Super Cute

One of my favorite things about my school is that we have spirit day every Friday. Last week, each mentor group got to choose their own theme. Usually my mentor group (thorough all fault of my own) lacks spirit when it comes to this sort of thing, but this time they were all in. (Maybe because they know that spirit days are one of my favorite things ever?) We voted on a superhero theme, so E. bought masks for everyone and I brought in felt and markers so we could make L's to pin on capes and shirts. Look at how adorable they are! We were by far the most spirited, most awesome mentor group of the day (sorry "Jeans and a white t-shirt" group). 

My favorite part was how much they got into it making the costumes. Multiple kids commented that it was our most focused, most productive mentor time in three years. I do not disagree.  As soon as E. passed out the masks, everyone put them on and got to work. 

 

And then they stayed in costume. Even superheroes have to take tests.  (Another teacher snapped this for me from our office window). 

 

What is... awesome?

Most of my celebrity crushes fall along the usual hot movie star lines, but somehow I developed a massive crush on one skinny, blonde, Mormon trivia nerd. So imagine my delight when I found out that Ken Jennings was speaking about his new book, Maphead, in Oakland.

Morgan and I with my hero:

Best autograph ever:

Another Addition to the Banned List

Awhile back I wrote a post detailing some of the phrases and teaching strategies I would like to see banned from our nation's math classrooms. There are always little things that make me wonder why a teacher chose a certain strategy ("When you multiply by 1 it stays the same because 1 looks like a mirror, so it reflects back the number." Do you think that kids couldn't reason out why multiplying by 1 doesn't change the value?). But there's been a big one coming up lately that's kind of been driving me out of my mind.

"Reducing" Fractions
I understand why we say reduce, especially when accompanied by the phrase "to its simplest form," but I what do you think of when you think of something being reduced? You think of something lessening, you think of it having not as high of a value, you think of it not amounting to as much as it originally did, etc. Kids in the US have a lot of trouble with fractions, particularly with the concept that fractions represent a specific type of comparison of a part to a whole. When one 'reduces' a fraction, an important conceptual aspect is that even though the numerator and denominator change in a way that lessens their respective values, the fraction as a whole does not change in value at all. To say that a "reduced" fraction is equivalent to its original form is kind of an oxymoron--I'd love to see a sale where the reduced prices are equivalent to the original prices. When we use the word "reduced," are we surprised that kids don't understand fraction equivalence?

So what's the better option? Simplify. I love this word for a few reasons. First, it's preferable to "reduced" because it makes sense that a simplified version of something still has the same meaning/value as the original--now it's just in an easier-to-understand form. Second, I want kids/people to realize that any value can be represented in infinite ways, but we prefer some ways because they are easier to work with, compare, interpret, manipulate, or use in a given situation. Would you want to go to a restaurant where a sandwich cost $1-3^(0!)+300/(4x10)? Mathematically, there's nothing wrong with that price; realistically and emotionally, it's just annoying. If we simplify the price (not reduce because the restaurant still wants the same amount of money), we get a value that's more useful for our brains because the simplified value is easier to compare to what we already know about sandwich prices. Is  $1-3^(0!)+300/(4x10) expensive? Cheap? I have no idea until I simplify it to a value that looks like the other values I could compare it to. It's the same reason why we change the form (not the value) of a fraction when we need to add it to another fraction, or why we sometimes factor a quadratic into a binomial and sometimes multiply a binomal into a quadratic, or why we convert linear equations into slope-intercept form. Math is only useful if we can make meaning from it, so we manipulate values, expressions, and data sets until we can mold them into something that makes the meaning easier to find. We're not reducing anything when we rewrite 32/40 as 4/5; we're simplifying it into an equivalent form that's more useful.

Happy Holiday

About a month ago, I got this in the mail:

Unfortunately, I did not heed the urgency of Atlas Pen & Pencil Corp's envelope and once again Pi Day has snuck up on me before I even realized it. But thanks to the nerdy blogs I read and even nerdier company I keep, next yet I will be prepared with an arsenal of Pi Day-related fun. Here, for your celebratory enjoyment:

This is so freaking cool. Is it worth the time to cut out all those apple and pie crust slices? Probably.

Thanks to this useful allocation of government time and money, I now know what "squaring the circle" means. Dear State of Indiana: do not try to legislate mathematics because it is above the law. Or, more accurately, mathematics is the law.

