Do You Believe in Algebra?

(Cross-posted on The Huffington Post).

Let me clarify. I'm not asking do you believe in Algebra in the same sense as do you believe in the tooth fairy (full disclosure: I do not). I'll posit that Algebra exists. Rather I'm asking if you believe in Algebra as a separate course/curriculum that we should teach in high school.

After my last post, Dean Shareski wrote a thought-provoking post that asked whether it was possible to offer a customized educational experience in a standards-based system of education.

Our current system and structure fights personalized learning with nearly every new policy and protocol it can generate. The system craves standardization while we desperately need customization. These competing ideals butt heads constantly and for those teachers who do believe in personalizing learning, they live in perpetual frustration. . . In the end, without a restructuring of time and current curriculum requirements the best we can hope for is small pockets of success or the .02 percent of students whose passion happens to be trigonometry or Shakespeare.

Dean later acknowledges, however, that while he wants personalization, he also wants students exposed to a broader range of ideas:

While I'm busy advocating for changes that might support an education that fuels and fosters students' passions, I worry that we lose sight of what a liberal education is all about. They don't know what they don't know. Providing students with broad experiences that invites them to develop a variety of skills, understand and appreciate diverse perspectives and potentially uncover hidden talents and interests speaks to a fairly well accepted purpose of school. . . If we were truly starting education from scratch today, I can't imagine we'd build the same system we have. There would be lots of discussion as to what types of content all students need. Even if core content and skills could be determined, we'd never teach them all as segmented subjects taught in isolation in 45-minute increments.

And therein lies the dilemma - is it possible to provide in a systemic way a customized educational experience for all students that both allows and encourages them to pursue their passions, but also exposes them to the wide range of human endeavors that they may have little or no knowledge about and therefore wouldn't be able to even know if they were passionate about in the first place?

Which brings us back to Algebra. I teach in Colorado, which recently adopted the Common Core State Standards. In general, I believe the Common Core Math Standards (pdf) are much better than most standards that came before them. First, there are fewer of them, with 156 standards for grades 9-12. In addition, 38 of those standards are identified as "advanced" standards, which leaves us with 118 standards for all students spread out over four years of high school, or just under 30 per year. That's much, much more doable then what we had before, and I believe targets much more of what I would consider mathematics that is essential for people to know.

But it still begs the question of whether all students need these 118 standards. For example, do you believe that all students (scratch, that, all people) need to know "there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real?" (CCSS, N-CN 1). Or how about "prove the Pythagorean identity sin²(x) + cos²(x) = 1 and use it to find sin(x), cos (x), or tan(x) and the quadrant of the angle?" (CCSS, F-TF 8).

(My not-so-modest proposal is that no state legislature is allowed to require standards that they couldn't demonstrate proficiency on themselves. Since they are clearly successful adults and they are saying that these standards are necessary for all students to be successful, surely they'd be able to demonstrate proficiency by taking the same tests our students do. But I digress.)

As G.V. Ramanathan recently asked in the Washington Post:

How much math do we really need?

In an age of information abundance, when Wolfram Alpha can do pretty much all of high school math quickly and at no charge, do all students need to be able to know all 118 standards? When instructional videos (either homegrown or created by others like Khan Academy) exist that replicate many aspects of a traditional math classroom and allow students to learn the skills at a time and a place of their own choosing, what activities should be taking place in our math classrooms?


Consider these statistics:

1985: 3,800,000 Kindergarten students
1998: 2,810,000 High school graduates
1998: 1,843,000 College freshman
2002: 1,292,000 College graduates (34%)
2002: 150,000 STEM majors (3.9%)
2006: 1,200 PhD's in mathematics (0.03%)

(source: presentation by Steve Leinwand, American Institutes for Research at NCTM Regional Conference in Denver on October 7, 2010. His source U.S. Statistical Abstract)

There's lots we could talk about with those statistics, but I'm just going to focus on what percentage of our students truly need the Common Core Math Standards. I would suggest that it's most likely somewhere between the 3.9% and the 34%, which makes me wonder how "core" they really are. While I think Common Core, combined with replacing Calculus with probability and statistics as the capstone to high school mathematics for most students, would be an improvement on much of what we're currently doing, I'm still not sure whether teaching Algebra as a separate course is the best way to accomplish it - even for that small subset of our student population that is passionate about math and science.






