Tuesday, January 29, 2013

Purpose and Motivation

Purpose and motivation--these are two of the most basic elements of education, yet understanding them is a difficult task. What should children learn in school? How do we motivate children to take active roles in their education? Teachers and policy-makers have debated these questions for decades. Over the past century, prominent educators and educational researchers, including Mortimer Adler, Jerome Bruner, and John Dewey, have written profound works around these questions.  Watching two of my favorite school-themed films, Dead Poets Society and To Sir, With Love, over the weekend gave me new perspective on these questions. On the surface, the power of the school-movie genre appears to be its ability to touch our hearts and give us hope. While their plots are often exaggerated with unrealistic elements, these films' real power lies in the important truths they reveal about our schools.


In Dead Poets Society, English teacher John Keating (played by Robin Williams) challenges his students with an abridged version of this this poem from Walt Whitman:
Oh me! O life! of the questions of these recurring,
Of the endless trains of the faithless, of cities fill'd with the foolish,
Of myself forever reproaching myself, (for who more foolish than I, and who more faithless?)
Of eyes that vainly crave the light, of the objects mean, of the struggle ever renew'd,
Of the poor results of all, of the plodding and sordid crowds I see around me,
Of the empty and useless years of the rest, with the rest me intertwined,
The question, O me! so sad, recurring--What good amid these, O me, O life?
Answer.That you are here--that life exists, and identity,
That the powerful play goes on, and you will contribute a verse.
"What will your verse be?" Keating then asks his class.

In just one and a half minutes of speech, Keating summarizes Adler, Bruner, and Dewey's beliefs about the purpose of education. The purpose of education is to learn how to live. Through education we discover and develop our existences both as individuals and as parts of the greater society.

Our professions are a part of our lives, but so are our passions and our relationships. Perhaps this is why purpose and motivation are so tightly entwined. Each is necessary to drive the other. Both Dewey and Adler explain why education fails when it fails to balance profession with passion. Dewey writes, "the child, after all, shared in the work, not for the sake of the sharing but for the sake of the product" (p.18). When this happens, school stops being about the students. While education is important for improving society as a whole, that improvement cannot be made at the cost of the individual. Dewey's words remind me of the current push for improved math and science education. I'm a scientist, so I fully support the promotion of scientific and mathematical literacy and a push toward innovation. However, I am bothered by the fact that I only hear that American schools are failing because our test scores are lower than those of other countries. How does our students' problem-solving abilities compare to students internationally? How much scientific innovation is coming from our laboratories and universities compared to those worldwide? Are the policy-makers complaining about test scores mathematically literate enough to understand fully the meaning of data they present? We cannot educate students in math and science without understanding the purposes of math and science, and we cannot educate students without understanding the purpose of education.

Keating also says, "We don't read and write poetry because it's cute. We read and write poetry because we are members of the human race, and the human race is filled with passion." Adler reflects on a similar sentiment:
A part of our population--and much too large a part--has harbored the opinion that many of the nation's children are not fully educable. Trainable for one or another job, perhaps, but not educable for the duties of self-governing citizenship and for the enjoyment of the things of the mind and spirit that are essential to a good human life. (p.7)
Curriculum, whether it be mathematics or social studies or wood shop, must address all facets of education's purpose. It must prepare students for the intellectual, physical, social, and emotional challenges of adult life. While Adler's context focuses on students with socioeconomic and intellectual disadvantages, his point applies to all students. Students in both Dead Poets Society (Caucasian male boarding-school students from wealthy families) and To Sir, With Love (ethnically-diverse co-ed students from inner-city London) show what happen when education's focus is too narrow. In To Sir, With Love, first-time teacher Mark Thackery (played by Sidney Poitier) quickly realizes that his senior class lacks both intellectual and social skills for life beyond high school. He gathers the sleepy class's attention by throwing his stack of textbooks loudly into the garbage. "Those are out. They are useless to you," Thackeray says. He understands that kids cannot learn to become adults from books alone, especially from books students are not really reading. While we contemporary teachers have to worry about tests and standards, we can still address the standards through hands-on life lessons. In Dead Poets Society, Neil Perry (played by Robert Sean Leonard) is an outstanding student under tremendous pressure from his middle-class family to become a doctor and raise his status. However, Neil finds his passion not in the science lab but in the theater, where he is cast as Puck in a local production of Shakespeare's A Midsummer Night's Dream. His father disapproves of Neil's acting career and other extracurriculars, which he believes will distract Neil from becoming a doctor. The conflict between what he wants to learn and what his family and school believe he should learn break Neil; his academic studies have left him unprepared to deal with such incredible emotional stress. Neil ultimately chooses death over a life he believes is no longer his own. The purpose of education is to learn how to live. In the most desperate way, Neil shows that boarding school has taught him nothing. 

