"Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common." - Albert Einstein

Friday, November 30, 2012

"The Geometry of a Chocolate"

The following is a talk from TEDx. It is re-posted here to provide a refreshing vision of teaching math in primary and secondary schools:

From Bring technology and chocolate into the classroom: Nigel Nisbet at TEDxOrangeCoast
Despite the technological growth of the past century, test scores have barely risen. Nigel Nisbet believes that technology in the classroom today isn't being used to its full potential and demonstrates techniques to promote active learning through virtual lessons. 
"Math is the new literacy for the 21st Century", says Nigel Nisbet. Armed with a degree in mathematics, and early success as a rock musician, Nigel began his education career teaching at an idyllic private all-girls school in rural England. After moving to theU.S., he taught Mathematics, Physics, and Computer Science at Van Nuys Senior High, pioneering the use of technology in the classroom, and project-based learning. Leaving the classroom in 2006, he became a Mathematics Specialist for the Los Angeles Unified School District, the second largest school district in the United States. A passionate believer in the power of all students to learn mathematics conceptually, Nigel joined the nonprofit MIND Research Institute team as Senior Mathematics Specialist in the spring of 2010, becoming the Director of Content Creation in early 2011. Here, Nigel devotes his time to reaching into the structure and beauty of mathematics, finding ways to build engaging, interactive visual games that teach all students how math really works. AboutTEDx. TEDx was created in the spirit of TED's mission, "ideas worth spreading." The program is designed to give communities, organizations and individuals the opportunity to stimulate dialogue through TED-like experiences at the local level. At TEDx events, a screening of TEDTalks videos -- or a combination of live presenters and TEDTalks videos -- sparks deep conversation and connections. TEDx events are fully planned and coordinated independently ...

Thursday, November 29, 2012

Finding Space and Time to Learn at Home

Providing a child both space and time to read and learn is one of the suggestions made by Harris Cooper, a professor of psychology at Duke University and a leading researcher on homework. It is widely accepted that factors outside school can affect learning and at times, these external factors may have a heavier influence than teachers do. Growing up, I did not have a room of my own, but my parents made sure that I had enough space and opportunity to go over my studies. In fact, my mother sometimes would wake me up as early as four in the morning to study and review. I got also excused from household chores like washing dishes or cleaning the floors if I had an assignment to finish.  School supplies were limited but I managed by not wasting. Books were limited and of course, there was no internet then, but I managed by copying what I read from books that I could find in libraries or in my friend's homes. I used to envy those homes that had an encyclopedia. Without copiers and permission to take out books on loan, I had to copy manually the text that I saw in those books and even tried to draw some of the figures I thought were important. In spite of not having all the resources, it was made clear to me by my parents that studying was a priority. I felt not just encouraged but actually obliged to study.

Studying at home, whether it is doing a homework, reviewing for an exam, or simply reading or exploring, can be a major part of learning. The question is how much should parents be involved. My parents did not take advanced science courses so when I was taking calculus, I was already very satisfied that they at least gave me the space and time to do my calculus homework assignments. I was involved in a school project in high school where we were trying to extract methane from the algae spirogyra and my parents simply watched what I was doing while I tried to dry the algae on the rooftop. My parents were equally curious when I was trying to use various tropical fruit rinds to repel mosquitoes. There was no question that I had their support eventhough they could not really do my homework.

My son in the above video is just reading  "The Cat in the Hat", so I could certainly read the entire book for him. I certainly do not know what would interest my son later on, but I am hopeful that it would be more advanced than simply reciting a first grade book. How much a parent should do is really an important question. A recent article in the Wall Street Journal tries to address this question:
"Homework can be as monumental a task for parents as it is for children. So what's the best strategy to get a kid to finish it all? Where's the line between helping with an assignment and doing the assignment? And should a parent nag a procrastinating preteen to focus—or let the child fall behind and learn a hard lesson?"
The questions above are being addressed by education research, and as cited by the Wall Street Journal, work at Johns Hopkins University tries to elucidate how parents influence student learning. The following was a recent webinar held at the Center on School, Family and Community Partnerships at Johns Hopkins:

Downloaded from Joyce L. Epstein's Presentation
The first slide of the presentation, I think, summarizes the important elements for an excellent education:
Downloaded from Joyce L. Epstein's Presentation
According to Epstein, there are six ways through which parents can be involved in their children's education:

  • Parenting (Parents provide time and space for learning at home while schools assist and guide parents as well as understand the conditions at home),
  • Communicating (Schools and parents establish and maintain a way of sharing information regarding the progress or challenges both at home and in school),
  • Volunteering (Parents participate in school programs and activities),
  • Learning at Home (Includes homework and projects), 
  • Decision Making (Parents Teachers Organizations allow parents to be part of school governance, decisions and advocacy), and
  • Collaborating with the Community (Involves a larger outreach, not just parents of schoolchildren, but the entire community).

