img.latex_eq { padding: 0; margin: 0; border: 0; }

Monday, September 21, 2009

Counterintuitive Discovery

Today I taught a lesson that went horribly wrong. I was being observed by my cohort leader, so I was already nervous, but some additional time constraints made me feel very rushed. As the lesson progressed and time slipped away, I started talking faster, pausing less between questions, and taking the first raised hand that presented itself. Needless to say, the kids were completely baffled.

After class, I had a couple of postmortem conversations with my mentor teacher and my cohort leader. I came to the surprising discovery that you can actually go faster by slowing down. Had I spoken slower and paused more, I would never have gotten so far ahead of my students. It's as though I was racing them to the end of the lesson. What purpose does that serve to get to where you're headed before the students do?

In the future, I am going to make a concerted effort to linger. I believe that by doing that, I will actually cover more information in less time.

Monday, September 14, 2009

Everything's in Motion

Today we had an assembly sposored by Honneywell and NASA about Newton's laws of motion. The presenters used hip hop, humor, and interactive displays to keep the kids involved. I'll give a more detailed critique later, but for now check out the handsome sumo wrestler in the blue trunks.

Wednesday, September 9, 2009

Tuesday, September 8, 2009

Excuse Me..But Your Question has an Open End

I inadvertently sat in on what turned out to be a rather clever little lesson on open-ended questions. While I still think that name could be retooled a bit, the demonstration itself was quite useful, and surprisingly, it was aimed at students in a 7th grade health class.

As teachers we need to get into the habit of asking questions that probe just a little deeper. If your question can be answered with a single word, you probably aren't delving all that deeply into the subject. In the lesson I witnessed, the teacher challenged to students to ask her open ended questions. She made a game of answering with as few words as possible. At first, she was able to deliver yes and no type answers, but gradually, some of the students started to get it. By the end, she was getting a lot more "why do you like that?" and "what do you think about that?"

The teacher may not have known I was eavesdropping, but I am thankful that I did.

Wednesday, September 2, 2009

Let the Testing Begin

Three days into the first week of school and already we're talking about state testing. Within the first two months of school, our students will spend 5 days, a full school week, taking norm referenced standardized tests. That's five days right at the beginning of the year, before they've even brushed of the summer malaise, where they won't even have an opportunity to learn new thins.

I haven't had the opportunity to ask kids what they think about all the testing. They are probably used to it by now, since evidently it has started in kindergarten. Still, it seems excessive to me.

Sunday, August 30, 2009

Teacher Colleges Beneficial in Only in Theory?

I just read and interesting article in the New York Times debating the relevance of teacher colleges and education degrees. Sure, getting that Masters will raise your salary, but how much does that degree really help your kids? I am going to take the easy way out and let the article speak for itself, especially since my own school cohort leader peruses this blog from time to time.

Saturday, August 29, 2009

Friday, August 28, 2009

Welcome to Westbrook Middle

My first day as an intern began with a district wide breakfast at the high school. I say "the" high school because there is only one of them. For some of you, this may be par for the course, but coming from where I grew up, it will take some getting used to. I lived in a suburban sprawl, where entire neighborhoods appeared overnight and new schools were always being unveiled. There were at least ten high schools in my district that I can recall offhand, and my graduating high school class was nearly 600 students. Here in New England, that numbers dwarfs the populations of many schools, including faculty and staff.

Even though it is sometimes surprising to me, and the administrative costs must be astronomical, I find that I really enjoy the tight-knit community structure. Already, I am on a first name basis with umpteen faculty and staff members, which certainly helps assuage any nervousness I may feel as the new guy on the block.

Also helping me gain confidence was the crisp new $20 bill I received courtesy of the state teachers' union. As part of her presentation, the union rep distributed raffle tickets to the audience. When she emphasized a benefit to union membership, she called out a number and rewarded the ticket holder with $20. Mine was the second number called. Frickin' sweet!

Next, there was a series of introductions and gifts for faculty members. The longer you had worked for the district, the better your gift. Five year tenure earned you a corsage; forty year tenure earned you a windbreaker and a totebag. So on your first day as an intern, you get twenty dollars to do with as you please. After 40 years, a totebag. Does anyone else see the irony?

