teaching philosophy

Selling mathematical thinking the Apple way

After reading Gizmodo’s post on the recently created blog Applefied Ads, I started thinking about the relationship of good advertising and the public relations problem that learning mathematics has.

Most people think of math class as that “special” time of day when you learn step-by-step procedures on how to do something. I’ve posted on this before, so I don’t need to go into it in detail. The common idea that math class is a time for nothing more than skill development is the reason this problem exists.

One thing that’s interesting about Apple is that their advertising is always focused first on what it allows someone to do. Some companies often focus on the speed of the processor, the number of ports available, or installed memory. While these are things that Apple might mention in their ads, it isn’t the first thing that is said about a product. Without exception, Apple focuses on how the product will improve things or be different from what is already possible. Despite the media rich world we live in, it does so in a strikingly minimalist fashion.

Textbook companies are faced with the task of engaging with media overloaded students and connect with the oft repeated goal of making math education focused on “the real world”. In doing this, they usually stuff their pages with as many pictures as they can be found, contrived examples, and carefully crafted “investigations” that usually are nothing more than a series of guided steps to a single end. Dan Meyer does an amazing job of pointing out how Pearson has already tried to do more of the same in creating electronic textbooks in this post.

Dan has also done incredible work in getting the mathematical problem to jump off the page or screen, but in an understated and minimalist way through the power of multimedia. If done correctly, you don’t need a bunch of fluffy text or pictures to explain a math problem to a student. A question and a picture or video, and often just a picture, is all that is required to set a student off investigating and developing problem solving skills. In math, these are the skills that will have lasting power and utility for a student beyond a single school year, not the steps of an algorithm.

I wonder what happens if we make a concerted effort to sell math (or any subject for that matter) in the same way that Apple does. What does it enable us to do? How does it let us look at the world in a new way? How can its elegance and beauty be captured through a picture and a few carefully chosen words? How do we get students to think about it as a philosophy?

My purpose is NOT to dress mathematics and mathematical thinking as a ruse to fool students into being engaged by it. This is what many of the textbooks do already. I’d love to see what draws students in and gets them thinking mathematically without our having to mess it up by talking or explaining it further. Less is more.

How would you sell the classes you teach in a way that engages students without tricking them? How would you show what your course is about on the first day of class? Can you do this with a picture and a few words? Try it and share what you create.

Can ideas and a little money be a bad thing?

I was having a conversation with someone recently about technology in education. I brought up Udacity as an interesting model for using video and interactivity for learning. My example was (expectedly) countered with Khan Academy. I shared my opinions about its strengths and weaknesses and we had a really great discussion about what its existence means. I felt good about being able to share some of the ‘other side’ of the argument that Time and CBS haven’t really covered.

One point that was brought up has stuck with me, and I want to explore it a bit. Here’s the basic idea with my own paraphrasing.

Here’s a smart guy with an idea. He sees a problem and wants to help, so he puts his own time and resources into solving that problem. Other people noticed what he was doing and thought it was a good idea, so they put money into his project. What could it hurt?

What could it hurt?

My focus has nothing to do with the fact that many people have benefited from Khan’s resources and his website. Many teachers have used the site as a tool to help their students in skill development. I also don’t want to focus on the fact that many learning professionals have questioned the pedagogy of Khan’s videos given the fact he has no teaching background. Many others have already fleshed out this line of reasoning pretty effectively.

The big problem I see comes from applying how business investment works – a business starting up needs investors so it can start getting what it needs to generate revenue. If the business is actually fulfilling a real need in the market, it will increase in value through the income earned and the equipment and intellectual property generated or acquired by the business. Venture capitalists research companies and their ideas to see which ones have potential to be successful in the market and then select those that, based on their experience in the field, are most likely to succeed. Often these capitalists invest in a number of different ideas to maximize the potential that one will be a real money maker – they understand that not every investment will actually be a winner.

Here’s why I see the hubbub about Khan Academy as an indication of a bigger problem: We get things backward when we see a major investment as a measure of its value, whether in an idea or a business.

So much has been made out of the fact that Bill Gates and Google have invested in the Khan Academy that people might thing it’s a good idea specifically because Gates and Google have done so. Don’t get me wrong – Google has invested in many really great causes (FIRST being one of my favorites) but they don’t always get things right. As I said before, this is the nature of investment though. Not everything works out. I challenge anyone to defend the content of the video below as really, honestly, being truly deserving of a major investment to help it be implemented in schools:

[youtube http://www.youtube.com/watch?v=SXwh0A3YP5s&w=560&h=315]

This is the Explicit Direct Instruction initiative that Google recently supported in the Mountain View school district. The manager of community affairs says in the linked article that EDI “…seemed like a really successful program that we want to continue to support.” Google wants to help solve the complex problems of the educational problem, and based on the manager’s assessment, it will continue to do so.

Why might this situation hurt rather than help?

The news story was all about Google’s generous donation in support of the initiative. A person reading this article might make the mental connection that if Google is supporting the idea, then the idea must be one that will effectively address an educational issue. Google’s donation (and subsequent coverage of the donation) have consequently turned it from a company that just wants to help, into a ‘player’ in the educational reform world. What was this originally based on? A manager that saw kids ‘engaged’ because they were compliant, which to her meant that learning was going on in the classroom. What does she know about education?

Many people think they are experts in education because they went to school and they know what worked for them. Salman Khan has been reported to be good at explaining concepts through solving problems – he has said himself that procedures are how he and everyone he knew learned. He makes videos that primarily show procedures, though there are some exceptions. Investors see this and contribute millions. The media picks up on this and says that because of these investments, school has been “rebooted” and education has been revolutionized by his contribution.

Money talks. If the money goes toward Khan, EDI, and other flavors of the week, a few things can happen. The media pounces and says that these ideas that have attracted investors must be what will revolutionize education. Not the genuine ways that many teachers have individually used technology to improve instruction in their classrooms. Not the ways teachers are able to have improved communication with parents and students about their progress. Administrators looking for quick solutions to achievement deficiencies in their districts might sink considerable resources into these ideas without consulting with the teachers responsible for implementing them. Parents can demand that teachers spend less time creating rich explorations and applications of topics in their classrooms in order to focus on this ‘innovative’ idea they learned about on TV or the internet. As I have said before, there is no silver bullet in education, not any one piece of technology, not a single pedagogical technique, nor a single textbook. Solutions to problems in a learning community must be influenced primarily by the parents, teachers, students, and administrators in that community, and not by what the news says is innovative because of a million dollar donation.

It is possible that the involved players can act with a bit more restraint. I know there are many administrators that do. We are so reactionary these days. We want a quick fix. The media’s tendency to hype, the power of the internet to exponentially transmit ideas, and the ability money has to set our priorities: these form a dangerous formula that could lead us to rapidly pursue options that really don’t resolve the issues we face. Hopefully we do not lose sight of what we really value in education. I don’t believe it is too late.

