Technology

I like technology.  I really do.  Calculators, computers, tablets, cell phones...facebook, twitter, class websites...I use them all, and I like using them all.  They make a lot of what I am able to do in and out of the classroom as a teacher possible.  From exploring mathematics to answering questions and giving homework hints to keeping up with former students (not to mention hearing from people I have never met in response to this blog), so much of this simply wouldn't be possible without technology.

And yet, if you were to look around my classroom on any given day, you would often wonder if technology was even present.  The kids have their calculators, and every once in a while they'll reach for them. If they need a definition they may reach for their phones and look up the term in question.  But most of the time the focus of the in-class discussions is on the concepts and the content, trying to understand the mathematics rather than mindlessly plugging in numbers or relying on calculator-produced graphs.

Which got me thinking this week: with the huge push from seemingly everywhere to incorporate more technology into our lessons, are we using technology for the sake of looking modern, or are we doing so to actually improve the quality of the learning that is happening?  As we encourage the kids to make use of the technology, are we also teaching them to discern when the technology is being helpful and when it is actually getting in the way?

And then there is the bigger question: for as connected as we are and with all of the forms of communication we have at our disposal, how are the kids at one-on-one communication?  While there are plenty of kids who are fine when it come to having a face-to-face conversation, for others it is a definite weakness.  Most of the kids are comfortable having a texting conversation, but when it comes to actually talking with another person the percentage drops drastically.  And by encouraging the use of technology (for instance, discussing a reading assignment on a wiki instead of in class), are we inadvertently denying our kids an opportunity to work on and develop a skill they lack?

Just some thoughts from the week as I was sending out homework hints on twitter, looking around my classroom watching the kids have face-to-face conversations with one another every day, reading the self-assessments they submitted online, and wishing former students "happy birthday" on facebook.

The Advantages of a Large Class

Thursday and Friday of this past week, the band students in my classes (and there tend to be quite a few of them) were on a trip to Indianapolis, which for two of my classes took the number of students down to 15 or less.  So, rather than sitting at separate tables, those classes sat as one group and discussed the exercises.  Since it was only one group, I didn’t need to circulate and sat at the “table” with them the entire bell both days.  The atmosphere was, as you might expect, completely different in those two classes.  The most striking thing to me was the way that most of the kids presented the material to me instead of the group.  There was an almost constant look of, “I’m doing this correctly…right?” in their eyes as they kept turning toward me about every five seconds as they presented their solutions.  It took a lot of reminders to get them to refocus on presenting to each other, interacting with each other, questioning each other, etc.  Friday was definitely better than Thursday, but even then there still wasn’t the level of interaction that normally pervades the classroom.  These two classes are my morning classes, so it made for quite a contrast to the afternoon, where things were running normally, with three or four tables going at once and me checking in visually and verbally with each group rather than sitting with them the entire bell. 

From this, it occurred to me that there may actually be an advantage to having enough students in the classroom to force the move to more than one group.  Specifically, the students are forced to become more self-reliant.  If I’m constantly at the table with them, it becomes really easy to fall back into the old habit of relying on the teacher for everything from moral support to verification of the correctness of answers.  (I avoided asking questions and/or agreeing with their answers until the end of each presentation, allowing plenty of time for the other students to catch any mistakes and ask any questions, but the request from their glances was there almost constantly.)  If, however, there is an understanding that I need to keep track of other tables and that I can’t be with any group the entire time, then the responsibility of running the conversation, catching the mistakes, asking the questions, and thoroughly investigating an exercise falls to the students by default.  And normally the kids rise to this responsibility, especially by this point in the year.  Despite the fact that we just began the new trimester on Tuesday and that these kids have not been together in my classroom before (they’ve had the first half of the course so they know how things are supposed to run, but it’s a new distribution of the students each trimester), the afternoon classes are already running smoothly, and I’m sure the morning classes will be next Monday with the return of the band kids.  However, the fact that the instinct to look to me rather than to each other is still there is something that I found disconcerting to say the least.