Doing homework is only one of the six. And for homework, the best a parent could do is to provide ample time and space, and instilling a positive attitude towards learning. My parents did exactly just that.

The Center for Disease Control (CDC) and Prevention of the United States also highlights the importance of health to the success of education. In this area, the role of parents is also important. The following links to a brief presentaion from the CDC.

Click Parental Engagement Slides to view the presentation
Bringing quality to Philippine basic education requires so much more than just a new curriculum. A new curriculum by itself simply cannot promise quality education without addressing these external factors.

Wednesday, November 28, 2012

Which Scientific Findings are Applicable to Basic Education?

I recently read a commentary by Dr. Leonardo L. Leonidas, "Jump-starting our kids' math ability" on the Philippine Daily Inquirer. The commentary made the following claim:
Chinese children in grade school and high school are more advanced in counting and in math. There are many reasons for this fact, and one big advantage of Chinese children is their language. 
By far, their language depicting numbers is simpler. The Chinese have only 10 one-syllable words that can be used in combination to form higher numbers. From one to 10, the words are: yi (one), er, san, si, liu, wu, qi, ba, jiu, and shi (10). 
In English, there are 29 words needed to express numbers. Many of the English word numbers are even of two syllables, such as seven, fourteen, sixteen, etc....
Well, here is my reaction.

"McKayla Maroney: "Did I just do the 'Not impressed' face with the President...?" Yes."
Downloaded from http://www.facebook.com/barackobama?fref=ts
My son is currently in first grade and some of the activity worksheets we use to teach him addition and subtraction look like the one below:
Sample worksheet downloaded from http://www.math-aids.com/Mixed_Problems/

Except for the header of the above activity sheet, there are really no English words. Arithmetic is really taught using Arabic numerals. In this particular sheet, red and blue dots are shown to aid in counting which helps children add and subtract numbers. Of course, if the activity sheet is read aloud, then English words (or words from the medium of instruction) will enter the scene. Doing the activity in silence clearly places a minor or even a non-existing role for language. Associating each Arabic numeral to its corresponding English word seems easy enough for children to grasp. Children in the kindergarten class where my son attended this past school year do not seem to have any problem counting up to twenty, for example. On the other hand, addition and subtraction seem to feel much more challenging at the moment.

We do find articles in mainstream media that highlight scientific findings. Most are in health since that subject seems to be a topic of great importance or interest to a wide audience. Once in a while, we stumble upon items that relate to education. The presentations in these popular articles differ greatly from how the scientific finding has been presented in a peer-reviewed journal. Oftentimes, the language used is more liberal and popular, in other words, less accurate and precise. Thus, to get the most out of reading these articles, a critical mind and experience in science are both required.

There are resources on the internet that can help us navigate through the vast array of scientific claims on how to improve education. This blog, for example, has found an excellent source that does exactly what is needed to sift through these claims and findings: It is another blog, the blog of Virginia psychology professor Daniel Willingham: "The Science and Education Blog". This is not the first time his ideas are being cited in this blog. The following are past posts that have mentioned or highlighted Willingham's works:

Oct 20, 2012
What Does Science Tell Us About Teaching Kids to Think? This is the same title of an article that came out in The Atlantic early this month. It was written by University of Virginia psychology professor Daniel Willingham.
Jul 29, 2012
Professor of Psychology Daniel Willingham at the University of Virginia arrived at an excellent analogy to describe the teaching profession. Teachers are neither scientists nor artists. Architects are a much closer comparison.
Nov 19, 2012
Daniel Willingham, a psychology professor at the University of Virginia, recently cited new research re-confirming what so many of us have known all along: Math and science teachers leave the profession at or around the ...
Professor of Psychology Daniel Willingham
Professor Daniel Willingham has written numerous articles on the magazine American Educator of the American Federation of Teachers providing timely and relevant discussions of issues affecting basic education:

How to allocate study time
Why transfer is hard
Why students remember or forget
Why students think they understand when they don't
Why practice is important
Why people love and remember stories
Why knowledge is important
How to teach critical thinking
Why reading comprehension strategies are less useful than most people think
What will improve a student's memory?
What goes into mathematical thinking?
Motivation--role of praise
Motivation--role of rewards
Has technology changed how students think?
Can teachers increase students self-control? 
Why does family wealth affect student outcomes?