A Response to Slate: How the recent article on technology misses the point.

Ah, summer. A great time to kick back, relax, and have time to write reactions to things that bug me.

I read through the article on Slate titled ‘Why Johnny Can’t Add Without a Calculator’ and found it to be a rehashing of a whole slew of arguments that drive me nuts about technology in education. It also does a pretty good job of glossing over a number of issues relative to learning math.

The problem isn’t that Johnny can’t add without a calculator. It’s that we sometimes focus too much about turning our brain into one.

This was the sub-heading underneath the title of the article:

Technology is doing to math education what industrial agriculture did to food: making it efficient, monotonous, and low-quality.

The author then describes some ancedotes describing technology use and implementation:

An experienced teacher forced to give up his preferred blackboard in favor of an interactive whiteboard, or IWB.
A teacher unable to demonstrate the merits of an IWB beyond showing a video and completing a demo of an electric circuit.
The author trying one piece of software and finding it would not accept an answer without sufficient accuracy.

I agree with the author’s implication that blindly throwing technology into the classroom is a bad idea. I’ve said many times that technology is only really useful for teaching when it is used in ways that enhance the classroom experience. Simply using technology for its own sake is a waste.

These statements are true about many tools though. The mere presence of one tool or another doesn’t make the difference – it is all about how the tool is used. A skilled teacher can make the most of any textbook – whether recently published or decades old – for the purposes of helping a student learn. Conversely, just having an interactive whiteboard in the classroom does not make students learn more. It is all about the teacher and how he or she uses the tools in the room. The author acknowledges this fact briefly at the end in arguing that the “shortfall in math and science education can be solved not by software or gadgets but by better teachers.” He also makes the point that there is no “technological substitute for a teacher who cares.” I don’t disagree with this point at all.

The most damaging statements in the article surround how the author’s misunderstanding of good mathematical education and learning through technology.

Statement 1: “Educational researchers often present a false dichotomy between fluency and conceptual reasoning. But as in basketball, where shooting foul shots helps you learn how to take a fancier shot, computational fluency is the path to conceptual understanding. There is no way around it.”

This statement gets to the heart of what the author views as learning math. I’ve argued in previous posts on how my own view of the relationship between conceptual understanding and learning algorithms has evolved. I won’t delve too much here on this issue since there are bigger fish to fry, but the idea that math is nothing more than learning procedures that will someday be used and understood does the whole subject a disservice. This is a piece of the criticism of Khan Academy, but I’ll leave the bulk of that argument to the experts.

I will say that I’m really tired of the sports skills analogy for arguing why drilling in math is important. I’m not saying drills aren’t useful, just that they are never the point. You go through drills in basketball not just to be able to do a fancier shot (as he says) but to be able to play and succeed in a game. This analogy also falls short in other subjects, a fact not usually brought up by those using this argument. You spend time learning grammar and analysis in English classes (drills), but eventually students are also asked to write essays (the game). Musicians practice scales and fingering (drills), but also get opportunities to play pieces of music and perform in front of audiences (the game).

The general view of learning procedures as the end goal in math class is probably the most destructive reason why people view math as something acceptable not to be good at. Learning math this way can be low-quality because it is “monotonous [and] efficient”, which is not technology’s fault.

One hundred percent of class time can’t be spent on computational fluency with the expectation that one hundred percent of understanding can come later. The two are intimately entwined, particularly in the best math classrooms with the best teachers.

Statement 2: “Despite the lack of empirical evidence, the National Council of Teachers of Mathematics takes the beneficial effects of technology as dogma.”

If you visit the link the author includes in his article, you will see that what NCTM actually says is this:

“Calculators and other technological tools, such as computer algebra systems, interactive geometry software, applets, spreadsheets, and interactive presentation devices, are vital components of a high-quality mathematics education.”

…and then this:

“The use of technology cannot replace conceptual understanding, computational fluency, or problem-solving skills.”

In short, the National Council for Teachers of Mathematics wants both understanding and computational fluency. It really isn’t one or the other, as the author suggests.

The author’s view of what “technology” entails in the classroom seems to be the mere presence of an interactive whiteboard, new textbooks, calculators in the classroom, and software that teaches mathematical procedures. This is not what the NCTM intends the use of technology to be. Instead the use of technology allows exploration of concepts in ways that cannot be done using just a blackboard and chalk, or pencil and paper. The “and other technological tools next to calculators in the quote has become much more significant over the past five years, as Geometers Sketchpad, Geogebra, Wolfram Alpha, and Desmos have become available.

Teachers must know how to use these tools for the nature of math class to change to one that emphasizes mathematical thinking over rote procedure. If they don’t, then math continues as it has been for many years: a set of procedures that students may understand and use some day in the future. This might be just fine for students that are planning to study math, science, or engineering high school. What about the rest of them? (They are the majority, by the way.)

Statement 3: “…the new Common Core standards for math…fall short. They fetishize “data analysis” without giving students a sufficient grounding to meaningfully analyze data. Though not as wishy-washy as they might have been, they are of a piece with the runaway adaption of technology: The new is given preference over the rigorous.”

If “sufficient grounding” here means students doing calculations done by hand, I completely disagree. Ask a student to add 20 numbers by hand to calculate an average, and you’ll know what I mean. If calculation is the point of a lesson, I’ll have students calculate. The point of data analysis is not computation. Just because the tools take the rigor out of calculation does not diminish the mathematical thinking involved.

Statement 4: “Computer technology, while great for many things, is just not much good for teaching, yet. Paradoxically, using technology can inhibit understanding how it works. If you learn how to multiply 37 by 41 using a calculator, you only understand the black box. You’ll never learn how to build a better calculator that way.”

For my high school students, I am not focused on students understanding how to multiply 37 by 41 by hand. I do expect them to be able to do it. Usually when my students do get it wrong, it is because they feel compelled to do it by hand because they are taught (in my view incorrectly) that doing so is somehow better, even when a calculator sits in front of them. As with Statement 3, I am not usually interested in students focusing on the details of computation when we are learning difference quotients and derivatives. This is where technology comes in.

I tweeted a request to the author to check out Conrad Wolfram’s TED Talk on using computers to teach math, and asked for a response. I still haven’t heard back. I think it would be really revealing for him to listen to Wolfram’s points about computation, the traditional arguments against computation, and the reasons why computers offer students new opportunities to explore concepts in ways they could not with mere pencil and paper. His statement that math is much more than computation has really changed the way I think about teaching my students math in my classroom.

Statement 5: “Technology is bad at dealing with poorly structured concepts. One question leads to another leads to another, and the rigid structure of computer software has no way of dealing with this. Software is especially bad for smart kids, who are held back by its inflexibility.”

