I received an announcement about a board sponsored teacher work shop to increase teacher competency in teaching algebra; it prompted this little rant1.
I suspect the workshop is part of our system’s reaction to the PISA test scores and its mistreatment for political or economic concerns in the media (or just plan inadequate and incompetent) which has lead us to believe that math scores are falling compared to the rest of the world and that this is a problem. While I strongly disagree with those tenants, that’s not the issue I’m having. Algebra is part of the curriculum and sure, there are teachers who could stand to build competency in this area. Teachers who don’t know what they’re doing in math, as in any subject, are likely less effective and therefore waste the time and efforts of their students. The problem I am having is we are focusing our resources in the wrong stand of math; we are focusing on a strand that will have little impact on our student’s lives and we are neglecting a strand that teachers, as a group, need to build competency in.
Many people frustratingly argue or express dissatisfaction with math because they fail to see its relevance in their life. “When am I going to use this?” and the like, are questions we uncomfortably endure during the teaching of algebra. In Real Life, most situations can be done using the same sort of subtraction that identifies number families in primary without “let statements” or other algebraic strategies. True, algebra does get amazingly complicated where proper procedure is necessary, but not in real life. People can live their lives without algebra without disadvantage. One reason why they never solidify their understanding or that skills are allowed to degrade is there are so few practical applications. This is part of a problem with our school curriculum. Our system is a sort of pre-calculus model; we teach math focused on, and heading towards, calculus as a mathematical goal. The problem with that is, beyond some engineers, very few up us will end up learning/needing/applying calculus in our lives. It has been 21 years since I took calculus—I don’t remember how to do it, but I have never had an opportunity where I needed it; I have not suffered for want of calculus. Calculus may be a stunning example of human brilliance; it may be invaluable to engineers, but to the rest us, it is impractical and unnecessary.
That’s not necessarily a bad thing. Aristotle taught that education is both a good unto itself and what you can do with it. Esoteric knowledge is not necessarily a bad thing, but in this case, it might be as it has a serious negative consequence. The math we need in life; the math we need daily to understand or solve our current problems is the math our system least values even though it is most relevant. The negative consequence is our studetns are short changed on relevant math when we, as a system, focus on pre-calculus. We should be focusing on Data-management and probability as a system. Understanding the importance of standard deviation would be so much more useful to people that calculating the area under a curve.
Many teachers and students think that these 2 units are easy and of little value; this is mainly the case because that’s how our curriculum teats them. Each year they make their surveys and walk around the school collecting data (and interrupting classes) so they can graph their “authentic experience” in whatever graphing style they are learning. In probability, students spin spinners, roll dice, and pull marbles from imaginary bags—boring and pointless. As a result, Psychology students struggle unprepared through their Stats course in first year university; teachers nod dutifully when Sir Ken Robinson tells them a test resulted in 98% of kindergarteners scoring at genius level, we fill in our school plans for continuous improvement without discussing significant difference, mean or standard deviation; we don’t understand in what ways the ambiguities of “average” and how it’s being used to mislead us; in short, we don’t know what we’re missing, ignoring and short changing our students on. I was lucky; I met a teacher that loved both…he taught me! I learned.
Hand out a diagnostic test and realize that by grade 7 and 8 everyone can make a bar graph—fix the odd problem with scale and move on!
Now you can:
1) Present David McCandless on TED.com and the artistic/beauty of graphing. Combine graphing to tell a different story…a picto-scatter graph, a three dimensional bar graph, a bar graph were the width of the bar displays other data, etc.
2) Present Chris Jordan…graphically display something that so large we can’t deal with intellectually—only emotionally.
3) Present Dan Ariely on TED.com and see the predictable mistakes we make with data everyday…advertisers know them…so should your kids
4) Watch Hans Rosling tell a story with data in “the river of myth” or “200 countries over 200 years.” Turn your data into stories.