By the end of the day, I was beginning to wonder why my mentor teacher signed on for this. The year is already packed with changes and transitions for her. She is implementing a new math program designed by the NSF. I believe it's called Connected Math. In December, the entire school moves across town to a new facility. With that move comes a new name. Wescott Junior High will become Westbrook Middle. And on top of all that, my mentor teacher announced to our team that she is pregnant and due in March.

I can't wait to find out what revelations today brings.

Tuesday, August 25, 2009

Gender Bender

There's a story emanating from the track and field World Championship in Berlin last week that I think has a lot of bearing on our classrooms. You may have heard about Usain Bolt's record-breaking sprints and his virtually uncontested gold medals. While Bolt held center stage on the field, the subject of this post is another athlete who remains in the news even after closing ceremonies.

South African runner Caster Semenya took the gold medal in the woman's 800 meter last week. As challenging as that competition must have been to her physically and emotionally, this week she must face a far greater challenge than she could possibly have imagined. As a reward for representing her country, Semenya must undergo gender testing. You see, she has sort of a deep voice and a lot of muscle mass. So instead of celebrating a hard-earned victory, she must submit herself to a barrage of demeaning tests designed push her firmly into a well-labeled little box.

I almost don't even know where to begin.

Semenya is not accused of trying to cheat, but of perhaps unknowingly having a
medical condition that blurs her gender and gives her an unfair advantage over
other female runners.

Maybe I don't understand what a "fair" advantage is. No one claims we ought to revoke Bolt's medals due to his unusual height. Don't his long legs give him an unfair advantage over shorter runners? Don't all great athletes have something that sets them apart from the rest? How do we decide when things are unfair? I recognize that I have an extremely unfair advantage in life as a white male. Should I give back all the awards or recognitions I have received?

For female athletes, the answer is always the same. Women from Babe Zaharias to the present have had to defend their abilities by defending their gender identities. Not so for men. They may have to submit to drug testing on occasion, but no one asks them to prove their manhood. Why do we continually ask this of women? What would we do to them if they started to win against men, instead of merely proving themselves against fellow women?

I think maybe some of the debate stems from our mistaken notion that gender and sex are synonyms. Gender simply means kind or type. So although our species has but two sexes, it has many different genders. By confusing the two terms, we invite these kind of arguments. I wonder what this might lead to in the classroom. As girls make steady gains in stereotypically male subjects like math and science, should we be expected to call their gender identity into question?

"Great job on the math test, Sarah. Now please pee in this cup. What's that? No, we don't think you cheated, per se. We just think that your brain might be wired differently than the other girls. You may have an unfair advantage."

Maybe some of my readers can point to the flaws in my reasoning, but it seems to me that a persons identity is their own business. We ought to be celebrating the triumph of the human spirit, whether on the track or in the classroom. No one ought to be punished for excellence, and certainly not by a committee with DNA tests.

Friday, August 21, 2009

Ropes Courses and Rain Checks

The funny thing about experiential learning is that you never know exactly what kind of experience you're going to get. I am currently sitting on my couch when I had fully intended to be enjoying s'mores around the campfire with my ETEP cohort. Unfortunately, impending thunderstorms and threats of tornadoes sent us scurrying for the cars.

Before the sudden exodus, we had been enjoying a fun filled day of low ropes courses and team building type activities. Some I enjoyed more than others and the high ropes course whispered seductively to me throughout the day, but despite that disappointment, I really do feel as though I got a lot out of the exercises. The lessons we learned could probably have been presented as easily through an in class video or a Powerpoint slide show, but I suspect that what we learned today will be more fluidly transferred to other contexts. Often times, epiphanies made in the classroom never filter out to other environments. I really think the ripples of today's lesson will continue for some time.

Still, I really would have enjoyed a good zip line.

Thursday, August 20, 2009

Praxis Makes Perfect Part II

Well, according to the education professionals over at ETS, I am officially qualified to teach. I passed both my math and science content tests with flying colors.

Wednesday, August 12, 2009

In Defense of Blogging

I go to bed early. I do my homework. I read ahead in the assigned text. I sit at the front of the class.