Looking at computers used purely as rote instruction tools, I completely agree. That is a fairly narrow view of what learning mathematics can be about.

In reality, technology tools are perfectly suited for exploring poorly structured concepts because they let a student explore the patterns of the big picture. The situation in which “one question leads to another” is exactly what we want students to feel comfortable exploring in our classroom! Finally, software that is designed for this type of exploration is good for the smart students (who might quickly make connections between different graphical, algebraic, and numerical representations of functions, for example) and for the weaker students that might need different approaches to a topic to engage with a concept.

The truly inflexible applications of technology are, sadly, the ones that are also associated with easily measured outcomes. If technology is only used to pass lectures and exercises to students so they can perform well on standardized tests, it will be “efficient, monotonous, and low quality” as the author states at the beginning.

The hope that throwing calculators or computers in the classroom will “fix” problems of engagement and achievement without the right people in the room to use those tools is a false one, as the author suggests. The move to portray mathematics as more than a set of repetitive, monotonous processes, however, is a really good thing. We want schools to produce students that can think independently and analytically, and there are many ways that true mathematical thinking contributes to this sort of development. Technology enables students to do mathematical thinking even when their computation skills are not up to par. It offers a different way for students to explore mathematical ideas when these ideas don’t make sense presented on a static blackboard. In the end, this gets more students into the game.

This should be our goal. We shouldn’t going back to the most basic textbooks and rote teaching methods because it has always worked for the strongest math students. There must have been a form of mathematical Darwinism at work there – the students that went on historically were the ones that could manage the methods. This is why we must be wary of the argument often made that since a pedagogical method “worked for one person” that that method should be continued for all students. We should instead be making the most of resources that are available to reach as many students as possible and give them a rich experience that exposes them to the depth and variety associated with true mathematical thinking.

What my dad taught me about learning.

The first time I saw the word ‘Calculus’, I was staring at the spines of several textbooks that sat on the bookshelf at home. I didn’t think much of them; I knew they were my parents’, and that they were from their college days, but had no other awareness of what the topic actually was. I did assume that the reason there were so many of them was because my parents must have liked them so much. After further investigation, I learned that they were mostly my dad’s books. His secret was out: he must have loved Calculus. I believed this for a while.

When my older brother took Calculus, these books came off the shelf occasionally as a resource, though I don’t know if this was his decision or my dad’s. From what I knew, my brother breezed through Calculus. I know he worked hard, but it also seemed to come fairly naturally to him. I remember conversations that my parents had about not knowing where my brother got this talent from. They admitted at this point that it couldn’t have been from either of them. My dad had taken Calculus multiple times and the collection of textbooks was the evidence that hung around for no particularly good reason.

This astounded my young brain for a couple of reasons. It was mind-boggling to me that my parents ever had trouble doing anything. They always seemed to know just what to do in different situations – how could they not do well in a class designed to teach them something? It was also the first time I ever remember learning that my dad was not successful in everything he tried to do. This conflicted deeply with what I understood his capabilities to be.

As I understood it, he just knew everything.

When I was nine and my parents had bought me a keyboard to learn to play piano for the first time, there was no AC adapter in the box I had unwrapped only moments before. My dad scrounged around among his junk boxes and drawers and found one with the correct tip, but the polarity was wrong. I knew I wasn’t going to be able to start jamming that night – it was late and a trip to the store wasn’t an option. He wasn’t going to submit to that as a possibility – he took the adapter downstairs to the basement and had me follow him. There was soldering involved, and electrical tape. I had no idea what he was doing. Moments later, however, he appeared with the same adapter and a white label that said ‘modified’. We plugged it in to the keyboard and it lit up, ready for me to play and drive my parents crazy with my rendition of . I now understand that he switched the wires around to change the polarity – I did it myself with some students recently in robotics. At the time though, it seemed like magic. I just knew I had the smartest dad in the world.

His mantra has always been that if it can be fixed, it should be fixed, no matter the hilarity of the process. I watched him countless times take in the cast-off computers of other people who asked him if he knew how to fix them. Thinking back, I don’t know that he ever specifically answered that question. His usual response was (and still is) “I’ll take a look.” So he would work long hours with a vacuum, various metal tools, and a gray multimeter (that I think he still has) laid out like a surgeon investigating a patient. I rarely had the patience to sit and watch. I would see the results of his work: sheets of yellow legal pad paper filled with notes and diagrams scrawled along the way. In the end, he would inevitably find a solution, though often at this point the person who had asked him to fix the item had gone and bought a new one. I don’t recall ever believing my dad thought it was a waste.

We also worked on things together to try to get closer in my early teens. We both took tests to get amateur radio licenses. I came to really enjoy learning Morse code and got the preparation books to climb the license ladder. He commented repeatedly as I zipped through the books about memorizing the books and not understanding the underlying theory of resonant circuits and antenna diagrams. That was true – at the time I just wanted to pass the tests. I didn’t understand that the process of learning was the valuable part, not the end point. I didn’t see that. I just continued to believe that the tests were a means to an end, just as I viewed through my thirteen year old brain that his herculean efforts to fix things was a means to getting things fixed., and nothing more.

My dad is one of the smartest people I know. As I’ve grown older, however, I have come to understand that it wasn’t that about knowing everything. He instead had been continuously demonstrating what real learning is supposed to be. It was never about knowing the answer; it was about finding it. It wasn’t about fixing a computer, it was about enjoying figuring out how it can be fixed, however much frustration was involved. It wasn’t just about saving money or avoiding a trip to the store to buy an electric adapter. It was about seeing that we can understand the tools we use on a regular basis well enough to make them work for us.

I have seen time and time again how he mentors people to make them better at what they do. I have seen it in the way he mentors FIRST robotics teams as a robot inspector at the Great Lakes regional competition in Cleveland. I have seen it in the way he has spent his time since selling the company he founded with partners years ago. He chooses to do work that matters and makes sure that others are right there to learn beside him. There were times growing up when, admittedly, I just wanted him to fix things that needed to be fixed. To his credit, he insisted on involving me in the process, even when I protested or became impatient.. I didn’t see it when I was younger. Knowing how to go about solving problems is among the most important skills that everyone needs. I was getting free lessons from someone that not only was really good at it, but cared enough about me to want me to learn the joy of figuring things out.

One of my students this year was really into electronic circuits and microcontrollers. He soldered 120 LEDs into a display and wanted to use an Arduino to program it to scroll text across it. The student’s program wasn’t working and he didn’t know why. I had only been tangentially paying attention to the issues he was having, and when he was visibly frustrated, I pulled up a chair and sat next to him, and then said ‘let’s take a look.” We went through lines of code and found some missing semicolons and incorrectly indexed arrays, and I asked him to tell me what each line did. I was only a couple steps ahead of him in identifying the problem, but we laughed and tried making changes while speaking out loud what we thought the results would be. At one point, he said to me “Mr. Weinberg, you’re so smart. You just know what to do to fix the program.”

