Education ∪ Math ∪ Technology

Tag: education (page 6 of 13)

Lecture – from a student’s perspective

What does your classroom lecture look like from a student’s perspective? I had my students video tape my lesson from a few different places in the room, and I’ve created these videos to demonstrate what it might be like for students with various learning differences. I’m by no means an expert in this area, but I want to add another perspective on why classroom lecture might not be the best pedagogical tool.

 

 

 

 

(Thanks to @marynabadenhors for the translation!)

Can you think of what class might be like for these learners? Are there other types of learners that might suffer in a one-style-fits-all classroom? 

The relationship between family income and FSA score

The Fraser Institute released their annual "report" on the Foundation Skills Assessment (FSA, a standardized exam given to 4th and 7th grade students in British Columbia) results. As usual there have been complaints about the validity of the results, and some interesting side stories. I decided to look at the Fraser institute’s results from a particular perspective. I took the FSA data and isolated the "parent income" and available FSA results (out of 10) from the Fraser Institute data. (I could have used the data from the BC government’s education site, but the Fraser Institute data was more convenient to work with.)

After writing a script to scrape the data (download the raw data here) from the PDF provided by the FSA, throwing away schools for which either FSA results or parental income was unknown, I graphed the data.

From the graph it seems clear that there is some sort of relationship between the two variables, but it is not clear how strong the relationship is between family income and FSA scores.

So I’ve calculated a couple of regressions for a linear fit and a logarithmic fit between the two variables. The value of the correlation coefficients are approximately 0.485 and 0.517 respectively (square roots of the r2 values given above), which given the large number of data points is statistically significance, showing that there is a moderate to strong relationship between the mean family income of a school, and the mean FSA scores for a particular school.

This type of analysis has been done before for other standardized tests, most notably the SAT exams in the United States. What this type of analysis shows is that standardized exams like the FSA are better measures of the wealth of a community than the strength of the schools in that community.

The Fraser Institute rankings are a flawed comparison of schools. It is not possible to fairly rank schools of different socio-economic status because of this strong relationship between scores and the family income. What would be more fair would be to re-rank the data and break it down into different sub-classes based on socio-economic status and not try to compare apples and oranges. 

What would be even more fair would be to throw out the exams all together. What we really want to know is how effective our schools are at ensuring that our students are successful. Given the enormous complexity of this issue, and the wide variety of variables involved, finding a solution to that issue will be extremely difficult. A standardized exam is like a fast-food approach to collecting data, it is cheap and fast, but not very filling. 

Blended Learning: The Importance of Face to Face contact

Here’s a great story (shared on the Huffington post) about a student who is attending his school remotely, through a robot. Watch the video below.

The robot has become a proxy for face to face communication, and this family considers face to face communication so important, they are ignoring other, probably easier, solutions for his education. Lyndon could be going to a virtual school and learning remotely through initiatives like the Khan Academy, but he’s not. Instead he and his parents have chosen to send a robot in his stead, which Lyndon controls via his computer. 

In any blended learning model, it’s important to remember stories like Lyndon’s and remember why we would use blended learning over pure e-learning. Although e-learning has the potential to allow for a much greater degree of personalization of learning, it is a poor substitute for face to face interaction. The ability to quickly communicate a lot more than just the course content is a critical aspect of face to face learning. Lyndon has joined this school virtually because he wants the emotional contact with other people his age. He’s not just content "knowing" stuff, he wants to know it through other people’s eyes as well, hence his comment on "the other student’s point of view."

As educators, we do this too. Although we have a thriving community on Twitter, many of us will jump at an opportunity to see each other face to face. We’ll spend collectively spend vast sums of money on going to conferences like Educon and ISTE, or spend hours planning local unconferences. The online interactions are great, but nothing beats a face to face conversation.

Mumbo Jumbo

Algebra is just mumbo jumbo to most people. Seriously.

If you asked 100 high school graduates to explain how algebra works, and why it works, I’d guess that 99% of them couldn’t, not in sufficient detail to show that they really deeply understand it. Remember that I am talking about high school graduates, so these people have almost certainly had many years of algebra and algebraic concepts taught to them. Most of these people will only be able to give you some of the rules of algebra at best, and some of them don’t even remember that much.

Algebra is an amazing tool for solving problems though! Formulate a problem as an equation, and unless the equation is too complex, there is an algebraic algorithm to solve that equation, and hence the problem you formulated.