There are so many more articles on his blog, and for a preview, here is Willingham's most recent article; (It shows where I got an idea on what to use to convey an "unimpressed" response)

Source: http://www.danielwillingham.com/1/post/2012/11/neuroscience-applied-to-education-mostly-unimpressive.html

Neuroscience reporting: unimpressive

An op-ed in the New York Times reported on some backlash against inaccurate reporting on neuroscience. (It included name-checks for some terrific blogs, including NeurocriticNeurobonkersNeuroskepticMind HacksDorothy Bishop's Blog). The headline ("Neuroscience: Under Attack") was inaccurate, but the issue raised is important; there is some sloppy reporting and writing on neuroscience.

How does education fare in this regard?

There is definitely a lot of neuro-garbage in the education market.

Sometimes it's the use of accurate but ultimately pointless neuro-talk that's mere window dressing for something that teachers already know (e.g., explaining the neural consequences of exercise to persuade teachers that recess is a good idea for third-graders).

Other times the neuroscience is simply inaccurate (exaggerations regarding the differences between the left and right hemispheres, for example).

You may have thought I was going to mention learning styles.

Well, learning styles is not a neuroscientific claim; it's a claim about the mind. But it's often presented as a brain claim, and that error is perhaps the most instructive. You see, people who want to talk to teachers about neuroscience will often present behavioral findings (e.g., the spacing effect)--as though they are neuroscientific findings.

What's the difference, and who cares? Why does it matter whether the science that leads to a useful classroom application is neuroscience or behavioral?

It matters because it gets to the heart of how and when neuroscience can be applied to educational practice. And when a writer doesn't seem to understand these issues, I get anxious that he or she is simply blowing smoke.

Let's start with behavior. Applying findings from the laboratory is not straightforward. Why? Consider this question. Would a terrific math tutor who has never been in a classroom before be a good teacher? Well, maybe. But we recognize that tutoring one-on-one is not the same thing as teaching a class. Kids interact, and that leads to new issues, new problems. Similarly, a great classroom teacher won't necessarily be a great principal.

This problem--that collections don't behave the same way as individuals--is pervasive.

Similarly, knowing something about a cognitive process--memory, say--is useful, but it's not guaranteed to translate "upwards" the way you expect.Just as children interact, making the classroom more than a collection of kids, so too cognitive processes interact, making a child's mind more than a collection of cognitive processes.

That's why we can't take lab findings and pop them right into the classroom. To use my favorite painfully obvious example, lab findings consistently show that repetition is good for memory. But you can't mindlessly implement that in schools--"keep repeating this til you've got it, kids." Repetition is good for memory, but terrible for motivation.

I've called this the vertical problem (Willingham, 2009). You can't assume that a finding at one level will work well at another level.

When we add neuroscience, there's a second problem. It's easiest to appreciate this way. Consider that in schools, the outcomes we care about are behavioral; reading, analyzing, calculating, remembering. These are the ways we know the child is getting something from schooling. At the end of the day, we don't really care what her hippocampus is doing, so long as these behavioral landmarks are in place.

Likewise, most of the things that we can change are behavioral. We're not going to plant electrodes in the child's brain to get her to learn--we're going to change her environment and encourage certain behaviors. A notable exception is when we suspect that there is a pharmacological imbalance, and we try to use medication to restore it. But mostly, what we do is behavioral and what we hope to see is behavioral. Neuroscience is outside the loop. 
For neuroscience to be useful in the classroom we've got to translate from the behavioral side to the neural side and then back again. I've called thisthe horizontal problem (Willingham, 2009)

The translation to use neuroscience in education can be done--it has been done--but it isn't easy. (I wrote about four techniques for doing it here, Willingham & Lloyd, 2007).

Now, let's return to the question we started with: does it matter if claims about laboratory findings about behavior are presented as brain claims?

I'm arguing it matters because it shows a misunderstanding of the relationship of mind, brain, and educational applications.

As we've seen, behavioral sciences and neuroscience face different problems in application. Both face the vertical problem. The horizontal problem is particular to neuroscience.