I immediately corrected him. I didn’t know what was wrong. We were able to make progress by talking to each other and experimenting. It wasn’t about knowing just what to do. It was about figuring out what to try next and having strategies to analyze what was and was not working. I learned this from a master.

On this Father’s day (that also happens to be the day before my dad’s birthday), I celebrate this truth: much of what I do as a teacher comes from trying to channel my dad’s habits while confronting big challenges. I don’t want my students to memorize steps to pass tests; I want them to understand well enough to be able to solve any challenge set before them. I don’t want to fix my students’ problems – I want to help them learn to fix problems themselves. I don’t want my students to be afraid to fail; I want them to understand through example that failure leads to finding a better way.

I am grateful for all that I have learned from him., and I try to teach my students what he has taught me about learning at every opportunity. It would be fine by me if I ever need to do Calculus for him – I’d still be in the red.

Electric Circuits – starting at the end.

We only have a couple weeks of class left, and there’s not enough time to do the traditional Physics B sequence that I’ve used for electricity with my seniors that asked for a non-AP physics course at the beginning of the year. Normally I do electrostatics for a couple of weeks, talk about electric fields and potential, and then use these concepts to motivate a treatment of electric circuits. I could have stretched that out, but given my freedom in pace and curriculum, I decided to switch everything around.

This year, I started at the end of my sequence to address a pretty big issue I’ve always seen with my students. As much as they talk about charging (mobile devices, laptops) and basic energy conservation such as turning lights off, they have a pretty fuzzy understanding of electricity and the origins of the energy they use everyday. Some of the last topics in my traditional sequence involve real voltage sources, batteries and internal resistance – the “real” electronics that you need to know if you want to actually build a circuit. You know, the actually interesting part.

There’s nothing interesting in looking at a circuit and calculating what current is going through an arbitrary resistor in a given circuit. It took me a while to come to this realization because I still have some brain cells clinging to the “theory first, application second” philosophy, the same brain cells I’ve been working to silence this year. These are the sorts of things I want my students to learn to do:

Build a charger for an iPod using a solar panel and some circuit components. What is involved in charging a battery in a way that the battery will actually charge up without blowing Nickel and Cadmium all over the classroom?
Create a circuit that lights up an LED with the right current so it can outlast an incandescent bulb.
Look at an AC adapter that isn’t made for a given device, and modify it so that it does work. The fact that it only costs $5 to buy a new one is irrelevant when you compare it to the feeling you get when you realize this is not hard to do. (Thanks Dad!)
Generate electricity. Figure out how hard you have to physically work to run your laptop.

This is what we did on day one:

I gave them a solar panel, some small DC motors and LEGO motors, a stripped down version of our FIRST Tech Challenge robot, some lemons, clip leads, and different kinds of wire, and said I wanted them to use these tools to generate the highest voltage they could. There was also a bag of green LEDs on the table there for them to play with. There was a flurry of activity among my five students as they remembered something vaguely from chemistry about sticking different metals into a lemon, and needing to connect one to another in a certain way. They did so and saw that there was a bit of a voltage from the lemons they had connected together, but that there wasn’t much there.

I then showed them one of the LEGO motors and had them see what happened on a connected voltmeter when the axle was rotated. They were amazed that this also generated an electrical potential. This turned immediately into a contest of rotating the motor as quickly as possible and seeing the result on the voltmeter. One grabbed an LED and hooked it up and saw that it lit up.

They then turned to the robot and its big beefy motors. They found I had a set of LED lights in my parts box and asked to use it. Positive results:

The solar panel was also a big hit as it resulted in us going outside. They were impressed with how “much” electricity was generated after seeing the voltmeter display over 15 volts – they were surprised then to see that it worked to turn on the LED display, but not any of the motors they tried.

At this point it was the end of the class block, so we put everything away and went on with our day.

Some of the reasons I finished the day with a smile:

There was never a moment when I had to tell any of the students to pay attention and get involved in the activity. The variety of objects on the table and the challenge were enough to get them playing and interacting with each other.
While I did show them how to play with one of the tools (i.e. DC motor acting as generator) , they quickly figured out how they might transfer this idea to the other items I made available.
They made bits of progress toward the understanding that voltage alone was not what made things work. This is a big one.

The next day’s class used the PHet circuit construction kit to explore these ideas further in the context of building and exploring circuits. We had some fantastic conversations about voltage of batteries, conventional vs. electron current, and eventually connected the idea of Ohm’s law (which was floating around in their heads from middle school science) to the observations they made.

I was struggling for a while about how to approach electricity because I have always followed the traditional sequence. In the end, I realized that I really didn’t want to go through electrostatics – I wasn’t excited to teach it this time around. I also realized that I didn’t need to do so, either in order to teach my students what I really wanted them to learn about electricity.

I think this approach will help them realize that electricity is not magic. They can learn to control it. I admit that doing so can be dangerous and expensive if one doesn’t know what he or she is doing. That said, a little basic knowledge goes a long way, even in today’s world of nanometer sized transistors.

Tomorrow we attempt the LED lighting assignment – feel free to share your comments or suggestions!

Results of a unit long experiment in SBG and flipping.

I’ve been a believer in the concept of standards based instruction for a while. The idea made a lot of sense when I first learned about the idea when Grant Wiggins visited my school in the Bronx a few years ago to present on Understanding by Design. Dan Meyer explored the idea quite a bit using his term of the concept checklist. Shawn Cornally talks on his blog about really pushing the idea to give students the freedom to demonstrate their learning in a way they choose, though he ultimately retains judgment power on whether they have or not. Countless others have been really generous in sharing their standards and their ideas for making standards work for their students. Take a look at my blogroll for more people to read about. For those unaware, here’s the basic idea: Look at the entire unit and identify the specific skills or you want your students to have. Plan your unit to help them develop those skills. Assess and give students feedback on those skills as often as possible until they get it. In standards based grading (SBG), reporting a grade (as most of us are required to do) as a fraction of standards completed or acquired becomes a direct reflection of how much students have learned. Compare this to the more traditional version of grading that consists of an average of various ‘snapshots’ on assignments, on which grades might be as much a reflection of effort or completion as of actual learning. If learning is to be the focus of what we do in the classroom, then SBG is a natural way of connecting that learning to the grades and feedback we give to students. My model for several years now has been, well, SBG lite. Quizzes are 15% of the total grade and test only a couple skills at a time. Students can retake quizzes as many times as they want to show that they have the skills in isolation. On tests, (60% of the total grade) students can show that they can correctly apply the set of all of their acquired skills on exercises (questions they have seen before) as well as problems (new questions that test conceptual understanding). As much as I tell students they can all have a grade of 100% for quizzes and remind those that don’t to retake, it doesn’t happen. I’ll get a retake here or there. I am still reporting quiz grades as an average of a pool of “points” though, and this might leave enough haziness in the meaning of the grade for a student to be OK with a 60%. For this unit in Geometry and Algebra 2, I have specifically made the quiz grade a set of standards to be met. The point total is roughly the same as in previous units. It is a binary system – students either have the standard (3/3) or they don’t (0/3), and they need to assess each standard at least twice to convince me they have it. I really like Blue Harvest, but my students didn’t respond so well to having twowhole websites to use to check progress. While a truly scientific study would have changed only one variable at a time, I also found that structuring the skill standards this way required me to change the way class itself was structured. This became an experiment not only in reporting grades, but in giving my students the power to work on things in their own way. This also freed me up to spend my time in class assessing, giving feedback, and assessing again. More on this ahead. The details:

