patterns from visualpatterns.org

VisualPattern1

These patterns are SO cool!  All of the students were engaged some of the time and some of the students were engaged all of the time (thanks, Abe Lincoln), but the conversation was never lively and I felt like we never really accomplished anything .  So often, when I try something new, I have a interesting activity and I know what I want the kids to do or to learn, but I have no idea how to get there.  I don’t know how to plan a classroom discussion.  How do I get the conversation started?  How do I facilitate a student-driven activity and yet accomplish specific learning objectives?   (Looking for some feedback here!)

Some things I know I did wrong:

  • I didn’t start with a question that everyone could answer.  I probably should have said, “Tell me something you notice about this pattern,” and then written down all of the student ideas.  (any other ideas for good starter questions?)
  • I revealed too much information at the beginning.  The website gives the answer to the 43rd pattern and asks for the equation.  I should have just shown them the pattern first without the additional information.  I think students were intimidated by the question about the equation.
  • I should have taken the time to anticipate possible student answers and plan out my questioning strategy ahead of time instead of winging it!

Thanks to two wonderful bloggers for their inspiration and help:  Michael Fenton’s recent posts about his One Minute Makeovers of his old assessments helped me to realize that trying something new and failing is normal and is better than not trying something new at all.  I can learn and grow better at this!  And Dan Meyer’s post today on Teaching the “Boring” Bits  was especially timely and full of helpful advice as I navigate the new and uncharted waters of facilitating meaningful classroom dialogue.

MTBoS Mission #5

Did my first Twitter Chat last Thursday.  It was a good experience, but not my favorite way to spend an hour and a half on a school night.  I felt like it took a lot of time to say very little, although I did glean a few useful ideas on which to follow up.  The best part was discovering some more like-minded Precalc teachers to follow on Twitter and possibly exchange ideas with later.  I’m not sure if I’ll do it again, but I am definitely finding Twitter to be a wealth of wonderful people and enough ideas and resources to make my head spin.  I think I tend to be more of a blog person.

MTBoS Mission #4

I listened to a podcast, the one “that started it all.”  I enjoyed listening to the discussion between Ashli Black and Daniel McMatherson, two teachers who are as passionate as I am about trying new things and who also struggle as I do with those new things they are trying!  Daniel switched to SBG cold turkey, just as I did, because he wanted to force himself to really think about what he was teaching and why, saying it has been hard but definitely worth it.  I switched to SBG because it offered more authentic grades, but soon found myself forced to plan much more carefully and deliberately than I ever have before,so I understood exactly what he was talking about.  Hearing him talk about how hard it has been for him makes me feel better about my implementation of SBG.    The two of them also talked at length about those days when they ended up apologizing to their students after teaching a lesson that no one really understood.  I’ve been there, too.  Listening to them validated my efforts this year to keep trying new things even if they don’t work the first time around.  And I loved Daniel’s “gift” at the end–wishing that all teachers could have another like-minded teacher with whom to “talk math teaching.”  I was beginning to despair of finding such a person outside of the occasional conference until I stumbled across MTBoS.  I’d love to listen to some more of the podcasts, but they are so long.  An hour is a lot of time for a busy teacher.

SBG Trials and Triumphs

Continuing my Precalculus journey…

So I decided to try Standards Based grading this year.  I forgot to mention that we are also  moving to Bring Your Own Device next year and maybe going paperless? (The contract on our copiers runs out after this year and our principal has asked us to move to a paperless environment–another issue that the math department needs to deal with and probably the subject of another post.) I am the department head, so I think it is important for me to be the first one to try new things so I can help others in the department with the nuts and bolts of the transition.  So I have invested a lot of time in exploring online resources, checking out apps and various devices, and making videos of lectures and posting all of my notes and handouts and lots of extra resources on my website, in addition to changing to Standards Based Grading.  So how is it all going?  Amazingly well, considering the enormity of the undertaking.

I will start by explaining what SBG looks like in my classroom, since SBG is a broad concept whose details look different from school or school or from teacher to teacher.

