Month: January 2011 (page 3 of 4)

I got owned by one of my students today in math class which doesn’t happen terribly often to me. Here’s the situation, see if you can tell whose solution is really a better way to approach this problem.

My student, instead of approaching this problem from my algebraic method using the distance formula drew some triangles and using the Pythagorean theorem to solve the problem. Her solution was much easier to understand and easier to work out. No one even completed the problem the way I was suggesting to do it. So I got owned.

You can’t discover these kinds of interesting solutions to problems if you require rigid step-by-step solutions. I got some professional development today and some advice from my 16 year student. She said, "Triangles are your friends." I gotta say, I agree with her.

Sandy Hirtz of CEET BC asked this question over at the CEET BC Ning.

"British Columbia Liberal leadership hopeful Kevin Falcon says public school teachers should be paid according to their teaching skills, not their length of service or level of professional training. He thinks a merit-based pay system should be implemented. What do you think?"

Here is my response.

When we think of merit pay, it is an attempt to turn the skills teachers have into a commodity. This works for some other professions because it is easier to attach financial value to what people do.

If you work in a profession where your work has a measurable financial impact, you can determine which of your employees has had the greatest financial impact by looking at various factors, including total sales in a marketing or sales profession, number of cases won and settled in law, etc… So it makes more sense to reward your employees for the good work they’ve put in. If you follow the research Daniel Pink has collected though, you’ll find those rewards don’t help the people in those professions work better, in some cases it actually hinders their profession.

Whether or not merit pay will improve teacher [performance] is a moot question however since there are no obvious financial gains from a teacher who performs well, or at least no gains that one can see in any useful time frame. If we buy the argument that people who are better educated make more money, and that a good teacher leads to better educated students, then over a time-frame of a generation, you could expect to see results if all of your teachers were suddenly better or worse at what they do.

In the context of schools though, this just doesn’t make sense. (Edit =>) We can’t wait a generation to see results and determine if teachers have actually been effective. So instead we are going to use ineffective measures which are not in fact related to the economic impact of good teaching, but are in fact a measure of the "turn them into factory workers" mindset of the 1860s.

However, I don’t actually think that the goal of merit pay is to pay good teachers more, or to bring an business model to education, I think it is actually intended to be used to pay teachers (overall) less. Essentially, the state controls the test, and the measures of how well teachers are doing, which means that what teachers are paid is not up to collective bargaining, but instead up to a bunch of factors controlled largely by the education ministry. I’d never want to cede that much control to an organization which has brought us such beauties as standardized testing, and BCESIS.

In the prisoner’s dilemma scenario, two prisoners are each interviewed separately and asked to cooperate with the authorities. Here is an except from Wikipedia on the dilemma.

"The classical prisoner’s dilemma can be summarized thus:

In this game, regardless of what the opponent chooses, each player always receives a higher payoff (lesser sentence) by betraying; that is to say that betraying is the strictly dominant strategy. For instance, Prisoner A can accurately say, "No matter what Prisoner B does, I personally am better off betraying than staying silent. Therefore, for my own sake, I should betray." However, if the other player acts similarly, then they both betray and both get a lower payoff than they would get by staying silent. Rational self-interested decisions result in each prisoner being worse off than if each chose to lessen the sentence of the accomplice at the cost of staying a little longer in jail himself (hence the seeming dilemma). In game theory, this demonstrates very elegantly that in a non-zero-sum game a Nash equilibrium need not be a Pareto optimum."

So how does this apply to schools? Let’s replace the word "prisoners" with students and the word "authorities" with "school administrator or teacher." We actually replicate the exact circumstances of this dilemma in schools every time we "try and get the bottom" of a situation between two students.

Instead of the highly negative choices for the students being prison sentence, they are detentions, or reduction of marks, or a million other consequences we apply to children when they misbehave. Further, children will apply their own consequences for "snitching" so that even if the adult administering the punishment goes easy on the child who tattles, and acts harshly on the child apparently "responsible" for the dilemma, there is often a consequence for the child who tattled; they may be ostracized by their peers or even face physical violence.

