Algebra 1

So it turns out that running a Harkness-based, standards-based algebra 1 classroom is exhausting.

It's not impossible...far from it.  The kids who are on-board with the method - which is most of them - are doing fine.  The discussions are lively, the kids are learning, and life is good.  I am able to give the kids a lot more individual attention than I have in the past, and as a result I have a better feel for where each of them is with the material.  All good things.

As you would expect, the kids have a lot of questions.  In general, more questions than the honors pre-calc kids, and they're less shy about asking.  Giving some kids individual attention makes the other kids want individual attention, and now I have a room essentially full of kids who want my help to learn algebra, which is a very good thing.  This is what teaching is supposed to be about: me helping the kids learn.

This is a natural fit for a standards-based grading system.  Individualized, daily, formative assessment for individualized learning.

But it is exhausting.

That's not a complaint, by the way.  Quite the opposite.  The fact that I have freshmen who start class by themselves before the bell rings is great.  The fact that I was able to do conferences last week without needing to print out a grade sheet or anything like that because I know the kids well enough to speak about their strengths and weaknesses is great.

But there is a price to pay for it.  Giving the kids constant chances to demonstrate they have learned or retained the material - whether in the form of short quizzes every day or kids asking to come in before or after school to show what they know - is time consuming. It cuts into time needed to do all of the other things that go into preparing for the class.  Things that, of course, have to happen.  So really it cuts into the time spent on other things, like writing a blog you're using as a means of reflecting on how things are going.

It's worth it.  The kids are focused on learning and retaining the material.  The rapport with the students is good.  The year is rolling along nicely.

But it's time for bed.

Not Grading

Of all of the tasks that are part of the job description for "teacher", grading is probably the most elusive to pin down in terms of how to do it well.  Some teachers I know just mark what the student got wrong without any explanation, emphasizing the idea that this is a judgment, along with a numerical label, of the student's ability.  Sometimes, the number of points "taken" for each incorrect response corresponds to a detailed rubric, from which the teacher, for the sake of fairness, does not stray.  Other times, the teacher will take points according to a more holistic feel for how well a student did on a particular exercise, making notes about what they have done on previous tests to make sure the grading is consistent from test to test.  It is rare in either case that the teacher will provide meaningful feedback about what they were actually looking for compared with what the student provided on the test.  And even if such feedback is provided, it is often ignored by the student, who tends to only be interested in the numerical grade at the top of the test, leaving the teacher to wonder why they even bothered to put the more detailed information on the graded test in the first place.

While there are certainly other things that are wrong with education in our country, this emphasis on grades and not on learning should be really close to the top of the list.  Many teachers and students (as well as many parents, administrators, politicians...) have reduced education to a game of numbers. As long as the grades are ok, learning must be happening, right?  If we're honest about it, the correct answer to that questions is, "No."  If the grades meant the students were actually learning the material, then the disconnect between high school grades and college placement tests (ACT, SAT, or from the colleges themselves) would not exist, the amount of review currently present is subsequent courses would not exist (example: how much of the beginning of algebra 2 is actually algebra 1 revisited?), the number of remedial courses in colleges - courses that contain material from classes the students actually passed in high school - would not exist....you get the point.  If we're honest about it, grades actually detract from what should be the goal of education, namely: help the students learn.  Instead, the focus has become the grades themselves, and not if they are accurately reflecting the learning.


Enter the first round of testing this year in both algebra 1 and honors pre-calculus.  First, as I mentioned in the previous post, I'm calling the assessments "checkpoints" this year, hoping to emphasize the idea that we're just seeing where the student currently is and where we still need to work.  Second, I created a feedback form for each of these first checkpoints, listing the skill that I was checking for, with options for "mastery", "proficiency" and "developing" next to each, along with room for me to write any comments.  For honors pre-calc, I made the mistake of putting a number (5-mastery, 4-proficiency, and 0-developing) next to each exercise, so the kids were somewhat instinctively drawn to look at the numbers rather than at the comments.  On the sheet for algebra 1, no such number existed - just a checkmark next to the level along with the comments.  For both classes, the opportunity to show me within the next couple weeks (the requirement is before the next checkpoint) that they have developed proficiency in those areas that were marked as developing exists.  This is not a second opportunity on a similar checkpoint; rather, the students need to create an exercise, get my approval that its successful completion will demonstrate the level of proficiency for which I am looking, and then answer the exercise they created.  This set-up made the comments important, since they contained the information about what I didn't see on the checkpoint, and therefore what the student needs to include in the exercise they created and show me in their solution.  In other words, the emphasis was on the material and not on the grade.


