Why teachers like me support unions

Why teachers like me...

What's a "teacher like me"? That would be a young third-year teacher with a masters' in mathematics, teaching mixed level courses at a small city school offering only the challenging IB programme to kids who generally are from low socio-economic groups in Stockholm, Sweden. I love my work, LOVE it, and spend way too much time striving to develop effective teaching based on sound research principles.

...support unions. 

I'm a member of one of Sweden's largest teacher unions, Lärarförbundet. Financially, and in terms of job security, there is no point in this membership - I have tenure and unions do not influence salary. Instead, the reason I support unions is because it is important to offer organized resistance to changes initiated, and sometimes even determined, by the many levels of school leaders.
Examples of such changes are increases in teaching hours as well as in administration and class sizes, all of which means decreases in the time we have to do a good job.

I am always astounded by how little non-teachers seem to be aware of how much work it takes to plan a good lesson. I have friends who teach at in universities, as teacher assistants; they have 4 hours for each hour of "lesson" (more like a seminar, really). Usually high school teachers have about one hour per hour of teaching, and this is supposed to cover preparing the lesson as well as marking any work collected from the students during the lesson. Teachers at lower levels typically have even less.
At the same time, teachers are blamed for not being good enough at explaining, engaging, motivating, fostering, caring, investigating, communicating with parents, cooperating with other teachers, organizing events, devising individual development plans, following new research, taking part in professional development, and documenting results. The expectations are wildly unrealistic given the constraints; as a result teachers get sick, get cynical, get divorced, or leave for something different. Meanwhile, what is happening with the students of these sick, cynical, sad and absent teachers?

These kinds of changes are happening in Sweden, where currently there is no limit on the number of hours a teacher can be ordered to teach. Some twenty years ago the average was about 14 hours (60 minutes) per week - I currently teach 18.5 hours and in other schools teachers teach up to 30 hours per week. We also don't have any restrictions on how many other tasks a teacher can be assigned, and there is no lower limit for how much time for planning and marking a teacher is entitled to. The only limit is when a teacher is assigned so much work that he or she becomes overworked and sick, and even then measures taken are to temporarily repair the damage, instead of permanently fix the situation.
Does anyone think this is reasonable? Does anyone think that teachers who are talented or lucky enough to have other options, will want to stay at a job such as this one?

This is the reason I support unions: by myself I can achieve little to improve even my own situation, and much less anyone else's. Together we can resist and maybe even reverse some of the developments which over the last couple of decades have undermined the high quality in education that we as teachers, as students, and as a community, are striving to achieve.

What is this job?

I just saw the final episode of a Swedish TV-show called Class 9A.  The idea is very interesting: a school is in trouble because the teachers and principal are not doing their jobs well, and one ninth-grade class in particular is singled out to receive help from expert teachers. These experts come a few times per week during one term (August through December) and coach the regular teachers while at the same time teaching the troubled class. This is the second season of this show, the original aired a few years ago in a different city and school than the current season. Interest for this show has been very high, probably in part because it ties in well with the current political emphasis on school reform.

The team of expert teachers - come to save class 9A at Mikaelskolan

One prominent feature that distinguishes the expert teachers from the regular teachers is the amount of effort the experts put into each student. For instance, at one point Stavros, the expert math teacher, spends 2 hours giving one student private tuition and in the previous season of this show, one teacher fetched one student from home every morning to help the student come to school. Overall, the experts imply that one reason things are not going well is because teachers are not doing enough for the students.
In general, it's not difficult to understand that these expert teachers are probably given MUCH more time and many other resources not usually afforded to regular teachers. I understand that what they are doing is not realistic for regular Swedish teachers who, on average, have a little more than one hour for preparing (and marking) each class.
But then, how can you tell what amount of effort is realistic, how much is enough?

Another issue, related to the first, is what it is we are aiming for. In this show, the goal is phrased exclusively as "getting all students to pass and be admitted to high school". The principal says this, the experts say this, the regular teachers say this. Yet, surely this is absurd.
First of all, education for me is about learning, not passing. I would find my job utterly meaningless if I thought of it primarily in terms of getting students to pass, or even getting students to achieve high marks. I teach because I love and believe in the power of education - because education opens a window on understanding this world we live in, and gives tools which increase ones chances of leading a rich and meaningful life, and because it is a privilege to see and assist students' growth.
However, there is a second problem with the goal that the point of school is to get students to pass: in Swedish school systems the teachers themselves are setting the grades. Guess what happens if the teacher is aiming to pass as many students as possible? They pass. And then they come to high school and I wonder what on earth they have been doing for nine years when in tenth grade they cannot even do multiplication with negatives.
This becomes especially ludicrous in the context of Class 9A, because it is set like an experiment and everyone is asking all the time "how is this going? are we seeing any results from this awesome and costly and highly publicized intervention we're conducting?"  There is a reason scientific experiments are often conducted blind. Researcher expectancies can have a tremendous effect, and doubly so when the researchers are the ones evaluating their own work and under great pressure to succeed.
Yet passing rates and grades and standardized tests remain the most clear cut and simple way we have to measure and compare learning. So how can we formulate goals that do justice both to education for its own sake, and to the reality of grades and test-scores?

