My ultimate career goal

Mathematics is wonderful, beautiful, expansive, powerful. But I'm afraid that students rarely leave our current American secondary mathematics education system with that conviction.

By the time most people graduate high school, I would venture to say that, whether they themselves think they had a good or bad experience with mathematics, they actually have a very small idea of what math is. And it is at this point in their lives (when they graduate high school and enter college) that many choose (some more passionately than others) to stop learning math, or at least to avoid learning math (avoid taking college math courses) as much as possible. I'm not upset that at this point they choose to stop taking math classes in pursuit of achievement in other great fields of knowledge and practice, because their desired majors of study may not coincide with more math classes -- we all have different interests and we should each pursue our own unique interests and that's great. But I am upset that at the point of high school graduation, I believe most people haven't learned enough of the right things about mathematics to understand its true nature such that they are able to make a well-informed decision about the degree to which mathematics should be a part of the rest of their lives. They don't have an accurate idea of what it is they're turning away from when they decide that math is not "for them". It's like deciding that you don't like chocolate before you've ever even tasted it. Of course, in turn, these high school graduates become the adults and the citizens of our society that continue to go and live clueless of the wonders in mathematics right under their noses. And this is simply a tragedy.

There are really fantastic supplementary materials out there to help "normal people" access the wonderful, true, beautiful expansive, powerful nature of mathematics (much especially from England comes to mind). I continue to learn and love so much from the passionate work and sharing of resources of individuals like Brady Haran (the Numberphile guy) and Marcus du Sautoy (the mastermind behind "The Story of Maths" among other projects). But why would anyone choose to spend their time looking at supplemental math stuff if they have a poor opinion or even just an inaccurate perspective of mathematics from their school experiences that actually draws them away from the grandeur of mathematics rather than towards it? The opportunity to recognize said grandeur of mathematics should not have to come from some supplemental or extracurricular thing outside of school. Rather, students' regular, mandated, daily mathematics education must be driven by helping students to understand and appreciate what real mathematicians do and what real mathematics is.

My ultimate career goal is to be the liaison connecting every child and youth to authentic mathematics in all its beauty through the schools that they attend every day.

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If you aren't familiar with Brady Haran / Numberphile or Marcus du Sautoy / "The Story of Maths", check out some of these short and engaging YouTube videos!

1) Here are a few of my favorite Numberphile videos:

• "Philosophy of Numbers"
• "The Mathematics of Crime and Terrorism"
• "Mathematical Way to Choose a Toilet"
• "Unexpected Shapes"
• "Fair Dice"
• "Was YOUR Vote Counted?"
• "Batman Equation"

2) Here's a trailer for "The Story of Maths": https://www.youtube.com/watch?v=eDwFElncCxc

The Problem With Many High School Mathematics Course Pathways

Because of the way that secondary mathematics courses are often structured and/or sequenced, many high school students (who then grow into many adults) have a very limiting linear view of the different disciplines of mathematics and furthermore of mathematics as a whole field. I say that students have a "linear" view of mathematics because they usually take a fairly linear sequence of mathematics courses in 6-12 education: Algebra 1, then Geometry, then Algebra 2,... one course after another that has been predetermined for them in a sequence that usually places AP Calculus as the "ultimate" (from the average student perspective) high school math course.

Occasionally, there may be some variation in this linear mathematics course pathway, e.g. a high school student may have the option of taking a statistics course somewhere in the mix, which is wonderful, but unfortunately I've often seen this statistics course referred to (by students and staff) as the alternative to a calculus course for those who "aren't as good at math", which, though it may end up being somehow to some degree true about the course because of the way it's taught and/or the way it's been perceived over time (e.g. it's become a self-fulfilling prophecy for Statistics to be the "easier" mathematics course), it is a huge insult to "real" statistics. But, I digress... And perhaps I'll be qualified to write a more in-depth piece specifically on statistics and statistics education a year from now after I've piloted my school's first statistics program.

In actuality, mathematics as a field is not a rigid linear sequence of courses; rather, its structure ought to be considered more like that of science or even history. In science, there are fields like biology, physics, chemistry, etc. We understand that they are distinct sub-fields, yet we also understand that they have shared natural principles, and although perhaps we must begin by studying one at a time, we can thereafter consider how one affects the other in nature, producing disciplines of study like biochemistry or biophysics, and there is even the study of string theory that seeks the elegant union of all sciences. In history, we understand the distinction of US history, European history, and Japanese history, but we also understand that they do at times interact, for how can the story of the US be told without telling the story of the land from where its founders came, or how can Japanese history be complete without mention of its military exchanges with the US? The histories are at those junctions intertwined, two sides of the same story.