And I blog.

These are all things that a younger version of me would have found terribly amusing. I used to stay up late for no particular reason, aimlessly flipping channels from one TV movie to another. I used to coast by on my innate intelligence, ignoring those homework assignments that weren't graded and procrastinating on the ones that were, knowing that my exam scores would save me.

And I used to mock and berate anyone self-involved enough to think the Internet community wanted or cared to read their quaint little journal entries. Even using the word blog was enough to illicit a sneer.

After two and a half years and roughly 250 blog posts, I will now explain with perfect clarity why I am glad I changed my tune.

As a teacher, I can not afford to stagnate. Just as I chastise my mother for not being able to program the VCR (or for still owning a VCR,) my students will mock anyone who isn't on Facebook or Twitter. One of our first assignments in grad school has been to build a wikispace. While many of my peers have been stumped by issues of formatting and functionality, I have breezed through, having experienced this process already. I am not bragging, but I am thankful for having anticipated the role technology would play in my classroom ahead of time.

In another week, I will be assigned to my mentor teacher. I can only hope that he or she is as influential in my life as the edubloggers that have guided my development for these past two years. I hope he or she is as innovative as Dan or as supportive as Jackie. Thanks to blogging, I have mentor teachers all over the world.

Admittedly, i have a long way to go. I still don't tweet and I text in complete sentences with full punctuation. I will never be able to completely keep technologic pace with my students. But as long as I can stay just a few steps behind, I ought to be able to communicate with them at the times when I really need to.

Monday, August 10, 2009

Hula Hoops and Bovine Poops: Day One of Grad School

Today I began the nine month boot camp that will shed the intellectual flab and give me the superior training that will transform me into a secondary educator. As first days go, it was pretty much what you would expect from a classroom experience, regardless of whether your role as teacher or student. You plan and plan and brainstorm every possible question or expectation, and just when you think you have all your bases covered, reality knocks to firmly on your ass.

I arrived on time and in style, sporting the first of some fancy new digs that my lovely wife Sarah helped me to pick out. She has been lecturing me about my total lack of style for years now, and with a shiny new ring on my finger and grad school teachers to impress, she figured this was the perfect time for a much needed make-over. As I donned my black sweater vest and stylish Chuck Taylors, I thought to myself, I'm glad I will be in an air-conditioned classroom or this would be a really bad idea. Note the not-to-subtle foreshadowing.

For the first hour, our cohort leader laid out the plans for the coming weeks. After some standard Q and A, she turned the reigns over to our exceptionality instructor. Our first week was going to be devoted to special needs learners, a topic which has always intrigued me. I benefited greatly from a TAG pull-out program myself, but it always struck me as odd to remove students from a mainstream class instead of allowing the varied skill levels and learning styles to augment one another.

Within minutes, and much to my chagrin, we were outside. Several games ensued, including one in which we linked hands and passed a hula hoop from person to person without unlinking. It was an excerise in learning, as the latter half of the circle watched the techniques of the first. Before I was completely drenched in sweat, we escaped back to the AC.

Our next and most substantial portion of our day consisted of reading about the former state-run facility at Pineland, ME. Before a person can truly understand where they are or where they might be going, they must appreciate where they have been. When the topic is exceptionality and special needs education in the state of Maine, looking backward means learning a little something about Pineland. The bulk of today’s activity was devoted to reading about the Maine School for the Feeble-Minded, a politically incorrect reminder of eugenics past.

As a relatively new arrival to Maine, I had never heard of the facility or what went on there. Sadly, I suspect the story is far from unique. While I believe it is important to judge men’s actions by the standard of the times in which they lived, it is hard to believe how quickly the road to hell is paved with good and superficially scientific intentions. It is both surprising and unsettling that this institution lasted as long as it did. In the future, should I ever feel hamstrung by exceptionality regulations or frustrated by special needs students, I will remember the shameful mission statement of Pineland and with that will come the empathy and understanding required.

As a demonstration of how things can change, we ventured the 45 minutes northward to visit the Pineland campus. While dining and socializing in the shiny new building atop the hill known as the Commons, it was hard to reconcile the history of atrocities of which we had read with the elegantly manicured landscaping and attractive architecture surrounding us.

