Monthly Archives: April 2013

How much should teachers do?

A recent post by Lisa got me thinking: how much should a teacher do? Lisa mentions that during an observation some of her students were not very engaged and that was reflected in the observation feedback.  A number of comments responding to her post outline different strategies that other teachers use to maintain student engagement.  However, it seems to me that this is not a one-way street: student engagement depends on the students as well as on the instructor.

Last week, I gave my Algebra I students an exam on systems of equations. I noticed that one girl, who has not paid attention all year and who is currently getting 5 F’s and 1 D in her courses was now, for a change, paying attention and taking notes. When I scored the exams I was blown away by the fact that she got a perfect score – actually she was the only student in three sections of Algebra I that did so. After I handed back the tests, I pulled this girl out in the hallway and, after congratulating her, I asked what changed. She said “I studied”. I asked her “Why now? Why did you waste a full year?” Well, it turns out she is in the judicial system – she was caught stealing and part of her probation is to get/maintain good grades.

I submit that some students (unfortunately too many in my classes) will not respond to teachers trying to engage them, especially in math. I submit that, while none of us wants to be a boring teacher, there is a large degree of responsibility on the students have to be engaged in class. I submit that we should stop beating ourselves up if some of our students are not engaged. If the horse does not want to drink, it will not drink no matter what song and dance we do.

As the case mentioned above illustrates, sometimes extrinsic motivation can be very powerful. I submit that our educational system does not provide sufficient such extrinsic motivation. If you fail a course, you can always take it in the summer – where teachers are many times easier. If you don’t get a good GPA, you can still go to college (albeit a junior one).  If you don’t score high enough on the placement exam, you can still take basically your high school courses over again.

The mantra in education seems to be that all our students will be successful and we will ask the teachers to explain, engage and entertain so no one falls behind. But, by trying to be inclusive we are too loose and too many of our “successful” students do not measure up to college or job demands. We are asked to engage the students, but there is no rubric on the observations forms for “teaches students to accept responsibility”.


Flipping the classroom – Algebra 2

“Flipping the classroom”, also known as “blended learning”, is a teaching technique that is currently very much en vogue. In summarizing blended learning , a KQED report states: “blended learning programs involve teachers who use home-time online discussions and collaborative projects as fuel for content and discussion in the classroom.”

The main advantage claimed by the flipping technique is that when students debate with each other the truth among the explanations presented to them, they achieve a better understanding of the concepts than when the instructor lectures from the stage.

The flipping technique started in an intro physics class at Harvard, with Professor Eric Mazur as the instructor. Professor Mazur has a number of videos that explain how the idea was born and how he implemented it. (

This year I decided to implement the flipping technique in my Algebra II classes (freshmen and sophomores). In this post, I want to describe how I set up flipping and my conclusions about using flipping at this level in high school.

At the beginning of the course I announced that I expected every student to have access to the Internet and that many assignments will involve watching videos on the Internet – either videos produced by others, or by me (via a software called Explain Everything, used on the iPad).

A legitimate question regarding flipping the classroom is what to do about the students that do not have Internet at home. For those students, I suggested that they use the school library or the public library. (When I suggested to one student that she use the town library to watch the videos assigned, she told me “I have a life” and switched classes the next day. Unfortunately, that pretty much summarizes most of the students I deal with and the school, which has a pretty liberal policy of allowing students to switch teachers.)

In addition to insuring internet access, I gave every students a set of 3 X 5 colored cards, each of a different color, each color corresponding to a choice and marked with an A, B, C, or D respectively.


The first day of a new topic, we had a full period lecture with a lot of practice problems. This introduced the concepts and gave the students an opportunity to see what kinds of questions would be asked. The homework assignment consisted of two parts. First, I asked the students to watch a video on the topic under discussion and/or a textbook reading.  Second, I asked students to send me, by 9 PM, 3 or 4 bullet point descriptions of the main ideas in the video/reading and a list of questions on the concepts that they did not understand.

Both the bullet points and the questions counted for the homework grade together with whatever problems I also assigned. Often students start with the problems instead of the reading and this way I wanted to make sure that at least they perused the video and/or the text.

I cut and pasted the questions from every student so I had a list of questions for the whole class. Often, groups of students had the same question, so I knew that to be a concept to emphasize. Based on the compilation of student questions I then made up 6 – 7 “concept questions”. These were all multiple-choice questions, as in the following example:

Which of the following represents abs(x + 4) = –5x + 6?


The idea here was to help students visualize the absolute value equation and to start a discussion on the number of roots possible in such equations. Another potential benefit is that students learn how to eliminate some of the “bad” choices among the possible answers.

After the first day’s lecture and reviewing the student questions, I then put on the screen the concept questions. For each concept question, I asked the students to read the question and think of the answer for about 90 second. Then, I asked the students to vote by raising the appropriate color card.

Often, what one sees in this procedure is that two of the possible answers get most of the votes. After looking over the raised vote-cards I then say “Turn to your neighbor and discuss your answers”. The class discussion is also part of the students’ grades – I look for a serious discussion and listen to the arguments presented.

At the end of about 2 – 3 minutes of discussion, I ask that students vote again. Most of the time, the second vote migrates towards the correct answer. I then conclude with the instructor’s take on the problem, stressing what I believe to be the key points.


I drew a number of lessons from implementing the flipping technique in Algebra II.  The first lesson is that for this technique to be successful, it must be implemented on a regular basis. When I originally discussed flipping with the administrators in charge of evaluating me this year, they expressed the worry that I would not lecture and that the kids and they would “have to learn on their own”.  This from people who say they want to promote self-reliance on the part of the students. As a result, I held back on using the flipped classroom as a regular teaching technique.

A second lesson – and perhaps the most important one – is that concept questions are most useful when students have a handle on the fundamentals. My Algebra II students often are still shaky on some fundamental Algebra concepts such as manipulating equations, graphing lines and squaring binomials.  There is an unresolved tension in mathematics education between teaching the fundamentals (“drill and kill” type of problems) and teaching for understanding (“critical thinking” type of problems). I have the feeling that flipping the classroom would benefit most those students who have mastered the fundamentals and are ready for a higher level of thinking, not impeded by procedural missteps.

A third lesson is how difficult it is to write good conceptual questions. I spent more time on coming up with good conceptual questions than I spent on any other part of the flipped classroom. I have a feeling that this would be either in more advanced, “richer” courses, such as AP Statistics or Math Analysis. In more elementary courses the concepts are simpler and fewer. For example, when we teach systems of (2) equations in Algebra, the only concept I can come up is that the solution is the point of intersection of two lines – most everything else is procedural.

The fourth lesson is that students need encouragement to participate in productive classroom discussions. Too many of my students are shy about discussing a math problem, even with their peers.  I still have not resolved to my satisfaction how to give credit and encourage serious class discussions for every student in my class.

However, I do think that flipping the classroom has a lot of merits and I will certainly try to do more of that next year.