It has only been a couple days since I returned to first checkpoints, and many of the kids - algebra 1 and honors pre-calc alike - have completed the second chance, and I've changed the mark from "developing" to "proficient" accordingly.  Only a couple kids have mentioned the grades.  I even figured out a way to get the grading program my school uses to report only the levels and not a semester grade, so that even the online report is about the material and not the numbers.  The rest of  the kids are focused on demonstrating that they now know the material.  The first after school help session, which occurred last Thursday, was the best attended session in years - well, other than those that occurred the day before a test/IES/checkpoint/whatever-we-called-it-that-year.  Kids getting help with material they didn't understand, kids demonstrating that they actually do understand the material but drew a blank on the day of the checkpoint, kids explaining things to other kids...all good things, and all of which I hope happen every Tuesday and Thursday after school.


Just to be clear and complete, the grades will show up eventually, but not until the unit is actually "closed" and the marks for that unit are "final" - meaning, the "grades" for unit 1 will appear after the checkpoint for unit 2 has been taken.  Until then at least, the focus will be on demonstrating knowledge of the material.


So, is it possible to change the focus to learning and away from grades?  For the time being, it seems the answer is at least a short-term yes.  Hopefully the remaining kids will come around soon.  Regardless, I'm going to enjoy the fact that the majority of the students are currently focused on learning and not on getting grades, work toward getting everyone on board, and try to find a way to have this focus continue even after the grades are posted.

2015-2016

Summer is over, and the new year is off to a good start, with this year's docket consisting of four honors pre-calculus and two algebra 1 classes. It was a full and enjoyable summer, with a week at Exeter, a week with EMI in Mason, a four-day weekend at Deerfield Academy participating in a PBL Summit, and lots of family time riding roller coasters, including a few days at Holiday World for our 25th anniversary.  The PD was inspiring, to say the least, and provided the impetus to take the discussion exercises created last year for algebra 1 and organize and expand them so that this year the course can include the discovery and inquiry that were, in many ways, missing last year.  In other words, Harkness has fully arrived in algebra 1.  There are several of us using the new algebra 1 materials this year, and the focus of the blog this year will be on the implementation and the adjustments as we go.  And after four days...

(1) Yes, the kids can do this.  The conversations have been good, the kids are making discoveries, and today they were already putting their work on the board before the bell rang to start class.

(2) No, not everyone is on board yet.  Some of the kids are trying to get by in the same way they have in the past, where not doing work at home and not participating in class menat that the teacher would swoop in and save them by giving them notes and finding other ways to spoon feed them the information.  Needless to say, that's not happening this year.  On the good side, each day another student or two has gotten with the program, so hopefully it won't be too long before we have everyone in the fold.

(3) Yes, there is a slight difference between what I'm doing in algebra 1 and what I'm doing in honors pre-calculus.  Namely, we spend the last five or so minutes of class in algebra 1 discussing the day's exercises as a whole group, as a way of summarizing things and giving the kids a chance to check their notes and make sure they caught the important information for the day.  Honors pre-calc doesn't receive this from me on a daily basis, as part of the point is for them to begin to discern  this for themselves...a college-readiness skill if ever there was one.

In addition to this, the way I'm reporting grades is changing this year.  Specifically, we are going to a more standards-based model, with only formal assessments (which we're calling "checkpoints" this year) contributing to the semester grade.  Homework, participation, etc., will be reported online but will not be included in the calculation of the semester grade.  If a student does not show proficiency on a particular topic, we have laid out a process (at the heart of which is them finding or creating exercises that cover the topic in question) by which they can continue to work on the topic, show proficiency, and replace the grade from the checkpoint.  My hope is that this will nudge any holdouts over to doing the necessary work to learn the material "the first time" (i.e., in class through the daily preparation and unit checkpoints) rather than having to work through the make-up process for the old material while trying to learn the new.  Either way, I'm trying to place the focus squarely on learning the material and not on the grade, and I'm certain that a few posts will be updates about how this process is going as well.

