Matthew Daly

Well, I've been absolutely horrid at posting. I had a grand notion of reflecting on each of my classes after they happened, but, well, I didn't. Just a week left of classes yet, which will be followed by a few finals culminating activities, and then a month and a half of decompression.

One thing I didn't want to let go was my philosophy of (inclusive) education.  I think this is like the third or fourth time I've had to write one, but this is supposed to be the final one that will allegedly work its way into my job applications and whatnot, and so this one was actually read and critiqued by my professor.  He seems to get a kick out of it; as a school psychologist, he says that he has too much experience with seeing first-year teachers who are disillusioned by the reality of classroom management., so getting to ask ORLY at this phase in our professional development is a good move.

Anyways, I submitted enough drafts that my professor either ran out of questions or got sick of reading it, so here is my final draft which already got full credit.  SPOILER ALERT: I am either planning to be a radical educator or I am the king of snowing my professors with the current generation of dynamic buzzwords.

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I affirm the inherent worth and dignity of all people, and I strive to use all of my talent, energy, and passion to provide a personally meaningful and practical mathematical education for all of my students. Every decision I make inside and beyond the classroom is, in some sense, a conscious reaction to my pursuit of this purpose. The following is a detailed but non-exhaustive list of specific strategies I undertake to achieve that ideal.

I define mathematics as “the systematic and objective process of making optimized decisions efficiently.” This includes learning how to perform numeric calculations, solving word problems, and other similar general tasks of primary and secondary mathematics. In the end, though, I believe that productive members of society must understand the range of decisions that they make throughout the day and the ways in which data is acquired, analyzed, and evaluated to make good choices and the ways in which both the choices and the processes are evaluated so that future decisions can be more easily and correctly rendered. For instance, if my students learn enough from about percentages and unit prices to pass a standardized test but not enough to be more strategic shoppers, then I will feel as if I have let them down.

To achieve that end, I believe in the principles of constructivist learning. As the mathematical tools students learn will be used by them throughout their lives, students must have an individual and intimate comprehension of those tools and how to apply them. When we teach a single perspective on a lesson and train students to apply it to solve a specific model of word problem, it should come as no surprise when students are unable to retain that knowledge past the unit test, much less when the lessons are built upon in future mathematics and science courses or in the real world. Only by giving students the resources and motivation to assimilate their knowledge into their own schematic understanding of the world will we provide authentic learning that the student can apply throughout his or her educational life and beyond.

Critical tools I use to showcase these diverse perspectives include small-group inquiry, peer learning, and a diverse array of multimodal media to explore problems in mathematics and the range of applications they have in the real world (focusing where possible on professional careers that require strong mathematical skills). An example that I often steer my students towards is the Khan Academy, which offers a thoughtful mathematical perspective that is often different from both my technique or the textbook's.

I believe that a teacher must be aware of and sensitive to the diversity of race, ethnicity, gender, religion, sexual orientation, gender identity, exceptionality, age, and socioeconomic status throughout our society. However, such a multidimensional cultural profile is only the first stage in forming authentic and respectful relationships with our students. Multicultural awareness is beneficial for roughly interacting with a group of people without unintentionally giving offense, but we must seek to destroy our stereotypes as quickly as we build them as we strive to know and serve our students as individuals. These plans require a foundation in a classroom culture of respect: my overt and consistent respect for all of my students and for the curriculum, my students’ respect for both me and for each other, and the students’ having respect for themselves as individuals, learners, and teachers.

To create this effective and inclusive classroom, I subscribe to the philosophy of culturally responsive teaching. My students have a diverse array of perspectives and differ in terms of the best strategies for educational success, and so I would be negligent to teach only in a way that benefited most of them or only in the way in which I was taught. For instance, lessons and projects should be customized to match the interests of a class to maximize their engagement, and vocabulary lessons should be structured around the linguistic strengths of each student. I also strive to take advantage of the diversity of perspectives and mastery amongst my students and use peer learning to further promote personal inquiry and self-constructed meaning, because there is no more effective and authentic teacher for a struggling student than the peer who just came to comprehend the material.

