Category: Blog

The Hardest Question

What is the hardest question a teacher has to answer?

As teachers, especially math teachers, we face this most painful question all too often, rarely do we have a good answer to it, and even more rarely does our answer enlighten students. The question is less a query and more a bleating call for relevance. For students, it is one more reason to ignore or at best inattend to a teacher’s presentation. For teachers, it reaches into the deepest sense of who we are and what our job is. Our inability to answer it directly and cogently can feel like a failure in the traditional analog classroom where our primary role is threefold, present concepts and skills, develop examples as prototypes, and motivate students to attend and learn. Our inability to give meaningful answers to the hardest question destroys their faith and our ability to motivate.

I always found the effort to motivate learning to be the most taxing part of my job as a teacher. Learning is work, pure and simple, and to get students to learn we have to get them to work, motivate them by placing what they have to learn into context, making it part of an interesting story, providing a strong rationale, finding a reason for students to care, or as the last resort bribing students with grades.

In our digital age the Web is the resource center, a library for concepts and skills. Whether the result of a Google search, a YouTube video, or Facebook connection, students today can find information, concepts, and even demonstrations of the skills they are to learn. The traditional roles we long assigned to teachers as presenter and prototyper are now generally obsolete. (Technology has even replaced most of the traditional teacher evaluation role with computerized high-stakes tests.) The motivator role remains, which brings me back to the hardest question teachers face all the time.

“Why do I have to learn this?”

Difficult, if not impossible to answer in the traditional analog classroom, it can be even more painful in a digital one that follows the traditional form, because in this time of accelerating change, amazing tools, the Web as an infinite library, and cell phones as communicators, our usual answers are all too often irrelevant!, Therefore, in the digital age, the student who has to answer the hard question. The student has to find his or her own meaning, we cannot give it to them. And to do that the student obviously has to have interesting assignments and choice.

The only way I know to give students interesting choices is to make our assignments project-based! So when you next get that hard question, think digital and think Project-Based-Learning.

Personalizing Learning

Envisioning technology that reinvents our schools not automates them should, I believe, be our goal and our dream for personalizing learning.

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Curiosity

The words curious and curiosity do not appear in the Mathematics Common Core Standards document, yet they are arguably the most important words in mathematics education. If there is any single habit of mind or critical skill I want our students to learn, don’t you agree, it is to be curious, to question, to experiment, to wonder, to imagine what we will do or become. Isn’t this what it means to reason quantitatively?

Curiosity is certainly the most human of traits. It is the reason we explore, the reason we invent, the reason we question, the reason we love mysteries and games. We are naturally curious. And curiosity is at the heart of mathematics as well. We wonder if particular numbers form a pattern, we want to know whether all triangles that fit in a semi-circle are right, whether all right triangles have two sides that when squared are equal to the square of the longest side. We wonder if our business will make money or our budget will enable us to buy that new computer. We are curious big and small, is the universe infinite or finite, is the chance of winning the lottery worth the price of the ticket, is global warming really that bad.

At What if Math we are all about curiosity. How many of the products in a 12 by 12 times table are odd numbers? If we choose any whole number and divide it by 2 if it is even and multiply it by 3 and add 1 of it is odd will repeating that pattern always make a sequence, 4, 2, 1…? What if we make a table using 1 simple rule, add the two cells in the row directly above it? What does the graph of a quadratic equation do if I change the b term? Was Ted Williams or Joe DiMaggio a greater hitter in the 1941 season? Was Napoleon right about using the Great Pyramid to build a wall around France or Moore right about the exponential rate of growth of microprocessors? What does absolute value do to the graphs of polynomials? Is the rate of change of C02 increasing or decreasing? Should I lease or buy that new car?

If curiosity is so central to our lives, then I am curious to know why it doesn’t appear in our math standards or in all too many of our math classrooms. I am curious to know whether students can care about what they are learning in their math classes if they are not curious about the problems we give them or the concepts they are supposed to learn. I am curious to know whether learning math can be fun for kids if they are not curious about it. I am curious to know…

Art

The Los Alamos Primer

Or how to build an atomic bomb.

One of the best curriculum ideas I ever had was to use this book as the text for an intro to physics course. It was written in 1942/3 by Robert Serber who had been tasked by Robert Oppenheimer to teach a course to newly arrived scientists and technicians on the fundamentals of the Manhattan Project they were involved with. It is a fascinating book, released from its top secret status only in 1992. It is a fascinating overview of the most important concepts in physics in 1942 that were both fundamental and essential to building the bomb.

I suggested it to my son Brenan who was assigned an intro high school physics course at a private high school without any time to prepare or text or materials to use. He planned to combine some of its simple lessons in physics with lessons in history and morality. For just as the physicists at Los Alamos questioned its ultimate usage, he sought to engage students not only in physics concepts and real-world problems but in the responsibility that physicists and all of us have in use of the ideas we develop or support. It was a brilliant and creative way for him to begin a physics course and engage his students in this great subject. Unfortunately, his classes started on September 10, 2001. Needless to say, he ended up pivoting in a different direction.

But it is still well worth thinking about the lesson and ask, “How do we connect our physics classes with the world our students are living in?” “What do our students have to know to prepare themselves for their future?” “Would you rather learn fundamental physics by dealing with the atomic bomb problem or by learning the definition of time, distance, and velocity?” And when we think about engaging students during those critical first six weeks of a physics course gets me wondering the same about our math courses. What kinds of projects can we develop into our math classrooms to bring them alive, to insure our students crave learning math and do not sit back asking what is perhaps the ugliest of all questions, “Why do I have to learn this?”

When I think about project-based-learning I picture The Los Alamos Primer, Leo Szilard’s The Voice of the Dolphins, and Brenan’s moral questions.

Art

Rows and Columns

This picture from a recent blog post sends shivers down my spine. It is our picture of a “modern” classroom with the desks lined up as they have been for 200 years in rows and columns, students looking at the backs of the heads of other students and the back of the head of the teacher talking and writing on the board. Principals should ban this arrangement, ban rows and columns classrooms.

How is it student centered? How does it enable students to work together on projects or problems? How can it make our modern schools interesting places where students want to be? It looks like the world of business did in the 1920’s, not today. It is a constant reminder that schools are places where you sit at attention and focus on the quietly listening, not active, not collaborating, not communicating with other students. It is a static place not a dynamic place, a place where the teacher is the focus and not the student, a place you cannot wait to leave and not do not want to go. The moment you walk into such a classroom you know you are in the past and not preparing for the future, you feel you are in a problem-making room and not a problem-solving one; a room where students are not valued and where creative thinking out-of-the-box is not encouraged.

It is a room I do not want to be in, why would I want our kids to be in either.

Art