Maybe it is such a useful tool that people don’t really need to understand how it works, maybe they can get by without a deep understanding, but still be able to follow the rules of algebra and use it to solve problems. I don’t really buy that argument though, simply because people who don’t understand something are prone to make mistakes, and not be able to check their work with a reasonable level of accuracy.

Computers are also mumbo jumbo to most people. If you asked people to explain how computers work, most of them cannot. There are actually very few people in the world who can explain from start to finish how a computer works, and there is no one that can explain every single piece of a computer. Computers are still amazing tools though, and give people the ability to solve problems that would otherwise be intractable.

I think computers are a useful tool despite our lack of understanding of how they work. Like algebra, computers are a block box in which we put our inputs and get outputs and don’t understand how the inputs are related to the outputs. Given this similarity, we should look at other reasons why using a computer might be superior to algebra.

There are some significant differences between using computers to do computation, and using algebra to do computation. The first is that using a computer, the error rate is much lower. Obviously you can still press the wrong buttons, enter the wrong information, read the information the computer gives back to you improperly, so there is error, but I’d argue that this error is much less than the standard error rate for algebra. The second benefit of using computers is that they are much faster than doing even moderately complicated algebra by hand, including entering the computation into the computer. In the case that doing it by hand is faster, then I’d say you should do the calculation by hand. 

The largest difference between using a computer to do the calculation and using algebra is that algebra is a single use tool. It can only be used to turn an equation into a solution. A computer can be used for so much more.

Granted we should consider computational mathematics to be a broader tool than just plain algebra, if we want a more fair comparison with a computer, but I’d argue that all of the same problems exist with other areas of computational mathematics. As we increase the scope of computations we can learn how to use, the power of the computer becomes even more evident. It takes much less effort to learn how to compute a broader scope of problems using a computer than learning all of the individual computational methods. Witness the power of Wolfram Alpha, for example. Enter in a search phrase and all sorts of useful information comes up.

So in the consideration of using computers for solving computations, over a by hand approach, we can see postulate that the computer will produce less errors, be generally faster, and is more multipurpose than the pencil and paper model is. Furthermore, the computers can do a lot more as a tool than what you can do with algebra.

Another issue I see is that our current mathematics curriculums leave very little time to learn more important skills than computation. As Dan Meyer (@ddmeyer) points out, the formulation of a problem is more important than the actual solution. Learn how to formulate problems and understand how to verify that what you are doing makes sense, then spotting errors in computation becomes that much easier. Furthermore, I’d like to see mathematics education be much more grounded in what is relevant, than be a collection of different types of math which are taught for historical purposes or because they are the ground-work for calculus.

The question for me is, why aren’t we using computers more to do mathematics in elementary and secondary education? It can’t just be because people are scared of change, can it?

Manufacturing Demand

Thanks to @rmbyrne and his Free Technology for Teachers website, I just saw Annie Lenox’s "The Story of Bottled Water" video which is recommended viewing, but chances are those of you coming to this blog know the story she’s telling already.

In the video, she talks about the process of manufacturing demand, in which a company uses advertising to turn something people don’t need, into something they do. I thought about what she said, and agreed that I myself own many things that I almost certainly do not need. I also thought of the parallel process that is happening in the United States.

Right now educators, parents, and students are being sold a myth of an education system in crisis. By all standards, nothing has changed in education in 40 years across the US, so why is everyone in so much of a panic to change the system? While no one can claim that the US public education system is perfect or isn’t in serious need of improvement, to imply that we should be in a state of panic is at best irrational. When people panic, they will grab at any solution which seems plausible. The US public are being sold a lie, a false-hood, and the solution to the problem all at once.

The US President’s state of the union was fairly uninteresting according to accounts I’ve read because he really said nothing new on education. I didn’t watch it, but he had a pretty simple mesage according to the commentaries I’ve read. "We must do better because we are being beaten. We must do better because the American school children do better." Attached to this message is Race to the Top which encourages charter schools, teacher accountability through standardized testing, and national curriculum standards.

The question you should ask is, if I wanted to change the US education system to be more privatized, how could I convince the US public that this is necessary? Oh right, we’ll just do what we did with the Gulf War, we’ll manufacture a reason why there is a problem, and then provide the solution at the same time, and imply that the only solution lies with greater accountability of teachers.

