Dear Lucky One (Reflections on a pond...or high-school math course.)

Dear Lucky One,

As I have just spent fourteen weeks learning the balancing act between being a student and a teacher, an informational source and an informational dumping ground. In this letter, I provide you with some of my best insights. As you read these, note that many of them are invaluable truths of which you are already aware. You may even raise one eyebrow and think, “Really? She thinks I don’t know that?” To that, I respond with a condescending shake of the head. Take special notice of the ones that appear most obvious: those are the ones you need taped to the steering wheel or the bathroom mirror, written at your desk or on your hand. Those are the ones that I forgot about on a daily basis and remembered only after I ignored or avoided the truths somehow, so they are included in your advice.

· Believe in the students first.

No matter what experienced teachers, administration, previous report cards, or your personal beliefs may tell you, you need to believe in the students first. Believe in the students before you give up, and believe in the students even if other teachers, parents, or the students themselves do not. You may not be the only person believing in them, but if you are the only, you are the student’s first. The students may not live up to your expectations or dreams for them: do not see that as a direct consequence of you as a teacher. There is always more that one can do for the students and the course, but we will never reach perfection. Use the students who are not meeting your expectations as one source of your motivation to improve, but do not let those students dictate your attitude toward the course, the class, the teaching profession, or your outlook on life. We are attempting an impossible task – to go to the “lost sheep of Israel” (Matthew 10:6), whichever students you view as the lost, discouraged, lonely, or unheard or misheard lost sheep, have them understand and perhaps even enjoy mathematics. The task is daunting, and my apex was realizing that not all students will meet my expectations. I would much rather have some students miss the mark than have no mark or expectations for those same students. Believing in the students is much more important than lowering your standards to fit the lost sheep in your classroom.

· We face a daunting task: students believe in math’s bad rap.

Times it appeared to be okay to like math:

1. As a joke – This is indicated by a smug glance around the classroom and a smattering of chuckles from around the classroom and the student himself or herself.

2. When a difficult objective is suddenly understood – This is indicated by an “OH!” or an “Aha! I like this!” almost immediately followed by a sudden self-awareness of what was just said. Then self-awareness is followed by silence, and perhaps some blushing, depending on who heard the student’s positive attitude toward math.

3. When it’s “okay.” – This only happens on your best-planned, best-enacted lesson. Hours and hours will be put into engaging activities that encompass multiple levels of Bloom’s taxonomy, stopping just shy of teaching your students to save the world. In this case, a few students may admit, even openly, that the lesson, perhaps even math in general, is “okay, I guess.”

Because math has a bad reputation, due to proofs, right answers, a certain brain that American students appear to lack, among other things, it is important for you as a teacher to be excited about math, all areas of it. Being excited for a piece of a lesson will incite students to catch onto your excitement. For example, I gave a very awful math pun at the end of a slideshow lesson. I cautioned the students to not share the answer with other classes, making a very big deal for such a small portion of the lesson. By the third class, students were walking into the class telling me bad puns and mockingly saying, “I know the answer to your joke!” If only the students had realized they were actually excited to get to class, even if it was just to know what the acorn said when he grew up. (“Gee, I’m a tree!”) Excitement is contagious, even if the students do not want to admit it. It is important to like math and to have lessons that you don’t have to pretend to enjoy, but that you actually do enjoy. The students will feed off of your energy and enthusiasm much better than they do your apathy or disinterest.

· Review past course material whenever possible.

Remember the readings you have done reporting ’80 percent of algebra material is new’ compared to ’70 percent of pre-algebra material is review’? They are true. Students are given new ideas – letters as changing numbers? Only if they’re at the end of the alphabet? Constants at the beginning? Adding and dividing and exponentially increasing the alphabet? Greek letters as one number? Greek letters? And students who understood enough to not fail algebra were still placed in geometry. Purposely creating problems that combine algebraic knowledge and geometry offer moments to re-teach and remind students about algebra, along with showing uses of algebra. I learned to go through the algebraic steps to solving geometrical problems, at least the first few times, before skipping over the steps. Students do not learn the geometric concepts if they are focused on the algebraic steps and mistakes. When finding area of a regular polygon, do not take it for granted that students know how to multiply to find perimeters, or complete the algebraic steps necessary to find a leg of a triangle with the Pythagorean Theorem.

· Use technology to your advantage.

Many teachers shy away from the internet because it might allow students to cheat and find answers: don’t succumb to that belief! Students can find answers on the internet, and they might. Use it to YOUR advantage – make the questions a little harder or a little more in-depth. Give students a website to look at; it will really throw them off. They are often shocked when you know what’s on the internet, just like they are shocked when you know the answers to the odd problems are in the back of the book. I also really recommend playing with blogs, wikis, or educational social networks (ning.com.) If students are provided with time in class to prepare their sites or additions to the class sites, they will spend time learning when they do not realize they are learning. Wikis allow students to edit a main page, and have a history so the moderator can see who made which edits. Blogs are great sources of information; I designed one describing the class projects. Students can click on a “label” that interests them and see what projects fall into that category. Ning.com is a social networking site, allowing each student to have an individual page and a classroom group or page that all students can edit. It is simple to post word documents, podcasts, or updates with this site, and one English teacher found that a number of students were entering in interesting discussions with their comments on other students’ profiles.

One last benefit to accepting technology: Word’s 2007 automatic formatting is a lot less annoying. Those extra spaces? Better formatting for online work.

· Emphasize that more than one road leads to Rome.

Sure, there are wrong ways to work math problems. But there is typically more than one correct way. If the students give explanations of their procedures, especially if students have differing procedures, then they will see solving math problems is not just about one procedure and one answer. Math is not as cut-and-dry as people like to believe! By pressing for “hows” instead of just an answer, you have shown students the importance of math as a constructed area of knowledge and not just something that pops magically out of the heads of those with the “math gene.”

· Be interruptable, aware, and helpful.

Jesus allowed himself to be interrupted by a man whose son was dying in John 4:43-54. The story does not say what Jesus was doing when the royal official came up to him, but one can imagine that Jesus was not sitting alone in Cana simply waiting for the official. Instead, He allowed himself to be interrupted and I assume it was even without a frustrated sigh or an “okay, but make it quick” qualifier. He was interruptable, and therefore welcoming. He was also aware of the man’s shortcomings, not fooling Himself to think that the royal official was perfect. The first thing Jesus says to the man is, “You will not believe without signs and wonders.” Jesus was honest, not naïve, and aware of the sin in the world around Him; that makes His approachability and interruptability even more awe-inspiring, as it does the story’s end: Jesus is helpful. He does what He can for the official, healing the son. Should we go doing everything people ask? No – notice that Jesus does not subscribe to the man’s request of returning to Capernaum in order to heal the son; Jesus heals Him in a way unexpected by the royal official. With preparation and a God-centered focus, we can consistently make judgments on our own actions to best help the students and all we interact with. It may not always be what is asked for, but at the same time, action is taken with what we see as beneficial and helpful. The issues are not forgotten, set aside, ignored, or downplayed, but we react accordingly and provide the help we are capable of giving.

Using a quote from F. Scott Fitzgerald’s The Crack-up, I conclude my pearls of wisdom with a grain of salt. After all, it is a single grain of sand irritating an oyster that creates a pearl.

“The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function. One should, for example, be able to see that things are hopeless and yet be determined to make them otherwise.”[1]

---

[1] Fitzgerald, F. Scott. (1936). The Crack-Up. Esquire, February-April.