Can we find a way to have students whose passion is math and science explore rich, meaningful mathematics that isn't divided up into courses (Algebra), semesters (first semester linear, second semester non-linear), and units (Chapter 5: Writing Linear Equations)? Can we do this in a meaningful way for all students, even those who currently don't have a passion for math and science? Can we do it in a mathematically coherent way that doesn't impact a student's ability to progress to higher-level mathematical thinking should they choose to do that? Can we do this within a system that - at its heart - is an assembly-line model designed to mass produce a fairly standard product?

I think this is essentially what Dean - and many of us - are asking ourselves. Is there a way to combine the best of both? The best of passion-based learning and a liberal arts education that exposes students to some "standard" body of knowledge that we believe all people should be exposed to. Can the current system - with all its flaws and all its successes - adapt to a personalized, on-demand, anytime, anywhere learning environment? Or do we have to start over with a system that is designed to meet the needs of the learner and one that - at its heart - is antithetical to a standards-based system?

I honestly don't know. Because while I do believe the current system is designed to meet the needs of a rather small portion of our students, I'm not sure I can clearly define what mathematics education would look like in such a new system. As I stated in a previous post, I believe we can have high standards without standardization, yet like Dean I struggle to envision exactly what that looks like in practice in any kind of systemic way.

So, do you believe in Algebra as a separate course/body of study in high school? Or, like the tooth fairy, is Algebra - and standards-based, one-size-fits-all education - something we should've outgrown by now?

A Conversation with My Students

(Cross-posted on The Huffington Post. Regular readers will recognize that this is essentially this earlier post with the intro and conclusion slightly adjusted for HuffPo, but several folks suggested it was worth re-posting.)

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I had a conversation with my Algebra class about a month ago. I realized that I hadn't done a good job of conveying my thoughts and beliefs about the class, of sharing my passion, of explaining why I setup class the way I did and what I was expecting from them -- and what I was hoping for them.

So here, more or less, is what I said. I'm sure it wasn't quite this smooth, as when I write I automatically edit and tweak, but this is pretty close (and definitely the spirit of what I hope I conveyed).

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I wanted to talk a little bit about this class and why I'm doing the things I'm doing. Mr. Krause, one of our English teachers, is doing a project right now where his students are asking people how they define success. I answered that for several groups of students, but I wanted to talk for a minute about how I'll decide if I'm successful with you guys in this class.
I won't think I'm a success if you do well and get a good grade in Algebra, although I certainly hope you do and I'm going to try really hard to help you do that. I won't think I'm a success if you score well on tests like CSAP or ACT, although I hope you do, and even though a lot of well-intentioned people think that's how I should define success. I won't even think I'm a success if you go to a good college and then get a good job, although I certainly want you to do that because I'd like to retire someday and I need you all to have good jobs to support me.

No, I'll consider myself successful if you turn out to be good, kind, caring adults. If you're a good spouse, child and parent. If you contribute to the world and to your community and help those around you. If you participate. And learn.

Here's the deal. The education that I received was a pretty good one. But it's not good enough for you guys. Not anymore. You see, in a rapidly changing, information abundant world, the people who are going to be successful -- both professionally and personally -- are the learners. And by "learners" I don't mean people who just learn what we teach you here at AHS.

Now, I want to be clear, that doesn't mean I don't think you should learn what we teach you here at AHS. I don't want you to go to your second period teacher, raise your hand, and say, "Mr. Fisch said I don't need to learn what you're teaching." Please, don't do that. That's not at all what I'm saying. Your teachers here work very hard trying to share important, meaningful and relevant knowledge and skills. And that's important, but it's not enough. Because to be successful you're going to have to be a learner, you're going to have to learn how to learn, and go after things on your own. You're going to have to be independent, curious, passionate learners, who don't just sit back and wait for someone to tell them what they're supposed to know, but who go out and try to figure things out for yourself. Who pursue your interests, your goals, your passions with intensity, and who actively participate in everything you do. Who go out and find other learners who are passionate about what you are passionate about and learn from them -- and alongside them.

The world has shifted. The world of school, and the world of work, and the world in general has shifted, and so I need you to shift as well, and that's what I'm trying to do in this class. I'm trying to get you to be actively involved in your own education, to be independent and curious learners in mathematics, even if Algebra is never going to be your favorite subject.

I believe you need the skills I'm trying to get you to learn for three main reasons. First, to be a successful citizen you have to be numerate. In order to deal with all the data that is going to get thrown at you, and to make good, responsible, effective decisions, you're going to need a lot of the skills we're learning in Algebra.

And, frankly, that's not necessarily true about all the math classes you'll take. Honestly, if you take Trig. and Pre-Calc., the skills you learn there are very important if you go into the math and sciences, but perhaps not so much in day-to-day life for most of you (some folks will disagree with that). But the skills we learn in Algebra you'll be using every day to make sense of all that data in the world, to be informed voters and decision makers.