What do you make of this?

On the subway, just now, I overheard two high school students talking about their math teachers:

- ...the old one? did you have him? He was f-ing horrible.  

- I heard so. 

- yeah cuz he gave us these difficult problems and no one got them and one time I was working on a different problem and he asked if I could do the one on the board and I said no and then he said, like in front of the whole class, "oh that means you have a lot to revise!".  

- jerk 

- yeah... 

(pause) 

- but you know then we had a different teacher and she was awesome! if someone didn't get something she was like "OK let's do this again!" and she explained it and was really patient. It was great.  

- yeah there are so few teachers like that, who can get contact with their students, no wonder at the end of high school everyone is so tired of studying.

Overhearing this exchange was really awesome for me, because it gets right to what I've been most concerned with all year: the differences in what students want, and what I want.

Because what these students are saying, what I think most of my weaker math-students would say if I asked them, is that teachers that give a lot of help, teachers who guide students through problems, teachers who make mathematics simple, are the good teachers. Teachers who give challenges, and then expect students to stick with the problem until they solve it, are the bad teachers.
Meanwhile, what I want is to engage students in thinking, to show them that they can do math more or less on their own, form their own conjectures and prove them, too. I hope that this way math comes alive and students develop interest and confidence as well as understanding and skill.

This is nothing new, and part of the invisible contract which Ben Blum-Smith wrote about beautifully in this post a year ago. But I do wonder about the effects of this discrepancy in teacher and student attitudes.
Could it be that these students are right? That, for them at least, and at this late stage in their relationship with mathematics, it is better to provide a crazy amount of scaffolding and to sacrifice ideals of creativity, fun and even deeper understanding for the benefit of getting the students to feel confident and safe in math class.
This has been my main question this year and I still don't know how to answer it.

Developments in Sweden

I haven't been writing about all the strange changes in education policy that are taking place in Sweden because the audience of this blog is mostly from the US and, frankly, I just assumed y'all don't give a damn.
But yesterday something happened which is just too weird for me not to comment on it.  A debate article calling for more direct instruction was published in our largest newspaper, DN.
The author? Our secretary of education Jan Björklund.

A little bit of history: 
Contrary to popular belief, Sweden is not very centrally controlled, and education has, since the early nineties, been controlled and paid by individual cities. We have, also since the mid-nineties, a large number of charter schools which operate under laws more lax than perhaps anywhere else in the world. The government occasionally updates the main law of education ("skollagen") and published standards and grading criteria for each course, but since the early nineties government has actively avoided regulating or even advising teachers on how to teach, and even what to teach. Now, however, everything is changing.
I'd say it all started  when Alliansen, our right-wing coalition (our right is still USA left) entered power with the explicit goal of getting rid of the wishy-washy education ideals that the left-wing had established over an (almost uninterrupted) reign of many decades. These wishy-washy ("flummiga") left-wing policies (transmitted to teachers not through laws, but rather through teacher training institutions) had long been emphasizing the individual freedom and responsibility of the students, the importance of social goals in schools, intrinsic motivation, and an avoidance of grades and (in the most extreme instances) homework. In Sweden, children still do not receive grades until 8th grade. For teachers, all this translated into trying to get students to lead their own learning while at the same time creating learning opportunities individualized for each student.

These kind of education policies have fallen into disrepute in part because of convincing research reports that teachers have been unable to implement individualized teaching the way left-wing policy makers have envisioned. Instead, teachers have approached the ideals of student responsibility and individualization with the kind of laissez-faire leadership which is actually the absence of leadership. Students have been assigned project-based group-work with very little structure, or just told to do individual work in the textbook. As a result weak students, left to their own devices, became even weaker. For this and other reasons (charter schools causing the inflation of grades, as an example) Sweden's results in PISA and TIMSS decreased substantially.

So when the right-wing coalition said they wanted to move in a very different direction, emphasizing structure, clear standards, and discipline, many teachers, parents and concerned old-timers felt that finally politicians were talking sense about education. It's likely that this convinced many voters to vote for the right-wing coalition for the first time in their lives. Recently, however, there is an increased awareness that while it certainly appears that Björklund is very sensible in these matters, this is only relative to the utterly unrealistic idealism that the left-wing coalition has been advocating for years. In fact, Björklund, maybe because of his military background (he was never a teacher), is looking for simple and rigid old-school solutions which may solve some problems, but are likely to cause others.