After lunch, we meandered down to the Pineland Farm, a working dairy farm adjacent to the main campus. In addition to caring for a herd of show quality cows and numerous other livestock, the staff at the farm maintains a thriving education program. It is precisely the type of program that allows exceptional students to engage in learning activities alongside of their mainstream peers. The variety of sensory experiences and depths of understanding possible make lesson plan differentiation much easier than traditional classroom settings.

And there I was...ninety degree heat, a brand new sweater vest and Chuck Taylors...standing scant inches from streaming cow excrement. A hell of a first day.

Friday, August 7, 2009

Married....with Children?

Now that Sarah and I have tied the knot, our discussions about the future seem to carry more weight. The topics are the same, but somehow the air around us seems thicker. Still enjoying our honeymoon, we have already begun discussing the pitter patter of little feet. My position on that issue has become cloudier than it used to be.

I have always wanted to become a father. Maybe it’s because divorce robbed me of a traditional relationship with my own dad, or maybe it’s just the strong pull of genetics. Regardless, I have long thought of hiking trips and bedtime stories with sons and daughters. But now that I am about to become a teacher, I wonder how I could possibly balance my passion for education with the family I intended to have.

One of my favorite things about attending school at USM is that class demographics are so non-traditional. Students range in age for 18 to 80, which makes for interesting group dynamics. As much as I love collaborating with the older students, I have noticed that they seem to be much less competitive than their younger classmates. It isn’t that they are less intelligent or less capable; it’s a matter of time. Most of them are parents who simply don’t have any time. Between force feeding recommended daily allowances of green vegetables, parent-teacher conferences, and shuttles to hockey games and dance recitals, there isn’t much time left for writing papers and studying for exams.

I know the kind of teacher I want to be. I know that I will spend as much time outside of class preparing and perfecting as I do in class with students. How can I possibly juggle fatherhood with that? How can I be the kind of teacher my students deserve while being the world’s greatest dad?

Tuesday, August 4, 2009

Saturday, July 25, 2009

My Morning with ETS

So I got to spend my morning with Henry Goddard's present day disciples (i.e. the good people at the Educational Testing Service.) But that's starting in the middle of the story.

By the time I registered for my tests, all of the local testing dates had passed. The only date available prior to the start of grad school was at a center in Salem, MA. Unfortunately, it was a week before my wedding and on the day of another wedding I was to attend. Nonetheless, I felt it was the best choice in the long run. Plus it was months away, so I had plenty of time to study.

Without too much more adieu, this morning arrived. My alarm went off at 4:30am and I suddenly realized that I hadn't really studied as much as I probably should have. Still, I sharpened my number 2 pencils and hit the road. On the way, I dropped off my lovely fiance at the marine animal rescue center where she volunteers. Google Map print-out and toll money in the passenger seat, I tooled on down the highway.

I had planned to get there with time to spare, but after several wrong turns, I arrived with seconds to spare. If you have ever tried to navigate through New England as a visitor, you know my pain. These states seem to make a game of obscuring road signs. As you are flowing through traffic, you must somehow glimpse the tiny non-reflective sign hidden behind two hedgerows, one giant oak tree, and any one of a dozen quaint New England landscaping features that that seem to exist solely to frustrate visiting drivers. Still, in the end I prevailed and arrived at Salem State College on time.

Four hours and 120 lead-filled bubbles later, I headed back home. I really hope I passed, because I don't want to go through this again.

Friday, July 24, 2009

Praxis Makes Perfect

I have to drive down to Salem, MA tomorrow to take back-to-back Praxis II tests for math and physical science content knowledge. I've been brushing up a bit on all my trig identities and special factoring formulas and such. I feel pretty well prepared, especially considering that I only have to get 60% of the questions right to pass. Isn't it great that we have such high standards for our children's teachers? I'll let you know how it goes.

P.S. I'm getting married in a week. Woo-hoo!

Friday, July 10, 2009

The Dreaded Word Problem

All across this great country of ours, math students grapple to the death with their arch nemeses- the dreaded word problems.