The second reason to learn the skills is that if you decide that you are passionate about math and science, you need these skills in order to progress to more complex topics and to go deeper.

The third reason -- and it's the one I think is least important but you may think is the most important -- is that right now in the short term you have to learn these skills to get a good grade in this class, to do well in school, and to get into college if that's what you choose. So while I prefer that you focus on the first two reasons, this one is still a valid one for many of you.

This is why it's critical you do the assignments I'm asking you to do, like watching the videos I've created for you. Those videos are designed to help you master the skills, and to become more independent learners. But they're also designed to free-up class time so that you can become more curious, active learners, in class, and so we can explore interesting (or not for some of you) applications of Algebra like the bike gear ratios or Tim Tebow's speed at the NFL Combine or a variety of other activities we'll be doing this year. In order to apply the skills in class, I need you to do the necessary work outside of class.

In order for that to happen, in order for us to use our class time to be the kind of learners I think we need to be to be successful, I need you to step up and take care of business. I need you to watch the videos, and use them as they're intended, and do the other things I ask you to do outside of class. And I really, really need you to participate in class, to be active learners. To ask questions, and be involved, and talk to each other, and help each other, and be willing to take risks in order to learn more, even if that makes you a little nervous or uncomfortable. I need you to do more of the talking in class, and me to do less. I need you to do more of the thinking, and the questioning, and the figuring out.

So I'm asking you to please, please consider what kind of future you want, not just for yourself, but for those around you, and make an effort to be as independent, as curious, as responsible, as passionate of a learner that you can be. And I promise that I'll bring the passion every day and do the very best I can to help you become that learner.

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In all the conversations around school reform, about standards and global competitiveness, about teacher tenure and accountability, about charter vs. public, urban vs. rural vs. suburban, I think we sometimes forget one of the most important conversations we need to be having -- the one with our students.

This conversation with my class continues. What conversation should you have with your students today?

What Should Students Know and Be Able To Do?

(Cross-posted at The Huffington Post.)

I'm a teacher. A parent. A citizen. Those are the lenses I view teaching and learning, educators and students, education and school through. That doesn't make me an expert, and I don't have all the answers, but I think I have some good questions, so let's get started with one of those questions.

This is the question that educators are constantly asking themselves.

What should students know and be able to do?

It gets back to an old argument in education, the argument about which is more important -- content or skills. Like most teachers I've talked with, I think that's a false dichotomy. I want both. I want students to know some content and have the skills to be able to use their knowledge. I don't want them to just "cover" the material, I want them to uncover their own understanding, and to think critically about the content.

My bias, however, is that too often in schools we err too much on the side of content. I once heard Cris Tovani, a wonderful reading teacher in Colorado, say,

Yeah, as a teacher I can cover my curriculum. I can get to that finish line. But often when I get to that finish line and look around, I'm all by myself.

That's even more true today, when we live in a rapidly changing, information abundant world. We live in exponential times. There's just too much content out there. As Eric Hoffer said,

In a time of drastic change, it is the learners who inherit the future. The learned find themselves equipped to live in a world that no longer exists.

He said that more than thirty years ago, and I think most of us would agree that the pace of change has only increased since then.

Schools were designed for an age when information was scarce, when students came to school because that's where the information was. It was in the textbook, it was in the teacher's head, and -- if they were lucky and had a good library -- it was in the additional resources the school library provided. But now, now we live in an information abundant world. I don't hear many people complaining that they don't have enough information (although they may complain about the quality of that information), yet schools are still designed around the concept that this is where you go to get information. That needs to change.

Which leads, I think, to an even more basic question. A question I think that, despite all the education reform lately, we haven't really talked much about.

What's the purpose of school? Is the primary purpose of school to meet the needs of society, or to meet the needs of the students?

There's a strong argument to be made that since society is investing so many resources into educating the young, that schools should be designed to meet the needs of society. After all, if schools don't meet the needs of society, why should society support them? This is the argument that is currently in fashion.

But I'd like to suggest an alternative, that the primary purpose of school should be to meet the needs of the individual. That if we meet the individual needs of students, we will ultimately meet the needs of all students. And if we truly meet the needs of all students, we will then meet the needs of society. I think this has always been the case, but it's even more important in a rapidly changing, information abundant world, a world where society doesn't even know what its needs are going to be in five years, much less in thirteen (for K-12 education) or longer (if you include post-secondary education).