The question I received the most as a high school math teacher (after "Will this be on the test?") was "When am I ever going to need this?" High school students often ask this question with their future professions in mind. They have heard the fallacy "education = job training" so much that even they believe it. For the students who want to be doctors, lawyers, or business people, the answer to the question is straightforward. For the students who want to be actors or mechanics or cosmetologists, traditional academics do not fit as easily into their plans. These students understand that the times when they pursue their passions are when they feel most human. However, the message from family and teachers that there is no place for these passions in school can cause these students significant inner conflict. Teenagers with conflict are rarely teenagers with discipline.

In the following scenes from To Sir, With Love, Thackeray takes a traditional approach on his first day. As we might expect, the results are less than spectacular.

Dewey and Bruner agree that the way to create discipline is to ease conflict. External discipline (like school rules and consequences for breaking them) often leads to external conflict (like students acting out). However, internal discipline (the motivation for self-improvement) eases the inner conflict that can explode into something external. Dewey suggests making the trades and arts larger parts of the curriculum, not only to allow students to gain job skills, but more importantly to gain the life skills that come from cooperation and creativity. Bruner examines how the relationship between teacher and student affects disciple. He writes, "Since this is a relation between one who possesses something and one who does not, there is always a special problem of authority involved in the instruction situation." (p. 42). Part of why both John Keating and Mark Thackeray are effective teachers is because neither man acts like he is smarter or better than his students--he is merely more experienced. Each shares honestly what he has seen outside the classroom to prepare his students for what will await them there. Keating uses poetry and "exercises in nonconformity" to remind them that boarding school is far from the reality of adulthood. Thackeray takes his class to an art museum to show them how their hairstyles originated in the 18th century and their clothing reflecting the 1920s. Being a teenager in the 20th (or 21st) century has some surprising similarities with being a teenager throughout history. Thackeray tells his students that the most important similarity is that all teenagers rebel in some way, and that rebellion drives the change in society that is each generation's duty to make. Both teachers maintain authority in their classrooms because their students trust and respect them rather than fear or misunderstand them.

Thackery tells his class, "I teach you truths. My truths. Yeah, and it is kinda scary dealing with the truth. Scary, and dangerous."

If we want to help our students find purpose and motivation, maybe we need to be a little more dangerous.

Adler, M.J. (1982). The Paideia Proposal: an Educational Manifesto. New York, NY: Macmillian Publishing Company, Inc. 

Bruner, J.S. (1966). Toward a Theory of Instruction. Cambridge, MA: Harvard University Press.

Clavell, J. (Director). (1967). To Sir, With Love [Motion picture]. United Kingdom: Columbia Pictures.

Dewey, J. (1900). The School and Society. Chicago, IL: University of Chicago Press.

Weir, P. (Director). (1989). Dead Poets Society [Motion picture]. United States: Touchstone Pictures.

Whitman, W. (2005). Leaves of Grass (150th Anniversary Edition). New York, NY: New American Library.

Tuesday, December 20, 2011

Music Videos as Teaching Tools

Blame the gym for this one.

I got the idea for this lesson before I decided to become a teacher. I went to the gym nearly every day during my last two years as an undergrad. Our gym only showed MTVU, and the constantly-played video at the time was "Bulletproof" by La Roux.

In this video, the 1980s vomit geometry everywhere. I love it! How many geometric figures in this video can you identify? I'll be asking my students the same question (and sharing an excerpt from the book Flatland by Edwin A. Abbot)  before they use geometric figures to tell their own stories. 

Of course, I can't stop there. Here are some other ideas for using music videos in math and science classrooms:

- A teacher from another Albuquerque high school uses the fabulous music of Andrew Bird to teach the idea of transformations to his geometry students. I haven't decided if this one is a good fit for my class yet, as they're more visual and hands-on learners than auditory learners.