A typical analysis of the prisoner’s dilemma indicates that the optimal choice for players of the game is to remain silent and accept the minor punishment, even if they haven’t committed the crime. When we place school children in the same situation, don’t they react exactly the same way? This is not what we want, simply because in order to help a child who has misbehaved, we need information in order to help them. We need to understand what is going on so it is not repeated over and over again, as is normal in unresolved disputes.

There are two solutions I see for resolving the prisoner’s dilemma in schools. One, don’t isolate the kids and have the conversation about the misbehaviour as a group. This breaks the conditions of the prisoner’s dilemma as now each participant is aware of the other’s response. Two, change how you define misbehaviour so that you don’t end up in this situation. My recommendation, if you are more interested in the second of these options is to check out Restitution, although I am sure there are other ways to do this.

Joe Bower posted this video on his blog.

Joe writes:

If we really cared about real accountability, we would first ask if kids like school, and then we would have to care how they answer. Until then, kids will continue to be victims of a system that cares more about sustaining its current self than serving students.

Here is my response which I left as a comment on his blog:

I love this video Joe. It frames what I believe to be true about education in a way which is catchy, interesting to watch, and (I feel) hard to argue with.

When we share these ideas with other people, they keep going back to the same argument: how will we know kids are learning?

So I think our challenge is to come up with an answer to that argument which parents will accept without having to make too much of a radical change in their life.

I mean, I know my son is learning because I spend a lot of time with him and I keep track of the changes I see. I know he’s learning because I listen to the questions he has. I know he’s learning because I catch him trying to read (he’s 4). I know he’s learning because I’m involved deeply in his life. I want this to always be true, although over time I also want him to really learn the skill of autonomy, so I want to be a participant in his learning, rather than the sole director of it.

Our system of education absolves parents of the responsibility of paying attention to their kids learning needs by giving them easy numbers and letters to look at which are substitutes for the measures we already have for learning. You will know your child is learning if you are a part of the process, and pay attention.

Our economic system requires that parents work harder than should be necessary to support themselves, often leaving them without the time to support their kids emotionally. Something is flawed with a society which devalues the relationship between parents & kids and suggests that only a stranger can best teach your child everything they need to know. 

The transformation in our education system will happen when we give students real choice about what they learn, when we take away the barriers to developing individuality, and when we stop pretending that it is possible to carefully select the curriculum students will learn from the millions of useful things they could be learning. One size fits all doesn’t work. There is no other industry I can think of which believes that every one of their "customers" has the same needs.

We can argue that good teaching doesn’t need technology, and I’m going to agree with that. There lots of really powerful learning opportunities you can do with students that require no technology at all. In fact, if it works better without the technology, don’t use it. You are just introducing the risk that the technology will fail and your lesson will flop.

However, there are some things you cannot do without technology, and they are interesting and engaging learning opportunities for your students.

For example, I want my students to understand that when a ball bounces, the heights of each bounce closely match an exponential function. We’ve talked before how they match a decreasing geometric sequence, but I want them to really see and understand this phenomena.

So I had students first video record a ball bouncing, and then use this video recording to accurately record the heights of each bounce. Students did their recordings, and right away had questions. Here’s an example.

The thing is, you can’t accurately find the heights of the bounces without technology. Trust me, I’ve tried. I’ve had students measure with meter sticks and do 10 trials and find the mean of the heights, and all sorts of other tricks, but every time there is at least one group with really bad data. Data which makes the whole point of doing the exercise useless. You really only need to learn the lesson about experimental error a few times before you either give up, or find better ways of collecting your data.

Here are some examples of what the students did to find the heights of the bounces. What I found interesting is that they didn’t really use new technology to do their measurements, they relied on what they knew how to do, which is measuring with a ruler. So I would say this activity so far is a mixture of new technology and very, very old technology.

Notice the student (in the photo below) is using stickie notes to keep track of different positions of the ball at different times. I really thought this was a creative way to help make the measurement taking easier.

