Falling in Love With Boat Building

Why I teach.

(A speech I gave to the Cum Laude Society at La Jolla Country Day School, later published in LJCDS360, a Country Day promotional publication, in Summer 2010. )

Why Collaborate? The Bullet Points

• students learn by doing
• reduce passive listening
• give students more autonomy over their learning
• empower students to express opinions, ask for help, help others
• gives me (eachother) immediate feedback on their understanding and engagement
• adapts well to students of different ability
• research and my anecdotal evidence shows it works
• it teaches soft skills: collaboration, communication, writing and creative problem solving
• CEO’s like those skills, research shows social skills are the #1 factor in future success
• forces me to teach better
• IB and Common Core are headed this way
• more interesting

Khan Academy, a learning institution

If you've read my post about collaborative investigation you've got an idea of what Khan Academy is all about. They've got a mission to provide instructive videos on nearly every topic, organized in an intuitively sensible way and paired with interactive practice problems. In this way, a student selects their own homework to support their work in class. These online tools allow teachers to abandon traditional lowest-common denominator lecturing and open up the classroom to deep exploration of mathematical concepts linked to real world problems. Indeed, this is the larger revolution which Khan Academy aspires to inspire.

Khan Academy is young, and they are learning as they go along. Their process is as collaborative and non-linear as that of our students. They adapt to unexpected realities, they adopt new tools when they make sense, and they model the creative problem solving which we hope to see in our students' work.

Learn how they learn here.

A1 Pre-Race Warm Up

Introduction

A1 Pre-Race Warm Up is the first investigation in a unit on acceleration. In my 9th grade math class, this unit is preceded by an inaugural unit on lines and systems, but as I am introducing this material to the blog in November I'll skip lines for now. In any case, I think the acceleration unit is rather more interesting and actually stands well on its own no matter where you are in your year of work with your students. Indeed, you might use it in any high school math class.

As you may have guessed, this unit is followed by a quadratics unit. You might think that students would need to understand quadratics before modeling accelerating objects, but actually the converse is true. The acceleration unit, driven by tables and graphs, eventually draws students to develop a quadratic function. As students approximate solutions to problems, they invariably ask me what algebraic tools they can use to get more precise results. Algebraic tools are introduced when a student has developed a need for the tool. 

Paintbrushes and wrenches, words and hammers, these tools of the trade are powered by the simple desire to order the world. For the toddler, before the hammer had any known application, hammering for the sake of hammering sufficed. But even the toddler's first word, "water," was arguably uttered for want of a solution to a problem, thirst. The question, "Why do we have to learn this," is evidence of a tool lacking a purpose. This acceleration unit flips the question to "Do you have any tools I can use to solve this more precisely?"

Collaborative Investigation and the Flipped Classroom

Introduction
My first year of teaching was in 1995 at an innovative, elite private high school in San Francisco named Lick-Wilmerding. The math department at Lick-Wilmerding employed a method of teaching which was unfamiliar to me and to most teachers at the time. Students worked in small groups of 3 or 4, exploring geometric relationships on a shared laptop and reporting their findings in documents written as if they were lab reports. Studying algebra, students used graphing calculators to explore functions dynamically and again, report their findings in written form accompanied by detailed examples and analysis. Students would receive direct instruction when necessary, but for the most part questions were explored and answered by members of the groups themselves. I adapted hesitantly to this new structure, as I myself had been taught by teachers and professors using lecture combined with repetitive homework. Over my subsequent years of teaching in the states I explored a range of methods tailored to the various cultures of the schools at which I taught. This included straight lecture and homework, a mixture of lecture and independent class work, and collaborative group work supported by a traditional textbook. Finally, now at the American School of Valencia, I’ve developed a suite of collaborative investigations which allow my ninth and tenth grade math students to explore mathematical concepts much as they explore scientific concepts in laboratories. This is supported by online resources which include videos and extra practice problems.

When are we ever going to use trigonometry?

In the summer of 1994 I worked at an outdoor education center in Montana. We lived in crumbling Forest Service barracks on the north fork of the Flathead River. The Douglas Fir forest swarmed with deer, at night we heard mountain lions. Every week a bus would ramble up the dirt road and empty a rabble of fifth graders versed enough to recognize a bull trout but still thrilled to see otters riffling the river, and recoiling in nervous delight from binoculars when they spotted a grizzly on the adjacent huckleberry mountain. Teaching kids about the outdoors in a place so wild was like teaching art history in Le Louvre.