When people don't seem to appreciate the difference, that indicates sloppy thinking. Sloppy thinking is a good indicator of bad advice to educators. Bad advice means that neurophilia will become another flash in the pan, another fad of the moment in education, and in ten year's time policymakers (and funders) will say "Oh yeah, we tried that."

Neuroscience deserves better. With patience, it can add to our collective wisdom on education. At the moment, however, neuro-garbage is ascendant in education.

Willingham, D. T. (2009). Three problems in the marriage of neuroscience and education. Cortex, 45, 54-545.
Wilingham, D. T. & Lloyd, J. W. (2007). How educational theories can use neuroscientific data. Mind, Brain, & Education, 1, 140-149. 

Tuesday, November 27, 2012

Digital Divide: Poor and Rich Children

How technology can enhance learning is quite a large area to study. One part involves classroom media and various technological applications to improve presentations and lectures. Other efforts center on developing learning materials that can be delivered to students via the internet. Technology can be used likewise to extend the reach of excellent teachers by broadcasting their lectures and creating virtual conferences that will allow for live interaction between a teacher and a remote classroom.

On top of all of these, the technology we now have also provides an entirely new social medium in which relationships can be established. The internet enables us to network with each other with so much ease. We are able to share information, moments and photographs instantly. Facebook, as an example, has indeed become a gigantic meeting place where one can share what one has just read, what one has just seen, what one has just heard. Electronic mails as well as messages or posts no longer require postage stamps and long waits. And if by chance, the two parties that are communicating are both online, the response could almost be instantaneous.

Social media truly add a different dimension to technology. These tools can certainly influence schools and learning in the same way other social interactions do. The classroom can extend much farther both beyond its walls as well as scheduled hours. The internet can indeed be a virtual learning experience. The internet allows people of different backgrounds, social status, and educational attainment to be connected. Sadly, in this new medium, the digital divide takes life beyond mere access to technology.

It is true that in a developing country, access to the internet is still a major impedance to utilizing technology for learning. However, access has been improving dramatically all over the world. The widespread activity and large presence of Filipinos on Facebook clearly demonstrate that the problem of access has been somewhat alleviated. Having access, however, is not enough to destroy the digital divide between poor and rich children.

A new digital divide can arise not from a lack of access to technology, but from a lack of access to the right people, helpful connection, and correct information. The new digital divide comes not from a lack of technology, but from not knowing how to use the social networks for the benefit of learning. Recently, I was delighted to receive an email from the Mai Uichanco, currently the national secretary general of the League of Filipino Students. The email speaks of a student leader, who is actively engaged in discussions concerning Philippine basic education. We do find support and new relationships on the internet. Such an introduction would not have been possible if Mai and I did not meet on the internet.

Being a social medium, the internet can serve as a source of support. Students can build and maintain friendships. These connections are very important for adolescents. The internet can easily become a place where students are able to share frustrations on a difficult homework or project. I recently posted a quotation from Einstein:
""Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common."
And in addition to the "likes" I got from friends on Facebook, I got the following response:
Angel,not only in school but also in the house and with some friends and relatives as what I've learned from you during the days we spent in your house at Instruccion,the names of all the horses you bet in DIVIDENDAZO,seems inherited and received.......
Oops, I was just reminded of the times I used to spend on San Lazaro and Santa Ana (These, by the way, are not religious places, but horse racing clubs). Thus, by being with each other, even in a virtual sense, we are able to share ideas, experiences, and yes, even grief. These are all helpful connections.

The last one, getting the correct information, hinges in fact on the first two, the right people and helpful connections. It also depends on an ability to think critically, which is a must to filter irrelevant and incorrect information. Sadly, the internet is also full of hoaxes, misconceptions and in simple terms, garbage. Students have the responsibility to develop critical thinking, but as adults, it is our responsibility to provide the support they need on the internet.

Christine Greenhow, Assistant Professor in the College of Education at Michigan State University, works currently on how social networks can help education and civic engagement. Recently, she was a guest at the
American Public Media - American RadioWorks:

"For a long time it was assumed that a "digital divide" existed between rich kids and poor kids. But emerging research says kids from all income backgrounds are going online in large numbers - it's the way they're using the Internet that could make the difference in their success in school and life."

