Equity and Mathematics

Well, my last post was fun.  This one will probably only interest math educators.

Back in 1985 and '86, long before my current students were even born, I had the honor of leading freshman calculus workshops at UC Berkeley under the direction of Uri Treisman.  At the time, the workshop program, the Professional Development Program, was considered revolutionary, demonstrating that through a system of collaboration and high standards, students of color could perform as well or better than their peers.  Though I primarily took that gig to help pay for college, it served as the foundation for my beliefs in education and the power of education to address equity issues in our society.  Teachers don't often realize the influence they have on their students' lives, but Uri Treisman was one of the most influential people in my personal and professional development.

Recently, Uri gave a talk at the National NCTM meeting about equity and mathematics education.  It's data-heavy, which we math-wonks love, and it's rather long, but it is one of the most important talks on math education I have ever heard.  I have embedded a video below which Dan Meyer put together linking the slides with the talk.  Thanks, Dan!



In the talk, many major issues in math education and our society are addressed succinctly and convincingly.

• Equity and poverty
• Common core 
• Assessments
• Teacher performance evaluation
• Charter schools
• School reform
• PISA, NAEP, and TIMMS

There are so many remarkable takeaways, that I suggest you view the video yourself, a few times if possible.  Dan Meyer gave a very good summary of the most quotable points, so read his post on this as well.  I would like to highlight the primary takeaway for me - the effects of poverty and the increasingly pernicious problem of wealth inequality masking any efforts to quantify the benefits of teacher evaluation, charter schools, or the Common Core on education improvements.

Treisman points out that in our society, the only real wage increases in the past forty years have occurred in high-skilled jobs, and the primary indicator of whether or not you will obtain a high-skilled job is your math education level.  It is the single biggest factor in our upward mobility.  Math educators have one of the single most important jobs in this country. The "Land of Opportunity" depends on us.

Favorite quote:
As citizens, we need to work on poverty and income inequality or our democracy is threatened. As mathematics educators … we need to work on opportunity to learn. It cannot be that the accident of where a child lives or the particulars of their birth determine their mathematics education.

Poverty sucks.  Treisman was able to disaggregate PISA test scores by percentage of Free and Reduced Lunch students at the schools.  In doing so, he showed that students in the U.S. actually outperform European states with comparable poverty rates.  It is not crappy teachers, crappy curriculum, nor crappy facilities that bring down the average U.S. score, it's poverty.  The education system appears to be doing pretty ok.  Our social system needs work.

Improving education in America will need to take on the battles of poverty, income equity, and social justice.  It will not be fixed solely by changes in curriculum models, teacher evaluation systems, or by testing kids even more.  As math educators, we need to do what we can to ensure all students have mathematical opportunity; as Americans, we need to do what we can to ensure all citizens have social opportunity.

Why I love my school - and why I'm leaving

I love Summit Prep Charter School.  For seven years, I have toiled, sweated, and laughed as I have worked to get hundreds of kids into college.  I have taught algebra 1 and 2, geometry, and AP Calculus - both AB and BC.  I have been the official mentor to two different groups of students and the unofficial mentor of dozens more.  I have visited kids in the hospital, I have helped runaways reunite with their parents, and I have bailed kids out of jail.  I have spent multiple wedding anniversaries on camping trips and I have missed family dinners for expulsion hearings.  It has been the most stressful, lowest paying, and best job I have ever had.

Unless you have been a teacher, you do not understand the rewards that come from making connections with kids that aren't your own.  The love I feel for these kids, the heartache I share with them, and the joy I experience from seeing these kids grow has enriched me more than I ever imagined it could, far more than the wealth I gained from my previous career as an engineer.

I love my job.  And I am leaving it.

I came to Summit because it was an oasis in a vast desert of public schools that have lost their way.  Unions and administrators alike at my previous school were focused on their bottom lines, whether or not these bottom lines had anything to do with the best interests of the students in their schools.  Unions hellbent on protecting teachers and their salaries, administrators evangelizing about the importance of test scores; no one asking if students were really learning or really enjoying learning.

Summit has been a community of teachers and students working in common to provide the best college preparatory education possible in the the Bay Area on the pittance known as the revenue limit funding of California public schools, less than $7,000 per year.  It hasn't been easy, but for three years in a row we have been named one of U.S. News and World Report's top 100 public schools.  Newsweek magazine named us one of the top 10 transformative schools in the country.  This year, 100% of our sophomores passed the California HS Exit Exam, unheard of in a Title 1 school.