This is a problem for many of the current school reform discussions because, despite the rhetoric about leaving no child behind and racing to the top, they rely on a standardized view of success, a one size fits all approach. I think individual students are different, and to ignore that fact is to deny the evidence that is all around us, at least if you ever met more than one kid.

No, I'm not talking about lowering expectations. I think we can have high standards without being standardized. Standardized curricula create standardized minds. Standardized minds create collateral debt obligations and credit default swaps. You know all those folks on Wall Street aced their standardized tests. They were the best and the brightest, the success stories from our schools, at least by our current definition of success in schools. Yet clearly there must be more to success than just those test scores.

So, I would suggest we need to slightly modify the question we ask ourselves as educators. Instead, perhaps we should be asking,

What should this student know and be able to do?

I think the addition of just one word might just make all the difference.

A Fundamentally Different Place?

Some of you may recall that I announced way back when that I would be blogging for the Tech + Education section of The Huffington Post. Well, it ended up that they changed their minds and never launched that section. Instead, today they launched an Education section and I'll be one of many contributing bloggers (many of whom regular readers of this blog will recognize - and probably already read) to that section.

It was difficult to write my first post for them because I felt the need to "introduce" myself in this new space. That's not at all the style of HuffPo, people just dive right in with what they want to say. But, for me, blogging is still a conversation (or at least it should be) as well as a place of reflection, and it didn't feel right to skip that piece. I felt like people had to have at least some idea of why I had been asked to blog for HuffPo, some idea of the context, so I decided to write an intro piece even though it doesn't really fit with their style.

This is all a long way of saying that my first post probably doesn't say that much to folks who have been reading this blog for any length of time. Despite that, I hope you visit HuffPo Education and support the many folks there that you'll recognize. Join in the conversation, add words of support or push back, but don't let their posts languish in the shadows of the "celebrity" bloggers. I think you should comment on the celebrity bloggers as well, but I think if we take some of the passion and energy we have been a part of on our blogs and infuse that into the conversations on HuffPo Education, then perhaps we can expand this conversation outside of the relatively narrow and confined edublogosphere. And if we do that, then maybe, just maybe, we can create some of the change that we believe our students deserve.

I've cross-posted that first post below. Second post is in the queue at HuffPo, it will hopefully appear soon.

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I'm honored to have been asked to contribute to the Education section of The Huffington Post. I'm going to focus mostly on the impact technology has -- or should have -- on education. I'll talk about learning. And students. And teachers. And technology. And how best to do this thing we call school. I hope to have thoughtful discussions about how to leverage the creative, collaborative and connective powers of technology to help our students learn and grow. To help them be successful in school and in work, in their personal lives and as citizens.

Let's review how I got here. In reverse order and slightly abbreviated:

• Contacted by HuffPo to write for their new Education section.
  
• Mentioned in two HuffPo pieces, one by Jose Antonio Vargas and one by Arianna Huffington.
  
• Presentation gets shown to or used by various folks, including the National School Boards Association, the Senate Subcommittee on Intelligence (including the heads of all the intelligence agencies), Major League Baseball owners, various high-tech companies, politicians on the left and right politically, televangelists, Time Magazine columnists, and many, many others -- variations viewed at least 40 million times.
  
• Had presentation go viral on YouTube, in email and elsewhere.
  
• Had presentation go semi-viral in the education blogosphere.
  
• Posted PowerPoint presentation on my blog to continue the conversation.
  
• Was inspired by many in my learning network, so created a PowerPoint presentation to start a conversation among the teachers in my school.
  
• Attended some great conferences and learned from folks, many of whom were in my learning network.
  
• Had some great staff development conversations as a result of that learning network.
  
• Created my own personal learning network, both online and off.
  
• Started a blog to complement our staff development efforts.
  
• Started reading lots of blogs by following the links in that one blog.
  
• Started reading one blog.
  
• Read an article about a teacher that was blogging.

Now, the point of all this (and there is a point) is not to say how wonderful the presentation is or how great I am (this story is not about me, I just happen to be the one that gets to tell it). The point is that this PowerPoint ended up being an example of itself. If a simple little PowerPoint -- some folks would say simplistic, and they'd be right (it was supposed to be the start of a conversation, not the entire conversation) -- can start at least 40 million conversations around the world, then we live in a fundamentally different world than the one I (and most of you reading this) grew up in.

I know some folks would dispute that, and that's an interesting conversation in and of itself, but if you buy that -- if you buy that, on so many levels, the world is a fundamentally different place -- then it just begs us to ask the question of whether schools have similarly transformed from when we grew up. If your answer to that question is no, as I think it probably is for a large majority of you, and if you see a problem with that, then what should we do?