One of Greenhow's recent papers is the following:

Downloaded from Baywood.metapress.com

Technology indeed has a social dimension. This blog although it is maintained thousands of miles away, is visited mainly by readers from the Philippines. This blog attempts to provide perspectives and opinions as well as results from research regarding education. This blog collects views from people who are in the Philippines. I also spend time sharing links to the posts on this blog on Facebook. At the same time, I have made new connections, new acquaintances, new "friends".

Almost ten years ago, I was part of a group that helped elementary schools build a computer classroom. We were fortunate enough to have a supporting local government and throughout the years, people in this small town of Paete, Laguna have established a presence, a community on the internet. Providing access, however, is only the starting point. The digital divide can persist even with access to technology if such access is not used wisely and efficiently.


Recently, Congressman Palatino, the youth representative in the House, raised the importance of social media:

Youth solon urges DepEd to include social media topics in basic ed curriculum

21 NOVEMBER 2012
Following the growing number of “cyberbullying” incidents in the past weeks, Kabataan Partylist Rep. Raymond Palatino has called on the Department of Education (DepEd) to consider including social media topics in the basic education curriculum.
On November 20, Palatino filed House Resolution No. 2901, which urges DepEd to include topics on the use of social media in subjects taught in elementary and high school.
“More and more cyberbullying incidents are being reported in recent days. There are those who believe that Congress should be legislating laws to penalize such acts. However, we believe that teaching social media topics during the formative years of students could be a far better solution,” Palatino said.
“Many of us will remember that in our earliest years in school, we are taught good moral and right conduct. In the age of Facebook and Twitter, it is but apt to include topics on responsible use of social media in the basic ed curriculum,” Palatino continued.
According to a study done by Yahoo-Nielsen, around 50 percent of the youth between the ages 10 to 19 access the Internet and use social networking sites on a frequent basis. Various estimates, meanwhile, put the number of Internet users in the country to as many as 30 million.
“The use of social networking sites is speedily becoming the norm. Thus, it is important that we teach out youngsters how to use this communication platform responsibly so as to avoid cyberbullying incidents and other nefarious acts committed online,” Palatino said.
“Teaching computer literacy should be beyond imparting knowledge on the hardware and the input of data. It must also include the teaching of good online practices including responsible use of social media and proper conduct online,” Palatino explained.
“Instead of criminalizing cyberbullying, we should move towards teaching responsible use. In this light, we urge DepEd to include social media topics in our country’s basic education curriculum,” the youth solon added

Monday, November 26, 2012

Teaching Math and Science = Teaching Patient Problem Solving

We currently live in a world of "soundbites". Our span of attention continues to shrink as we watch shows on LED screens. With problems, we always look for quick solutions. Buying furniture from IKEA can be quite challenging. Finding the right pieces and assembling them in the correct order can sometimes take hours. But when we finally assemble that cabinet or entertainment center, we feel proud of our accomplishment. There are indeed problems worth solving. These are the ones that make us feel that we have made something.

Dan Meyer, a math teacher, points out that current ways of teaching math and science have lost the element of a challenge and therefore deprived students of a sense of accomplishment. He cites five symptoms of poor math instruction in classrooms:
  • lack of initiative
  • lack of perseverance
  • lack of retention
  • aversion to word problems
  • eagerness for formula
All of these symptoms reveal a lack of patience. Unfortunately, to address these problems, we apply quick solutions. Meyer proposes to do the following instead:
  • Use multimedia
  • Encourage student intuition
  • Ask the shortest question you can
  • Let students build the problem
  • Be less helpful
The above are presented elegantly in this TED video:

Transcript (http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html):