While Summit's stats are impressive, even more impressive - and more important in my opinion - is the community we have established.  Because we draw students from all over San Mateo County, our student body is incredibly diverse.  There is no ethnic majority and the socio-economic status of the student body is even more diverse than their ethnicities.  And it's important to note that, because we don't track, each and every classroom is equally diverse. This past weekend, I hosted an AP test prep party at my house for my AP Calculus students.  Twenty-one students took me up on the voluntary retreat.  For nearly twenty-four hours, students worked together on calculus, swam in my pool, did more calculus, played an impromptu game of "red light-green light", tackled even more calculus, hung around the campfire, did yet more calculus, and generally had a great time.  This group of twenty-one students consisted of  seven latinos, three asians, a pacific islander, eight white kids, and a couple of kids whose ethnicities would trip me up if I tried to guess.  It was a very special weekend illustrating the power of community on learning, learning that extends well beyond the textbooks.  These kids enjoyed each other and worked their butts off at the same time - together.  They are kids whose paths would never cross in most any other school, all working towards a common goal.  I simply cannot imagine such a scene repeating itself at any other high school I know.

And I doubt it will ever happen at Summit again, either.

You see, Summit itself has been co-opted; we have been a victim of our own success.  We are growing - we'll be opening our fifth and sixth schools next year - and as a result, we have grown into the bureaucracy I left when I came to Summit.  Even worse is that this bureaucracy is being run by "reformers" and "innovators".  The "Global Education Reform Movement" or GERM as Pasi Sahlberg refers to it, has taken over Summit Public Schools.  Well-meaning but (and I mean no offense by this) ignorant reformers are dictating the future direction of our school.  Summit is glomming on to the latest ideas in "competency-based learning" and technology in the classroom while community and enjoyment of learning are secondary.  People who focus on quantifiable results will never see what I saw happen in my backyard this past weekend.

Furthermore, Summit is being irresponsible in its implementation of these new ideas in education.  Perhaps the day will come when I am proven wrong in my estimation that this individual-focused movement does more harm than good, but until that day comes, dismantling one of the best systems known to anyone will certainly do harm in the short-term and perhaps in the long-term.  Why does anyone feel it is best to work alone?  Education should not be an individual sport.

Summit Public Schools (SPS) has been doing a great job documenting data and student feedback on their pilot program in San Jose, and they have been making nearly continuous iterations in the model to improve it over the past year.  But it isn't ready, and the quantifiable data isn't as good as the data coming from Summit Prep (the original Redwood City School that I work at).  By their own measures, SPS data indicates Summit Prep students show greater improvement and have higher test scores than do their counterparts in the San Jose schools, despite the fact that all San Jose students are working on math two hours a day.

I like the idea of students working on what they need to best help them learn each and every day, as competency-based learning offers, but there are larger issues that competency-based learning misses out on.  In my AP Calculus class, there are students who honestly would never get to that level of a class in a competency-based model - at least not in a four-year high school program - and that is what makes my class so special.  There are students discussing high-level analysis problems that can't really factor a quadratic equation consistently.  But think about it - what's more important to these kids once they get out of high school - analyzing the rate at which a graph is changing or factoring a quadratic?  Which are you more likely to encounter and need in the "real world"?  These students will unlikely become engineers, but they will be able to see a graph of a stock's price and argue intelligently about the rate of growth of that stock.  They can describe inflection points and local versus global maximum values.  Would they have been able to do that if they had been locked in a competency-based program which forces them to master each and every Algebra 2 standard before they move on?

But I haven't gotten to the real reason I'm leaving yet.

Believe it or not, I feel if there is a school that can pull off competency-based learning and maintain some aspects of a community-focused - rather than individual-focused - program, it's Summit Public Schools.  They are very thoughtful, intelligent, and experienced educators.  Most are former classroom teachers.  My primary objection to what is happening to Summit, and reason I am leaving, is that I have next to zero say in how this transition takes place.  When I started working at Summit, teachers developed curriculum, hired other teachers, developed school calendars and policies, reviewed budgets, and generally ran the place.  Now, decisions are made from on high, consensus is lip service, and dissent is silenced.  When I spoke up in January that I felt there is no compelling evidence to make a switch to the SPS competency-based model, I was nearly fired. That is not an exaggeration.