In the domain of assessment, I tend to be a follower of the theory of mastery education. Particularly in mathematics, there is little sense in advancing a student before he or she has a solid understanding of all of the standards that form the foundation of the new class. However, I believe that students deserve a broad range of options to demonstrate those competencies and that we should be open to the realities that many students do not do their best work on multiple choice exams under time constraints. For these students, the most authentic testing accommodation we can offer is alternative assessment, like journaling, oral examination, or service learning. If the grading criteria are tied to established objectives like the CCSS, calibrated against standard assessment measures, and performed with a passion for student success, I am confident that the result will be a measure of achievement that will provide a relevant supplement to the traditional measures. And when you demonstrate in word and deed that the education program can be catered to meet each student's’ talents and interests, the result is bound to be an increase in motivation and engagement that will enable the greatest possibility of positive outcomes.

I think it all starts with word problems.  This is contrary to the model of American math education, and maybe beyond.  We teach you the skill and then teach you how to apply it.

You know what, though?  I'm not the one who is backwards on this.  Remember Psych 101?  When a person is exposed to a new piece of knowledge, she will attempt to incorporate that fact into her worldview.  If she can't find a schema for it or hasn't developed an advantageous strategy for assimilation, then she's barely better off than if she hadn't been exposed to the fact in the first place.  On the other hand, if she can effectively identify a schema and assimilate the fact into it, then her worldview is expanded and she is embiggened by the process.

Not everyone has had Psych 101, I suppose, so I'll illustrate.  Let's say that a young child sees a German Shepherd, which is the first time that she recalls seeing a dog that is as big as she is.  She doesn't know what to make of it; perhaps she is inclined to think of it as a "big animal" like a pony or a goat, except that she has developed a sense of "dogishness" (that adults would call "canine") that this animal satisfies in many ways except size.  That sense is her schema of "dog", and when an adult tells her that German Shepherd are also dogs, she is able to broaden her schema to understand that dogs can be big and perform tasks beyond companionship. 

However, this model is exactly what we don't do in math education.  The skill comes out of the textbook through the blackboard without giving any sense of how it works into your worldview.  This is tragically short-sighted, since mathematics is actually the formalization of the modelling our ancestors did to solve their real-world problems.  Sometimes we are so busy answering "how" that we forget to ever get around to "why".  Some students can get it anyways, of course, but we're far too comfortable with thinking that when other students can't get it that the problem is with the students and not with the math instruction.  Back when I was in high school, if 80% of students barely understood math and 10% of students mastered the concepts, we'd have enough understanding to sustain society's population of alphas and betas.  We don't live in that world any more; machines are currently doing much of the work that used to be done by Deltas and the Gammas are next in line for reassignment.

Let me give you an example I use at the beginning of one of my pre-algebra lessons.  I am leading a full-day field trip, so I made some packaged lunches for the adults and children.  Each adult lunchbox contains seven crackers and five pieces of sausage, and each child lunchbox contains three crackers and two pieces of sausage.  If there are ten children and four adults on the field trip, what is the total inventory of food in the lunchboxes?  Go ahead and solve that problem: note that it is a moderately difficult arithmetic problem that requires a few steps.  Still, in my experience, it is not beyond the intuition of the sufficiently motivated student to understand that they want to "dump out" all of the lunchboxes and gather all of the similar foodtypes together.  I've got a follow-up question too -- did you come up with fifty-eight crackers and forty pieces of sausage as your solution, or ninety-eight food pieces?  Whichever answer you came up with, why did you settle on that as the better answer?

So, once people have worked out a few problems like this in small groups, I show how you would solve this in "algebra language":

10 ( 3C + 2S ) + 4 ( 7C + 5S )
30C + 20S + 28C + 20S
58C + 40S

See, I don't need to drag students on a trip to appreciate how to simplify algebraic expressions using the Distributive Law and collecting like terms.  They made that trip themselves.  My job as a teacher is to point out some of the highlights they'd have spotted along whatever journey they made, and they're going to be able to retain and apply that knowledge effectively because they had already engaged their schema for solving pre-algebra problems.

So I seem to have stepped out without turning off the lights first. Um, what to say....

First, I'm fine, and I've been fine. I've been working on having a more deliberate life (in Thoreau's sense), which in the context of the internet means a life made up of people that I can see and touch while I'm communicating with them. That has been quite an effort, and I can still see ways in which I need to continue to improve, but at the same time it has been entirely rewarding. I can see the value I'm bringing the world and aware that there are things that would have gone undone had I not been there to do them.