Can I ask you to please recall a time when you really loved something -- a movie, an album, a song or a book -- and you recommended it wholeheartedly to someone you also really liked, and you anticipated that reaction, you waited for it, and it came back, and the person hated it? So, by way of introduction, that is the exact same state in which I spent every working day of the last six years. (Laughter) I teach high school math. I sell a product to a market that doesn't want it, but is forced by law to buy it. I mean, it's just a losing proposition.So there's a useful stereotype about students that I see, a useful stereotype about you all. I could give you guys an algebra-two final exam, and I would expect no higher than a 25 percent pass rate. And both of these facts say less about you or my students than they do about what we call math education in the U.S. today. 
To start with, I'd like to break math down into two categories. One is computation; this is the stuff you've forgotten. For example, factoring quadratics with leading coefficients greater than one. This stuff is also really easy to relearn, provided you have a really strong grounding in reasoning. Math reasoning -- we'll call it the application of math processes to the world around us -- this is hard to teach. This is what we would love students to retain,even if they don't go into mathematical fields. This is also something that, the way we teach it in the U.S. all but ensures they won't retain it. So, I'd like to talk about why that is, why that's such a calamity for society, what we can do about it and, to close with, why this is an amazing time to be a math teacher. 
So first, five symptoms that you're doing math reasoning wrong in your classroom. One is a lack of initiative; your students don't self-start. You finish your lecture block and immediately you have five hands going up asking you to re-explain the entire thing at their desks.Students lack perseverance. They lack retention; you find yourself re-explaining concepts three months later, wholesale. There's an aversion to word problems, which describes 99 percent of my students. And then the other one percent is eagerly looking for the formula to apply in that situation. This is really destructive.David Milch, creator of "Deadwood" and other amazing TV shows, has a really good description for this. He swore off creating contemporary drama, shows set in the present day, because he saw that when people fill their mind with four hours a day of, for example, "Two and a Half Men," no disrespect, it shapes the neural pathways, he said, in such a way that they expect simple problems. He called it, "an impatience with irresolution." You're impatient with things that don't resolve quickly. You expect sitcom-sized problems that wrap up in 22 minutes, three commercial breaks and a laugh track. And I'll put it to all of you,what you already know, that no problem worth solving is that simple. I am very concerned about this because I'm going to retire in a world that my students will run. I'm doing bad things to my own future and well-being when I teach this way. I'm here to tell you that the way our textbooks -- particularly mass-adopted textbooks -- teach math reasoning and patient problem solving, it's functionally equivalent to turning on "Two and a Half Men" and calling it a day.(Laughter) 
In all seriousness. Here's an example from a physics textbook. It applies equally to math.Notice, first of all here, that you have exactly three pieces of information there, each of which will figure into a formula somewhere, eventually, which the student will then compute.I believe in real life. And ask yourself, what problem have you solved, ever, that was worth solving where you knew all of the given information in advance; where you didn't have a surplus of information and you had to filter it out, or you didn't have sufficient information and had to go find some. I'm sure we all agree that no problem worth solving is like that.  
And the textbook, I think, knows how it's hamstringing students because, watch this, this is the practice problem set. When it comes time to do the actual problem set, we have problems like this right here where we're just swapping out numbers and tweaking the context a little bit. And if the student still doesn't recognize the stamp this was molded from, it helpfully explains to you what sample problem you can return to to find the formula. You could literally, I mean this, pass this particular unit without knowing any physics, just knowing how to decode a textbook. That's a shame. 
So I can diagnose the problem a little more specifically in math. Here's a really cool problem. I like this. It's about defining steepness and slope using a ski lift. But what you have here is actually four separate layers, and I'm curious which of you can see the four separate layers and, particularly, how when they're compressed together and presented to the student all at once, how that creates this impatient problem solving. I'll define them here: You have the visual. You also have the mathematical structure, talking about grids, measurements, labels, points, axes, that sort of thing. You have substeps, which all lead to what we really want to talk about: which section is the steepest.So I hope you can see. I really hope you can see how what we're doing here is taking a compelling question, a compelling answer, but we're paving a smooth, straight path from one to the other and congratulating our students for how well they can step over the small cracks in the way. That's all we're doing here. So I want to put to you that if we can separate these in a different way and build them up with students, we can have everything we're looking for in terms of patient problem solving.So right here I start with the visual, and I immediately ask the question: Which section is the steepest? And this starts conversation because the visual is created in such a way where you can defend two answers.  
So you get people arguing against each other, friend versus friend, in pairs, journaling, whatever. And then eventually we realize it's getting annoying to talk about the skier in the lower left-hand side of the screen or the skier just above the mid line. And we realize how great would it be if we just had some A, B, C and D labels to talk about them more easily. And then as we start to define what does steepness mean, we realize it would be nice to have some measurements to really narrow it down, specifically what that means. And then and only then, we throw down that mathematical structure.  