So much of the current debate around education is only touching the surface of these issues. I hope to use my contributions to Huffington Post Education to explore these shifts further.

With you.

Together.

Please join me.

Welcome Huffington Post Readers

If you�re visiting this blog for the first time due to this article, welcome. I feel like I should have something profound to say, but it�s the end of May. And in my high school, that means finals week, projects, grades, graduation, scheduling and some reimaging of laptops and netbooks, so I�m fresh out of anything profound.

Actually, even if it wasn�t the end of May, it would be unlikely that you�d find much profound on this blog. But, if you�re interested in what goes on here, here are some links to some of the interesting stuff we�ve talked about over the last few years. Pick one and drill down into some of the posts if you�d like.

The Best (?) of The Fischbowl 2009
The Best (?) of The Fischbowl 2008
The Best (?) of The Fischbowl 2007
The Best (?) of The Fischbowl 2006

Thanks for stopping by. And, if you have a question to ask, you're welcome to ask it here as well. I have a feeling I'm not going to end up in the top five, so you might be better off asking it here.

Blogging for The Huffington Post: I�m Gonna Need Your Help

In the next week or so, The Huffington Post is going to add some new "blog topic" pages within their existing Technology section. One of those topic pages is going to be "Tech + Education," and I've been asked to be a contributing blogger to that section.

(Update 12-16-09: They've decided to delay the Tech + Education section until January 11th, 2010, so that it doesn't get lost in the holidays. This is perfect, as it gives me almost four more weeks to lose sleep over this.)

(Update 1-19-10: Now pushed back to January 25th.)

(Update 1-26-10: Now pushed back to February 8th.)

(Update 2-11-10: Now pushed back to March 1st. No really, it's going to be March 1st. Maybe.)

(Update 3-9-10: "Before the end of March . . .")

This was not an easy decision for me for a variety of reasons. The Huffington Post is a different space than this blog, and that brings with it both some good things and some not so good things. One of my concerns is that the conversations on that blog can get both off-topic and somewhat uncivil at times. Not only do I not have a very thick skin, but I'm not particularly interested in contributing to something that generates a lot of noise but doesn't actually move the conversation forward.

The Huffington Post is also generally considered to have a political bias, and � while I realize everything has a political aspect to it � I don�t want what I write about (and what we�ve all been talking about these last few years) to be viewed as being on one political "side" or the other. I'm not very much interested in "sides," I'm more interested in solutions. I know it's na�ve, but I don't view any of this stuff through a political lens, I just want to write about and think about and talk about learning. And students. And teachers. And technology. And how best to do this thing we call school. And I want it to make a difference.

So I thought about this for a while, went back and forth with myself, and finally decided to give this a shot for a couple of reasons. First, it's an opportunity to take this conversation to a wider and different audience than typically reads this blog. We've all talked about "preaching to the choir" and the "echo chamber," and how we need to engage with folks that typically are not present in our spaces, and this is an opportunity to do that. I've written more than once about teachers and students being willing to take some risks in their teaching and learning, so I guess I better walk the walk and take a risk myself.

Second, and this is the main reason for this post, I'm counting on a secret weapon to help me out with this.

You.

(Stop looking around, I'm talking to you.) I figure if I can bring all of you with me, then I have a much better shot at making this work.

So, here's the deal. Whenever I post to The Huffington Post I'm going to cross-post here, and I'm going to both ask and count on all of you to get involved in the conversation there as well as here. Now, I'm not asking you to always agree with me (although, you know, it would be nice if you occasionally did). What I'm asking is that you bring your perspective as thoughtful people that have been thinking and writing and commenting and struggling with these issues for a while now into a space where many of the folks reading and commenting are coming at this from a different perspective. That doesn't mean their perspective is wrong or that we can't learn from it, it simply means that we need your perspective as well. If you'll join me there, then maybe, just maybe, we can do some good.

What do you say?

Welcome Huffington Post Readers

So, if you're just arriving here as a result of this (update: and this) nice to meet you. You can probably find out more than you ever wanted to know about the presentation on the wiki, including this page which has links to posts that take you through the history of the presentation. The particular version that the Huffington Post featured is discussed here (update: subsequent article also talks about the original version, version 2.0, and version 4.0.

If you're at all interested in what this blog is about, then here are some other posts you might investigate:

• About This Blog
• The Best(?) of The Fischbowl 2008
• The Best(?) of The Fischbowl 2007
• The Best(?) of The Fischbowl 2006