The structure of mathematics must be understood the same way: a set of distinct yet interrelated sub-fields. Geometry is not "higher than" algebra, trigonometry is not "higher than" geometry, and calculus certainly is not superior over all the other high school mathematics courses, and certainly not the end-all of mathematics as a whole field (though it is so elegant and really beautiful). And don't even get me started about the so-called "Pre-Calculus" course... What the heck is that anyway? (I taught it for three years and I can't tell you.) I mean, what is it really? What is the essence of it? And does its content have any true relation with its name? (I think not, but perhaps more on that another time.)

Actually, some even consider mathematics as a whole to be a sub-field of science, at the same organizational rank as biology, physics, and chemistry. Biology is the study of life, physics is the study of matter and its motion, chemistry is the study of matter and its reactions with other substances, and mathematics is the study of patterns. And again, everything is interrelated, intertwined; understanding in one area grants enlightenment in the others.

Doesn't this wider perspective of mathematics make it so much more curious and fascinating? College math majors will understand this far-reaching, diverse view of the field of mathematics as they have to take a variety of math courses in their programs, many of which are not prerequisites to others (e.g. discrete mathematics, linear algebra, real analysis, game theory; but calculus is a prerequisite to many of them, demonstrating what I said before about calculus certainly not being the superior, ultimate epitome of mathematics). But of course, these individuals are not the ones who need to be convinced of the beauty of mathematics since they must have already glimpsed it to commit thousands of dollars to higher education in advancing their study of mathematics. Most others, however, come to this realization of mathematics too late, or not ever at all, their traumatic past experiences in the high school mathematics classes they've taken having made them callused to the very thought of every being intellectually stimulated and amazed by anything with the word "math" in it. How students view mathematics in school will 90% of the time be how they view mathematics beyond school. So it is my hope that secondary mathematics education can shift in ways that will steer students away from the rigid, linear perspective of mathematics as a field to a perspective of the truer, broader picture of mathematics as many distinct but wonderfully interrelated sub-fields before those students grow into adults that will perpetuate the former perspective.

I think one way to make this shift is to throw in as many forks as possible into the secondary mathematics course sequence, leading in to as many different diverse types of mathematics courses as possible. Here's one diagram for a diversification of mathematics pathways that I sketched over a year ago:

For starters at my school, less than 10 years old and still very much in its formative stages, I'll be teaching the very first statistics course of this school. I'm very excited to lead this first step at my school towards broadening students' perspectives of the wide, vast, beautiful world of mathematics.

a snippet of an email

A friend of mine who does ministry work in Oakland recently got her laptop robbed right before her eyes. This is a snippet of an email I wrote her in response to the news:

"...I'm so sorry to hear about your laptop getting stolen, but I'm glad that you're OK and I'm encouraged by your heart within your response to this incident. There was a recent event at my school that helps me to relate to your still choosing to be in Oakland despite the crime. A student brought a knife to school a few weeks ago. Praise the Lord that it was discovered and safely confiscated before anyone was hurt, but certainly the incident was and is cause for students, staff, and parents alike to question the delicate environment and culture of safety that we strive to create and maintain at our school. Several staff members shared how their own friends and family didn't understand why we choose to continue to work in an environment where our physical safety is possibly threatened. Headlines like "Student Brings Knife to School" invoke certain knee-jerk reactions (e.g. fear, blame, avoidance), and understandably so, but this is why context is important. Why did the student feel the need to have a knife with him? Why did the men (or women? don't mean to be sexist) who robbed you feel the need to do so? There are bigger systemic themes and issues and oppressive patterns at play here that you and I are in the work to disrupt, and it's really difficult if not impossible to explain that to those who aren't in the work..."

you can't understand... but i love you trying

I came across this post in which a high school teacher in southern Louisiana, Alice Trosclair, states a few reasons why teachers cannot live "normal lives" that non-teachers don't usually realize: http://www.washingtonpost.com/blogs/answer-sheet/wp/2015/02/05/why-teachers-cant-have-normal-lives/. This spurred me to share some of my own ideas.

