The 2016 Presidential Elections

President Donald Trump.

Words I never thought I would have to speak aloud, now my reality.

I admit that I spent the evening of November 8 getting more and more upset as the results came in. And I spent the day of November 9 wandering around my house, crying, doing chores, and pretending to work from home. But now it is time to get down to business and figure out what we can and should learn from this election.

There are a lot of things that worry me about the impending Trump administration. I worry that my right to marry my same-sex partner could disappear. I worry that law makers will make it legal to discriminate against me, my boyfriend, and my other LGBTQ friends. I am concerned that we elected a vice president who is anti-LGBT, anti-science, anti-intellectual, and anti-woman. I am nervous about the kinds of policies that a Trump administration and Republican Congress might put in place, with little opposition. But mostly I find myself deeply disturbed about how normalized hate-speech has become. I feel much more unsafe today than I did a few days ago. I fear that I will get called a faggot while walking down the street. I am sincerely afraid of being gay-bashed, for the first time in my adult life. And I dread that I will hear chants of "Trump! Trump! Trump!" as I get hit, as though his election justifies violence against my person. And yet, we must learn from this election.

In the past year and half, Trump called Mexicans rapists, referred to women as pigs, implied that all Muslims are jihadists, said that the inner cities (read: black folk) are terrible, mocked individuals with disabilities, and promised to strip away rights from LGBTQ people. If you are in one of those marginalized groups, like I am, you might have rejected his words and ignored his message. I know I did. His message to white, working class America was clear: you have been pushed out of the mainstream for too long and the America you love is gone; it is time to take our country back.

Trump's is a powerful message, if you can set aside the hate-speech. That this message resonated with voters should not be a surprise. After all, it was very similar to the message Bernie Sanders used to propel himself through the primaries. Of course, Bernie's message was that we should get government to work better for us and that we can fix it together. The core of Trump's message was government is broken and corrupt and he alone is the solution. Both men put together a populist platform. Bernie's was built on hope and optimism and collaboration. Trump's was constructed out of fear and despair and authoritative leadership. Maybe we would be having a very different conversation if it were Sanders vs Trump. Would Sanders' positive message have bested Trumps' hate-filled one? There is no way to know. But we must learn that people across America believe that politicians at the federal level are out of touch with the real day-to-day lives of good, hard-working folks.

Obviously Hillary Clinton did not prevail. Maybe her message was not strong enough. Maybe she was too disliked. Maybe she represented too much of the establishment. Those of us who supported her have to reflect critically on this election and wonder if maybe we were so excited to make the kind of her-story we wanted to see that we ignored the warning signs. However, we must remember that Hillary Clinton has gone farther along the path to the presidency than any woman ever. She didn't get the golden ring, but she did win the popular vote. There will be a first woman president of the United States. It just was not meant to be this time around.

Ignorance is its own kind of hate-speech. White, working-class, rural people have become a marginalized group in America. They feel ignored and dismissed by the ruling elites. I have to believe that not every vote for Trump was a vote for hatred. I know it is difficult to see that today. And maybe it will be difficult to recognize that for a long time. People vote for lots of different reasons. I know military and law-enforcement personnel who voted for Trump because he represented safety and security in a way the Clinton did not. There are small business owners who experience regulations which prevent them from running a thriving enterprise. They did not think about the LGBTQ implications of their vote because that issue is not as important to them. We have to learn about our differences and why what matters so much to you does not matter as much to me and vice versa.

This one is going to be a difficult pill to swallow for those of us with progressive mindsets. Many Republicans and those on the conservative right have spent nearly 40 years pounding away at the same set of messages: Government is broken, Politicians are corrupt, Liberals want to take away your guns, Democrats want to kill your unborn babies, Gay people are immoral, Immigrants will destroy this country, Free trade erodes jobs... The list goes on. All the other side has been able to say is something along the lines of "No, that's not true." Decades of being bludgeoned with mis-truths and outright lies cannot be countered with a simple refutation. If we want to move forward with a progressive agenda, we need to learn how to change the narrative.

I hope we learn, in time, that Trump's election was a watershed moment for American history. One that threatened to send our country back decades but instead thrust forward the next generation of progressive, liberal, intellectual leaders who fought for equality, decency, and prosperity.

The end of another year - Algebra 1 edition

As the school year has ended and vacation has been underway, it is important to reflect on the year that past and look forward to next year. By nature, I spend a lot of time dwelling on both the past and the future while not considering the present too often so this should be a breeze for me!