- The Fibonacci sequence isn't a part of the curriculum in any of my current classes, but someday I hope to use Tool's "Lateralus" in a math class. This video (created by a community college student) explains everything that is lyrically, rhythmically, and mathematically awesome about this song.

- A Rube Goldberg machine timed to music?! Thank you, OK Go!
EDIT: Rube Goldberg machines can be a great way to visualize the law of syllogism in logic/geometry. If the man starts the chain of dominoes falling, then the last domino will pull the lever. If the lever is pulled, then the model car will be released. And so on. The students can then visualize the conclusion: If the man starts the chain of dominoes falling, then the band will be hit with paint cannons! (Thanks for the idea go to Jacobs' Geometry: seeing, doing, understanding).

- Ratatat's "Neckbrace" is the latest addition to my collection. I saw this video for the first time this morning on "The Cool TV", a broadcast music station that I can only describe as "local access meets 90s MTV". I honestly think both the song and video are awful (saved only by the bird tessellations). My students will probably get a good laugh out of it.

If you know any good songs/videos to add to this list, please let me know!

Saturday, November 26, 2011

Why We Study Math

As we began our unit on logic, my geometry class assaulted me with the question "How is this stuff math?!" I explained that logic is the foundation upon which effective arguments are created, and in mathematics it would be how we show that ideas are true or false.

They refused to buy into it. They couldn't understand how something that didn't involve numbers and equations could be mathematics. They'd never seen anything else.

I think we as educators must completely rethink our attitude toward the purpose of mathematics. We spend so much time emphasizing the importance of particular skills--counting, solving equations, or measurement, for example--that the overall goal of studying math is obscured. Math, like any science, gives us a specialized way to investigate our world and create knowledge. When students leave any of my classses at the end of the year, I have the following expectations:

1. Students should have the confidence to take on complicated problems rather than avoid them.

2. Students should be able to use a variety of resources (calculators, computers, the internet, reference materials, collaboration with others) to investigate problems and form strategies for their solution.

3. Students should use logical reasoning to analyze information and make decisions.

Do I care if my Algebra II students memorize the process for finding the roots of polynomial equations? Not really. I didn't even touch the topic after high school until I reached a 400-level numerical methods class. I certainly don't expect the majority of students to need that blurb of information. However, I do care that they know how to develop a budget and that systems of linear equations can be a useful tool for optimizing their budget. I don't care if my Statistics class can recite the formula for standard deviation. I do care that they know to use standard deviation as method for determining if a data set is precise (and likely reliable). I don't care if my geometry students can prove that a particular triangle is congruent to another triangle. I do care that my students know how to prove ideas are true in a variety of contexts. 

I care that my students become more logical thinkers with the ability to analyze ideas and effectively communicate their thinking. That is why we study math.

I'm excited about New Mexico's adoption of the Common Core mathematics standards next year. They do a much better job of addressing the "big picture" goals of mathematics as well as describing the combination of skills students need to accomplish those goals. The current New Mexico standards separate desired skills into "process" and "content" knowledge, with a majority of the document addressing the mathematical content students should know. What little the standards address about process is vague, including things like "Students should solve problems that arise in mathematics and other contexts" (Ok...how?). The New Mexico content standards include "Students should use mathematical models to represent and understand quantitative relationships," which is followed by several sub-standards. The Common Core standards explain, "Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards." So many features of mathematics are intertwined with the idea of modeling real-world phenomena that it's difficult to accurately discuss modeling as a stand-alone topic. 

Even subtle wording differences between the sets of standards imply a greater depth of understanding required by the Common Core standards. The New Mexico standards want students to write equations. The Common Core standards want students to create equations. I often see students write and manipulate equations without really knowing what's going on. However, the creation of equations requires that students recognize the meaning of variables, coefficients, constants, and symbols in order to put together an accurate mathematical sentence.

Of course, standards mean nothing if we can't implement them effectively. That's where teachers must take the lead.

Friday, November 25, 2011


One of my goals in starting this blog is to address (and ultimately overcome) many of the fears I have as a first-year teacher. Before I go into detail, let me set up a little background for you.

