I was recently asked to share some talks which might inspire parents who have come from a traditional schooling system to think differently about how schools should be operated. Here is my list (please feel free to add your own in the comments below as I am sure I have missed some gems out there).
Author: David Wees (page 33 of 97)
The following was shared to me and I felt it deserved a wider audience, so with permission of the author, I am sharing it here. The author has asked me to point out that this writing is copyrighted by her, and that permission is required from her if you wish to copy it or publish it in another format. You can contact me through the contact link above if you want to get in touch with the author.
Ah, yes, homework.
To mark it? To leverage the pressure by counting the marks in the final average? Perchance not to assign it at all? Why can’t we seem to settle this, or at least find a way to get students to do their homework without all this agony? I believe we have met the enemy, and he looks familiar.
It is partly the system and partly ourselves creating this culture that teaches students in a perverse and relentless way to view the whole school experience as oppositional and adversarial, from mildly so to unbearable. However, when most of the work of learning is handed over to students, when performance happens only as they feel ready and at low risk, when acts of learning are full of interesting, varied experiences and fun, when learning happens within a really functional community of interacting,supportive peers, when every stage is completed so that students are fully competent to move on to the next, and when many or most things to learn are self-chosen, students become almost driven to work hard, and for their own reasons. Result: they learn like clappers. We all know it when we see it. It’s what teachers live for.
There are several sticking points on the way to achieving this, and then homework becomes almost a non-issue. One is the absolute refusal of the system to give up some control, especially over timing. The system overall has never paid anything but mealy-mouthed lip service to the part of our official Mission Statement that says people learn in different ways and at different rates. We seem to say "Sure…yeah…but you still have to complete FOM10 in one semester, or X number of classes, or you FAIL, get no credit for learning anything, and have to start all over again." "You have to move on to grade 6 now, and never mind all that grade 5 work you didn’t complete. Good luck to you."
This leads to "squeaker passes" and the awful pattern of moving on to the next thing when not ready for it, and probably another fail. It tells students in a loud voice that they don’t have to be really competent to "get out" of a year-grade or a course of study, and avoidance or disengagement has rewards (relief from stress, getting out of work they don’t want to do, elimination of risk, "sticking it to the man," declaring a pseudo-independence, status among peers, and more). Remove these pernicious rewards, and their origins, and avoidance vanishes (perhaps after a short period of trying frantically to make it work again!). Create an environment in which intrinsic rewards abound from genuine engagement, and they will come to the table. If they engage learning it feels fabulous; if not….well…nothing. And definitely not fabulous. And no way out but another chance tomorrow to get ‘er done. This is key: we have to learn patience, and WAIT.
We have never just accepted that learning mathematics, for instance, is a continuous process of acquiring knowledge and skills. As a student, it just doesn’t matter to you what age-appropriate or development-appropriate peer group of fellow learners you are with this year, or where any of those kids are on the continuum, as long as you are somewhere on the continuum, moving steadily forward, and riding on a solid history of competence in all of the previous work. We have to learn to trust kids to get there in their good time – with our help, of course. We have to let go of our insistence that every learner in a group must be nearly at the same place academically at any given time, and they all have to be doing the same thing at the same time, all day long.
Step back a bit, and it looks as crazy as it really is. Kids aren’t widgets and education is not mass manufacturing. "Scientific management" was NEVER appropriate for schools, and never will be. I am staggered by the human cost of this over the last two centuries, by the effects on millions of lives that we will never be able to guage fully, nor redeem. Despite widespread, largely unfounded belief, it’s not even efficient. In 2012, we know better, and yet we permit this one, tragically misguided set of notions about learning to dominate education worldwide to this day.
As competent, trained, experienced, caring adults, teachers do have the upper hand, but in many cases, we don’t use it as deftly as we could. Observing where the real intrinsic rewards and natural consequences fall can be disturbing, but very helpful. Interrupting the patterns of urging and resistance, of coercion and punishment, of risk and reward, means becoming very astute observers of what the school landscape feels like for students. How can we change their view of school from jail-like institution to a resource-rich playground where the goodies are?
Piaget so rightly did advise us that play is, above all things, "the Great Work of children". Play is hard work and results in rich, deep learning. Children do not have to be forced to do it. They are inwardly driven to play, and very inventive withal. Play is efficient, because it is child-selected, directed and timed; the energy and effort are focussed where they need to be, and exactly when. Maria Montessori proved how powerful this can be when we provide children with a truly rich environment, model civilized behaviour and true mentorship, and collaborate with children on their learning. How can we transform ourselves from authoritarian keepers, lecturers and judges, to become preparers and guardians of rich learning environments, protectors, mentors, record-keepers, directors of traffic, facilitators and fellow-learners? But that would mean reinventing our own identities somehow, and even adjusting our point of view, before we can transform learning in schools!