5) Teach them graphic manipulation techniques. It’s not wrong when a magazine or politician starts their graph at 50 rather than 0…its strategic–learn the strategies. Stop telling them it’s wrong to not start at zero and start telling them when they might want to (remember, “there are three types of lies: lies, damn lies, and statistics”…teach them how they are being lied to)
6) When should you use mean or mode or median….depends on the story you want to tell
7) How to use biases to your advantage…advertisers and politicians don’t avoid them…neither should you
8) Have them explain the math behind jokes (3 mathematicians go hunting; a duck flies by. The applied mathematician takes a shot but misses—2 feet too high. The Abstract mathematician takes a shot; he misses—2 feet too low. The statistician starts jumping…”we got him! We got him!)
Think it’s easy? Try this: if 72% of people prefer milk chocolate to dark chocolate, what is the probability of at least 8 out of a random 10 people survived prefer milk chocolate? Probability is great, because, like data we’re not very good at it and it is often counter intuitive–we have lots to learn
1) Look up “Linda bank teller” on Google and explore the conjunction fallacy with your students. How many chose option 2…was it the standard 85% even though it’s wrong?
2) Have fun even…look up Donald Duck and Flipism
3) If 5 friends are drawing straws or picking numbers is it better to go first or last? Prove it (it doesn’t matter—a beautiful little pattern emerges)!
4) Have you explored the Monty Hall problem…I like it because so many mathematicians were wrong…Why?
5) Penny’s game: try it! Explain it!
6) Try using black jack
7) Explain the birthday problem—why in a room of 23 people is the chance of 2 sharing a birthday 50%
8) Go to NLVM.com and find the coin flipper…talk about the law of large numbers–more chance of being close to the mean but less chance of being exactly the mean…cool!
9) Probability has multiple modes to solve problems which create multiple points of entry for different learning styles. There’s diagrams like tree diagrams, some formulas and calculation techniques, tables and charts, and experimental. What is the chance of getting a value of 7 rolling 3 dice is a great question because people will approach it differently
10) Then, if you’re really adventurous, try Bayesian logic…if your doctor gives you 3 months to live why will you likely live much longer than that?
While we hardly use algebra, we are constantly running data management and probability software in our heads but it needs constant upgrades to remain useful as we grow into more complicated situations. Algebra is great; it is one of my favourite units because I like the symmetry—it’s beautiful; however, I’m not fooling myself. Algebra gets them ready for high school; data and probability get them ready for life.
1While I came about these conclusions on my own and in discussion with a colleague, we were both delighted to be vindicated by Arthur Benjamin: “Teach statistics before calculus!” on TED.com when we found it. Some of the phrasing in this post is inspired by his presentation.
I failed! I started this year with many assets: I had a lot of experience working with digital technology and students, I had read/thought/learned a lot, I had 10 IPods, 3 Macs, 3 desk tops, and access to 3 ABEL laptops for ½ the day, I also had a nice, personable class of 28 students. With all these assets, I decided to operate a BYOD classroom with free and open technology to be integrated as needed in all subject areas. In spite of all these assets, it was with reluctance and regret that I found myself banning the use of all digital technology (at the suggestion of my principal) in our class on December 18. I hope that it’s only temporary, but I’m not sure. Having struggled for 4 months, I had to concede that it wasn’t enhancing their learner; quite the opposite, it was detracting from their learning.
How will I ever attend an edcamp again; how will I tell Heidi Siwak, Monica Batac, Stephen Hurley, colleagues at CEA and all the other individuals who helped me reach the point where I thought I could run a BYOD classroom?
The problem is I’m not quite certain why it failed. I couldn’t get the students to buy in. Very few of them use the technology to aid their learning. The primary uses were listening to music, playing flash games, and texting for social reasons. Using it for academic purposes was a distant 4th. I couldn’t get them to a point where they could resist the temptation of distraction and focus on their learning tasks/goals.
Sure, there were some who used it well and seamlessly in their learning. They’d make a quick search to find something to add to a discussion, or look on Google images to see examples of art to help them learn technique; however, this was not the majority experience. Whenever my back was turned (or sometimes right in front of me) or my focus on helping individuals, there was always more than a few who took advantage of me, their agreement, and the technology to do as they pleased.