Teachers have somehow lost the respect of our society, and this is the number one reason teachers leave the profession before five years.  It is why it has become harder and harder to attract highly-intelligent, highly educated people to the profession.   It can hardly be called a profession; we aren't treated as professionals.  Competency-based and online education seem to be dedicated to taking the teacher out of the equation.  But it's through my relationships with my students that I find my greatest joy and my greatest successes.  There is research to back-up my own observations as well; my students learn because I know them and I know what they need - both in the classroom and outside the classroom.  I spend time with them and I get to know them.  And I grow to love them.  This will not happen in an individually-based, online-centered system.  And Summit will be making the transition to this system regardless of what the teachers at the school believe is best.

I have been depressed ever since I announced I was leaving.  Every time I think of the current Summit kids who I will not get to teach I get choked up.  I am moving on, but I feel like I am turning by back  on the school I love so much.

Poor Sal Kahn

Anyone who has been at all connected to math education - whether as a student, a parent, or an educator – is aware of Sal Khan and the influence his Kahn Academy videos and exercises have had on the progression of online education and independent learning.  The work he has done is incredible, and people have noticed.  The Gates Foundation, Google, O'Sullivan Foundation and others have donated millions to his company to further develop the idea of online education and self-help instruction.

So, why would the title of this entry imply that things are going poorly for Mr. Kahn?  Well, they’re not, but education in general appears to be at a crossroads, with differing opinions on which road should be taken, and Kahn has – wittingly or not – put himself right at the center of the crossroads.  Or is it the center of the crosshairs?

Kahn believes that his website provides a good supplement to the critical work that teachers do on a daily basis, and use of his materials can free up teachers to do more personalized, targeted instruction with smaller groups who require more intervention.  Others believe that Kahn’s materials can be used to replace teachers, reduce staffing and cut costs. One rather controversial report that took this position was released by the Pacific Research Institute and argued that is precisely what Kahn Academy should be used for, and governments should reduce the red tape and bureaucracy, including the influence of teachers unions, that is limiting large-scale changes like this.

While Kahn has earlier presented some similar arguments about the videos providing primary instruction, he no longer feels that reducing the interactions with teachers would be beneficial for students.  He envisions Kahn Academy dovetailing with a flipped classroom in which meaningful interactions with teachers fill the day while lectures can be done at home with the aid of his videos.  However, PRI is looking to trim government – read, teachers – and is essentially using his words and his tools to further their agenda of busting unions, shrinking government, and privatizing schools.

And on the other branch of the crossroads are teachers who criticize Kahn’s pedagogy.  A viralvideo put out by Dave Coffey and John Golden critiques several of Kahn’s methodologies.  Sal Kahn is a very smart person who creates mostly very clear videos on an incredibly wide variety of topics.  But he is not a teacher – he even felt his short stint as a teacher was disastrous, and teachers are attacking him, perhaps out of fear for their futures, but also because he does make several pedagogical mistakes and mathematical miscues.  The Coffey/Golden video led to a lot of back and forth on the internet, including much from the author of one of my favorite blogs – Dan Meyer.  

I think we need to find ways to embrace technology, but as soon as the technology is used to eliminate teachers instead of supporting teachers, education is doomed.   

Math Anxiety - Blame me

For most of my career I have pushed back - gloriously unsuccessfully - against the onslaught of standardized testing.  From the time Americans start learning addition, they are subjected to timed tests. Having myself been a parent of second- and third-graders forced to complete hundreds of addition and multiplication facts in five-minute increments, I have been a first-hand witness and, if I really want to be truthful, a perpetrator of the stress-induced onset of math anxiety.  My kids seemed to have survived this traumatic period in their lives, but there is considerable research that shows these timed tests are the beginning of the "I just can't do math," mindset that so many people in this country suffer from.

Jo Boaler wrote in an Education Week article last July how stress-inducing time tests have a physiological response on the brain and that kids as young as five years old show signs of math-related stress.  She writes

. . .and the level of interest in the subject is at an all-time low. This is a result, in part, of schools in the United States heading down a fast-moving track in which the purpose of math has been reduced to the ranking of children and their schools. Math has become a performance subject. Children of all ages are more likely to tell you that the reason for learning math is to show whether they “get it” instead of whether they appreciate the beauty of the subject or the way it piques their interest.

More and more we are applying a corporate model to education where everything except student satisfaction in their learning is quantified.  It is as if we have come to believe that students improve by assessing and ranking them, rather than through the actual instruction.