Another issue is our very difficult and uncomfortable relationship with the concept of evaluation. Although we have all kinds of ways to determine whether a person can perform a skill or demonstrate knowledge at any number of levels of mastery (recognition, recall, application, synthesis, etc.), we are still collecting marks from early performance, or even formative stages, and averaging them with information from summative performance, sticking in some "credit" for what amounts to compliance or engagement attitudes, and claiming that this represents some kind of accurate picture of competence in a scope of challenges. I have struggled with many iterations of this, none of them even in the ball park of real validity. And none address the likelihood that skills may improve with time after instruction.
Many teachers do have a good grasp of the use of rubrics, checklists, and testing theory, and use them every day. More and more are finding ways for students to demonstrate levels of mastery for summative evaluations that really do represent what students can do reliably and independently after learning and practice. Too many of us are still wallowing in a miasma of mixed messages, imprecise language, unsupported beliefs, crossed wires, lack of guidance, administrative confusion and just plain muddleheadedness about what we’re really trying to do here. And you can’t write comprehensive anecdotals on 150 kids every couple of months. Get real.
The first thing is to admit that this is a much bigger, wholly systematic problem, and cannot be fixed with a few hints about marking or not marking homework. We have work to do. (Don’t we always?) Psychologists speak of the "dances" of dysfunctionality, and admonish us that if we don’t like the dance we’re in, there’s only one way to move toward something better. Each of us can only act individually; we can’t change others. But if we change our own steps, we change the dance, and that can make all the difference.
When we do it together, we can change the world.
Oh, and in the short term, make a Big Deal of homework. VALUE it. Assign adjustable amounts of work (according to self-assessed need for gaining competence). Assign tasks that are very high quality and meaningful. Be sensitive to students’ need to have a life outside of school. Teach students explicitly how to know when they can perform a task confidently and independently. Set and insist on very high standards of work and presentation. Talk about it, go over some of it in class. Require completed, fully-documented corrections before checking off. If it isn’t done right, it isn’t done. Keep records. Don’t count them, but show them to parents. And there’s always after school. On Friday. 😉
KT Pirquet
KT Pirquet is a professional writer/editor and retired high school mathematics and science teacher. Katie lives near Victoria, B.C., where she is currently a writing instructor at the Western Academy of Photography.
"If I am to have faults, I would rather they be my own." Vi Hart
Vi Hart is somewhat critical of math teachers in this video, and of systems which prevent exploration into mathematics in their desire to ensure that all students have equal exposure to mathematical ideas. Of course, as she points out, students rarely have exposure to mathematical ideas. Instead, what they usually experience are mathematical procedures to solve problems that aren’t their own.
This is another in a series of posts about how one could find mathematics in the world around us.
My son loves to play with train tracks. A few days ago, while playing with his train tracks, he observed, "Daddy, I can’t turn a train around." I asked him what he meant. "No matter which way I go on this track, I can’t get my train to start facing in the other direction. I’d have to pick it up, but that’s cheating." (Note: I’m paraphrasing here)
Observations like this are mathematical observations about the world. He has abstracted from his train tracks to a property of his train tracks, specifically the direction his train is able to travel. He has then attempted, and I watched him do this, to verify this statement is true by running his trains around the track in every possible comination.
My wife and I spoke about this later, and she came to the observation that in order to be able to turn around his train on the track (without "cheating" by lifting it up), he needs a closed loop with a single entrance and exit point included in his track somewhere, and this entrance and exit point has to connect to the rest of the track in a certain way. So I asked the question, does he have the right track to be able to create a closed loop? If you look at the picture above, you may be able to answer this question yourself.
The area of mathematics that deals with these kinds of issues is called graph theory, and it was invented by Euler for a very different purpose many years ago. It is unfortunately not in most school curriculums, but it is certainly an interesting area of exploration, and one which is accessible to students.
While I was at my mother’s house the phone rang so I picked it up.
"Hello?"
"Hello Sir," said a female voice on the other end of the line, with a slight accent, "We are calling you from an independent computer security company. We want to let you know that we have received numerous reports that your computer has downloaded viruses and malware, and we would like to help you fix your computer." In the background, I could hear the unmistakable background noise of a busy call centre.