Regardless of how they are dressed up or repackaged, most math textbooks are still pretty much the same. A particular lesson or skill set is explained, several examples are given, and then two to three pages of exercises follow. At the very end of these practice problems, buried in the back so they are easily ignored are the much maligned word problems. While the future mathematicians relish with excitement the chance to challenge themselves with these rhetorical abstractions, the average students find ways to conveniently skip over them, like peas being pushed around an otherwise empty plate.

Despite our efforts to reassure the students, to give them problem solving techniques and confidence boosters, we must admit that we are sending mixed signals. Anyone who truly understands mathematics realizes that word problems are not only a key part of math, they are the only part of math. Mathematics is a way of thinking about our world. Seldom does one find themselves confronted by a floating quadratic function demanding to be solved at gunpoint. Instead, we encounter normal, everyday questions or problems that can be illuminated using the tools of mathematics. This means translating the idea into language and translating that language into a mathematical construct. Thus, by hiding these problems at the end, we allow our students to skip the only problems that they really ought to attempt at all.

Rather than work umpteen practice problems, already laid out in clearly defined mathematical language exactly mirroring the guided examples, the students should skip directly to the world problems. Too often I hear my pupils tell me that they understand everything but the word problems. I politely respond that if they don't understand the word problems, they don't understand anything. Instead, they are confusing familiarity with understanding. They think because they can generate the expected answers with a series of repetitious algorithms, that they are preparing themselves for the exam and beyond. There curriculum is a mile wide and an inch deep.

What I would prefer is this: fewer practice problems investigated with greater depth. I would like the answers to come in narrative form, where the student explains to me and to themselves exactly why they made the decisions they made and what axioms of mathematics allow them to employ the techniques they chose. Take the following example:

An Internet service provider charges $9.95/month for the first 20 hours and
$0.50 for each additional hour. Write an expression representing the charges for
h hours of use in one month when h is more than 20 hours. What is the charge for
35 hours?

I don't want to see 9.95 + 0.5(h-20) = Cost (h) ; Cost (35) = 17.45. I want to see the following:

The Internet service provider is offering 20 hours a month of internet usage for
a flat rate of $9.95. This means that regardless of how many hours we use, our
bill will be at least $9.95. In other words, this value is a constant. If we go
over our allotted 20 hours, we will have to pay an overage fee of $0.50 for each
additional hour. Since the number of hours we use will change each month, we can
represent that value by the variable h. (We label it h out of convenience, since
hours starts with the letter h.) It is important to note that we only pay
overage fees on the hours we use beyond 20. An expression for those extra hours
would be h – 20. Therefore, our total bill will be $9.95 plus $0.50 for every
extra hour, or in algebraic terms,

Total Cost = 9.95 + 0.50(h – 20)

To evaluate the expression where h = 35 hours, we simply plug 35 in for h and solve.

Total Cost = 9.95 + 0.50(35 – 20)

9.95 + 0.50(15) = 9.95 + 7.50 = $17.45

That, ladies and gentlemen is how you solve a word problem, and until our students are able to clearly explain every step, they aren't mathematicians. They are walking, talking abacuses.

Thursday, July 2, 2009

Intro to Chem Lab

Last semester I was forced to endure the most painful chemistry lab. As is typical for labs, the amount of work required is disproportional to the one hour credit earned, but that was not the source of my frustration. A scientific laboratory is by its nature about discovery, but this lab was really just about pedagogy. We were really only there to learn how to run columns or pipet solutions, yet we were to write our lab reports as though we were conducting real science.

Evidentally, some of the faculty members shared my concern. This summer, the entire general chemistry curriculum is being retooled. A new textbook has been selected, one written by the American Chemistry Society and centered around the most abundant and familiar molecule on the planet- water. Subsequently, the labs must be rewritten as well.

I have been working for the chemistry department this summer, researching procedures regarding using titanium dioxide to remediate environmental contaminants. The work was done toward designing some new modules for the analytical chemistry lab. The idea was to give the students all the requisite data to design their own lab procedures instead of following a cookbook recipe. That way, they get to appreciate what science really is. Yesterday, I finished that project. The professor I was working with is also involved in retooling the aforementioned gen chem labs. When I was given the option to turn my attention toward those, I jumped at it.