So, I'm back, and I've got some thoughts about what an internet soapbox offers to me in this chapter of my life. My brain is cramped with all of the facts and debates of educational philosophy and praxis. I need to sort out how to be an effective and authentic partner in learning and development and how that interfaces with the epistemological and pedagogical realities of the secondary mathematics curriculum. (Trust me, I have a graduate school vocabulary and I'm not afraid to use it.) I'd like to get it sorted out in the company of thoughtful people so that it will come out clearly in a job interview or a conference. If my classes are any indication, publicly wrestling with my own synthesis is productive for others whose journeys are like mine. And it's nice for me to be able to re-incorporate all the dear people who are outside the range of my eyes and hands.

So I promised in an earlier post that I would talk about the anti-racist mathematical movement as I understand it (which is admittedly not well yet).

At a certain level, it seems to be a web of issues and I will mention them and then leave them without support or defense. One complaint is that mathematics is taught from the perspective of how it came to be understood in Europe, which often times ignores that virtually all of elementary mathematics was independently discovered by every culture in history (Chinese mathematics in particular often beat key European discoveries by a millennium or more) and that mathematical discoveries that Europeans knew were often the product of Arab, Indian, and Egyptian influences but we often don't highlight those contributions as such. This bleeds over into the same sorts of "dead white man" issues that literature and the physical sciences have faced over the years -- both that mathematical discovery is closed and that people of color have no talent for it anyways, which will discourage a student of color from mastering the material and furthermore from contemplating a career in a mathematical field. And that, in turn, is connected to all of the other ways that we fail to expect mathematical mastery (let alone excellence or prodigy) from students of color.

As I say, there is no lack of very important discussions to be had there. And my role in those various discussion would range from pulling out my cheerleader uniform to mildly defending the status quo all the way to heavy skepticism. I cannot help but become more informed as my own education continues, so perhaps I will someday come to know enough to speak on some of them in the future. In the mean time, I will speak of my first-hand experience with an issue here that I do know.

(For those who haven't been following along at home, my experience is as a math tutor for students studying for the GED and other related math tests at around the 8th grade level in the United States. My students are mostly black and Latino, nearly all female, I suspect virtually all living in poverty, and a significant number attempting to overcome learning disabilities and similar challenges.)

I will illustrate with an actual example that happened in the past week. About half of my students are taking a formal GED math class that my tutoring sessions are intended to supplement, and this past week they took the Official Practice Test. (A sufficiently high grade in this test would allow them to "graduate" to being allowed to retake the Math portion of the GED.) Here is a relevant portion of a question from that test. I won't display the rest of the question because the last thing I need is a cease-and-desist letter from the ACE, but trust me that an understanding of this sentence is a fundamental part of solving the problem. Again, I want to highlight that this is not a third-party product but an actual question generated by the American Council on Education that is a part of the gate-keeping process for GED diplomas.

"A restaurant menu lists 5 appetizers, 6 main dishes, and 4 desserts that are specialties of the house."

When I reviewed this question in my class, one of my best students shot up her hand and said "I'm sorry, but what does 'appetizer' mean? I'm sure I've seen the word before -- I mean, it's not like I've never been to a restaurant -- but I don't know if I've ever had one." And a few of us kind of talked out that it was like a plate of potato skins or chicken wings or shrimp cocktails that everyone at the table could share while they were waiting for the main dishes to be served, and she seemed to get it (although it was an embarrassing topic for her so I can't be certain).

But you see what happened there. If you're a middle-class white kid like me whose family ate out at sit-down restaurants on the average of once a week, you're answering an easier question than that student of mine did. Because we know that an appetizer isn't a specific sort of main dish, so we just multiply those three numbers together and move on. My student has to go looking deeper for contextual clues to figure out how to process these numbers. I can accept the argument that those clues are buried deeper in the problem, but there is a larger probability that she's going to miss those clues, and even if she does find them she will have less time and less morale than someone who "just knows" these non-mathematical facts.