So, one more thing to add to the to-do list: make sure the kids understand that they can and should rely on themselves and on one another, not only in my class but in others as well.  I’m there to double-check and refine their results, but I’m not the driving force behind the conversations.  I thought I was already doing this, but clearly I need to do a better job.  Hmmm…

Cause or Effect

In every discipline, there are some pieces of information that simply need to be memorized.  Each subject has its foundational definitions and fundamental facts: names and dates in history, proper grammar and syntax in language, basic arithmetic in mathematics...all of these need to be fairly automatic to be successful in understanding the content of the subject at hand.  However, I've been giving this some thought lately, especially with final exams this past week, and the question I have is this: should memorization be part of the cause of understanding the content of a subject, or should it instead be the result of understanding the content? 

For example, is it necessary to sit down with flash cards and memorize the important names and dates as part of the process of understanding historical events, or, instead, should the memorization of the names and dates be the natural result of understanding the events?  Does memorizing the formula for the area of a rectangle actually help me understand what it is I'm finding, or instead, does understanding what it is I'm finding result in the memorization of the formula?

The reason this came to mind this week is I noticed that some of the kids who had, up to the point of the exam, earned As on the tests were lightly reviewing for the exam, whereas others with As were studying rather furiously.  Those who were lightly reviewing were participating in the discussion during the in-class review in a very relaxed, almost nonchalant way, and through their contributions it showed that they have a solid understanding of the material.  On the other hand, those who were studying furiously seemed to be attempting to re-memorize the material, and their conributions to the in-class review discussion were more in the form of double-checking their facts rather than demonstrating their knowledge. 


My conclusion after watching this was that both directions (memorize to understand vs. understand to memorize) are viable methods of achieving success on tests.  Both groups of kids had As on the tests, so both, from a purely data-driven perspective, were doing well in the class.  But looking more deeply into that success, it became obvious to me that only some kids were being truly successful when it came to actually learning the material.  And those were the kids whose memorization of the material was the result of understanding it, and not the other way around.

I wonder how prevalent this is in every class, regardless of the subject matter.  I wonder how much I have missed during my teaching career, thinking that if the kids were doing well on the tests (perhaps even the AP tests when I taught those classes) they were understanding the material.  And I'm grateful to have found a means through which I can at least partially discern which kids are truly understanding the material and which ones, despite their grades, are not. 

Just one more reason to use and promote discussion-based learning.

I Can't Imagine

There is a group of teachers in my building who are doing some professional development about discussion-based learning, and as part of the preparation for a day that we will be spending with one another next month we are doing some peer observations.  This week, one of the other teachers came in to watch one of my classes, and while she was in my classroom she asked the kids some questions, wanting their perspective on Harkness so she could share their feelings with the group.  While the other teacher didn’t share all of the responses with me, she did share one, and it absolutely made my day.  The question she put to the student was simple enough: “How do you feel about learning this way?”  The response from the student?  “At first, I wasn’t sure if I liked the class being run this way or not.  But now, I can’t imagine learning math any other way.”

I love this answer as it sits, but it got me thinking.  It’s now been a year and a half since I’ve lectured on any kind of a regular basis, and I’ve reached a point where I can’t imagine teaching any other way than I am now.  Whether it’s in my high school classroom where as close to Harkness as I can get rules the day, or my evening college classes where I run things on more of a flipped model, I can’t imagine running things any way other than through discussions.  The assessment information I get from the discussions, the rapport I am able to build with the students, the general atmosphere of the room…all of this has improved since I started running my classroom through discussions.  Not that it was bad before – it wasn’t - but the improvement from my perspective as a teacher has been priceless.  I get constant feedback, the students have a real sense that we are in this together, and the room is relatively relaxed.  OK, there’s some frustration when a student isn’t understanding a concept, both for the student and for me, but it’s productive frustration and certainly better than before when there were many times that students didn’t ask questions until right before the test when the urgency of the situation made the frustration far more intense.  The discussion-based classroom alleviates a lot of this type of frustration by all but forcing the kids to speak up and ask their questions, as well as forcing the teacher to pay more attention to the individuals than to the class as a whole.

Nope, I can’t imagine teaching math any other way, and for at least one of the students, they can’t imagine learning math any other way.  I doubt the student is alone in feeling this way, and after gathering next month, I hope that I’m not alone, either.