Many have written that we shouldn’t take the technology away; that we wouldn’t take a pencil away if they were misused it. I guess I disagree- if the pencil became a constant distraction, a danger, if it were constantly abused, I hope that we would take it away and look for other more successful options.
I still think that BYOD classrooms can work, once equity can be guaranteed. I still see many aspects of the learning process that digital technology can enhance. As I said, I have failed, not the program.
Many have been writing recently about how failure is necessary to learn. I haven’t figured that part out in this situation yet….any suggestions?
Often, again among educational circles on the internet, you hear the phrase / command to “stop asking questions whose answer can be found on Google.” Firstly, I think implicit to that statement is a devaluing of factual knowledge that I have addressed http://tuckerteacher.wordpress.com/2011/06/04/in-defense-of-facts/ where I argue that having factual knowledge is the basis of skills and is vastly different from having the ability to find factual knowledge, and in a corollary form http://tuckerteacher.wordpress.com/2011/06/25/im-not-dead-i-think-ill-go-for-a-walk-said-the-expert/ ; however, a few things remain to be said:
I have often replied to individuals who advocate the above with: “can you give me an example?” Mostly, the call is ignored but occasionally, an individual replies with a broad statement about asking students for opinions. To this, I’d respond 2 ways. 1) To have an opinion, you require facts; opinions are a response to a fact. They need a base or are merely a pseudo-opinion that may mimic the syntax of an opinion, but are valueless. Thus, you must at least start with facts (that can be googled) that are firmly understood in order to have an opinion. 2) Have you met the Internet? One is tempted to say that the majority of statements on the internet are opinions or pseudo-opinions. Why can’t a student copy / mimic an opinion as much as a factual statement? I wait in earnest for someone to give me a question that can’t be googled but can be answered by my students. The only think left is to create—are they advocating jumping to the top of the beloved Bloom’s Taxonomy each and every time with everybody?
Many skills are also an application of factual knowledge. Are people suggesting we shouldn’t ask a student to demonstrate a serve in volleyball because we can look up how to do it on the internet? Don’t paint a picture to demonstrate balance because you can just find one on the internet. Don’t write a poem about beauty because Shakespeare’s been digitized. Don’t do any math question because you can find the answer on line. Being critical or creative is an application of knowledge; many fine examples can be found on the internet, but surely there is value for students to do these independently. Is it different with a content question in science?
The organising of facts into a coherent answer is an application and a demonstration of mastery. Like the above art examples, to have a student create an answer to a math or science question requires them to turn their understanding into the complex symbolic language of writing. Even if it doesn’t involve opinion, it requires many skills, clarifies their thinking / understanding, and improves their understanding and memory for later application.
Implicit to the statement is also the assumption that it is better to seek information from the internet instead of class questions or discussions. This is troubling for 2 reasons. It is partial (at least) absurd, and it fails to appreciate the complexities of learning online.
It is partially absurd because it is such a generalization. It has in its core, either the idea that information on the internet is always inherently better, or that learning this way is always inherently better. Should students learn to speak from the internet? Learn the letters and sounds? Can they learn to turn the computer on from the internet-sure they can, but perhaps it would be less problematic to be told how to by a teacher, even if it can be googled. I invite you to take a break now and go to Google. Type in “how do i goo” and see the list of suggestions from instant search feature; don’t the suggestions hurt just a little? There are many factual based content areas that are better learned from teachers or other interactions; how to share and why is sharing important are easily googled, but not easily learned from this exposure.
Many contents on the internet are hard for students to decode without context from the teacher first. “Is radiation good for you?” is a good question to ask and to discuss in class because a search on the internet will likely reveal to the student that indeed radiation is good for you (try it and pretend you don’t already know). “Is global warming real?” is another great question to ask in class even though the answer can be googled. This is because a student without factual knowledge beforehand will almost certainly come to the conclusion that it is fake (try it!). “Evolution?”-try it! “Which religion is the best?” – try it! Critical thinking without prior knowledge relies heavily on internal inconsistencies as you cannot spot the omissions without prior knowledge—that’s what makes the internet a dangerous place.
What’s wrong asking questions that can be googled? To retell and repeat doesn’t just demonstrate understanding, it improves it.