And this is the sort of thing that you find quite a bit of once you're looking for it (and it is even easier when you have students who are comfortable enough to "admit" that it's their fault that they don't understand poorly-worded questions). How many days are there in June? What is the standard restaurant tip? What is an "at large" delegate? What does "reservoir" mean? Some of these questions are less unfair than others, and reading comprehension and setting up word problems are truly valuable skills that need to be tested. But when the word problems that you set up are biased against some classes or cultures, you really don't get to then dump on those classes and cultures for underperforming on the test.

I should start getting used to talking about me, especially since I'm doing some interesting stuff that I'll probably have to be talking about before long.

I've been spending the last handful of weeks as a volunteer math tutor for the Rochester Educational Opportunity Center, helping folk to get their GED and qualify for an LPN license and similar sorts of job training and college prep opportunities. The organization I am working for is a non-profit affiliated with one of our local state universities that does all this training tuition-free for qualified prospective students (and it seems like pretty liberal standards to establish the economic need) and it really seems to do a lot of good in helping people to chart out a better future. For me as well: it's not a paid position and doesn't even count as field work for a Masters in Education (even though the affiliated university is the one at which I'll be studying), but it'll be a leg up to have the experience in both the schmoozing sense and in being actually prepared for a room full of adolescents.

And so far it's been going really well. The staff is thrilled to get all the help they can, and they've been very helpful and welcoming. The students have been very generous with their praise as well, and even though there is selection bias in my hearing primarily from the sorts of student that I am helping, I can also objectively see that they are growing from one class to the next. That has more to do with my students being eager to be taught and willing to invest the time and brainwork than in the role that I'm playing, but again I am a critical catalyst in that reaction and if I don't give myself credit for my part then I can hardly expect people down the road to independently offer me future opportunities.

At the same time, it has been very challenging and I have yet to even comprehend the scope of the challenges. Math anxiety is a significant hurdle, and I don't have any specific strategies for dealing with it. (Nor do I have any personal experience with it at this level no matter how much I know about other sorts of anxiety.) I have also come to appreciate that people who talk about anti-racism math have their thumb on a very real and important problem. Again, I see it when I see it, but I'm still soaking in it and I've got to figure out how to confront that. 95% of my students are women, 90% are people of color, and I'll go ahead and guess that at least 95% of them aren't commuting from my upper middle-class neighborhood. In short, the only thing that comes easily to me in this class is the math.

But those last two paragraphs are both true and coexist in balance. My best isn't good enough, and my students deserve even better than my best. But that doesn't mean that I shouldn't do what I can do. The alternative to me teaching this class isn't Jaime Escalente taking over the class for me; the alternative is no class at all. I need to fail a little bit better every day, because a lot of people are still going to succeed in spite of me because of me.

I voted today.

In the New York primaries.

They don't have the awesome tamperproof mechanical voting booths any longer.

The replacement technology doesn't have a big red lever that makes a definitive and satisfying KA-CHUNK sound when you pull it and register your vote.

...

That is all, I guess.

NORMAN, Okla. — Prolific mathematics and science writer Martin Gardner, known for popularizing recreational mathematics and debunking paranormal claims, died Saturday. He was 95.

Martin Gardner was the most influential of my math teachers in junior high. I didn't get credit for his classes, but he taught me that math was far more interesting than what the official curriculum was revealing. He, along with Raymond Smullyan, turned me from a student who liked math into a nascent mathematician. I cannot imagine how my life's journey would have been different had I not been exposed to his work.

Rest in peace, Mr. Gardner.

So shortly after writing yesterday's post, I got an email from my Census boss saying that those of us who didn't get enumerator jobs could maybe do some clerical work this week since it is OMGWTFBBQ week preparing all of the casebooks for everyone who didn't mail in their forms. He gave a phone number which ... didn't get answered by a person and the voicemail was ignored for at least an hour. I then made another one of those bold decisions that I've become capable of, that since I know where my grandboss sits I can go see her even though if I don't know the number of her direct line. The worst that could happen is that I get escorted out by security.

The best that could happen is what did happen. I said "I heard you need help", thinking that she'd tell me when to come back. She brightened and said "let's find you a chair!" and I spent twelve of the next thirteen hours working. And and my chair turned out to be right next to the superboss who was the most capable of being concerned about my falling through the cracks and working to get me into the final round of training next week when all this dust has settled. That's no sure bet, but at least this time I'll know. But at the least, making the decision to seek my fortune instead of waiting by the phone probably made me nearly a thousand dollars in income this week alone. There's probably a moral in there somewhere.