Geometry

I started the unit by defining the seven skills I wanted the students to have by the end on this page. The unit was on transformational geometry, so a lot of the skills were pretty straight forward applications of different types of transformations to points, line segments, and polygons. I had digital copies of all of the materials I put together last year for this unit, so I was able to post all of that material on the wiki for students to work through on their own. I adjusted these materials as we moved through the unit and as I saw there were holes in their understanding. I was also able to make some videos using Jing and Geogebra to explain some concepts related to using vocabulary and symmetry, and these seemed to help some students that needed a bit of direct instruction in addition to what I provided to them one on one. I also tried another experiment – programming assignments related to applying transformations to various points. I said completing these assignments and chatting with me about them would qualify them for proficiency on a given standard. Assigning homework was simple: Choose a standard or two, and do some of the suggested problems related to those standards. Be prepared to show me your evidence of study when you come into class. Students that said ‘I read my notes’ or ‘I looked it over’ were heckled privately – the emphasis was on actively working to understand concepts. Some students did flail a bit with the new freedom, so I made suggestions for which standards students should spend a particular day working on, and this helped these students to focus. I threw together some concept quizzes for the standards covered by the previous classes, and students could choose to work on those question types they felt they had mastered. Some handed the quiz right back knowing they weren’t ready. I was really pleased with the level of awareness they quickly developed around what they did and didn’t understand. I quickly ran into the logistical nightmare of managing the paperwork and recording assessment results. Powerschool Blue Harvest, whatever – this was the most challenging aspect of doing things this way. I often found myself bogged down during the class period recording these things, which got in the way of spending quality face time with students around their understanding. Part of this was that I was recording progress for each standard, whether good or bad, in the comment field for each student. “Understands basic idea of translation, but is confusing the image and pre-image” is the sort of comment I started writing in the beginning. While this was nice, and I think could have led to students reading the comments and getting ideas for what they needed to work on, it was a bit redundant since I was having actual conversations with students about these facts. Here is where Blue Harvest shines – I can easily send students a quick message explaining (and showing) what they need to work on. Even more powerful would be recording the conversation when I actually talk to the student, but that would be more practical with an iPad/cell phone app to avoid lugging my computer from desk to desk. Still, I wanted the feedback to be immediate and be recorded, so I knew I had to change my approach. The compromise was to only record positive progress. If a student’s quiz showed no progress, it didn’t get a comment in Powerschool. If they showed progress, but needed to fix a small detail in their understanding, they might get a comment. If they clearly got it, they got a comment saying that they aced it. Two or more positive comments (and my independent review) led to a 3/3 for each standard. The other promise I made was that if they clearly demonstrated proficiency on the exam (which had non-standard questions and some things they needed to explain) I would give them credit for the standard. The other difficult issue was creating a bank of reassessment questions. My system of making a quiz on the spot and handing it out to individual students was too time consuming. I created an app(using my new Udacity knowledge) to try to do this, the centerpiece being a randomized set of questions that emphasized knowing how to figure out the answers rather than students potentially sharing all the answers. They quickly found all the bugs in my system, and showed that it is far from ready for being an actual useful tool for this purpose. I appreciated their humor and patience in being guinea pigs for an idea. As you might notice from the image above, there is a pretty strong relationship between the standards mastered and the exam scores. Most student exam scores were either the same or better following this system in comparison to previous exams. The most important metric is the fact that most students weren’t hurt by going to this more student-centered model. Some student took more notes while working to understand the material than they have all year. Other students spoke more to their classmates and both gave and received more help in comparison to when I was at the front of the room asking questions and doing mini-lessons. While there was a lot of staring at screens during this unit, there was also a lot of really great discussion. I would have focused conversations with every single student three to four times a class, and they were directly connected to the level of understanding they had developed. Some needed direct application questions. Others could handle deeper synthesis and ‘why is this true’ questions about more abstract concepts. It felt really great doing things this way. I have always insisted on crafting one good solid presentation to give the class – the perfect lesson – with good questions posed to the class and discussions inevitably resulting from them. I have to admit that having several smaller, unplanned, but ‘messier’ conversations to guide student learning have nurtured this group to be more independent and self driven than I expected before we started.

Algebra 2

The unit focused on the students’ first exposure to logarithmic and exponential functions. The situation in Algebra 2 was very similar to Geometry, with one key difference. The main difference of this class compared to Geometry is that almost all of the direct instruction was outsourced to video. I decided to follow the Udacity approach of several small videos (<3 min), because that meant there was opportunity (and the expectation) that only two minutes would go by before students would be expected to do something. I like this much better because it fit my own preferences in learning material with the Udacity courses. I had 2 minutes to watch a video about hash functions in Python while brushing my teeth – my students should have that ability too. I wasn’t going for the traditional flipped class model here. My motivation was less about requiring students to watch videos for homework, and more about students choosing how they wanted to go through the material. Some students wanted me to do a standard lesson, so I did a quick demonstration of problems for these students. Others were perfectly content (and successful) watching the video in class and then working on problems. Some really great consequences of doing things this way:

Students who said they watched all my videos and ‘got it’ after three, two minute videos, had plenty of time in the period to prove it to me. Usually they didn’t.. This led to some great conversations about active learning. Can you predict the next step in the video when you try solving the problem on your own? What? You didn’t try solving it on your own? <SMIRK> The other nice thing about this is that it’s a reinvestment of two minutes suggesting that they try again with the video, rather than a ten or fifteen minute lesson from Khan Academy.
I’ve never heard such spirited conversation between students about logarithms before. The process of learning each skill became a social event – they each watched the video together, rewound or paused as needed, and then got into arguments while trying to solve similar problems from the day’s handout. Often this would get in the way during teacher-centered lessons, and might be classified incorrectly as ‘disruption’ rather than the productive refining and conveyance of ideas that should be expected as part of real learning.
Having clear standards for what the students needed to be able to do, and making clear what tools were available to help them learn those specific standards, led to a flurry of students demanding to show me that they were proficient. That was pretty cool, and is what I was trying to do with my quiz system for years, but failed because there was just too much in the way.
Class time became split between working on the day’s standards, and then stopping at an arbitrary time to then look at other cool math concepts. We played around with some Python simulations in the beginning of the unit, looked at exponential models, and had other time to just play with some cool problems and ideas so that the students might someday see that thinking mathematically is not just followinga list of procedures, it’s a way of seeing the world.