In truth, I have had an extremely difficult school year. This, without doubt, the most challenging group of students I have dealt with in 17 years of teaching mathematics. There have been ups and downs and while it is easy to focus on the bad stuff without acknowledging the good stuff I want to try to give equal treatment to both.

My 9th grade Algebra 1 students were tough... tough to manage, tough to motivate, tough to encourage, tough to engage, tough to have them think... Many of them came from special education classes where the teacher never taught a full year's worth of math. They had low expectations from the adults in their lives and they had low perceptions of themselves. Despite the deck being stacked against them in pretty much every way possible, we managed to work our way through the entire Algebra 1 curriculum with two weeks to spare before the state test. I am incredibly impressed with what they accomplished this year. Maybe we went a little too fast but I am reasonably confident that most of the students can solve an equation, graph a line, calculate/identify/interpret slope, add/subtract/multiply/factor polynomials, and perform some data analysis. What more can I ask? Well, I suppose I could ask for my students to comply with requests the first time I ask. In fact that is probably the single biggest reason why this year has been so challenging in Algebra 1. I ask nicely for a student to do something and he/she refuses because he/she simply does not want to do it. These are just a few samples of the exchanges I've had:

Vignette 1
M: Please put your phone away. 
S: No, man. Why? 
M: Because I asked you to and because we are going to take notes and you won't need it right now. 
S: I pay attention better when I'm listening to music.
M: You probably don't. Please put your phone away.
S: I'm not even using it.
M: That doesn't matter. Please put your phone away.
S: Fuck you, man. I don't have to listen to you.
M: I've asked you nicely several times. I'm going to ask you one more time. Please put your phone away.
S: No.
M: OK, please go to the office.

Vignette 2
M: Please get away from the window.
S1: (ignoring me, speaking to another student) Yo man, you won't drop your phone out of the window.
M: Please do not drop your phone out of the window. Please get away from the window.
S2: How much will you pay me?
M: Please get away from the window. Please do not drop your phone out of the window.
(S2's phone gets dropped out of the window and students cheer. S2 runs out of the room to retrieve his phone)
M: S1, please get away from the window. (no response) 
M: S1, please get away from the window. (no response)
M: S1, please get away from the window.
S1: Chill, bro. You don't have to yell.
M: I was trying to get your attention. I asked you several times to get away from the window.
S1: You don't have to be a fucking dick about it.

Vignette 3
M: S3, please stop talking and write down what's on the board.
S3: Why should I stop talking, S4 is talking too.
S4: You never shut up. Just do what he asks.
M: Both of you please stop talking. I will worry about who is working and who is not working.
S4: Yeah. You should do your work. You're so annoying.
S3: Shut up. You're annoying.
M: Both of you! Stop talking and copy down the notes. 

An exchange like one of these happened at least once per period. It has been demoralizing and depressing and debilitating. Every two steps forward was met with one step backwards. I know that's a bit of a cliche, but it feels so true. Setbacks are a necessary component of learning and a natural part of school but to be in a near constant state of rehabilitation and recovery has been mentally and physically exhausting. If I had to measure the good and the bad and weight them against each other I think Algebra 1 would be pretty balanced. The significant academic growth my students made was systematically offset by considerable behavioral issues.

I know that I am teaching Algebra 1 again next year. I am not sure how I feel about it. I recognize that I get this class because very few teachers in my department would be willing to teach this class (or "these students") and I think that the administration believes that I can handle it. I know there are things that I have to do better this year, starting with a new classroom management plan. Luckily, I get to spend the summer contemplating what I need to do to make this coming school year run more smoothly.  

NCTM 2016 - Making Sense of Logarithms

Powerpoint and Notes

Thank you for the attendees who noticed that I have an error in the slides. I have a decimal place in the wrong position: 
10^3 * 10^0.6435 should be 1000 * 4.40, not 1000 * 0.440

My Review of "Building a Better Teacher"

I've been struggling with my classes this year, so I've been revisiting some books about teaching. When none of them gave me any insight into my dilemma this year, I decided to try some new material. Aimlessly browsing through the neighborhood Barnes and Noble, I came across Elizabeth Green's book with the incredulous title "Building a Better Teacher: How Teaching works (and How to Teach It to Everyone)". After skimming a few chapters and recognizing some names from the world of education (Lee Shulman, Deborah Ball*, Magdalene Lampert, Doug Lemov) I decided to give it a try.