By implying that teachers are the problem, the US DOE has managed to drive a wedge between teachers and their long time supporters, the parents of the kids they have in their classroom. "Can we trust this teacher," a parent will think, "or are they just trying to save their job?" While fortunately most parents seem to continue to be satisfied with their schools, it is only a matter of time before their (the reformers trying to change the system) message gets through. "American public schools are in trouble and we know the solution."

I don’t see the US system as being entirely in crisis. What I see is a lot of dedicated individuals who are working in a system for a world which needs transformation. I see a lot of educators who like what they do, and would be happy to work differently, but are trapped by the imposed bureacracy around them. I see a system which is failing a lot of students because of its lack of flexibility and inability of US politicians to solve the problem of poverty within their own country.

Instead of the greater accountability movement being pushed on US public education, schools actually need more freedom to pursue an education for children which would actually work. If we think about Zoe Weil, and her work for an education system dedicate toward building a more humane society, we might wonder where that would fit in our current educational model. Could it fit within the greater accountability model? Or would we need to rethink schools completely?

What is it about these people that make them think they can bamboozle the US public so completely? Oh right, because they’ve done it before.

Update: Just so people don’t think I’m making this up, check out this post about how little data these decisins are based on.

What if we treated grades like leveling up?

So I was responding to comment on this blog about student retention, and the person used the word "level" and it made me think of "leveling up" which is this process by which your fantasy character becomes more powerful as a result of the experience they gained. This video below describes the process of leveling up in World of Warcraft (an online fantasy role-playing game). I also remember reading about a professor who was planning on giving experience points for assignments rather than grades.

The thought I had here is, grades on assessments are the "experience points" our students gain, and their school grade (K to 12 in the US & Canadian systems) is their "level." Experience points become a measure of how much your fantasy characters have learned over time, and when you have learned enough, your character gets promoted. As your fantasy character gains levels, they gain abilities, much in the same way students gain skills & mastery of content.

I think this simplistic view of how school works is wrong for a couple of reasons. First, many assessment students do, particularly under assessment of learning systems (as opposed to assessment for learning) are not learning activities, so the idea of applying experience points breaks down here. They simply aren’t gaining experience from the activities in a nice smooth linear fashion. The second reason is that what students are capable of doing does not come in nice neat quanta as suggested by the metaphor of levels. Instead students are complex organisms which grow and develop over time. There may be times when they make leaps and bounds, but really their development comes in small incremental changes, rather than suddenly gaining new capabilities.

So if you buy my argument from my previous paragraph, now our concept of traditional grade levels becomes a bit questionable. We treat students like they are capable of more in 8th grade than they were in 7th grade. How many times have you heard yourself saying "now you are in 12th grade, you shouldn’t act like that!" Our current school system makes hardly any allowances for students who are at different points along the learning continuum. Instead we treat students almost exactly like my analogy.

Retaining students, or complaining of social promotion are just symptoms of a larger problem. We need to stop grouping students by their perceived "experience point level" and start grouping them by what they skills they have mastered.

 

Improvement, not Innovation, is the Key to Greater Equity

Here is an excellent presentation by Ben Levin.

Improvement, Not Innovation, is the Key to Greater Equity from CEA ACE on Vimeo.

Here’s a great quote from his presentation. "How many of you have been involved in a pilot project? Okay almost all of us… How many of those pilot projects are still in operation? Virtually none of them…" In other words, schools have been spending too much time on innovation and not enough time implementing strategies which are known to work.

His observation that we have cycled through many times in education in innovation. Here’s a picture of what I think he means.

According to Ben Levin, we should "take what we know to be effective practices and ensure that these practices are used in every classroom…We could go into school after school after school and look for the practices we know that work, and not see them being used." I’m not sure that I want every classroom be identical, but maybe he is right, there should be more similarity. If something is known to work, and it works in every context it is used, then it should be used in every context, in every classroom.

I like what he has to say, but I’m going to push back a little. Obviously not every single new school program has died, maybe only most of them. However some of them have thrived and expanded and turned into things schools just do. We need a balance between what we know works, and a small number of educators pushing at the boundaries of what we know.

To do this, we need to become better at sharing, and we need to break down the barriers we place between schools. We need to find ways to allow educators to move more freely between schools and thus share their expertise. You can talk all you want about a good practice in education, but these things are complicated, and unless I see it in action, I’m not likely to implement it. We need more sharing of what we already know.