Finally, as a result of presenting "Harkness for Thirty" at Exeter and Deerfield over the summer, I have had a few email conversations with teachers from across the country providing requested information and advice as they make their first attempt at discussion-based learning.  It is a bit humbling and a bit overwhelming to think that my advice is worth asking for.  It has also got me thinking about putting together a workshop that I could do for math departments who would like help putting together the materials to implement discussion-based learning.  Not sure if there's a need for this, but it's probably worth considering at the very least.

So, a lot to work on this year.  Just the way it should be.

Training vs. Educating

In his new book, Creative Schools, Ken Robinson makes a distinction between training and educating students.  The essence of the difference is that educating a student is more holistic, whereas training refers to learning a specific skill or piece of information.

This distinction got me thinking.  When, for example, we teach a student how to factor by showing them several examples of each "type" of quadratic that we want them to factor, and then having them practice each type tens or hundreds of times, are we actually educating them, or are we just training them for a specific skill?  I would contend that this is training, and not educating.  And if we're honest about it, it's training them for a skill that is very limited in terms of its usefulness.  I'm willing to bet that even those who are currently working in a STEM-related field have not needed to factor, foil, integrate - the list goes on - at any time in the recent past.

However, if we help the students learn to factor by leading them to discover the process and allowing them to work through the different "types" (especially in the context of applications), and in the long run become just as proficient at the skill of factoring, we have, by the way the material was covered, educated them instead of trained them.  In addition to the specific skill, we have also improved their problem-solving skills, allowed them to make sense of the material themselves thereby making it more meaningful and more permanent...you get the idea.

I think this gets to the heart of one of the main issues in education.  If we look at a curriculum - any curriculum - and see a list of skills, and understand our job as getting the students to be able to do those skills, then our focus will change from educating the students to simply training them.  The assessments we give will focus on whether or not they have learned the skills, and so long as the students can accomplish this - regardless of whether or not they actually understand what they're doing, why they're doing it, or how it can be useful - then we will have done our job.

Of course, the current standardized testing - PARCC, AIR, etc. - isn't about just the skills (though they are still important), but rather is about the using the skills, especially in ways that are not seen in the textbooks, and therefore are not normally seen in classrooms.  These tests are not about second-guessing the kinds of questions that are going to be on them so we can be sure to cover those "types" of questions in class, but rather are about checking the kids' problem-solving skills.  So even if a teacher thinks that teaching is all about training the kids in specific skills, the standardized tests should get them to rethink their position at least a little.

Needless to say, since I'm solidly behind educating the students rather than training them, I'm not worried about any changes that may come to state testing. If you educate the kids instead of training them, then they will be ready for both a skills test and a problem-solving test...and will not recoil from whatever may be thrown at them, since they will be accustomed to working on exercises the likes of which they have not seen before.  Sounds good to me.

An 85

So, if a student "has an 85" in your class, what does that mean?  Well, it depends on how you view grading.  Among the things I have seen in practice from colleagues and friends:

1. Grades are payment for what the student has done in class.  In this scenario, the teachers sees the grade as what the student has earned by being in the class.  Normally, everything from homework to tests to bringing in paper towels to extra credit figure into the grade, so that "an 85" is meaningless.  It almost certainly doesn't mean that the student has learned 85% of the material.  With enough extra credit, homework (done with "help" from others) and paper towels, a student who barely knows any of the material could have an 85.
2. Grades are the average of the test scores, and nothing else.  In this scenario, a series of "snapshots" from the grading period are the only means the teacher deems as valid to  determine whether or not a student has mastered the material.  The student gets test anxiety? Not important.  The student has a learning disability that makes taking a paper-and-pencil or an online test difficult if not impossible?  Irrelevant.  The student has stayed after for extra help, and during those sessions has demonstrated a deep understanding of the material through the explanations they give? Nope. Only the grades on the tests matter.  Does an 85 here mean that the student understands 85% of the material?  Probably not.  In fact, the percentage is probably higher than that, but the grade won't show it.
3. Grades are a means of ranking the students from best to worst. The best kids in the class, whether they have demonstrated it or not, get the A.  The worst kids in the class, whether they deserve it or not, get the F.  The difference between the two? It can be anything from their reputation (other teachers said this is a good/bad student) to their personality to their effort to their ability to "brown-nose" the teacher.  What's missing from this is anything related to the material.  The "85" says nothing about the student's understanding.