Often, in educational circles, I hear the statement/complain that schools and classrooms look the same as they did a 100 years ago with the implication that this is harmful to student learning. I feel this is a ridiculous statement; it is either untrue or at best, irrelevant.
I think the first way to respond can be found in this article: Dear Hollywood: “School Doesn’t Look Like This”
http://plpnetwork.com/2012/06/15/dear-hollywood-school-doesnt-look-like-this/ In this article, some of the differences between today’s classrooms and those of the past are presented. Focusing on, teaching style, digital tech integration, desk or table arrangement, etc. Of course this is not an exhaustive list, and anyone familiar with today’s classrooms should be able to expand it. The troubling implication here is that so many in the education field don’t. There are so many other differences in content and pedagogy to point out. I once got a tweet from a digital art teacher who wondered if we were teaching the same as in the past; this from a digital art instructor! He later revealed he was refering to the fact that we still teach them in batches based on age. I have addressed that here: http://tuckerteacher.wordpress.com/2011/09/13/organizing-schools-by-ability-instead-of-age-is-harmful-to-children/ Even if you don’t agree with me, we can’t perseverate on this one similarity…it doesn’t alone justify the hyperbolic claim of “sameness.” Some similarities or consistencies will always be there (eg. schools will be to educate people).
Is your classroom just the walls and desks? Surely you don’t teach the same as 100 years ago? How many of us are teaching Latin or Classic civilizations (well grade 5’s are)? Are your students in single rows? Are you in a one room school house? In Ontario, at least, aren’t you using a curriculum radically different from the one used in the 1990’s (which was of course different from the one used 100 years ago)?
In our board, we go to the Heritage School House or Pioneer Village to experience the differences and to learn about how different schooling was 100 years ago. Sure I recognise the building, sure I recognise the front desk as the teacher’s…but there’s a world of difference between same and similar. Writing the word “once” is a similar act to writing a novel that starts with “Once upon a time…” I also recognise cars, houses, churches (even of different traditions and even 1000 of years old), boats, and all manner of other things. Being recognizable is part of it’s essence or even Platonic quality; chair appearance hasn’t changed to the point that its unrecognizable, but the tech to build one and the ergonomics have certainly improved. Do we need a new chair design to the point where it isn’t recognisable to prove to overly concrete and limited thinkers that it has changed? How about schools, just because they don’t look like an airport or submarine doesn’t mean they are the same as 100 years ago.
Being old is not the same as being obsolete or irrelevant. Anyone over 20 should intuitively agree. Would the people who suggest that schools are obsolete because of consistent design be willing to make a similar aguement with religious people. Would they be willing to say, “Your moral code is from the Bronze Age; you need to replace it!” to Christians and Jews. Should old people be considered obsolete as well?
My students can instantly recognise hotels, planes, cars, hospitals and banks no matter how old they are. Lots of things look the same but still work differently. Schools continuously change…often teachers grumble about that. We have a board plan for continuous improvement (change), and a school plan for continuous improvement (change)…never mind the dozens of changes implemented by Ministry and Board employees each year. Never mind the changes that I implement each year. You can go to school online now—can you travel online or go to a hospital online?
To reiterate: old does not mean obsolete. That is an epistemology that has developed over the last generation or so in the Western World. It is created largely by the market place; a market place of innovation sure, but also one of planned obsolescence, disposal-ability, and replace-ability. A market place that sold new things by creating false needs, or by creating the desire for newer products as a value. We used to repair now we replace and recycle. We used to value tradition over transience. Sometimes, things/ideas/building have staying power because they elegantly solve a problem, or because they so successfully create positive utility.
The better something is designed, the longer it lasts. Perhaps the persistence of the classroom model should be celebrated! It has lasted a very long time; where’s the evidence that your innovative model (or vague concept) will be better? Where’s the staying power of your innovation? Have you analyzed the unforeseen consequences? Do you have enough evidence to argue it is better and therefore classrooms need to change even more than they already do?
The endurance of our school/class model is evidence of it’s strength, not it’s stagnation.