 

School Bells Interfere With Learning

I hate being interrupted in the middle of a good learning session with my students. It has happened hundreds of times in my career because of an archaic device we use in schools known as a clock. The clock itself isn’t evil, but the way we use it in schools has serious ramifications on how our students learn.

First, because we partition students into neat packages called subjects, they are implicitly taught that learning is something we do in compartments. If you try and introduce a little bit of another subject in your subject, students object, saying "This isn’t English, Mr. Wees. Teach us Mathematics." (I’ve actually had students tell me that). Where in the real world is learning sectioned off like this? Mathematics use English (and other languages) when they explain their discoveries to other people. Biologists use geography to decide where to start their research. All of what we learn is interconnected, and more of these connections need to made obvious to the students. This is not easy to do in a school with nine 45 minute separate blocks.

Next, we tell students to stop working on a particular project when the time is up. We enforce time limits on learning! While I’ll grant that real life has deadlines and limits, it very rare indeed that someone has to complete a task "within the next 15 minutes because class will be over" (I’ve said this in my classroom, so many times I can’t keep track). Maybe you have to finish something by a particular day, or by the end of today, but you are in charge of how much you work on the subject, and not the clock. It is ridiculous the number of times I’ve seen students actively engaged in learning and have it wrecked because the end of class came. Worse, I’ve filled the last 10 minutes of a class with a meaningless activity just to ensure that I use every minute I’ve got.

We also assume that each subject area needs the same amount of time each week, and try to make sure that everyone gets their equal share of the carefully apportioned time for courses. In our school I teach IB Mathematical Studies, which requires at least 150 hours of in class instructional time. My school has carefully arranged for about 160 hours, just in case I lose some to field trips, student illness, snow days, and other time sinks. Oh right. Field trips, those banes of our teaching existence which make it so hard to plan. It’s not like any REAL learning happens during field trips anyway.

Clocks are part of the systems world of a school but they have come to rule our life world. We have let ourselves become subject to fixed schedules, daily routine, and the drudgery of a factory-like system. I’m not saying that we can do without the clocks, but maybe we need to find ways for our system to be more flexible, to allow the learning to extend when necessary, and even send off kids early for another opportunity to learn, when their lesson with us is done. Maybe we should even rethink how we schedule kids, and consider other instructional models. There are schools where there are no bells, no classes like what you would see in a traditional school, just kids (and adults) learning.

Learning through Guided Inquiry

My son has started to learn how to ski. He tried last year, and failed miserably, in fact he gave up in the first five minutes of the lesson, which ended up being a pretty expensive day for a 5 minute skiing lesson. It wasn’t his fault the lesson failed, he wasn’t ready for it. He was probably too young, and had strong expectations about what he should be able to do when we started skiing.

We had been to Science World in Vancouver, where they have a simulator that lets you pretend to be a professional skiier. You can race down alpine slopes at frightening speeds, but whenever you crash, the simulation resets and pushes you into the right direction. The problem with the simulation is that my son tried it, and at his age, that’s what he thought his first experience of skiing would be, and when he wasn’t immediately racing down the mountain, he got upset, and his lesson ended.

Now he’s a year older and we’ve tried a different tact. We bought skis and ski boots for him and put them in his play area. Periodically he’s put them both on and walked around our little livingroom. He hasn’t played the simulation at Science World in a long time, and so his expectations are different. We’ve talked about the need to practice to get good at something, and he’s learned a lot of patience. We set up a private lesson for him, instead of the group lesson which failed so badly last year.

He’s learning through what I would call guided inquiry. If we had just put the skiis on him and set him loose, he wouldn’t learn very much about skiing because there are some subtle things which are not obvious, like how to stop or turn. On the other hand, we can’t tell him everything about how to ski, he has to learn through practice and trying it out for himself. His private instructor, a friend of ours, guides him instead of instructing him. He doesn’t go through an experience with the other ski instructors in the big group which I liken to the factory model of education, instead his instructor spends most of the time skiing backward and asking Thanasis to "come here" without telling him too much about how to do it. Periodically she would give him pieces of advice and feedback, but by and large he figured it out himself.

More of our education system should be like this. Guided inquiry as opposed to factory instruction.