Why I Made the Switch

A few of the other teachers in my building have begun to implement some discussion-based teaching in their classrooms a couple days each week.  During a conversation this week, one of these other teachers made the observation that teaching this way is exhausting.  This came as no surprise to me, but it often comes as a surprise to many to whom I try to explain the way things are run in my classroom.  My assumption is that they imagine me just sort of sitting around watching the kids work.  Or worse, that I sit at my desk while the kids flounder, and every once in a while I descend from the heights to make sure the kids are still working.  Of course, the reality is that if you're running a discussion-based classroom "correctly", you're constantly walking around the room, constantly listening to the conversations, constantly assessing how well the kids are understanding the material, and so on.  The walking is not necessarily physically exhausting, but it's certainly more physical activity than I experienced when I used to lecture.  The real exhaustion, though, comes from how mentally taxing running a discussion-based classroom is. When lecturing, I could prepare the "script" for the day pretty well, especially after teaching a course for a few years and gaining both a solid knowledge of the material and the ability to second-guess the common questions that would come from the students.  Realistically, I wasn't doing a whole lot of daily assessment, and certainly wasn't doing the kind of constant analysis of the students' understanding I'm currently doing.  So, in this regard, running a discussion-based classroom is definitely more exhausting.

Interestingly, during a phone interview this week one of the questions I was asked was, "Do you find this way of teaching to be more difficult?"  My first reaction was that the interviewer clearly understood what actually happens in my classroom, because this is the first time I have been asked if teaching this way was more difficult.  I don't know if I would qualify running a  discussion-based classroom as being more difficult, though, since preparing a lecture can be fairly labor-intensive.  Although, after teaching a class for a few years, the preparation portion of a lecture-driven class can get easier.  Similarly, the preparation portion of a discovery-based class is fairly labor intensive; however, in my own experience, this year has been easier than last year in terms of preparation, and I can directly attribute that to the fact that we have the year of experience behind us.

All of this then begs the question: Why?  Why make the switch from a lecture-based classroom where I was comfortable?  What reasons could I give someone to include at least some discussion-based activities in their classroom?  Ultimately, I don't think it comes down to how the material is delivered to the students.  As I have said previously, I firmly believe that I cannot make sense of the material for any of my students, and that ultimately they need to make sense of the material for themselves.  In this, I firmly believe that discovery-based exercises followed by discussion is the best way to make this happen.  But to try to "sell" this to someone who is not including any discovery or discussion in their classroom can be difficult if not impossible.  Instead, I believe the more important distinction lies in the depth and the amount of the assessment I am able to do.  The big advantage from my perspective is that I get a much better feel for how well my kids have understood the material on a day-to-day basis.  The one thing I never realized was missing from  my classroom in the past was the day-to-day pulse of the learning that was happening (or not happening) in my classroom.  In particular, I never really knew how well the kids had caught what I had thrown to them until the next day when we went over the homework.  And even then, I really only knew that a few specific kids had trouble with a few specific exercises.  I didn't get the depth of understanding about where the kids were having trouble, where specifically they were making their mistakes, where precicely the holes in their understanding were...not even close.

The other question that commonly comes up is whether or not I think someone could include some discussion-based activities "tomorrow".  Honestly, I would say yes.  Even someone who uses a lecture-based format for delivery of the material could break the lecture up into smaller pieces and have the kids do an exercise or two in groups based on the short lecture.  The exercises could be discussed, with someone putting the proposed solution on the board while the teacher circulates among the students to assess whether or not they understood the new material.  The only additional preparation necessary would be having a few practice exercises on hand for the students to try.  And even in this it may not be any extra prep, since the teacher could simply take a few of the examples they had planned to do during their lecture and let the kids try them instead.  Would this be easier? Nope, it would be exhausting, since there would be a sharp increase in the amount of analysis of student work being done.  But sitting on the other side of this fence, the information gathered from this analysis would be more than worth it.

Thinking through all of this during the week, I came to the following conclusion: the goal of education is not for me to explain the material to the students.  The goal of education is for the students to correctly explain the material to me and to understand what it is they're explaining.  Running a discovery and discussion based classroom allows me to see, day-by-day, how well this goal is being met in my classroom, and this, more than anything else, is why I made the switch.

My Best Year of Teaching

I remember my first year in the classroom.  I taught choir, introduction to music, pre-algebra, algebra 1, and algebra 2.  I was teaching at a small school with only one part-time and three full-time math teachers.  Like most first years of teaching about which I have heard from other teachers, it was rough.  Looking back, I did a lot of things right and a lot of things wrong.  But the general consensus was that I had done well enough, and that after a few years of teaching things would get easier.  Which they did.