Number of external standardized tests students in my high school take in their four years: 25 - 30
Number of external standardized tests students in Finnish high schools take in their four years: 2

Finland, which is regularly touted as one of the best, if not the best school system in the country, has gone the opposite direction from the U.S.  And the few tests students do take (with the exception of their summative test at the end of high school) are low-stakes tests used for teacher professional development and a means to measure student growth, but not teacher nor school accountability.

In Finland, only 7% of students state they feel math anxiety.  In the United States, the number is greater than 50%.  While there are many, many reasons the Finnish school system is more successful than the US system, and I encourage people interested in delving into those reasons further read Finnish Lessons by Pasi Sahlberg to better understand those reasons, certainly the obsession on testing in the U.S. is inconsistent with the successful approach employed in Finland.

I want to teach in a way that students "appreciate the beauty of the subject," but I so often feel I am employed by a test-prep center, knowing that I am doing harm to my students' long-term appreciation of the subject I love.

I MOOC, therefore I am

MOOCs (massive open online courses) are all the rage these days.  I have been curious - and a bit skeptical - about them, so I thought I would give one a try myself.  In the interest of full disclosure you should know that I am a skeptical thinker by nature.  I consider myself an early adopter and I have always made efforts to incorporate technology into my teaching where I think it makes sense, but I always feel there needs to be a compelling reason to try something before I expose my kids to it.

Call me compelled.

I am currently enrolled in Robert Ghrist's Single Variable Calculus course out of Coursera and the University of Pennsylvania. I have found Dr. Ghrist's approach to teaching calculus interesting, relevant, and refreshing. His introductory lessons were on Taylor Series of all things, and he expands (pun intended) on their use and meaning in his subsequent units on differentiation and integration.  He demonstrates how calculus is used in the ever-so-lofty "real world" with approximations and other applications.  He has given me great ideas for how I will be teaching the topic of series in my Calc BC class.

But, I remain skeptical.

I am a very disciplined person - not crazy, but disciplined. I floss daily.  Yet, I am having a hard time maintaining focus, staying on schedule, and doing all the work.  I have found myself skipping videos and homework.  Yes, I already know calculus pretty well and I am not learning a lot of new stuff, but this course is intended for someone who has previously seen calculus and the material is quite challenging, and I really do want to participate fully.  It's just that in my busy schedule, I find it easiest to jettison something to which I have no financial or social commitment.

I'm not the only one.

Dan McFarland, a professor in Stanford's Graduate School of Education recently offered his Organizational Analysis course as a MOOC.  He required his Stanford students to sign up and take the course and provide feedback. They were among the 44,501 students who registered for the course.  The vast majority had the same commitment issues I have with my MOOC.  Of the initial registrants, only 2,375 took the final (I couldn't find out how many actually passed), and only 291 actually wrote a paper for the class that would give them an advanced certificate of completion.

McFarland's students had mixed feelings about the course as well.  Some found the isolation difficult; when they wished to ask a question, no one was around; many found it difficult to focus on the video lectures as they sat watching them alone.   MOOCs attempt to deal with this isolation in different ways. There are discussion forums in MOOCs, but they require you to post a question and wait for a response.  Some have live lectures where you can participate in live chat, but chat rooms with thousands of people are never efficient and often distracting and can do more harm than help.

I want MOOCs to work.  They would be a great way to offer students at my small, poorly-funded school more learning options.  And they can offer access to high-level educational opportunities to people that would never dream of having such access.  Think of a poor farmer in Bangladesh learning programming or a Tibetan teenager discovering democracy through a social sciences course.  I do see them as potentially transformative.

But much work needs to be done to motivate participants.

I'm encouraged by a recent development in the course I am taking. It appears that Dr. Ghrist's course and a few other Coursera courses may be receiving accreditation which could lead to offering credit for these courses.  That would be a big step in the right direction.  But I don't see that motivating me; after all I didn't sign up for college credit in the first place.  I, and the students in Dr.  McFarland's course, have a different issue with MOOCs - the lack of social interaction.  I learn best as part of a collective, bouncing thoughts and questions off of each other.  I feed off the collective energy of a group of students working together toward a common goal.  This is true whether I'm the student or I'm the teacher.

MOOCs have potential, and that potential, in my view, includes the effect of propagating an ever-increasing malady in our society, the illness of individualism. Learn alone, achieve alone, fail alone. The "I built it" theme at the Republican convention this past summer was emblematic of this disease of "me."  I fear MOOCs and other trends in education like competency-based learning could contribute to this problem, and I worry the primary reason I got into teaching - to develop better human beings - is going to suffer if individual achievement is stressed over the accomplishments of society.  Yes, I am a "It takes a village" kind of guy, and I suspect I am a bit paranoid, but I love seeing my students collectively do great.  And I want to be part of that whenever I am a student, too.  I'm not ready to embrace the MOOC phenomenon yet.

