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


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.

Feeling very “amateur, but experienced” today

I had one of those days which probably went OK for the kids but didn’t seem to flow at all well for me.  Here is what happened.  Yesterday the students took a learning target quiz.  Since students would be finishing at different times, but there was still a lot of time left in the period, I gave them the assignment to connect to the internet and watch a video after the quiz that went over some introductory notes about logarithms and converting between exponential and log form, a topic they had previously covered in Algebra 2.  That went smoothly, amazingly enough.  Internet access worked and everybody watched the video and got the notes done.  Today I used my Navigator system to check for understanding.  The problem was that we had to update calculator operating systems, remember how to all log in, etc. etc, which was a necessary evil, but it ate up some class time.  Meanwhile my SBG trained kids just started working on the two worksheets they had picked up, before and during the Navigator review, so some students were far ahead of others, but that, I guess, was OK, too.  The formative assessment (FA) showed about 75% mastery of concepts, which was not bad for the first day of reviewing something from Alg 2, so that was OK.  I did a bit of reteaching as we went through the FA, spent a few minutes introducing a couple of log properties, and then did the first problem with them on another worksheet about exponential growth, leaving them to finish up both worksheets and check keys online.  As I look back on it, nothing was really negative, but I felt like I was jumping all over the place with not coherent plan to my lesson and the kids were all doing their own thing, some paying attention, some just working on their own, so I wasn’t sure if students were getting the point of what I was saying, especially my weaker students.  And coming from 16 years of structured lecture, followed by practice, the whole thing just seemed sort of loosey goosey to me and I felt like I had blown it–very amateurish when it comes to the whole SBG flipped classroom experience.

Guess what?  After writing this, one of my weakest students popped into my room to ask a question.  I asked her how class had gone for her today–was it too chaotic, hard to follow, etc.  She said very nonchalantly, “It was fine. I understood everything.”  She had already done most of the worksheet and just needed to clear up a few details she had questions on.  Eureka!  I am not a failure.

Sad, but glad

Two day ago, I used the cricket chirp/temperature relationship and had students come up with a linear equation to describe the relationship as an introductory activity to mathematical modeling.  The sad thing:  Some students still had to be reminded how to find a linear equation from two points–in Precalculus!   Students were thrown by the context of the problem.  Too often, they only see:  “Here are two points (3,5) and (-2,8).  Write an equation of the line containing those points.”  But two points in real life context just messes up their neat math world and they don’t know what to do.  In fact, one student told me that he never before realized that you could actually use  the equation of a line to figure out something in real life.  How sad that he is first encountering this in Precalculus!  But how glad I am that I get to help open their eyes to a little bit of what math is all about!

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.


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.


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.


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.

The evolution of a precalculus teacher

I have been teaching Precalculus for about 15 years.  I learned how to teach Precalculus using Paul A Foerster’s excellent Precalculus text and gradually began adding in my own ideas and worksheets as I got more and more comfortable with the material.  So the textbook went from being my teacher and sole source of instructional material to just one of many resources and finally to a thing the kids carried around but often didn’t use for weeks at a time. Then it came time to adopt new textbooks and the Indiana Department of Education recommended that we postpone adoption for a year until the new (CCSS) standards came out.  The next year, we tried Springboard (a one year commitment since the text is consumable),  but none of us liked the way it was structured.  So, sans textbook, and still waiting for the IDOE to finalize the high school standards, I just did my own thing with worksheets I created.  I missed having the textbook as a resource — “Turn to page 123 and do #1-25 odds”– but I made it through year one.  Year 2 was easier, but I still missed having a resource to which students could refer for help. Year 3–still no textbook and still no definitive high school standards.  Finally, Indiana adopts Common Core.  Then the legislature decided to postpone for a year and think about it.  They are still arguing and we are still in limbo about CCSS and our high school standards.  For four years now!   Arghh!   (Precalculus won’t be tested in any end of course exam, probably because no one quite agrees on exactly what Precalculus is.  The CCSS for Precalculc is mostly just trig and then a bunch of unconnected stuff they didn’t know what to do with.  They eviscerated Precalc and dumped way too much in Algebra 2.  But it sure would be helpful to know exactly what Indiana will be requiring for Algebra 2 so I know what I’ll have to cover in Precalc!  Come on, Indiana!  But I digress.)

Back to my evolution.  No matter what I do, I am never fully satisfied with my curriculum because there isn’t time to do everything, so I always struggle with what to leave out and wrestle, as all math teachers do, with striking the right balance between “covering the material” and providing students with time to think and experience mathematics in a meaningful way.  I also struggle, as all math teachers do, with how to meet the diverse needs of students who learn at different speeds.  I always seem to have a handful of students who stick it out in Precalculus, working hard all year, only to end up with a D or even an F, because they need a lot of extra support and just can’t learn everything as quickly as everyone else.  Just giving them a test they fail and then moving on seems so pointless and unfair.  So when I read about Jo Boaler’s free online course How to Learn Math, I signed up and found that what was bothering me about math education bothered other people as well.  To make a long story short, I watched Jo’s videos (you can see some at her new website  http://www.youcubed.org), read a bunch of blogs and discovered Standards Based Grading.  Two weeks before school started, I decided to take the plunge and do SBG in Precalculus this year. .  . alone . . . unaided . . . and without any training.  I also thought I’d throw in some flipped classroom.  What was I thinking?!  But I was so convinced that I needed to make the change, that, against my own inner warnings (this is going to take so much time and so much extra work, Jane, and it might not even work) I did it.

Next blog:  What has happened so far with SBG