There are other scenarios, of course, but you get the point.  For the most part, the perception by someone reading a transcript is that "85" means the student understands (or at least understood) 85% of the material.  Anyone who has ever put a grade on a transcript knows that this isn't the case.  So if "the student has an 85" is meaningless, why do we continue to label kids in this way?

Because there's not an alternative.

Oh really?  Let's look at the report card I received when I was in kindergarten.  There was a column containing a list of skills (things like "knows numbers from 1 to 10" or "can buckle boots"...not kidding), and another column where the teacher would mark if I had the skill mastered, or if I was making progress, or if I hadn't demonstrated the skill at all yet.  On the other page of the report card were the "behavior" skills (takes turns, raises hand, etc.), along with a similar set of marks.  If anyone looked at that report card today, they would know exactly what the expectations of the class were, and what I was able to do (or not do) at the end of the first semester of kindergarten.

So why can't we give a similar report in a high school classroom?

No, seriously: why not?

We could if we actually worked with the kids as they were learning the material.  We could if we actually got in the arena with them and participated in their struggle and gave them every opportunity to demonstrate their understanding of the material.

Lecturing alone can't do this.  Testing alone won't be enough.  It takes real, meaningful discussion with each and every student to achieve this.  And don't tell me it can't be done, because this is what happens in my classroom pretty much every day.

Job Description

As we approach the end of the year, my email begins to fill with summer professional development opportunities that tend to come in a limited number of varieties.

The first type, and overwhelmingly the most common, is something along the lines of “this will help your students do better on tests.”  The PD is training in how to implement their program and use their materials.  Nothing in the advertisements for these opportunities mentions helping the students do anything other than pass tests, be they chapter or unit tests in the classroom or state or national standardized tests.  Testing is everything, and these programs are here to help your students succeed…at taking and passing tests, anyway.

The second type is something along the lines of, “this will help you keep your kids be quiet and well-behaved.”  This classroom-management type of PD focuses on keeping the kids quiet but engaged with the material.  The pictures from these advertisements show kids seated in rows or in front of their own computer, working quietly and independently, and the description of the PD emphasizes that your classroom can look like this…under the assumption that I want my classroom to look like that.

The third type is something along the lines of “this will help you present the material in your class in a better way.”  The emphasis of these is how to improve your method of delivery, how to be more clear in your lectures, how to produce better worksheets, and so on.

Notice that none of these opportunities mentions helping the kids actually learn the material.  Not one sentence in all of the advertisements mentions the kids comprehending anything.  It’s bad enough that people outside the profession think that the job description for a teacher should be dominated by keeping the kids quiet and giving them information.  But for the folks running these PD session - folks who are supposedly inside the profession - to be spewing this nonsense is irritating to say the least.  More disturbing is the idea that teachers are actually signing up for these sessions, which means, at least implicitly, that these teachers also see the job as primarily involving keeping kids quiet and giving them information.  Sorry, folks…that’s not what the job is about, and the job description I would give is essentially antithetical to everything being promoted by these opportunities. 

Teaching is about helping kids learn. Period.  The sooner we can bring everyone to the realization that testing, classroom management and giving information are not the focus of teaching, but instead are only useful if they help the kids learn, the better.

It should be clear by now that my idea of “classroom management” is very different than the one described in the PD advertisements.  It should also be clear that me giving the kids information is, in my opinion (and in the opinion of most current research), not the best way to help them learn.  But what about testing?

I still struggle with the idea that any test on any given day is the best way to measure how well a kid understands the material.  With that, I have really been struggling lately with the idea of putting a letter or number grade on every assignment, be it homework, quiz, test, or whatever, to the point that I’m questioning whether or not grades are good at all.  Let’s be honest: the kids and parents look at the grade first, and any comments or other feedback intended to help the kid do better next time are often, if not entirely, ignored.  Without a grade on which to focus, however, the feedback becomes more important.  And if the feedback is focused on improvement and resubmission of an assignment, then learning becomes the focus of the classroom.  We have implemented a strategy of this kind this semester with the review projects we assigned.  We gave the kids five broad topics from the first semester of the course, and the kids need to create an exercise that covers the topic, get the exercise approved by us, type up their solution, and submit it online for us to review.  The only grades possible are 0 or 15 (full credit).  If the solution as presented is not a “15”, the student receives specific feedback on what is missing, where improvements are needed, etc., and has the opportunity to turn in another draft of the project.  This process continues with each project until it is a “15”.