I'm not sure what I was expecting when I brought it home, but what I read wasn't it. That said, I liked the book. It was an enjoyable read and I would recommend it to anyone with an interest in teacher education. It probably would have been more accurately titled, "A layman's guide to the history of the research on teaching from 1980 through 2015", but who would buy that book? I thought it would be helpful to write a short review of the book to help me process what I read.

Truthfully, I'm not sure that I read a lot that was very new to me. I knew that it had been long argued that teaching is difficult intellectual work. I was pleased to see that Green was not at all dismissive of the challenges of the classroom, as are some writers on educational issues. What was helpful for me was Green's agnostic and critical stance on schools of education and educational entrepreneurs. She argued that each camp was engaged in the same goal: to describe and classify effective pedagogy so that it can be taught to aspiring teachers. However, she was careful to acknowledge that each camp was differently equipped to attack the problem. Schools of education are often fighting a culture and value war about what teaching should look like, what Dan Lortie called the apprenticeship of observation in his seminal work, Schoolteacher. The education start-ups entered the fray explicitly rejecting what schools were in the hopes of creating what schools could be. Many schools of education are research institutions which means (hopefully) that they are thoughtful about what teaching methods to try and how to try them responsibly. And they should be well-positioned to collect and analyze the data in both a qualitative and quantitative way. The charter schools were more or less haphazard in collecting information about student achievement and trying to match it to effective teachers. 

What both camps seem to have in common is the belief that good teaching can be taught! That is a pretty revolutionary idea. I've heard a lot of people say that good teachers are born not made. I've had administrators tell me that I'm just a "naturally good" teacher. I believe that the notion that some people have a gift for teaching and others don't is dangerous for (at least) two reasons. For teachers who work very hard at improving their craft, being told that they are "naturally good" demeans and discredits the effort they have put forth. For teachers who think that teaching is a talent, it releases them from any responsibility to get better; it absolves them from all pedagogical sins. How can we improve as a profession if we don't acknowledge that some instructional practices are more likely to result in student learning and others are less likely to bring about the desired results?

In the conclusion to Green's book, both camps constructed lists of effective pedagogies. Deborah Ball and colleagues put together what they call "High Leverage Practices" which are a set of "fundamental capabilities" that they believe all teachers should master. All of the practices and more are available on their website dedicated to improving teaching. Meanwhile, Doug Lemov published a book. "Teach Like a Champion" that documents his taxonomy of effective teaching "techniques". I know that some people have been dismissive of Lemov's approach because it feels like behavior modification. But, Ball's cognitive stance could be critiqued for emphasizing thoughts over actions. I don't think it's fair to compare them. I think that a thoughtful and critical teacher should be reading and using both of them to inform and improve his or her practice. That's what I'll be doing. 


*Deborah Ball is a widely recognized authority on mathematics education and I had read much of her research. Also, my graduate school advisor was a student of Deborah Ball so I like to think of her as my academic grandmother.**

**You know, a grandmother who lives halfway across the country, whom you've never met, and who most likely has no idea what you exist. So, we're not close.

Monmouth University - February 15, 2016

Thank you for allowing me to speak about my research. Here are links to PDFs of some relevant additional information:

Power Point Slides

Task Interview

Framework

Classroom Vignettes

Nuts & Bolts of Online Teaching

After reading a chapter from Kristin Kipp's book on online and blended learning, I couldn't help but think, "why didn't we read this weeks ago?". The chapter provided some very grounded suggestions in creating a syllabus, managing student information, and how to maintain teacher presence. All of which were exciting to read, but I felt much too late in the sequence of readings. This chapter, and maybe more chapters from her book, could have been used to ground some of the other more theoretical readings. Don't get me wrong, I love reading about learning theory. I really do find it an interesting subject! I just wish we had tried to create more of a bridge between theory and practice. 

That said, what I mostly got out of Kipp's chapter was that online instructors must put a lot of thought into their course design. But, face-to-face teachers should put a lot of effort into their course designs also. In an online or blended format, teachers also need to consider how the user interface could affect how students engage with the course content. Well, face-to-face teachers should probably consider those things too. How does the classroom environment influence what and how students will engage with the content. Teachers should think about the environments in which their students will learn whether online or blended or face-to-face? Yup.