I initially did things this way because a student needed to go back to the US to take care of visa issues, and I wanted to make sure the student didn’t fall behind. I also hate saying ‘work on these sections of the textbook’ because textbooks are heavy, and usually blow it pretty big. I’m pretty glad I took this opportunity to give it a try. I haven’t finished grading their unit exams (mostly because they took it today) but I will update with how they do if it is surprising.

Warning: some philosophizing ahead. Don’t say I didn’t warn you. I like experimenting with the way my classroom is structured. I especially like the standards based philosophy because it is the closest I’ve been able to get to recreating my Montessori classroom growing up in a more traditional school. I was given guidelines for what I was supposed to learn, plenty of materials to use, and a supportive guide on the side to help me when I got stuck. I have seen a lot of this process happening with my own students – getting stuck on concepts, and then getting unstuck through conversation with classmates and with me. The best part for me has been seeing my students realize that they can do this on their own, that they don’t always need me to tell them exactly what to do at all times. If they don’t understand an idea, they are learning where to look, and it’s not always at me. I get to push them to be better at what they already know how to do rather than being the source of what they know. It’s the state I’ve been striving to reach as a teacher all along, and though I am not there yet, I am closer than I’ve ever been before. It’s a cliche in the teaching world that a teacher has done his or her job when the students don’t need you to help them learn anymore. This is a start, but it also is a closed-minded view of teaching as mere conveyance of knowledge. I am still just teaching students to learn different procedures and concepts. The next step is to not only show students they can learn mathematical concepts, but that they can also make the big picture connections and observe patterns for themselves. I think both sides are important. If students see my classroom as a lab in which to explore and learn interesting ideas, and my presence and experience as a guide to the tools they need to explore those ideas, then my classroom is working as designed. The first step for me was believing the students ultimately ~~want~~need to know how to learn on their own. Getting frustrated that students won’t answer a question posed to the entire class, but then will gladly help each other and have genuine conversations when that question comes naturally from the material. All the content I teach is out there on the internet, ready to be found/read/watched as needed. There’s a lot of stuff out there, but students need to learn how to make sense of what they find. This comes from being forced to confront the messiness head on, to admit that there is a non-linear path to knowledge and understanding. School teaches students that there is a prescribed order to this content, and that learning needs to happen within its walls to be ‘qualified’ learning. The social aspect of learning is the truly unique part of the structure of school as it currently exists. It is the part that we need to really work to maintain as content becomes digital and schools get more wired and connected. We need to give students a chance to learn things on their own in an environment where they feel safe to iterate until they understand. That requires us as teachers to try new things and experiment. It won’t go well the first time. I’ve admitted this to my students repeatedly throughout the past weeks of trying these things with my classes, and they (being teenagers) are generous with honest criticism about whether something is working or not. They get why I made these changes. By showing that iteration, reflection, and hard work are part of our own process of being successful, they just might believe us when we tell them it should be part of theirs.

What my mom taught me about patience.

Looking back over the students I’ve taught over the past nine years, I can say that I’ve worked with some phenomenal youngsters. Many of the proudest moments have been those that have required a great deal of patience in moving them forward and helping them develop. There are many times when I’ve felt I owe it to the world to be patient because, well, I know others were patient with me. When a toddler sits behind me and plays the ‘kick-the-seat’ game on a flight, I just sit and take it. I played that game. Actually, I did worse – I perfected an imitation of the call-button ping so that flight attendants would hear the sound, and then look around frantically for the light indicating which row needed attention. I would giggle hysterically; my mom (I assume) hid her face and shook her head.

ejmd — Me, Josie, and my parents in a Shanghai garden, during my parents’ visit to China last fall.

My mom’s patience has always been boundless. When I would make messes in the kitchen with my experiments, she would kindly ask that I clean up after myself. In the many cases that I didn’t, she would remind me, often while I stirred my chocolate milk, loudly. Then I would slurp it, spoon by spoon, each successive clink of the spoon on the glass louder until she would snap, screaming my name sharply to tell me to just drink it. One more clink, then compliance.

I wasn’t the only one that pushed the limits of her sanity. As the middle child of three brothers, we were the worst/best when we worked toward the common goal of mayhem in her midst. Shopping trips at the grocery store were opportunities to get extra things into the cart. In spite of her vigilance, we often succeeded in getting giant rubberband balls, quart containers of honey, and boxes of sugar cereals she subsequently kept from us.

In spite of all of the ways we tested her, she still went out of her way to give us the enriching experiences that shaped who my brothers and I have become. She signed me up for magic lessons at the library. She not only tolerated my interests in collecting insects and animals and getting unbelievably muddy during the process, but scrounged up things like mason jars and film canisters and all the books, field trips, and camps she could find to learn to do these things well. She has always kept me honest. She would look up the facts I claimed were true to see if I was full of it, as I had repeatedly proven I could be. She was the one that broke the news to me that the reason my hamster couldn’t walk that morning because it had a tumor. After tolerating my tears and anger in the midst of the devastating tragedy this was for me at the time, she followed with a completely straight-faced phone conversation with a veterinarian about how one might go about putting down a hamster.

One of the reasons I can maintain a positive outlook on things is that I know that good people are looking out for me. I do my best when people demand the best I have to offer, but understand that there will always be setbacks and failures along the way. My mom was doing this long before I ever realized or appreciated it. Striking the balance between being strict and direct with rules and directions and granting the freedom to try and explore and learn from one’s mistakes is the hardest part of being a teacher. But I get to go home and try again the next day with my students. She put up with my stomping around and singing for no pay in the same house, and had only a crossword puzzle to hide behind.

She managed this balance like a pro, despite the working conditions. I still push her buttons and put my smelly feet on the kitchen table. She shoots the same look she gave me when I was nine. This sort of consistency is rare. It is also what makes me smile knowingly when my students start playing the button-pushing game with me. I just smile and nod to defuse the situation, and that works well enough for me.