The math serves the conversation, the conversation doesn't serve the math. And at that point, I'll put it to you that nine out of 10 classes are good to go on the whole slope, steepness thing. But if you need to, your students can then develop those substeps together.Do you guys see how this, right here, compared to that -- which one creates that patient problem solving, that math reasoning? It's been obvious in my practice, to me.  
And I'll yield the floor here for a second to Einstein, who, I believe, has paid his dues. He talked about the formulation of a problem being so incredibly important, and yet in my practice, in the U.S. here, we just give problems to students; we don't involve them in the formulation of the problem.So 90 percent of what I do with my five hours of prep time per week is to take fairly compelling elements of problems like this from my textbook and rebuild them in a way that supports math reasoning and patient problem solving. And here's how it works. I like this question. It's about a water tank. The question is: How long will it take you to fill it up? First things first, we eliminate all the substeps. Students have to develop those, they have to formulate those. And then notice that all the information written on there is stuff you'll need.None of it's a distractor, so we lose that. Students need to decide, "All right, well, does the height matter? Does the side of it matter? Does the color of the valve matter? What matters here?" Such an underrepresented question in math curriculum. So now we have a water tank. How long will it take you to fill it up? 
And that's it.And because this is the 21st century and we would love to talk about the real world on its own terms, not in terms of line art or clip art that you so often see in textbooks, we go out and we take a picture of it. So now we have the real deal. How long will it take it to fill it up?And then even better is we take a video, a video of someone filling it up. And it's filling up slowly, agonizingly slowly. It's tedious. Students are looking at their watches, rolling their eyes, and they're all wondering at some point or another, "Man, how long is it going to take to fill up?" (Laughter) That's how you know you've baited the hook, right?And that question, off this right here, is really fun for me because, like the intro, I teach kids -- because of my inexperience -- I teach the kids that are the most remedial, all right? And I've got kids who will not join a conversation about math because someone else has the formula; someone else knows how to work the formula better than me, so I won't talk about it. But here, every student is on a level playing field of intuition. Everyone's filled something up with water before, so I get kids answering the question, "How long will it take?" I've got kids who are mathematically and conversationally intimidated joining the conversation. We put names on the board, attach them to guesses, and kids have bought in here. And then we follow the process I've described.  
And the best part here, or one of the better parts is that we don't get our answer from the answer key in the back of the teacher's edition. We, instead, just watch the end of the movie. (Laughter) And that's terrifying, because the theoretical models that always work out in the answer key in the back of a teacher's edition, that's great, but it's scary to talk about sources of error when the theoretical does not match up with the practical. But those conversations have been so valuable, among the most valuable. 
So I'm here to report some really fun games with students who come pre-installed with these viruses day one of the class. These are the kids who now, one semester in, I can put something on the board, totally new, totally foreign, and they'll have a conversation about it for three or four minutes more than they would have at the start of the year, which is just so fun. We're no longer averse to word problems, because we've redefined what a word problem is. We're no longer intimidated by math, because we're slowly redefining what math is. This has been a lot of fun.I encourage math teachers I talk to to use multimedia, because it brings the real world into your classroom in high resolution and full color; to encourage student intuition for that level playing field; to ask the shortest question you possibly can and let those more specific questions come out in conversation; to let students build the problem, because Einstein said so; and to finally, in total, just be less helpful, because the textbook is helping you in all the wrong ways: It's buying you out of your obligation, for patient problem solving and math reasoning, to be less helpful. 
And why this is an amazing time to be a math teacher right now is because we have the tools to create this high-quality curriculum in our front pocket. It's ubiquitous and fairly cheap, and the tools to distribute it freely under open licenses has also never been cheaper or more ubiquitous. I put a video series on my blog not so long ago and it got 6,000 views in two weeks. I get emails still from teachers in countries I've never visited saying, "Wow, yeah. We had a good conversation about that. Oh, and by the way, here's how I made your stuff better," which, wow. I put this problem on my blog recently: In a grocery store, which line do you get into, the one that has one cart and 19 items or the line with four carts and three, five, two and one items. And the linear modeling involved in that was some good stuff for my classroom, but it eventually got me on "Good Morning America" a few weeks later,which is just bizarre, right?And from all of this, I can only conclude that people, not just students, are really hungry for this. Math makes sense of the world. Math is the vocabulary for your own intuition. So I just really encourage you, whatever your stake is in education -- whether you're a student, parent, teacher, policy maker, whatever -- insist on better math curriculum. We need more patient problem solvers. Thank you. (Applause)

How we tackle problems in Philippine basic education is also a matter of diligence, perseverance and patience. A straightforward formula is not available. The solutions are as diverse as the communities a school serves. One thing is clear, however, education reform must be grounded inside the classroom. No solution will succeed without the wholehearted participation of a teacher.