I do believe, and find myself somewhat frequently saying that non-teachers simply cannot truly, completely understand the difficulties of being a full-time classroom teacher, especially in under-served, low-income communities. I don't mean to say that in an arrogant or a condescending way; simply in a factual way. There's just no way that you can know without actually experiencing the flurry of real, nonstop day-to-day highs, lows, joys, sorrows, busyness, ambiguity, confusion, craziness, wonders, etc. of teaching. Basically, there's no way that you can claim to completely understand something that you haven't actually experienced yourself. Certainly by the same token, I readily admit that I cannot (at this moment in time) completely understand what it means to work in the corporate world, or in the medical field. Those sectors have their own unique set of difficulties that I won't pretend to be able to fully relate to. There is just no way that I could completely understand, having never worked in those sectors. However, sometimes people don't apply that same principle when it comes to the education sector because most people have spent over a decade of their lives in classrooms as students, growing up and getting an education. So, they do have an extensive amount of experience in the classroom, and so it's understandable to me (but not agreeable) why they think they know something about teaching. But I strongly encourage those people to reconsider because the student experience and the teacher experience are very different. It's not a perfect analogy, but it's kind of like saying that you know how to play basketball really well because you've watched a lot of games. Sure, watching games does help, analyzing them helps more, but if you've never been on the court, you are some combination of arrogant, foolish, and ludicrous to claim that you're a good basketball player. Such things can also be said of non-teachers who think they know what it means to be a teacher.

Again, I say this with the intention of being informative and not condescending. I don't want this to become an excuse for me or other teachers to be moody or to complain all the time, to be inconsiderate of others, or to have to be accommodated all the time, like a man who uses having had a bad day at work to exasperate his wife and children when he gets home. I also don't want to brush aside non-teachers who genuinely want to understand. Everyone has their difficulties, and it's often part of relationships to empathize with them. Just because you can't completely understand, doesn't mean that you can't show your love and support. And in fact, I feel very blessed to be surrounded by many non-teachers in my life who get this, and I dearly appreciate when they lovingly empathize with the struggles that I face as a teacher without pretending like they completely understand them. It only irks me when people talk as if teaching is easy and nothing more than glorified babysitting, and/or a back-up plan because I couldn't do anything "better" with myself (e.g. "You know what they say; those who can't do, teach!") Boy, that really riles me up. Don't get me started. But I would venture to say that Trosclair, the author of the aforementioned article that motivated this post, has heard that, or things like it, from one too many persons, resulting in her article coming off as perhaps a bit -- abrasive? (in my humble opinion). I hope that, while holding the views that I've stated in this post, I can be gracious in my lifetime in trying to correct the misperceptions that people have about teaching. Nonetheless, Trosclair brings up some honest considerations for non-teachers, and I hope that you can read them informatively to construct for yourself a more accurate (though incomplete) picture of what it means to be a teacher.

"Maybe it is selfish for people to be angry at other people for leaving. But that's only natural... That's how we survive."

The school that I work at is essentially in its fourth year in operation. The first year, 8 faculty members left in the middle of the year. The second year, there were 6. Last year, there were 2. The number was decreasing, and it was an optimistic sign that our school culture was improving, that we were moving towards better establishing ourselves as a stable community supporting the academic and personal growth and development of students and their families. Three weeks in to this new school year, 2 faculty members announced their leaving within the next week. This sparked a variety of reactions, emotions, and comments from the rest of the faculty that I found at the least very thought-provoking. These 2 faculty members are leaving to take other jobs. I don't know all the personal details of why they're making these moves to other jobs at this time three weeks in to the new school year, nor do I need to know. I know they both have contributed so much to this school and value our students so much that they would not be making this move at this time unless they pretty much had to. I trust them in that. I have to. That's what a safe, productive urban school has to be built on. But no one can overlook that something like this does have a huge impact on students. In a profession that is so based in relationships, in an urban community where it is not uncommon for students to come in with pre-existing emotional scars from parents walking out of their lives at a young age, and in a school that has already historically had a hurtful teacher turnover rate, the damage that teachers leaving can do has the potential to be absolutely devastating. It's so different than perhaps in the corporate world when, for the most part, people celebrate you and throw you a little good-bye party when you've contributed a lot to the company and now are moving on to bigger and better things. In education, you're almost blamed for leaving in the middle of the year because our work in education is so personal, so built on relationships and community, and when you leave in the middle of the year, you leave a void in that community. Should it be this way? I want to be empathetic to my peers who are upset and angry over our fellow faculty members leaving, but I have to explore the possibility that they're angry because of selfishness. They hurt because of the difficulty that they'll have to deal with and the pain of the students that they'll have to see. But saying that makes me feel insensitive. Maybe what I need to understand is that I can't understand because I've never faced loss like some of our students have, like some of our faculty have. I've never had someone who was (or who was supposed to be) a guardian, a role model, a mentor to me walk out of my life, abandon me, forsake me. I can't understand how much that hurts. I can't understand how much that complicates your feelings and your experiences. Maybe it is selfish for people to be angry at other people for leaving. But that's only natural. That's only human. That's how we take care of ourselves. That's how we protect ourselves. That's how we survive. Is it wrong for my peers to be angry? I can't answer that. You feel how you feel. It's about how you cope with it and what you do next that matters.