Next semester, when students download their chemistry labs, they will be reading my words. Pre-lab questions, procedures, post lab review- all written by me. Hopefully, I can spare them from the boredom I experienced.

Sunday, June 28, 2009

Writing to Learn Math

I have a new tutoring student starting tomorrow. She has always gotten A's in math, but she works very hard to do so. Next fall, she begins Algebra I and her parents have opted to put her into the accelerated program, fearing she would be bored in the standard pace. To give her a bit of a head start, they asked me to work with her once a week for the rest of the summer. We got a copy of the actual textbook she will use from the school and I have started preparing some lessons.

Since I have curriculum design on the brain, I am making a concerted effort to design an actual curriculum, rather than just work through the text. Her favorite subject is language arts and she loves to write. As a pre-assessment, in addition to having her complete a skills review, I have asked to read some of her writing. I don't have a lot of time to get to know her and I thought that might help. Additionally, I have purchased a bound sketchbook which I am going to make her math journal. I want her to keep all of her notes and assignments in it, but I also want her to have a place to jot down her thoughts and questions about math. Ideally, it will be equal parts mathematical notation and writing.

I'll let you know how she responds to it.

Friday, June 26, 2009

What's in a Name?

Je m'appelle Tony. Mi chiamo Tony. Ich heisse Tony. My name is Tony.

And that's my problem. My name isn't Mr. Lucchese. I understand that formal address is meant to be a sign of respect, but it makes me uncomfortable. I prefer to be addressed as Tony, regardless of the age or station of the speaker. I have worked around people of varying ages in a variety of capacities my entire life, and I have never had trouble commanding respect as Tony.

So how do I reconcile my own personal preference with the fact that the administration of most schools is going to frown upon such informality? I've been trying to come up with compromises. On one hand, I could call my students Mr. or Ms. followed by their surname. At least then we'd all be equally uncomfortable. Or maybe the students and I can come up with an appropriate nickname, like teach or chief or oh captain, my captain.

Did anybody else have this problem?

What's in a Name?

Wednesday, June 24, 2009

And That's My Final Answer

Recently, American audiences got an Academy Award winning look at how easily traditional assessment overlooks cognitive gains made outside of formal classroom instruction. Slumdog Millionaire, a film about an improbable winner of the Indian version of Who Wants to Be a Millionaire, provides a kind of case study in multiple intelligences and learning styles, particularly those with cultural components.

The protagonist, Jamal Malik, along with his brother Salim and friend Latika, demonstrates a tremendous intelligence born from the streets of Mumbai. When circumstances call for him to test his abilities in a formal, albeit fantastic environment, Jamal’s surprising success is met with suspicion and accusations. By assigning him the label slumdog, the world has placed restrictions on the paths to which he may aspire. As educators, we often perceive limits to our students’ understanding based on our own cultural paradigms. The damage brought about by these unfortunate assumptions is made transparent when children like Jamal rise above them.

When their parents are killed by an anti-Muslim mob, Jamal and his companions leave their already impoverished life behind. Orphaned and alone, these three musketeers must learn to navigate the physical and political labyrinth of the Juhu slums. The tests they face are far removed from the ruthlessly efficient norm-referenced exams synonymous with Western culture. Their tests are ones of sheer survival, and these amazing youths score in the top percentiles. In a country where potable water is a luxury, accepted codes of ethics offer no particular advantage. Jamal and Samil learn that it is better to steal than starve, just as it is better to kill than to be killed. Though both boys exhibit clear intelligence, their ways of knowing are as individual as students of any classroom.

Samil, only marginally older and physically developed than Jamal, keenly reads the threads of power that hold their violent world together. He knows who is weak and who is strong. He knows when to strike out and when to run. These skills are recognized almost immediately by Maman, who begins to groom Samil for a role in his organization. Later, when Samil is forced to kill Maman, he does so with calculation, not passion. At a young age, he has learned to leave behind corpses, not enemies. In a situation that would break most adults, Samil follows one cold decision with another when he uses Maman’s death to curry favor with Javed, a rival crime lord. This way of knowing might translate to the playground, or even the boardroom, but it would not gain high marks in a classroom setting. In fact, students in Western schools showing similar aptitudes are typically branded as bullies and troublemakers, and despite its obvious merits, interpersonal intelligence is ignored at best and punished at worst.