My students were super-excited that they are going to graduate in very important year, Pi Day-speaking. For the only time in any of their lives, it is their senior year of high school when we will get to have a completely legitimate Pi Day on 3.14.15. Some were more excited than maybe they should have been.

Finally, in case you forgot to celebrate today, fear not. There are many more mathematical holidays yet to be turned into Hallmark occasions and/or crappy math lessons. Some seem to be taken a little more seriously than others.

Happy 'Sorry Your Math Teacher Didn't Serve You Baked Goods (Mostly Because She Wants You To Learn The Correct Spelling Of The Greek Letter)' Day!

A Terrifying Realization

I have not left the country in almost 18 months.

Life just starts passing you by and all of a sudden there you are, your passport glaringly devoid of stamps. My passport is not even taunting me because it's buried in a drawer somewhere. Drastic times may call for drastic flight itineraries.

I could use a little of this right about now:

Sometimes high schoolers are cute

I already gave my final exam, so there is now some down time for my kids who don't also take algebra. I had nothing planned for today, so I broke out the pattern blocks. This group decided they wanted to work together to make one giant, cooperative pattern.

Now they are sitting in almost complete silence, completely engrossed. Every once in awhile they discuss what color or shape to place where. Who says that kids today are only interested in constant, passive stimuli?

I love these kids.

Who Can't?

There was an interesting letter published recently from members of the Palo Alto High School math department about why they disagree with the proposed change to their graduation requirements that all students pass algebra 2. While I am disturbed by the tone of their letter and some of its implications, I will say that I sympathize with what they're dealing with because lately I have been questioning what some of my students are capable of.

Let me start out with a fundamental belief that I hold: all kids can learn and all kids want to learn. I don't believe that each person possesses a limited quantity of intelligence or potential. In fact, I don't even want to consider the possibility because of how that could impact my interactions with my students. I HAVE to believe that all of my students can learn because if I don't, what's the point? I also do not believe that the students are ambivalent toward learning; all of my students want to learn both because they want to be successful and because they value knowledge. Not every student translates their desire to learn into action that leads to success, but I do believe that they all want it.

The Palo Alto teachers state that for "objective reasons" some kids "can't" pass algebra 2. Coming from the belief that all kids can learn, that's a pretty tough statement to swallow. But I have also been wondering lately about some of my own students and, objectively, whether they can pass my class. I am shocked by the math that I'm seeing this year. I am used to kids coming in with weak math backgrounds, huge misconceptions, and severe lack of exposure to concepts one should know by 9th grade, but there are some really tough cases this year. For example, this weekend's homework asked students to measure the circumference, radius, and diameter of five circular objects at home. Then in class we used the data to explore the relationships between those measurements, blah, blah, oh look it's pi, etc. I knew that kids would measure imprecisely, but I was not prepared for glaring errors in the objects they actuall chose to measure. Below, two students' work:

Yes, I had students who think that a knife and an oven and a cell phone are circular. Honestly, what am I supposed to do with these kids? I have to expect that my students come in with certain prior knowledge, and it seems fair that 14-year olds should be able to identify circles. Like the Palo Alto teachers, I have to wonder, can these kids learn high school geometry, let alone algebra 2?

My answer has less to do with can or can't and more to do with WHO is incapable. What I feel is not that these kids can't learn high school geometry, but rather that I am the one who can't. In the context of their past math experiences, and our current school and its resources, as their teacher I cannot give them what they need for them to learn even basic high school geometry by this June. Call it a failure of their previous schools, a failure of the system, and absolutely a failure of my teaching skills, but I can't call it a failure of these students' predestined potential.

Even then, we're still left with failure. I feel like a failure every day when kids aren't learning the things I intended. I look at the systems that have failed my students over and over again by letting them get to ninth grade not knowing what a circle is, or, more importantly letting them go hungry or without a place to live. I don't know whether the failure of all these people and all these systems means that kids should or should not be required to pass algebra 2 in order to graduate, and I don't want to suggest that failures beyond a teacher or a school's control alleviates anyone's responsibility to educate and care for a child. But I get nervous when words like "can't" get thrown around and assigned to parties with little exploration of what is actually impossible.

This is not all meant to sound hopeless, but instead hopeful. Maybe I "can't" teach some students geometry or maybe some of them "can't" learn it, but only when limited by the time and resources we're all working with. But what if there were more time and resources? What if we as a system poured our energy into the belief that all kids can learn? Just as I believe that all kids are capable of learning, I believe that we are capable of educating them. And it's our responsibility to figure out how to make that happen.