1.  I don’t grade homework at all.  Students can do as much or as little as they need to do to learn a concept.  Complete answer keys for all assignments, with work shown, are posted online, along with all worksheets, notes, and other online resources.  (I use Google Drive, a Google site, and YouTube)  Here is the link to my most recent unit on my website.  After trying various ways to organize my resources, I like this one the best so far.  You are welcome to use my stuff, but my videos are not high quality–strictly amateurish.

2.  Videos explaining all concepts (mostly made by me) are posted online.  Some are repeats of lectures given in class. Some are assigned to view outside of class (partial flipped classroom).

3.  Students are given a list of learning targets (standards to master) for each unit.  Here is an example.

4.  Students are quizzed twice in class on each learning target (LT). There might be several LTs on each quiz, but each LT is scored separately as a 10, 9, 8, 7, or 5, (I also use 7.5, 8.5, or 9.5), which correspond to A, B, C, D, and F in our grading scale. (The reason that I give a 5 instead of a 0 is because I realize that this is a grade in progress and I don’t want students to lose their eligibility to play sports, for example, until they have had a second try.) The score for each LT on the second quiz replaces the first.  However, if the second grade is lower, I will only lower the first grade by one point. (I may change this to averaging the two scores. A student who gets an A and then an F on a standard doesn’t deserve a B, in my mind.  I want them to retain the information.) Two 5’s in a row becomes a 0 in the gradebook, because if a student doesn’t show any improvement at all, then their grade needs to take a hit at that point, to force the student to do something about it.
Students can then retest on any individual LT outside of class.  After the third try (2 times in class and one outside of class), the maximum score a student can get is a 9.

5.  Class time is spent in a mixture of whole group instruction, collaborative work, individual practice, and quizzing.  I don’t spend time in class going over quizzes or assignments, except to comment on certain questions missed by nearly everyone or to work with individuals or small groups on questions.

Positives:

1.  Students are actually doing assignments to learn instead of just to get a grade.  It took a few bad quizzes for some of them to realize that they still needed to do the work, even though it isn’t graded, but they soon realized that the effort they put in actually resulted in learning.  Some students who can master the concepts without doing much practice are not doing unnecessary (for them) busy work.  Students are even requesting additional problems so they can practice more.

2.  Students are becoming self-directed learners.  Because I do not grade homework, I can post answer keys and even videos explaining how to do some of the more difficult problems and encourage kids to use those resources to help them when they are stuck on something at home.  I have some students who watch videos multiple times and who reprint worksheets to do again for extra practice.  I have also recruited peer tutors and have paired them up with some of the students who struggle and now they are helping each other.   They are figuring out how to teach themselves and what works best for them and it is awesome to see.

3.  A clearly defined list of LTs helps the students to know exactly what they need to know and what they have mastered already and which areas they need to work on.  When students get back a quiz, the individual scores on each LT allow them to self-diagnose their strengths and weaknesses.  Clearly defined LTs also help me to identify the core concepts that require mastery and focus my teaching in those areas.

4. Grading is vastly streamlined and more informative.  I don’t waste time checking homework that may or may not reflect the student’s own effort and knowledge.  I can give harder problems and grade more strictly on assessments, not padding the grade with partial credit, because students can try again, if necessary.  I also have time to give more detailed feedback on assessments because that is the only grading I am doing.  Here is how I show scoring on a quiz.  Often multiple problems will contribute to a score and I grade holistically.

scoring

5.  Test anxiety is no longer an issue.  Prior to SBG, when students did badly on a test, a significant proportion of them would say that “I knew how to do the problem, but I always freeze up and go blank on tests.”  Sometimes that was true and more often it was lack of understanding or failure to prepare adequately.  But that is what they said.  Amazingly enough, no one says that to me anymore.  If students do badly now, they say things like, “I didn’t have time to study that” or “I wasn’t prepared” or “I need to get some help with that” and then say that they will be ready on the second quiz, and they usually are.  Test anxiety is not even mentioned.  Knowing they can improve their score seems to have taken off the pressure.