 If you're going to MOOC, MOOC responsibly.

Teach how to learn, not what to learn

I just finished reading a short book by Will Richardson titled "Why School?" It's based on a TED Talk he gave in 2011, and appears to only be available as an e-book, which fits with the theme of the book - technology in education. In this book he questions the fundamental purpose of schools in this age of the internet.  Having also read "Disrupting Class" by Clayton Christensen, I was expecting another book that was going to espouse software as the next great teacher.  We can debate if that is the point of Disrupting Class or not, but it certainly wasn't the point made by Richardson.

Richardson acknowledges that information and facts are in abundance, and there is no point in teaching facts.  Each student holds in his or her pocket a device which can retrieve those facts in a few clicks.  Unfortunately, driven by skills-based, high-stakes testing, this is what teaching has become more of, and it is how the majority of technology in the classroom is being utilized.  We fool ourselves into thinking we are cutting edge technologists by sitting kids in front of Khan Academy videos.  As Richardson asks, "What is the point of going to school for something you can do from home?"

I think most well-meaning educators share Richardson's view that school should be a place to develop deep inquiry, a place to explore passions.  Yet, a pitiful amount of that goes on in our schools.  More and more we are at the mercy of politicians and businessmen who are well-meaning but think that an education can be broken down into a few numbers.  And as a result of the ever-increasing push to increase test scores, schools are becoming test prep centers, not the places of academic enlightenment we believe them to be.

Our schools are driving curiosity and creativity out of our kids.  I recently received an e-mail from one of the hardest-working, most driven students I have ever taught.  It choked me up when I read it.  Here is an excerpt:

 Entering Summit, I: 1) read for fun all the time and 2) loved math
 Leaving Summit, I: 1) never read for fun and 2) was kind of sick of math, despite having an excellent teacher for three years of it. 

I can attribute some of that flagging intellectual curiosity to the social environment of public high school, but I still think Summit's academic environment didn't do enough to stimulate my love of learning. I truly believe in Summit's vision and mission, but I think that it is sometimes so standards- and test-driven that it forgets some of the most crucial goals of education. I realize there are a lot of other factors at play including the educational backgrounds, cultures, and goals of the Summit student body, but I think that genuine intellectual curiosity can be one of the most valuable qualities a person can have, and it can absolutely be fostered in Summit's classrooms.

This from a 19-year-old kid.  Why can't he be in charge of our state's educational policies?

We MUST change.  But how do we go about it?  Richardson gave one word of advice - Scream.  Talk to teachers, school boards, politicians, and even the high-powered foundations and institutions that are, more and more, the dictators of educational policies.  He boycotted his kids' schools during the end-of-year testing period.  What would happen if we all did that?

We need to teach how to learn, not what to learn.

In my next post, I think I'll chat about how I envision using technology to do that.  It includes some of Richardson's ideas, as well as my own based on experiences with incorporating technology in my own classroom.

Revival

So, if you dared to look at the posting history, you may perchance have noticed that I haven't used this blog except for the initial mistart when I thought I would use it as a communication forum for my algebra 2 class - THREE YEARS AGO!

That didn't work so well.

The reasons it didn't work were many and not worth going into at the moment.  Let's just say that I have chosen to use other methods to communicate with my students - e-mail, static websites, and Facebook for class-wide discussion.

I am reviving this blog with the intention of sharing my own thoughts, insights and summaries on teaching math in a time that I feel represents a crossroad in public education, particularly in the charter school world in which I have taught for the past six years.  The influence of big government, new standards, large foundations, technology, funding cuts, and  . . . well, the list is long . . . is putting pressures on teachers like never before.  Pressures to adapt, pressures to perform, pressures to comprehend all these changes and the expectation that we will be experts in adopting these changes to the best interests of our students.

It's daunting.

I am constantly browsing other math blogs.  In particular, I want to recommend a couple of my favorites: Dan Meyer's dy/dan and Sam Shah's Continuous Everywhere but Differentiable Nowhere.  They have different foci, and I hope mine will differ from theirs, but these are worth reading for any math educator.

I'm not sure what path this blog will take - focus on curriculum, teaching methods, use of technology, political pressures, . . . - but I hope to learn from other's learning and create exponential growth in all of us.