Admittedly, getting rid of grades entirely would require a massive shift the likes of which on teacher alone can't make.  But giving the kids more than one opportunity to "show what they know" and giving them a variety of ways to do so is making more and more sense the more I think about it.  For the time being, there has to be some sort of "happy medium", but I haven't found it yet.  Hopefully, between now and the beginning of the 2015-2016 school year, I'll find a way to make this happen.  Even better would be for the PD to help teachers find a way to shift the focus from the grades and the testing to the learning.  I guess we'll see...

At, To, and With

I’ve spent some time recently thinking about the real differences in the teaching styles of different teachers I know, to see if I can pare it down to the essentials.  While on the surface it would appear that there are many different teaching styles, I’ve come to the conclusion that there are basically three different ways that teachers run their class.

First, there are the teachers that talk at the students.  These are the teachers who have students falling asleep in class, texting in class, completely (or at least essentially) disengaged from the class, and the teacher doesn’t care or doesn’t notice. The teacher sees teaching as delivering the material, and as long as that happens, whether or not the students receive the information is irrelevant.  The teacher believes that in delivering the material, they have done their job, and the rest is up to the kids.  If the students aren’t learning, it’s their own fault, because the teacher has told them exactly what they need to know and what they need to do.  There is no real interaction between the teacher and the student in this scenario, and from what I can tell neither the teachers nor the students want any interaction.

Second, there are the teachers who talk to the students.  These teachers still see teaching as delivery of the material, but they also are concerned about whether or not the students are receiving the information.  These teachers notice when kids haven’t done their homework or aren’t taking notes in class, and will have a “conference” with the student to tell them what they need to change about their behavior to be more successful in the class.  Conference probably isn’t the right word here, because this is actually a monologue, with the teacher doing the same thing during the conference as they do in class: they tell the student what needs to happen, check whether or not the student has understood what was said, and it’s left at that.  While there is certainly more interest in whether or not the students are learning, the means by which the students are being given the opportunity to learn the material is one dimensional: the teacher is the fountain of all knowledge in the class, and the students must “give the teacher what they want” or they will not pass the tests.

Sadly, I believe that this form of teaching is the one that is valued by the teacher education programs.  At least from the perspective I have of having student teachers in the building and seeing the forms that the cooperating teacher is supposed to fill out, as well as seeing what it is the  professors are looking for when they visit, this second type of teaching dominates the paperwork.

The third way of teaching relies on the teacher talking with the students.  These teachers see interaction between the teacher and the students (and between the students) as vital to the learning process.  The emphasis in these classrooms is not on the teaching, but rather on the learning.  I have seen this style of teaching happen in classrooms dominated by discovery and those in which the teacher delivers lectures, though the lectures in these classrooms are much shorter than in the other styles described above, since there is time built in to every day for the students to work with one another to practice what they have learned, and for the teacher to discuss the material with the students after the lecture to check whether or not the students have understood the material.  

It is difficult for me to imagine a student teacher doing well on an evaluation being this type of teacher, when it is completely possible that the student teacher would be in front of the class for less than five minutes during an observation, which would make several sections of the form that needs to be filled out meaningless.  

Clearly, anyone who knows how I currently teach knows that I’m a “type 3” teacher, and that my opinion would be that the research supports the idea that a “type 3” classroom is the best for the students.  Go back four years, and I would say I was a “type 2” teacher.  And I would say that most of the teachers I know are “type 2”, though I also know a few “type 1” teachers.  The other thing that I have noticed is that the new teacher evaluation system being implemented in Ohio values “type 3”, seems like it will be ok with “type 2”, and will not be kind to “type 1”.  My opinion would be that, from the standpoint of educational and neuroscience research, this is absolutely the right thing to be doing.  However, it also seems like we are setting up the new teachers for difficulties since the way they should be teaching is not the one being emphasized in their training.

Hopefully, the education and neuroscience research will begin to have an impact so that teachers will move toward being a “type 3” teacher.  The move is possible. The only thing missing is the desire.