The thing I can never get right in the moment, however, the secret that I think my mom had figured out from the beginning is this: she always let me think I had won. I could go on to torture one of my brothers; she could get back to taking care of the important stuff, and being entertained by seeing us battling with each other. I can’t say for sure that this was her tactic. She knew a lot more than she let on when I was younger, but has always been modest enough to just say that I knew how to drive her crazy. I think that is true. I have this sneaking suspicion though that she has always had the upper hand.

I wish her a wonderful Mother’s day. I am committed to trying to be as patient with my students as she was with me, as well as to leaving my dirty socks on her computer in the near future. For the record though: I maintain that Ben was involved in the sandwich incident that resulted in my head getting cracked open.

Planning for instruction: Not just for humans!

My wife and I welcomed a new member to our family a couple months ago. Meet Mileaux:

His name is a play on the more standard Milo, with the end spelled in the Cajun way as a tribute to Josie (my wife’s) roots. He’s now around six months old. We’re not exactly sure what he is – the current theory is a mix of a Pekinese and a Pomeranian, but there are hints of a whole bunch of other dogs in his behavior. His hobbies include chewing on towels and begging on command with his paws clenched together like an Italian soccer player trying to get out of a yellow card call. You have to see it to understand how spot on this description is.

Training him has been really interesting. As with every other part of my life since I started teaching, it serves as yet one more source of data on how learning occurs naturally. A disclaimer:

Yes, I know that my students are not dogs. I am saying, for the purposes of understanding the learning process, that outside of the supremely unnatural structure currently called ‘school’, that some aspects of learning are universal. As another comparison with my students, I can say for sure that Mileaux doesn’t like when I lecture him either.

Mileaux shows a lot of behavior that makes sense when thinking about how learning really should happen. He responds more strongly to positive reinforcement than negative, and the negative (when we do resort to it) has the consequence of sometimes leaving him confused rather than corrected. He sometimes gets tired of learning when he’s had enough. Sometimes he just needs to take a break in order to get it the next time.

One command we hadn’t tried until today was to lay down. We hadn’t really figured out the best way to do it. Yes, there are videos with suggestions on how to do it, but it’s fun to try to figure out how to communicate what we want him to do. I went for a quick 20-minute run to think of how I wanted to approach it. Here was my process:

I knew what he already knew how to do – specifically to sit. That seemed like a good entry point into getting him to lay down.
He just had his Lepto shot yesterday and was consequently a bit stiff and sore today. I didn’t want to use a leash or pressure to urge him into the down position. I wanted him to be able to figure out what we wanted him to do, and do it on his own.
There would, of course, be treats involved in the process when he did exactly what I wanted him to do.

Since he knew how to sit, I could put a treat within his reach laying down on the floor in my fingers. Any time he got up to move toward the treat, I would again give the sitting command. After around five minutes of doing this, he figured out that he needed to stay seated, and chose to stretch out into an awkward leaning position with his head arched down toward the ground. Then came strained reaching and pawing toward the treat on the floor. Soon after, he realized that laying down was a much more comfortable option for getting the treat, and started doing that every time. Copious petting, treats, and praise followed.

The connections to teaching content?

There is no paragraph in the textbook introducing the concept of laying down. Mileaux and I didn’t read it together and then do a share-out. I just needed to clearly define what I wanted him to learn, and this didn’t involve words.
While it is true that the skill of ‘sitting’ is one that he needed to have beforehand for my method to work, if he didn’t, I would have chosen another entry point to the activity. He lays down every day. He knows what it is. My goal for him was to make the connection between this skill of laying down with the verbal command. The knowledge he already had was really useful in helping him understand what he needed to do, but the background knowledge was not necessarily a prerequisite for the task we were doing.
I posed the problem in a way that had constraints that he figured out on his own. I couldn’t tell him not to move his hind legs. That limitation needed to be obvious to him as part of the activity. Managing this limitation as part of getting the delicious snack was what led him to learn the command as quickly as he did.
I had him go through this activity from a number of different starting points – standing up in the kitchen, sitting next to the couch, begging in the doorway – because I needed him to see that in these different contexts, the one skill I wanted him to learn was to lay down on command. He figured out that it was the common thread, and not any of the other simpler cues or tricks he could have used as a crutch or shortcut.
He didn’t do exactly what I wanted him to do, and felt alright about that. He knew it was just fine to get things wrong. The key to his getting it right in the end was clearly communicating when he did what he was supposed to do.

Granted, this may be strained. I accept that this may not be immediately be applicable to everyone’s classrooms. I do think it’s important to think about what we are asking our students to do, how we are communicating those objectives, and how we are helping them develop a healthy mindset toward learning along the way. We need to be thinking about knowledge in the context of figuring out problems. Solving them is an innate part of living in the world, whether as a snail, a dog, or as a human. The more we can create learning experiences that connect to this need to challenge and interact with our world, the more effective these experiences can be for our students.

Topic for #mathchat: Do we need students to reach automaticity?

I was honored when asked recently to offer a topic for discussion on #mathchat.

My suggested topic:

Is it necessary for students to develop automaticity in their pencil and paper mathematics skills? Why or why not?

First some definitions and examples to clarify the intent of the question.

By automaticity, I also mean procedural fluency. A student that has developed automaticity is familiar enough with the mechanics of a particular task to not have to devote substantial thought to how to do it. It also is connected to retention over time – how well do the details stick with a student as more information is learned over time?

In an Algebra class, for example, do the details of arithmetic need to be automatic so that the student can focus on applying algebra knowledge to solving an equation? In Calculus, should students be able to apply the product and quotient rules efficiently when working on optimization or related rates? Or is it reasonable for them to figure out the derivative using basic principles or use a computer algebra system to take care of this step when it comes up?

I also refer specifically to pencil and paper skills because, for what I would guess is a majority of us that teach math, we tend to assess students by pencil and paper at the end of the day. A student can use a graphing calculator, Geogebra, or other piece of technology to explore a concept and check her/his work. The thing I often wonder about is how the use of activities and technologies help students perform mathematical tasks when these technologies are not available.

Is it necessary to do these tasks when these tools are not available? I don’t know. I think that’s open to interpretation and individual opinion. There are some cases, however, when that choice is not up to us. Standardized tests are one example. Given that they do exist (and independent of whether or not we agree with their content/quality/use), standardized tests are not typically electronic and are timed. These are often posed as opportunities for students to choose an appropriate method of finding answers to questions and then find those answers with a limited set of resources available.

Let me be clear – I am wildly inconsistent on this, because I don’t have a good answer to the question. I emphasize understanding through the activities I do in my classes – very rarely will I directly tell students how to solve a problem, have them practice the skills with me, and then send them home to practice those skills in isolation from others. I really appreciate Conrad Wolfram’s point about using computers to handle the calculating, and leave the thinking to us and our students. I have decided on occasion not to assign #1-30 for students to practice differentiation because my feeling at that time is that if they can apply it correctly several times, they get the point, and are ready to apply that knowledge to more interesting contexts.