I graduated with my B.S. in mathematics with minors in biology and chemistry about a year and a half ago. Having a vocal music/performing arts background as well as a passion for the sciences, I decided to pursue education rather than research for my career. I'm now 3/4 of the way through a master's degree in secondary education with a focus in math education. I also teach at a small (~140 students) charter school that emphasizes career-readiness and project-based learning.

Sounds positive, right? Well, I'm teaching six different classes (regular and honors Algebra I, regular and honors Algebra II, Geometry, and Statistics). My classes, while small, contain mostly at-risk students and several fully-immersed special education students (without support from a special education teacher, which violates several IEPs). I also have fewer resources and more administrative duties than I expected because we're such a small school. Add the stress of a complete administration overhaul and two weeks of medical leave taken after surgery (stories for another time, perhaps...), and it all adds up to what sometimes feels like the First Year from Hell.

And there you have the source of my many fears. I'm afraid that I can't relate to many of these kids. I'm afraid I can't reach some them no matter what I try. I'm especially afraid of failure despite what I tell my students about failure as a necessary element of creating knowledge.

I'm afraid that I can't relate to many of these kids.I don't have a rebellious bone in my body. Conflict makes me nervous (probably not a good trait to have as a high school teacher). I've always respected authority, even when I've questioned it. I've never been in a fight. I've never done drugs. I didn't drink until I was 21. I've never even gotten a traffic ticket. So, how do I compassion toward teenagers who aren't afraid to throw or take a punch, who don't fear consequences like Fs or suspensions, who approach problem-solving with emotion first and logical reasoning second (if at all), and who probably think I'm a giant pansy. How do I show them that I am, in fact, a real person and not a nerd-bot?

I'm afraid I can't reach some of them no matter what I try.
The students and I are fortunate to have such small classes because it makes differentiated instruction much easier to implement. However, that does not guarantee that I'm any good at implementing it. I'm really a terrible multitasker, so up to this point in the school year I haven't done well running different activities simultaneous. I've focused instead on differentiating the level of complexity and the presentation of material (auditory, visual, verbal, hands-on, etc.). I try to give students some choice in the style and context of questions they answer (though I believe nudging students out of their comfort zones is necessary for personal growth). Despite this, I have some students (and a good 2/3 of one class) who I struggle to engage in learning. I've tried creative projects. I've tried authentic contexts. I've tried structured activities. I've tried open-ended questions. I'm having trouble leading them to water, much less making them drink. On Monday/Tuesday, I plan to use the following as a warm-up activity in 3 of my classes: "Write me a letter. In it, tell me what your goals are for this class and for this school year. What do you enjoy about school? What do you wish were different? Suggest an activity for us to do as a class some time this year." I hope this will allow some of the "unreachables" and I to communicate with each other a little better. What else can I try to engage these kids?

I'm afraid of failure despite what I tell my students about failure as a necessary element of creating knowledge. The scientific method requires failure. We form hypotheses. We test hypotheses. We measure the results and compare them to the hypotheses. Very often, we analyze the failure in our results and use the failure to refine our hypothesis for a new test. Despite my understanding of this, there's still a stubborn part of me that feels like failure is something final that I can't recover from. FALSE. Recovery can be difficult, but it is possible. I assigned a project to my geometry class to analyze the logic of advertisements in which they write and study conditional statements and their converses, inverses, and contrapositives based on ads. This is the only project I've ever found on the topic of logical statements, and in hindsight it's a pretty awful one. Is analyzing the logic of advertising a useful activity for real-world decision-making? Absolutely! Are the converses, inverses, and contrapositives of advertising slogans useful tools for such analysis? Hardly. My students recognized this far faster than I did, and their response was to do anything other than complete the project. My confidence was temporarily crushed. My content knowledge of geometry is much weaker than I'd like (meaning I haven't had a geometry class since I was a freshman in high school; I focused on linear algebra, statistics, and numerical methods as an undergrad), so I was completely lost as to how I should approach the study of logic with this group. This situation leads me to several questions. How do I find a new way to do things when I don't really feel like I know what I'm doing? How do I make logic feel more like "math" in my students' eyes? How do I help my students grow from both my failures and their own failures?

Hopefully I'll answer all of these questions over the course of the year. I appreciate any constructive input I can get. Both the challenge and beauty of teaching is that there is no single right answer to any question. All I can do is approach it like a scientist: do my research to collect options, experiment, refine my hypotheses, and try again until I get it right.