6.  A higher proportion of students are mastering the concepts, including my weaker students.  That is the bottom line.

Negatives:

1.  Coming up with the list of learning targets is difficult and time-consuming.  If they are too broad, students don’t know how to prepare.  If they are too detailed, grading is tedious and you lose the big picture and the inter-connection of the concepts.  It is hard to strike the right balance, but it does seem to be getting better as I gain experience.  It is always a hard call to determine what is essential and what is not as essential for students to know.  I’m sure I will do some revising next year.

2.  I am spending a large percentage of my time in class quizzing.  Some of that has gotten better as I have streamlined my learning targets, but it is still taking a big share of classroom time, to the extent that I am not going to be able to cover as much as I did last year.  Maybe that will get better with practice, as well.  I was flying by the seat of my pants at the beginning of the year and we have had some internet issues at school, both of which have contributed to wasted time in class, as well, so maybe that was part of the problem.  Having each LT on two different quizzes in class is more time-consuming, but gives me much better information on what students really know and retain, so I am not ready to give that up at this point.  Maybe my learning targets are still too numerous and need to be even broader.

3.  My best students need more to challenge them.  I started adding in bonus opportunities for those students who master all of the LTs quickly on the first try and don’t need as much practice to master concepts.  They still have to take both quizzes, to demonstrate mastery and retention, but they usually finish so quickly that they have time to do a bonus topic or a challenge problem.  There is a cap to extra credit, but just having the opportunity to meet a challenge is an incentive for many students.  I also have been giving some extra credit assignments (no key posted) for students who are not necessarily fast on the quizzes but are willing to do extra work outside of class.

4.  How do I incorporate open-ended problems?  I want to do some projects or open-ended collaborative work but how do I assess those types of activities using SBG?  I’d love some feedback on that.

I’d love some comments from other SBG users.

Fun with Daily Desmos

My Desmos solution

My Mission #3 assignment with MTBoS was to explore one, only ONE of several excellent websites and write a blog about my experiences.  Since I just commented in my previous entry that I didn’t know anything about Desmos (and everyone who is anyone on MTBoS seems to use it) I decided that now was the time to learn it.  So I did a couple of the basic challenges on Daily Desmos and I was pleased with my trigonometric transformational approach.  I wonder if anybody else tried that.  The online Desmos graphing calculator is user friendly and the Desmos Challenge problems (matching graphs) complements my Precalculus curriculum very nicely, so I hope to incorporate it in my classroom.  I will have to Twitter some questions first…

Of course, I had to check out some of the other interesting websites:

Estimation 180:  Teaching estimation skills with pictures (similar to the visual approach of Dan Meyer’s Three Act problems)  I like the idea of using my own pictures to do some interesting warm-up problems.

VisualPatterns:  I can use definitely use these in the classroom (functions, sequences) and with math club.  Saves me a lot of work!  Woo-hoo!

Math Mistakes:  What a novel idea–posting student mistakes and then reflecting on the conceptual misunderstandings and implications for teaching.  I read some very insightful posts.  Here was a great one:

Mistakes, Radicals, Rational Exponents, and Partitioning?

One Good Thing: A forum for teachers to post something GOOD that happened in their classroom.  Very uplifting 🙂

And …. I just figured out how to embed the links to all of these in my post!  Another Woo-Hoo!

Twitterized

I just tweeted a few people and read some tweets. Nobody has tweeted back yet, but I have already found some amazing blogs and downloaded some great resources that I found on Twitter feeds. I can tell that my biggest problem will be managing my time and knowing when to stop.  I hope that I can cultivate a few like-minded Twitter pals to share ideas with.  I guess that the best thing I have learned is that all of these wonderful teachers who know how to use Desmos (I don’t) and attach links to Twitter feeds that have “bitly” in them (I don’t know how to do that either) and who use these amazing activities that I want to learn how to use still struggle with the same classroom issues and feelings of inadequacy that I have.  And they share the same joy when they try something new and it actually works!!