But when these same students that complete the short assignment, later struggle in finding anti-derivatives, I wonder if I should have drilled them more. My decision not to burden them with repetitive exercises because they are repetitive often has implications for the future of the students in class. Do I need to drill this to automaticity so that next year’s teacher doesn’t come complaining to me about how “your old students can’t XXXXXXXXXX” where XXXXXXXXXX = [arbitrary math skill that either (a) will mean the difference between getting into a top choice school during Senior year or (b)won’t matter at all ten years after leaving the classroom]?

So I call upon the collective brilliance of the #mathchat community to help find an answer.

For those unaware, #mathchat is a Twitter based chat held every Thursday night at 8PM in which all respondents use the hashtag #mathchat in their post so that everyone else following that hashtag is updated with the latest responses. If you aren’t up on using Twitter for professional development, you need to be. It completely changed my perception of how Twitter is useful and has put me in contact with some pretty amazing folks from around the world.

Reflections on EARCOS Teachers Conference 2012 – Friday

I decided to use a few digital tools to record my thoughts at the EARCOS conference. At other workshops, I tend to take notes on paper, leave them in a folder, and possibly go back to them when inspiration hits, if I remember I have them. Since I am on my computer so much of the time (and NOT digging around in a filing cabinet to see what is in there) I think this will keep the ideas from this conference fresh and nearby.

I attended a few fantastic workshops Friday and tweeted extensively about each one as important ideas came up. The #earcos12 archive and search function will be really useful for going back and reminding myself of the ideas that came to mind during those workshops.

Workshop 1 – The Geometer’s Sketchpad Workshop: Beyond Geometry with Nicholas Jackiw

It was really a treat hearing the person that defined dynamic geometry talk about the philosophy of his software that implements the model. Having learned mathematics using GSP back in 9th grade, I’ve always seen the dynamic geometry as a natural lens through which geometric concepts can be viewed. Nick mentioned that mathematicians initially had a problem with the concept because two triangles with vertices A,B, and C that aren’t congruent are not the same. Since dynamic geometry defines triangles in terms of the relationships of vertices, two triangles with the same vertices connected in the same way represent the same geometric object. This means that any triangle ABC can be turned into any other triangle ABC just by dragging vertices around the screen.

We went through the basics of plotting points, lines, and measuring slope using the tools of Geometer’s Sketchpad. I hadn’t used it for a while, but it still remains a great program. Nick is a genuine guy with a love for mathematics and what his software can do for students learning concepts. He has a solid grasp and had some great activities that could be used for students to actively learn concepts through exploration rather than listening to a teacher go through a list of boring definitions.

I had the pleasure of sharing with Nick that I used Geometer’s Sketchpad to use geometry in ninth grade and that I still had print outs of the assignments I did using the software. Back then we printed out computer assignments and turned them in, much different from today when turning things in electronically is quite easy. I was a little star-struck talking to him, but as with most good teachers I meet, he was really friendly and appreciative of my comments.

Workshop 2 – The Harkness Method: The Best Class You Never Taught – Alexis Wiggins

One of the things I want help doing is improving the quality of classroom discussions. The shelf life of the discussions we have isn’t much longer than the class period itself. I have been able to extend that a bit having students create wiki pages, interact onor create videos describing their understanding of problems.

I think this workshop provided a real possibility for restructuring my class to do this far more effectively.

Alexis shared how the Harkness method (originated at Exeter Academy) has transformed her classroom and itneraction with students. Students spend class time discussing, arguing, and critiquing arguments. In the process, they learn extensively how to be good community members, be constructive in their criticism, and communicate their ideas. She shrewdly hooked us math/science teachers at the beginning (why are we always the cynics?) by sharing that Exeter does this in their math department. Alexis also shared that she does need to do direct instruction once in a while – her ratio is around 60% discussion, 40% other methods. She also does not do this for the entire class period, particularly for the younger (9th grade) students. Modeling the process and explicitly teaching students skills that make this successful in her room is a key part of her process. She made clear that it takes time to get them to be good at it.

Alexis posted her materials at https://alexiswigginsharknessmethod.pbworks.com.

Workshop 3 – Rules of Engagement – Using Technologies to Motivate Rather than Distract – Doug Johnson

We are constantly having discussions at our school (which is 1:1 Macbooks) about how to maximize student time on task during class – I think this is something almost everyone in schools is currently battling. The presence of technology has so many potential positive applications for learning. It is easy, however, to fixate on the negative aspects almost entirely and stall the process of making these potential benefits available to students in the classroom.

Along with having one of the most useful handouts I’ve ever received at a workshop, Doug Johnson made a number of fantastically relevant points about how school communities can think about the issue. The question he posed at the beginning was “How do teachers compete w/ tablets, smart phones, netbooks, mp3 players, portable games, etc?” What I found most interesting throughout was that he showed how it didn’t need to be a competition. Instead teachers can capitalize on the opportunity

His emphasis on the distinction between entertainment and engagement really resonated with me, as I always wonder if the activities I do with my students are actually helping them learn or not. We then worked together to identify ways to make technology an active part of classroom activities, including a lot of modeling using gosoapbox.com and references to other similar sites such as socrative.com.

Doug’s presentations can all be found at https://dougjohnson.wikispaces.com/engage

Workshop 4 – Digital Citizenship: The Forgotten Fundamental Kim Cofino

This workshop from the excellent Kim Cofino was a perfect pairing with Doug’s workshop and a good ending point for the day. She clearly described her process at the Yokohama International School of rolling out (all at once, which she said was the best idea ever) her 1:1 laptop program with students.

The most important takeaway was how much deliberate planning and community collaboration went into not only creating the acceptable use policy but actively sharing that philosophy with the students, teachers, and parents. The school year started with two days of 1:1 boot camp activities – students discussing and debating different aspects of the policy. She also mentioned that the students will soon repeat some elements of this training and discussion now that the community has been through several months of living out the policy.

An important element of this is that students are explicitly taught and engaged in activities that teach them digital citizenship. She made clear that this does not happen by accident, or by hoping that students will know how to act when they are suddenly given the power afforded them by technology. This is one of the key things I will be taking back with me to Hangzhou.

Her presentation and resources can be found at http://dctff.wikispaces.com/overview

Comments:

This has been a really fantastic experience being at the conference this year – I am learning so much at the workshops and through meeting the incredible collection of teachers here. I appreciate that everyone has been so positive and open in sharing their work and ideas with me. I admit it – I’m addicted to this conference atmosphere. Thankfully, I’ll be able to keep in touch with the people I have met here, and continue learning from them well after I have left Bangkok.

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