"You know that’s impossible, right?" I responded.
"What’s impossible?" she responded.
"You can’t possibly, especialy as an independent computer company, know the phone number associated with a specific computer, even if you were somehow able to scan my mother’s computer remotely without her permission. You are trying to scam her. It won’t work this time. I teach people how to use their computers. I’ve taught my mother about you. You cannot scam my mother. I will record the phone call the next time you call, and forward it to Interpol. Leave my mother alone!" I said firmly. (I doubt Interpol would be able to do much about this scam, but hey, empty threats sometimes work.)
Click.
Warn your parents, your relatives, and anyone you care about who may be taken in by this scam. My mother got caught the first time, but with some help from me, we recovered her money, and I have hopefully helped immunize her from the scammers.
We are introducing 30 iPads to our elementary school next year, and we are currently exploring what apps to put onto them. We have some suggestions as a place to get started, but I’ve been tasked with coming up with a list of useful apps for the iPads. I’m currently looking through my list of resources I’ve bookmarked for the iPad and deciding which of these apps I’ve seen will be most useful in our school’s context. (The screen-shots below are taken from the linked iTunes page).
- Move the Turtle
- Tinkerbox
This app allows students to build equipment to try and solve puzzles (which are based on physics concepts). I’ve not tried it out myself, but it is free, and so I’m going to at least try it out with the students.
- Show Me
This app allows students to draw and record their voice while drawing, letting them create a voice-over narration. It could be used for student created tutorials, stories, and animations. According to the description of this app, the videos created can be uploaded and shared via the ShowMe.com website.
- Motion Math
The series of apps Motion Math makes for the iPhone and iPad are excellent, because they are more than just the typical flash card apps that are all too common in the app store for math. I’ve played with the fraction one myself (so has my son) and enjoyed using it, and seeing how it creates an alternate representation of fractions. This representation is hardly sufficient for students to completely understand fractions, but I’m sure it helps.
- Sketchpad
I’ve not used this app myself, but it comes recommended from Trever Reeh. From conversations with the mathematics teachers who work with Sketchpad, and from my time spent using Geometer’s Sketchpad a few years ago, I’m pretty sure this app will be useful. On the app description page, they note that they have activities built into it, which is encouraging.
- DragonBox
DragonBox is a puzzle-game which tries to teach algebraic reasoning. It replaces algebraic symbols with visual representations (which are still themselves an abstraction of some arithmetic concepts) and then allows students to manipulate the symbols to try and solve the puzzles, which are all equivalent to standard algebra problems. It has a PC version which runs in the browswer and I have tried out as well. This is not a flash app so students can practice algebra – this game will try and teach students.
- Shuttle Mission Math
I’ve not tried this puzzle-game out myself, but I have used the paper and pencil version of the types of puzzles presented in this game with my students, and I found them very useful. Through solving the puzzles, students will have to employ (and learn) algebraic reasoning skills, which are explicitly described on the support page for this game.
- Scribblenauts
This game allows students to type in words, get presented with images that represent those words, and use the images to solve a puzzle presented. The students have an enormous amount of freedom in what words they choose, and what images result. My son has loved playing this game, and spends his time playing it constantly asking us how to spell words, which he seems to be able to (mostly) remember for the next time he wants that particular item.
These are some of the apps I’m looking into. I’d also like further recommendations. I’m looking specifically for iPad apps which:
- Are not just skill practicing / flash card apps. There are thousands of these, so finding them is easy, should our teachers want to use them.
- I’m hoping to find apps which will actually help teach concepts, rather than just review existing concepts. I’d like this teaching to be of the non-explaining-type teaching style, and more of the discovery-it-yourself-inside-a-guided-framework style of teaching. I can find things like the Khan Academy for myself fairly easily, but finding apps which support our inquiry-based teaching program in our elementary school is a bit more of a challenge.
Here are some images I’m collecting for future presentations on technology. Each of the images is intended to ask a question, and to have people reflect on their own use of technology, and our society’s use of technology.
(Image credit: Andy Hooper)
(Image credit: Wikipedia)
(Image credit: T Coffey)
(Image credit: Michael Leung)
(Image credit: Susan Sermoneta)
(Image credit: Dom Nozzi)
(Image credit: Geek of the day)
(Image credit: Erik Johansson)
(Image credit: Daniel Martin Reina)
If you have any other images of various technologies that you think require their viewer to ask questions (or which easily lead to questions), please share them with me.
Students First (I won’t link to their website, you can find it yourself) has published a new video comparing the ranking of the US education system to a potential performance in the Olympics.