Despite widely published and often cited research on multiple intelligences, most Western public schools still judge pupils by traditional rubrics. Jamal’s success on the quiz show emphasizes the flaws in this style of assessment. The questions asked by the host represent a statistical sampling of fields ranging from history to popular culture. As with standardized selected response tests, the implication is that performance on sample questions is predictive of overall knowledge. Thus, Jamal is labeled either a prodigy or a cheat. The possibility that he may simply have been extremely lucky is overlooked.

By his own admission, happenstance was a key factor. While he knows whose face appears on the American hundred dollar bill, he would be hard pressed to name those appearing on most rupee denominations. This naturally begs the question, do we judge intelligence by what a person knows or their capacity for knowing. By the first standard, Jamal would likely fall short in most classrooms. By the second, he would be judged a genius.

His ability to mine sense memories for trivial facts gives the impression that he can recall relevant pieces of information at will. Whether triggered by the smell of a dollar bill, the fall of his mother, or a chance encounter with a pop icon, Jamal’s mind makes connections that allow for swift recall of seemingly useless data. It is important to note that his intelligence pushes far beyond rote memorization. He is able to reassemble his knowledge in new and creative ways. When he deceives gullible tourists into believing that he is a guide at the Taj Mahal, he deftly parries questions and clarifications with fabrications of the truth constructed on the spot. This requires gifts for both language and reasoning ability, areas in which he clearly excels, despite having no formal education. While Samil would probably have difficulties in most formal school systems, all evidence points to the possibility that Jamal might have been successful, if only he had been given the chance to do so.

A teacher’s job description is often convoluted. We are essentially charged with the task of making students smarter. To do so, we must understand that intelligence is not a rigid characteristic, but an ever changing capacity to learn. As more knowledge is acquired, more nodes exist for future connections to be made. Nor is any one way of knowing manifestly superior to another. It is possible to take advantage of student’s contextual experience and cultural foundation by building new ideas on top of previous models. The characters of Slumdog exemplify the need to recognize these alternative learning styles and to design classroom assessment with them in mind.

Sunday, June 21, 2009

The Odd Answers are in the Back

I have recently been contracted by a local publisher to proofread some of their math textbooks before they go to print. It is actually a lot of fun. Basically, I am getting paid to do middle school level algebra problems. Occasionally, I recommend sweeping changes to the text, and I wanted to run some of them by my readers to see what you think.

First, on the subject of quadratic functions, if the guided example demonstrates how to find the vertex of a parabola written in standard form, do feel as I do that it is exceedingly cruel to give the students an entire page of functions written in vertex form.

Second, on the same subject, when the guided example shows how to find the vertex from the vertex form, do you think it is unreasonable to give an example like f(x) = 2(3x-2)^2 + 4? Nowhere in the example does it discuss how to handle this case or describe a horizontal compression. I recommended either removing these exercises or added an additional example to show the students what to do.

What would you have done?

Thursday, June 18, 2009

Dividing Fractions

Does anyone know of an applet or animation online that clearly demonstrates the process of dividing fractions? None of the textbooks I've seen make any effort to depict it graphically. They do it for multiplication, but then bail out on division. I can draw it for individual cases, but I would really like something more dynamic, so that students can investigate multiple examples for themselves.

Wednesday, June 17, 2009

Out with the Old, In with the New

Yesterday I attended an informal luncheon for recipients of the NSF grant that is funding my graduate degree. It was a chance for the incoming class to pick the brains of those who had just graduated. The details of the program are not terribly complex, so we mostly asked them about how their student teaching placements had gone and what success they were having with the job hunt. Their answers were surprisingly varied. Some had been placed in classes with excited and engaged students who fought to answer as many questions as possible. Others were in classes where students rarely picked there heads up off their desks. Some had been accepted at the first school where they had interviewed. Others had sent out resume after resume with no success.

I suppose I had better cross my fingers.