Some reforms which are taking place this year:

• Grades (letters from F to A)  from 6th grade. 
• More specific national course plans for all national courses. Schools will no longer be required to produce their own interpretations of national course plans. 
• New grading system (our third in twenty years), in which it is more difficult to achieve the higher grades. It will be written in prose, however, and it is a challenge and a mystery to most teachers how to use this system for actual grading. 
• Students in vocational high school programs will no longer be eligible for university education, although the schools will be obliged to offer students additional courses  for eligibility should the students wish so. 
• Teachers will be required to obtain  a teacher "licence". This is just a word and a document, it does not require any more training or proof of competence than has been required up to now. Yet the unions and the government are sure that this piece of extra bureaucracy will magically increase the status of the teaching profession ("after all, doctors are licensed practitioners, and they have high status and salary"). I think this is a stunning case of correlation mistaken for causation, and I cannot for the life of me recall why, a year ago, I thought this was a brilliant idea. 

And finally, yesterday, Björklund writes that teachers must reclaim the position of authority in the classroom. 

He announces that the government will soon pass a law which states that students have the right to receive continuous and active support from the teacher through structured teaching. This could of course mean many different things, but Björklund explicitly states that the teacher should address the whole class as one group ("undervisning i helgrupp"). He also suggests that the teacher should maintain an active dialog with each student and together investigate different questions and problems. He does not seem to be aware these two suggestions are mutually exclusive; one reason why teachers often divide students into groups is because it is impossible to give each student in a large group sufficient attention and feedback. 

I am, however, not unhappy with this most recent development. For too long has direct instruction had a bad rep, and for too long have teachers struggled to teach every students according to that student's individual needs (and then felt guilty over not being able to meet such an overly ambitious ideal). Good direct instruction has it's place in teaching, as one instrument among many others. In general, what I hope Swedish teachers will take away from all this is that teaching is leading learners in learning, and that even though leading can mean very different things depending on whether one is lecturing or organizing group-work, it is the responsibility of the teacher to maintain control of the learning opportunities presented in class to all students.

How, and how not, to explain graphing trig functions

Graphing trig functions should be relatively easy for students who have already mastered general function transformations with quadratics and exponentials.  Nevertheless, there are so many steps involved that I think an emphasis on procedure and practice is justified in this case. With that in mind, I aimed to build on students' prior understanding of transformations while giving them an outline for how to graph trigonometric functions of the form f(x) = A*sin(B(x-C))+D. 
I completely butchered the first lesson on graphing trig function and promised my students (all patience and humor to the end of that horrid, horrid hour) to make amends by presenting the procedure crystal clear the following lesson.

What I learned from the failed lesson:

• Save your geogebra files before moving into the classroom, as the computer can and will have a fit and shut down unexpectedly (bye bye 30 minutes of work) when you plug in the projector.
• When creating a nice mnemonic for how to graph these functions (I came up with BC AD - Before Christ, Anno Domini, get it?) go ahead and check first that this is actually a reasonable way to graph these functions. BCAD isn't, in the sense that it doesn't allow you to place points each step of the way. 
• If something isn't working, stop doing it. I actually persisted for 40 minutes giving students one retarded way after another to graph trig functions, when I should have assigned some other work and taken a few minutes to think things through. It's a testimony to the loveliness of my students that they persevered and, when at last I came to my senses and called the whole thing quits, laughed with me (and, admittedly, at me). 

In my defense, when I immediately after the lesson googled how to graph such functions... NOTHING came up. Most websites and videos explain A, B, and D - but skip the C. I sat down with my colleagues and we  came up with the following method:

• D gives principal axis, so make a line there.
• A gives amplitude, so make lines at D+A and D-A. Now we know the range of the function. 
• C is the phase shift. For sine, put a point at (C, D). For cosine, put it at (C, D+A). 
• B is the frequency, and 2*pi/B is the period. Figure out how long one period is and place a point at (C+period, D) for sine or (C+period, D+A) for cosine. 

Now draw a full period of the function between the points you've made.

Mnemonic? I'll ask the kids to make one up. All my ideas involve dog ate cat bones and dingo ate chubby baby.

I'm afraid the lesson itself won't be any more exciting than demonstration and practice. But I think sometimes (especially after the havoc I put them through last time) demonstration and practice is what the kids want most of all. For homework, I give them a modeling activity involving the movement of the sun in three arctic cities.

Features of trigonometric functions

This Monday, a very basic investigation of trig functions/reinforcement of function transformation skills with a standard/honors junior class. I was toying with the idea of just throwing a matching activity to the students, but I'm still new to using those and besides they take so much work cutting and organizing.
The activity below is very characteristic of how I teach and what I'm aiming for is student ownership (discovery, confidence, etc) and connection to previous materials.
Students will be doing this in pairs, each pair doing either the sine or cosine activity. Afterwards, pairs will combine into groups of four so that each group has one pair which has done the sine and one which has done the cosine. They will then compare and discuss the question at the bottom.

Any suggestions for improvement are, of course, welcome.

Investigation Transformations of Trigonometric Functions