There are a huge number of issues with this analogy, but I’ll just bring up two.
- Countries which perform well at the Olympics outspend the other countries, have a larger population base, and more free political environments. So from this analogy, we can predict that the US will perform better in education if they spend more money, increase their population, and work on implementing a more democratic decision making system within their education system. Not what I think Students First is hoping for with their privatization agenda…
- The Olympics accept only the most elite athletes in their competitions. The US education system is intended to educate everyone.
What do I know about the most of the people with whom I connect online?
Nothing.
I know very little about their families, their history, their relationships, their beliefs about God, their dislikes, their intolerances, their emotions, and who they are. What I do know, I know only through their statements about themselves, so I know really nothing about them except what they have confessed themselves. What I know is their manicured self, their selves with the make-up on, and I do not really know them at all.
And of course I know that people tend not to share the uglier parts of themselves, and this is especially true in print mediums. I know that people tend to find it very difficult to view themselves objectively, and they (myself included, of course) have a tendency to exaggerate some parts of their personality, and ignore other parts. So what do I really know about the people with whom I connect online? Nothing.
And who knows about me? Who knows that I hated school until it became an escape from the bullies? Who knows that I once believed myself to be bisexual (and no longer do), mistaking a desire to connect and form relationships with the people around me with sexual desire? Who knows that I love to play games, often because the game is enjoyable, but mostly because I like to win? And who knows that right now, my favourite thing to do (and something for which I do not have sufficient time) is to wrestle with my oldest son, and gaze into the curious eyes of my youngest son as he observes the world? Who knows that I love my wife fiercely, and would do anything for her?
No one.
If you are reading this, even you cannot be sure these things are true, since you have not observed these in me yourself, you have only my (written) word for it. We cannot really know things about other people, except what we can predict is true about them from our observations of them. I know from my observations, for example, that John has a deep relationship with his God and his family, and that Mary Beth is passionate about coops, and that Shelley thinks her dog is the cutest dog in the whole world, but I know these things are true because I have talked with each of these people in person and I can see these things are true from the actions and words I’ve experienced while with them.
These are still shallow characteristics of who these people really are. John is not defined completely by his love of his family and God, Mary Beth is more than her passion for coops, and Shelley is deeper than just being a dog-lover. If I want to really know who these people are, I need to spend time with them, experience the highs and lows of their life, and this kind of relationship takes years to build.
We must be careful not to mistake interactions with the words of people online as friendships, and we must further be careful not to take away from the already precious time we have to build real friendships with the people around us. We must balance our desire to know more about the world that is away from ourselves, with building deep connections with the people surrounding us.
Here’s a thought experiment for you (h/t to Dan Meyer for the sports analogy).
Imagine you start learning the game of basketball by learning how to shoot free throws. At no point are you told what the point of shooting free throws is, or how being a good free throw shooter will help you play the game of basketball, or even that there is a game of basketball. Worse, you are occasionally asked to shoot as many free throws you can in a minute, and then judged against your classmates based on your performance.
You are at some point asked to start practicing all of your free throws blindfolded, possibly after unsuccessfully learning how to shoot free throws earlier. If you are lucky, your coach tells you how many free throws you sank, and how many you missed. You finally have some understanding that free throws are important in basketball after years of not having a clue why you were practicing them but no matter how many times you practice, you never seem to get better at free throws.
By way of analogy, this is almost exactly how addition and multiplication facts are taught to students. They spend the earliest years learning addition and multiplication facts with only a superficial explanation of how these facts might be useful later, and most do not learn how addition and multiplication fit into mathematics as a whole and they certainly never get to experience "the game."
In their later grades, their teacher (although lacking the time to give students feedback on their "basic skills") expects students to work on their higher level mathematics without a calculator or any aid of any kind for their foundational numeracy skills. The premise behind these calculator-less classrooms is that students will likely forget their addition and multiplication facts if they get to use a calculator, and so the use of a calculator is banned. Unfortunately, in most of these classes, very little time is spent reteaching addition and/or multiplication facts, and almost no feedback is given to students as to whether they have even done their addition and/or multiplication correctly, so if you are a student who never understood addition or multiplication in the first place, this further practice without support is unlikely to be useful.
If you are going to ban students from using calculators in your class for basic arithmetic operations, then you must at least take the blindfolds off of your students and help them improve their arithmetic skills. On the other hand, I prefer not to ban tools, but instead find ways that these tools are used productively (and unproductively) and change my teaching to compensate.