Here a student is measuring the distance directly with their ruler. At this point we had a great conversation about what this measurement meant. The question the student asked was, how do I find the actual distance the ball travelled during a bounce? She answered herself, and realized she could use the scale of the relationship between the height they dropped the ball on the screen, and the real world height. I pointed out that they could save themselves some effort, because the relationships between the bounces (what we were interested in) did not depend on the actual heights of the bounces, only on their relative heights.

So what we see a mixture of technologies the students are using and some obvious opportunities for learning to occur.

The technology is sometimes necessary to teach a particular concept in a constructivist way. In this case, the technology greatly increases the accuracy of the measurements the student is making. It makes enough of a difference that in the regression analysis the students did (using a spreadsheet program which is another useful technology) all of the students discovered that an exponential function is the best fit function for their data.

To make this point even more obvious, check out this high speed video footage of a drop of water landing in a pool of water.

You can’t see this phenomena clearly without technology to slow down time for us. It just isn’t possible. Some things worth learning in schools are impossible without using the appropriate technology.

@MrWejr and @GCouros have both recently posted about award ceremonies. I felt like I could contribute to the conversation, and I agree with their arguments. I just have a couple of other points to add.

George wrote a post called "Honoring All Students" in which he describes a two possible sets of students; those who receive rewards and those who do not. The students who win awards tend to focus on the awards themselves, rather than the activity they are being rewarded for. In fact, he links to research Daniel Pink has collected showing that rewards (and by extension awards) are detrimental to processes which require critical thinking. It is obvious that students who fall into the other camp will either be indifferent to the awards (or at least externally so) or feel hurt that they haven’t won an award. George also contents that having award ceremonies is for the adults, not the kids.

Chris writes 

June 1, 2010 marked the end of a tradition at our school – a tradition that awarded top students not for their efforts and learning but for their grades and achievements. The staff at Kent School decided to abolish the “awards” part of the year end ceremony.

His post is inciteful and interesting, and rather than quote all of it here, I recommend reading it.

Both of these posts are mentioned in a Vancouver Sun article suggesting that award ceremonies may be losing favour in BC schools. The comments on the article are either praising the ending of the practice at Chris’ school, or lamenting the end of the practice. The argument in the comments is quite interesting, but I find the arguments against awards to be mostly inciteful and well thought out, while many of the opposing comments are one-line sentences making fun of ending awards, like Chris isn’t an intelligent person with reasons behind his actions.

Both Chris’ and George’s well written blog posts come from a student centred perspective of educational philosophy. Rather than focus on the tradition of awards or our personal feelings about being awarded (or not being awarded) they focus on the outcome for the student. They ask the question, "Are awards helpful in promoting learning?" and both find that the answer is No.

There is another argument against awards that doesn’t rely on your perspective. I think it is a much weaker argument than whether we should approach awards from the student’s point of view or not but it is worth mentioning. The argument starts with the question, "How do we choose which students are awarded?"

First, we will assume that if you are handing out awards that you aren’t giving them to every student, because otherwise they wouldn’t be an external recognition of success, they would just be something everyone gets.

So now we aren’t giving the awards to everyone, we have to choose some criterion to select which students get awards. Those criterion will always be subjectively chosen and therefore it is impossible to objectively give awards to students. Awards based on grades will have bias since each teacher will be grading differently. Awards based on the judgement of a panel of teachers have obvious bias since each teacher will be rooting for "their student" (I’ve been involved in selecting awards in teacher committees before).

Awards for students seem like such a powerful message. "We appreciate what you do." It is a good message to send, but sending it once at the end of the year in a public assembly is problematic. It says, "we will reward you for your hard work but only in this special public way." Worse, when the message of recognition becomes a reward, especially a reward given frequently, it turns into an ugly monster where children stop being interested in what they do, and become dependent on the external motivators, or even demotivated by the awards.

Schools should be places where students love learning for the sake of learning, not for external rewards.