Actually, that there isn't really that much difference between high quality face-to-face teaching and online teaching is pretty much the same take-away I had from DiPietro et al's piece on best practices in online teaching. (As an aside, I think it was on Twitter this week that someone criticized the term "best practices" because it encourages copying the technique without analyzing its affordances and constraints and thus effectively shuts down innovation.) Their extremely detailed and extensively descriptive table of findings was interesting. While reading through it, I just kept thinking, "shouldn't all teachers be doing these things?". The medium is obviously different in online teaching, but the actions and intentions of the teacher aren't that different. Good teaching looks like good teaching whether in an online or blended or face-to-face format? Yup.

This entire semester hasn't really convinced me that digital technologies can supplant traditional ones. Supplement? Yes! Replace? Not sure. There's some research that suggests that writing notes by hand is better than typing on a computer. However students who need help visualizing some of the more esoteric and/or abstract mathematical concepts can reap huge rewards because of what digital technologies can do. Form should follow function. First we need to figure out what students are supposed to learn then we can choose the appropriate technologies.

Technological Tools for Teaching

Mishra and Koehler have a really interesting take on technology and teaching. I think I read somewhere that if you want to get ahead, you have to get a theory. It seems like they've done just that. Rather, they've expanded an existing theory to explicitly include educational technologies.

I'm pretty familiar with Shulman's construct of Pedagogical Content Knowledge. (In the math ed world, Deborah Ball and a few others have proposed a special domain of teacher knowledge called Mathematical Knowledge for Teaching (MKT) which is located partly within PCK and partly with Content knowledge.) I really liked Misha & Koehler's Venn diagram for PK and CK and how they included a separate but overlapping domain for Technology Knowledge. I couldn't help but wonder if there are aspects of MKT that exist within the sphere of TK or any of the other categories they created. I'm sure there is. 

I also couldn't help but wonder if TK is more correctly placed within one or both of the other domains. Is it really a distinct domain of teacher knowledge? Maybe it is. I could go either way on it. Maybe the tipping point for me is that TK is not just about knowing about and how to use both traditional (black/white boards) and advanced technologies (computers/mobile devices) but is also about the ability to learn about existing and emerging technologies. When we started to introduce Interactive White Boards at my school, there were more than a few teachers who resisted them and complained loudly that the IWBs were placed in the center of the existing white boards essentially removing at least 1/3 of the board space. I liked the idea of the IWB but was also wary about its location in the room. Now, I am so glad that my principal had the foresight to put it front and center in the classrooms. I cannot imagine teaching without an IWB now. Many of the same teachers never really explored what an IWB can really do for your instruction. Students used to marvel at things that I did on the board; things that seemed routine to me but that other teachers hadn't tried to do.* I always figured that I couldn't do any permanent damage and that I should just try some stuff. We used to characterize that kind of attitude towards technology as being a "digital native". Mishra and Koehler conjecture that it's part of a special domain of teacher knowledge. Perhaps it is.

Perhaps TK is becoming so much a part of what we do that it really isn't separate domain of teacher knowledge. Last semester I had the opportunity to teach a course on technology in mathematics classes. I had anticipated that the students in the class would want to know about how to use hand-held graphing calculators to enhance instruction. I was very wrong. We did a few activities but they students seemed mostly disinterested. I have a few ideas why: 1) graphing calculators have permeated mathematics instruction so thoroughly that the students in the class, who were both preservice and inservice teachers, had already developed a familiarity with what the graphing calculators could do ; 2) the way I was using the calculators had not really occurred to them before and what I was doing was maybe a little too weird and different to really understand ; 3) the graphing calculators have been around for a while and the graphing capabilities are subpar when compared with newer technologies ; 4) the graphing calculator has a pretty steep learning curve and it often produces static results while newer technologies are considerably more intuitive and are much more adept at producing dynamic results which makes the graphing calculator a difficult tool to use. These are just a few of the reasons why I think the students were uninterested in graphing calculator but did take to other technologies.

One anecdote can't make a theory, but it might provide a little evidence that maybe TK is just part of what we do as teachers. Teachers with better / more developed TK or TPCK can use all sorts of technologies better or more flexibly. They can also adapt to new technologies faster because they have that kind of disposition. And maybe they even seek out or invent new technologies when existing ones can't do what he/she wants. It's certainly an interesting construct and I'd like to learn some more about it.

*Kids used to marvel at the IWBs. Nowadays there's a lot less awe. I think its because the crop of students I have now have had IWBs for pretty much their entire school career. It's hard to get excited about something that's been part of your routine for 10 years.