However, during those next few years I taught a few other subjects and switched over from half-day music and half-day math to full-day math.  I taught geometry, statistics, and pre-calculus, and since I was teaching something new pretty much every year I was never really able to get into a groove and get comfortable with the material.  Of course, switching schools didn’t change this, and within my first 10 years of teaching I had taught everything from pre-algebra through AP calculus and AP statistics.  What I gained from all of this was a solid feel and appreciation for the scope and sequence of a math curriculum.  I got to experience how the different pieces fit together, and today I see that as a personal strength.  For all of the instability at the time, I wouldn’t trade the experience of those years for anything.

My current experience is completely different.  I have been at my current school for 13 years, and for the last 12 I have taught at least a few sections of honors pre-calculus.  There were even a few years, including the last two, where I have taught nothing but honors pre-calculus.  This has given me the time to delve deeply into the material contained in the course, so that at this point I can all but second guess where the kids are going to have trouble and find the mistakes they make much more quickly. 

All that being said, I have never, in either experience, felt that I have had my best year of teaching.  I have never reached a point at which I felt things were “good enough”, that the materials I was using were “good enough”, and that I could sort of coast for a while.  Sadly, I have seen this “I can coast” attitude in many other teachers.  They seem to think that a teaching career should, in the long run, consist of coasting once things settle in.  Once they have been teaching the same course for a few years, they should be asked to teach nothing but that course for the remainder of their career, and they shouldn’t be required to do anything differently than that which they have been doing.  There is no improvement necessary, no reason to do anything differently.  They are comfortable, and after this many years of teaching they deserve to take it easy. This, of course, is the stereotypical tenured teacher, and while it certainly doesn’t describe all of the teachers I know, it certainly describes enough of them to make the stereotype reasonably valid.

I completely disagree with this attitude.  I want my best year of teaching to be my final year.  I want to constantly look for ways to improve what I am doing in the classroom, ways to help the kids learn the material more effectively and more completely.  I never want to be so comfortable with my teaching that I simply walk in each day, set the “auto pilot”, and go.  And it’s easy to tell which teachers feel this way and which ones don’t.  Mention “best practices” to a group of teachers, and then spell out the practices that they should be incorporating into their classroom.  Those who are open to at least vetting the practices and trying out those they see as being a good fit for their classroom are the teachers I want to work with.  Those who immediately conclude that their personal practices are the best, regardless of any research, are those that frustrate me. 

We talk a lot about ways to improve education.  One of the steps necessary is to humbly admit that we have yet to have our best year of teaching, and to constantly look for ways to make this year the best year yet.

Snow Days

Last Tuesday, school was cancelled for the sixth time this school year, which in the past would have meant that we would need to “make up” the day at the end of the school year.  However, the Ohio Department of Education has given the schools permission to give online assignments to students in lieu of making up the day.  There are some limitations to this, but last Tuesday fell into this category.  So, we posted a set of five questions on the class website and the kids were responsible for doing the exercises and turning them in.  For me, that meant the kids had to take a picture of their work and e-mail it to me by 8pm.  That way, I had a good idea before we got to school on Wednesday as to whether or not the kids struggled with the assignment.

The exercises we chose were from the exam review, and we were careful to select exercises that were either well within the grasp of the students at this point in the trimester, or that would require a minimal amount of “mental stretch”.  Overall, the results were wonderful.  Aside from mistakes that fall into the careless category (of the variety “1x1=2”), the students did remarkably well.  Yes, there were a few kids who on a few problems simply wrote something along the lines of “I’ve been staring at this for 30 minutes now and I have no idea where to even begin this problem”; however, the overwhelming majority of the students were able to complete all of the exercises, and for the most part they got the problems right.

Contrast this with what I heard from a few other teachers who, giving their kids what they considered to be easy assignments, had the kids return the next day with nothing completed because the kids did not know how to do the majority of the assignment.  What the teacher saw as easy review, the kids saw as unreasonable and impossible because the assignment wasn’t about the current material, and therefore they weren’t even willing to try (even though they admitted the material was review).

If nothing else, I’m proud of the fact that most of my kids were at least willing to make the attempt to solve the exercises and complete the assignment.  The persistence they showed on that assignment spoke volumes to me.  The fact that for the most part they were successful is even better.  They are growing as independent learners.  Isn’t that the whole point?