The Lean Startup (by Eric Ries) redefines the metric of success for startup businesses. Traditionally, we might look at revenue or users to judge early success, but Ries calls these "vanity metrics", as they are more useful as bragging tools than as proof that you understand your customer and their wants and needs. Instead, he recommends using "validated learning" as the key metric. Validated learning comes from taking an assumption that is key to the success of the business, running an experiment with minimum cost and time, and demonstrating whether or not the assumption is actually true. One concrete example comes from the founder of the online shoe store Zappos.com: the key assumption is that people would be willing to buy shoes online. To validate this assumption, the founder created a small website that looked like a legitimate retailer of shoes and promoted it online. When people actually ordered from the site, he drove down to a nearby department store, bought the shoes at retail price, and shipped them to his customer. Every transaction lost money and was time consuming, but through this process he was able to figure out exactly what people wanted from an online shoe retailer without the financial risk of investing in a warehouse of shoes

*.*If the website completely failed, he would have moved on to other ideas with no major loss other than a few weeks of time and a few bucks. Instead, he bought himself lots of time to tweak the website and run additional mini experiments that tested different designs and policies to see how they affected sales and customer satisfaction. When he finally did commit to having a warehouse, suppliers, and employees, he already had a lot of the validated learning done and put his investment money into the right areas to quickly grow the business.

Taking a step back, I want to clarify that a startup is not a new business using a proven model, such as a pizza restaurant in a new town. It is an organization creating new products or services for a new customer. Many startups begin with hunches around a pain point or problem, but they don't know exactly what they are going to make or who is going to buy it. This is why advanced planning and business plan development are a massive waste of time for an early startup -- they have no idea what they need to do yet. Until they have validated that they have a product that a certain customer segment wants to buy, and they have even taken pre-orders for these half-fake products, they should not be wasting any time executing on the details that do not validate core assumptions of the business. This is hard for designers and developers with a product vision, which is why one of the huge themes of the book is discipline in business practices.

As an educator, I want to spend more time challenging the core assumptions that our school and curriculum are based on using experiments across different classrooms and with different teachers. True split testing experiments are difficult in a single classroom with one teacher, but there might be creative ways to move kids between teachers in the same block or give different tasks to half of a class in a more flexible environment. Below are a few assumptions that I and/or our team is already starting to question, but need better testing methodologies to fully understand:

*We should give students the solution key to self-monitor their progress*: my experience tells me that most students are poor self-monitors due to a mix of not understanding the difference between solution key answers and their answers, not knowing why they made a small mistake that actually occurred from a major misconception, and not caring if they are doing the problem right.*The most efficient way to group material is by similar topic:*After years of math was developed, we found efficient ways to compact the material. We put all of the factoring into a factoring unit and teach 4 methods for factoring different types of problems. When I rebuilt my Stats class, I placed content around the types of problems they could help you solve instead of in the traditional syllabus order so real-world projects could motivate and reinforce content work.*Students need two quarters to complete a math course:*This seems like an obviously flawed assumption. Despite this, I know of almost no schools that offer a continuous course called "math" that lets kids move at whatever pace they need to. Everyone has courses that advance at a single pace dictated by the content that needs to be covered and the time allotted to cover it.-
*The current sequence of courses and topics is the ideal way to teach them:*Teach number operations, then algebra, then geometry, then more algebra, and then calculus. Teach polynomials and all of their operations, then teach factoring in its many forms, and then jump into rational expressions and equations. Why couldn't you teach calculus concepts (it's just area and slope) to 3rd graders and give them tools to handle the nasty algebra? *Following the standards as prescribed is necessary:*I don't know anyone crazy enough to ignore the state's written standards, as a whole district, and teach what they think is best. If I were in charge, any factoring without a computer might get kicked out to free up time to build mathematical models of real-world systems. Just ignoring the standards related to factoring would eliminate an entire two week (block schedule) unit in Algebra 1 and Geometry and would save another week or more in the rational expressions and quadratics units. Kids would (probably) get more MCA problems wrong as a result and we would be intentionally ignoring a state mandate. I think this extra time could strengthen everything else we do and leave more time for meaningful application.*1:1 iPads are a tool for learning:*I think this depends on the task. In the "solve these same problems" environment that we created for our kids, the iPad doesn't have nearly as much to offer. It does allow for videos to quickly viewed on demand and saves paper, but a multi-purpose device that has so many built-in distraction tools makes it hard for kids to stay on task during long problems. Jury is still out here and we have little data to beyond teacher observations to go on.*A group-paced course is a better environment for the typical student:*Before a student is allowed to attempt Algebra 1/2 or Geometry credit recovery from an independent-paced math class, they need to fail or nearly fail a course. We do this because a computer-based math class costs more than using our own curriculum and we're afraid that it might be easier than our curriculum (kids trying to take the path of least resistance could avoid our material). What if everyone had a flexible-paced environment using our curriculum and cost wasn't a factor -- would that be worse than having large groups of kids moving through together?*Subject-separated courses taught by content experts is the best way to organize middle and high school:*This assumption drives me nuts. I have little proof on this being wrong and it is such a deeply ingrained conventional wisdom that is reinforced by the state's teacher licensing system that it would be hard to change even*if*there were experiments done that proved it wrong.

There are plenty more assumptions that I think stand on shaky ground. The Lean Startup has energized me to think more about these assumptions and think of creative ways to validate them as objectively true or false. As a statistics teacher, I especially feel like it is my calling to help in the design of experiments that can assess more causation than we're used to in education.

Much of what is done in math class is done by computers in the real world.

ReplyDeleteThe real trick is: How much math do you need to learn to understand how to set the computer up? How much math do you need to learn to recognize when the computer result is not right? When is a computerized task necessary to learn, because it is essential to understanding a required concept.

Factoring polynomials is a great example. Real world polynomial factoring is ridiculous to do by hand, but essential to understanding the behavior of systems. Finding the excluded values of a ratio of polynomials is the most important part of understanding many dynamic systems. Cancelling common factors between numerator and denominator can cause real problems, because real world numbers are never precise enough to do that.

Perhaps, teaching Newton's method for finding polynomial roots would be better than factoring. Can we teach finding the slope of the polynomial without calculus? Sure, not everything has to be derived for students to accept it. For the rare student that cannot accept it, an introduction to limits and solving Newtons formula for polynomials can be done as a side lesson (video).

Before the current swing toward standardized testing, the pendulum in education in MN almost reached PBL with the "Profiles of Learning". There was much push back from parents, because it appeared that there was less required content, and the measurement (assessment in eduspeak) was much harder to understand than "80% correct problems is a B"

ReplyDeleteBeyond teacher led PBL would be student driven PBL. Where each student (and parents) selects from a menu of PBL short courses. The student (and parents) own the responsibility for covering requirement territory supported by school provided "roadmaps".

Child driven PBL can work great for the talented like the grandchildren of Milton and Rose Friedman http://daviddfriedman.blogspot.com/2006/02/case-for-unschooling.html, but can we make it work for everyone?