So what's my role in this? What am I supposed to think? What am I supposed to do?

how long? how much longer?

As a young working professional in a social culture and era in which it is not uncommon for young professionals to change jobs a number of times before they decide to stay put for the majority of their lives, it is not uncommon for me to be asked how long I see myself working at the school that I'm currently teaching at. I probably even get asked a bit more frequently than your "average" young working professional since I moved 360 miles from where I lived for all of my life prior to moving, so family and friends from "back home" want to know when/if I'm coming back. Well, I don't completely know yet (who really does?), but my current plan is to stay put for at least two years. I don't believe you can fairly and fully enough determine how good a teaching job is until you've been there for at least two years, especially if one of those years is your first year of teaching ever. You've first got to be there for a full year to build rapport, assimilate into the school culture, and let the faculty and students get used to you. Once that's had a year to percolate, then you can get a true(r) feel for what it's like to work at that school and make a better determination of if you want to settle down there. So, as far as it's up to me, given no unexpected extenuating circumstances occur, I plan to stay put where I am for 2-3 years before I "re-evaluate my life". But although I may be postponing the "hardcore", thorough re-evaluation of my life, the biggest, probably-most-determining factor of that future decision is a recurring theme in my thoughts: how will I support the future family that I do desire to have? News flash: teaching is not exactly the most highly valued job in American culture. Sure, people will say nice things and give whole-hearted compliments, but at the end of the day, we see what people value by where they put their money, and it's not in public schools that serve 9 out of 10 U.S. students (http://www.huffingtonpost.com/jack-jennings/proportion-of-us-students_b_2950948.html). I don't care a whole lot about that for my sake -- I care for the sake of society and for the direction in which society is going in given what it values and doesn't value -- because I don't teach for the money in the sense that I don't teach to get rich, but I do teach for the money in the sense that I wouldn't do this for free because I like to eat and have a roof over my head. And one day, I would like to get married and raise kids, and when that day comes, I would like to be able to provide for my future wife and kids to also eat and also have a roof over their heads, and that's not something that I just gain the ability to do overnight. So I have to start asking now if my current position will enable me to do that.

This came to my mind because I was talking with a co-worker today who made the observation when she came to this organization a few years ago that there were many young employees A.K.A. singles with no children. Given that she was also a young professional at the time, I thought that that observation provoked a particularly mature pondering in her: is this organization conducive to being married and raising kids? Because it doesn't really look like it... Today, there are a handful of married employees in our organization (though I would say that the majority continues to be very young people, in their twenties, single with no children), but my co-worker has some serious questions about (1) how they do it and (2) how the quality of those relationships is (perhaps, to phrase it a bit more pessimistically: how much longer they can do it for). Is it just too consuming of time and energy to work at this organization, at least as it is now, and also have the commitment you ought to have (or the commitment I believe one should have) to marriage and child-raising? I believe that the answer is different for everyone because everyone is different and everyone has different capacities. But I'm not sure what the answer is for me yet.

A great day!

A blurb from some time in my first year of teaching:

Today was a great day! Had Restorative Circles with my 1st and 3rd period classes and talked about childhood favorite television shows and childhood dream jobs! These were great questions! They got really excited and into it! Praise the Lord for providing me with these topic ideas relatively spur-of-the-moment! It's been God's grace with these circles, and with my relationships with all my students in general, seriously. Then after school I got to play a scrimmage volleyball game against our girls' team since the team they were supposed to play a game against today couldn't make it anymore! The principal and I pwned them! Hehe! He is pretty good -- I need to find out how he started playing. He has good hands, got some hits, got one super sick block, and was generally commanding our court/captaining our team -- he is the principal after all! I got set up for a few good hits and got a few good serves off too. (I missed a lot of serves too though. :( Can't win'em all... yet!) I love beating my students! =]

Even though things started out rough this week with general rowdiness, things getting thrown around the classroom, and intense workout sessions with students, I think I'm slowly building those relationships and that rapport with students that smooths out rough spots. I still have a long way to go, but I feel like things are starting maybe to look up (or maybe I shouldn't speak so soon...). I was so thankful and encouraged that, of all the things my academic dean could have pounded me about in our meeting on Tuesday, he said his biggest takeaway from observing my classroom was that relationships with students were much better than two weeks ago -- students were more comfortable talking to me, asking questions, being themselves around me. Wow, I was relieved to hear that! Praise the Lord that every good and perfect gift comes from Him!