The work itself is routine office work with the printing and the collating and the cross-checking and the metric-keeping. But it's fascinating to be there. First off, during a recession, Census workers turn out to be the cream of the unemployed crop, so everyone is a caterer or a masseuse or a retired businessman with a lifetime of world travel. Plus we all get to comment on how inefficient the work processes we're doing are, and how we'd do things differently to make the work easier for people in the field. And I even get to share my bounty of Excel wisdom with a cow-orker who needed to make a spreadsheet report. So that was my lesson for the day, both in my work and in my work outlook: to find the awesome you've got to penetrate the corporation and meet with the people. They're awesome and smart even if they look neglectful and ill-conceived from a distance.

Also, holy cow I don't know for certain, but I think I printed out and ran my hands over 7000 pieces of paper yesterday. I'm not sure I've ever done that in a month before now. Now I've got to go make lunch and head back so I can collate and punch holes in those papers I think.

I've said it before, but if Wonderella and I agree that you are off the rails, then dude, you are seriously off the rails. However, people seem to eagerly argue that the KFC Double Down "sandwich" is the greatest abomination in fast food history.

Please.

Even if you handicapped them by putting a bun around it, it's a double chicken sandwich with cheese and bacon. That doesn't even survive the first round of the Fast Food Abomination playoffs. When I was living in California, Jack in the Box would routinely offer specials like double cheeseburgers with three slices of cheese, five strips of bacon, and ranch dressing. But this? Burger King has spent years with "buy one chicken sandwich, get one free" coupons, and you have to know that customers were routinely eating both of them in the same meal. Take a deep breath.

My only question is why people are going into a KFC and ordering processed products like this when their signature fried chicken is so outstanding and you can just SEE that it's made out of a whole chicken with breading and fried in oil and nothing mysterious except exactly what the specific herbs and spices are.

On a slightly broader and less silly note, Nate Silver at 538 does an interesting deconstruction of the issue (which is a great relief from that site's normal operation these days of relaying Obama's talking points without even pretending that it's about poll analysis or statistics any more), and I think he is onto a good point when he talks about the utility of understanding nutritional benefits and harm per calorie. I think that there are two tough parts about meal planning with an eye towards maintaining weight. The first is making sure that you're taking in the proper amount of calories considering what you burn off through your basil metabolism and exercise, and the second is making sure that you don't accidentally shoot your entire wad of sodium or polyunsaturated fats on a single small portion of it. And the data that we get doesn't always do the best job of driving that home. I don't think that Silver has the magic bullet right off the bat, but it's an interesting avenue for exploration.

Barring any surprises, the facility enumerating phase of my Census work ended this afternoon. Then more training next week (with our team being split into as many as twenty-one pieces waaaaah) for the door to door operation. It was a lot of fun, being a beautiful day and kind of a FUBAR dorm to count so we stretched out the schedule to make a few final passes of the floors that we were assigned to maximize our count and put off the inevitable breakup for an extra half hour.

But something happened. Yesterday I went through my floor interviewing the people I could find and leaving forms for the people I couldn't, except there was one woman who I met that was too busy for the interview so I left her the form. So I come around this afternoon to pick up the forms, and hers has a post-it note saying that she's a photography major and would I mind if she took some pictures of me?

And, I, uh, well, huh.

I know my powers of self-image are totally borked, and also that I'm not a horrific looking person especially if I make an effort to clean myself up. I can smile at babies in checkout lines and they smile back, so I'm aware that I'm not a freak. But I never like pictures of me. I don't know if it's the freezing in time or the perspective switch needed to form a two-dimensional image, but I can pretty much count the number of pictures of adult me that I've liked on one finger. In fact, the very reason I don't have a userpic here or on my LJ despite having a digital camera and a USB port is that this process is one of the things that I'm afraid of.

I'm going to sleep on it, but I think I'm going to agree to her proposal. I'm certain to learn something. But I can't stop looking at my bottle of clonazepam and asking WTF is in these pills that I could think of agreeing to model for a woman that I only met for twenty seconds. Strange days indeed.