Tuesday, June 16, 2009

Cultural Confusion

Consider the following phrases: "4 by 6" and "3 into 12." To which of the four arithmetic operations are these referring? If you said, multiplication and division, respectively, I can conclude one thing. You are not from India.

I recently began tutoring a young woman who immigrated here from India last year. Through a series of unfortunate events, she has experienced a 6 year gap in her education. At 18 years old, she is only eligible to attend public school for one more year. After that, she must pursue a GED. She is actually a very capable young mathematician, although she needs to build confidence.

During our first few lessons, she appeared to be confusing multiplication with division. After speaking with her father, I discovered that I was the one who was confused. Or rather, we were suffering from a miscommunication. Evidently, in India, the word "by" denotes division and "into" refers to multiplication.

Isn't that delightfully fascinating? I think so.

Monday, June 15, 2009

Certification or Bust

This past Wednesday I met with my graduate student cohort for the first time. There are roughly 20 of us and it seems we come from all walks of life. There are older professionals changing careers and eager young graduates alike. All in all, I think it's going to be good mix of personalities and perspectives.

Our first meeting was predominantly informational. We had a chance to introduce ourselves, or rather to be introduced by one of our peers. Beyond that, it was mostly paperwork and scheduling for the upcoming semester. We were given a few assignments, which I have begun exploring, and I am hoping to begin posting again at Pencils Down, as a secondary sounding board. I know I've promised that before, but this time I really mean it.

Tuesday, January 6, 2009

Pythagorean Lesson Update

I know the last few loyal followers have been holding their breath in anticipation of the results of my first efforts as a teacher. Sorry for the wait.

I was fortunate enough to teach this lesson three different times. As would be expected, each attempt resulted in a unique outcome. For my first effort, I had Sequence 2. This was the group of kids with whom I had spent the least amount of time. Although the three pre-algebra sections are not deliberately grouped by ability, a definite caste system seems to have materialized with Sequence 2 performing near the bottom. Still, I decided to teach my lesson as-is, despite advice to the contrary from my placement teacher. It turned out including the proof was a bad idea, as she had warned. It took way more time than I had estimated and consequently, I was not able to stress key aspects of the lesson. In looking at student work, I found that I had not clearly communicated the fact that c2 refers specifically to the hypotenuse and that it always goes in the same place in the theorem. For example, a2 does not equal b2 plus c2. I also discovered that my instructions on the handout could have been clearer, and that the students would have benefited greatly from working more examples together in class.

Next up was Sequence 5. I had worked with a few of these students before, so I was definitely more comfortable and my sentences flowed with greater clarity. I decided to cut the proof from the lesson and spend more time working through examples. Student work greatly improved as a result, but there was still some confusion over the order of the variables in the theorem, with several students jumbling the equation. Exit Slip feedback suggested that I had not stressed that the relationship only works for right triangles.

For the final group of the day, I had Sequence 4, which was the group that I had observed for EDU320. The lesson went much more smoothly as a result of the relationship I had established with those students. The simple fact that I was able to call them by name made things much easier. Despite my disappointment over skipping the proof earlier, I left it out again so that I could work even more sample problems and stress the importance of keeping terms in the proper order. One interesting thing did happen that I had not expected, though. I had made many efforts to make this a culturally sensitive lesson, and I made mention of great geometers from China, Egypt, Greece, and the Mayan culture. When I was mentioning the Egyptians method of using ropes to measure distance, I inadvertently suggested that this was an antiquated technology. One student in the class who is of South American heritage raised his hand to inform me that it many parts of the world, this is still the preferred method. He was pleased at my mention of the Mayas, and even took an opportunity to teach me some Mayan words, but it was clear that I had erred and should be careful of that in the future. He is typically a problem student, prone to gang related discipline problems, but his interest in his Mayan heritage helped him to focus on this activity. He did not finish the entire worksheet, but what he did do was correct and flawlessly organized.

In general, I thought it was a success. The students said that they enjoyed the hands-on activity with the ropes, though in the future, I would eliminate the 5-12-13 rope, as it was clearly too complicated for them. If I had another day, I would definitely revisit the proof, but only after the students had the main idea down cold. Access to a Powerpoint projector would have been helpful, but I know that I can not depend on technology, so it is probably better that I learn to work without it.