Alright, so in the name of honestly, and being encouraged by Kelsey's blog, here's how I'm currently feeling. I don't love math. I've always been able to pretty easily understand math concepts and get good grades on the test, but I've never really enjoyed it. Throughout the last few weeks I've been on a journey (as a junior in college) to figure out what I want to do with my life. For a while, I thought teaching was cool, and although I was never 100% hooked on it, it was my plan. I don't quite know what my plan is now. In this blog, I'm going to expand on some of those thoughts, and I'm going to talk about why this math class, and a couple others I've really enjoyed, was different for me.
First of all, I should clarify something. When I say I've never really enjoyed math, I mean that I've never been the type to totally "nerd out" about some math concept and learn extra than I have to about a specific math concept. BUT, I have liked math classes. I've had some awesome math teachers, and I've found a few common trends with these teachers.
From my experience, every good teacher is passionate about at least two specific things. (Hopefully more too, but at least two to make them a good teacher). They must be passionate about their subject area and their students. When I took geometry during my primary education years, my teacher & I did not get along very well. Both teachers I had for Algebra I & II, I loved. If you were to ask me if I'm more of a "geometry person" or an "algebra person", I would easily say the latter. Coincidence? I think not.
Those awesome teachers I had both loved math. And when I say they loved it, I mean they loved it. They would talk about it in conversation out of class, and you just saw they joy they had getting to teach it.
These teachers also loved their students. They wanted their students to do well not for the district assessment, for their payroll, or anything like that necessarily, but rather because they wanted their students to grasp the passion they had for math, and have that passion too. They loved the students they were teaching. There definitely is a place for people who love math and don't love the people aspect of it as much, but that place is not a classroom.
As I have been processing these things, the main reason I'm rethinking this whole teaching thing is because, if I'm being honest (which I am), I lack one of those. If you know me at all, you'd have no doubt that I LOVE people. But, as I mentioned, I don't absolutely love math. I want to be doing something I'm passionate about. Maybe, at some point, God will instill more of a passion for math in me than I have now, but at this point, He hasn't quite given me that part of the teaching passion.
Moving on to a slightly different topic though, I want to talk about why I still enjoyed this class. A math education class: a subject I don't necessarily love with a career I don't necessarily want to go into. So why did I still like it? Because my professor is passionate about math and passionate about people. He is a professor that desires relationship with his students, strives to build personal connection, and loves math (I'm talking going to math conferences, writing math blogs, participating in math-topic Twitter gatherings...you name it). Both of the passions, check. Enjoyable class, check. If you're not convinced yet, then I don't know what else I can do to convince you!
This class has involved so many fun ways to express these math ideas. We did many Desmos activities, played many online quiz games, had lots of discussion, and wrote a few blogs. This professor found a way to combine the math with the relationship. How sweet is that?
Another thing I love about this class: the professor is a facilitator, not an encyclopedia of information. Any idea you had of only students asking the questions, forget it. The professor would propose an intriguing question, and boom, awesome, animated class discussion.
Nothing we did in this class encouraged a fixed mindset. Everything told us to view things in a different way, see the multiple ways of doing it, open your eyes to new possibilities, even to old ideas.
During a recent conversation, someone said something to me along these lines: "If your passion for your students outweighs your dislike for things like writing lesson plans, you're gonna be a good teacher." If this professor doesn't have that kind of passion for students, then you have me stumped on who does. I don't just say that just because he's the one grading this, although he is, but because I truly think there should be more professors who love to teach what they are teaching as much as this guy.
And honestly, I'm not writing the blog for the grade. If I get a zero on this assignment, I don't plan on changing it. I'm writing it because I believe these things, I want to be honest with my thoughts, and maybe it's even another type of processing for me as I try to figure out this life, Outside the Glass Tank.
Ok, obviously there's not an exact formula for how to be an awesome math teacher, otherwise every math teacher would have plugged n' chugged already and would be awesome! There are definitely some things that you need to make true if you want to work towards it, though. I'll talk about a few of them that I've discovered, and once you read through those, you're welcome to comment qualities that you think make an awesome teacher as well!
1. Be Passionate About People
To me, this one is common sense. If you don't love being around people, why would you choose a job that is around people (besides grading) all the time? Maybe you're passionate about that "a-ha" moment. Maybe it's building relationships with students. I had a teacher in high school that thought of nicknames for their students all the time--Even simple things, like calling them by their last name--but it made them feel known and included. The reason I wanted to be a teacher in the first place was because I could truly invest in my students and care about them in an awesome, mentoring way. Maybe it's a combination of these things or more. My take on it, though, is that you should be passionate about the people you're working with, and desiring to instill that passion into them.
2. Be Passionate About Math (or Your Subject)
Why would you pick something to teach that you are not passionate about? If you loved social studies, would you become a grammar teacher? Absolutely not! There's honestly not too much more to this one other than: pick something to do with your life that you are passionate about!
3. Be Chill
4. Have a Sense of Humor!
This one is definitely my favorite of them all. A good teacher has a good sense of humor. If you can gain enough respect to make your students laugh, you have gained enough respect to teach them as well. Plus a joyful, happy atmosphere creates a more relaxed, less stressed atmosphere to learn.
For me, that about sums it up. There are a lot of subcategories of those and more categories in general that I'm sure I will discover as my career continues, but I feel strongly about those. I know this was a relatively short post, but I feel like I said what I needed to say. Please do comment below with your ideas, and I'll possibly even write a blog on one of your ideas as I explore it more!
I always imagined it would be hard to find a balance between being an authoritative teaching figure and being a friend to students in the classroom. Turns out, I was right! Especially with so many rules and guidelines teachers have to stay within to avoid legal trouble in the education system, finding that balance is tough. I have had teachers that have done this really well, and teachers that have avoided this "friend" dynamic completely. In this post, I would love to talk a little bit about one teacher who I think does this well, and highlight a couple things that I think he's doing right.
At 54th Street Academy, the teacher I have had the opportunity to observe (we'll call him Tom) has worked out this balance really well. He doesn't have it down pat, but he definitely does well with the balancing act. I would love to share a couple of stories with you, and with each story share why I think this is a good example of the balance. Good? Ok, great.
At the beginning of second hour every Thursday, or at least both Thursdays that I have been there so far, Tom starts off the class with "Good News". This is a time that has absolutely nothing to do with academics. He literally asks students for some good news in their life. Things ranging from "my friends and I are having a bonfire this weekend" to "I got coffee from Biggby this morning". I've been in a class where the teacher has actually done this (see his blog post here), but it was cool to be on the observing end of it this time. Tom intentionally made this time fully relational. He took interest in what the students were saying, and asked follow up questions. I could tell by the students' reactions that they felt loved. Then, when it was time to move on to the class lesson, he did so promptly, and the students were willing because of his authority.
The lesson during one class was about basic congruency proofs on triangles. As a review, he asked students to recall the various properties that they could use to prove triangle congruency. Students piped in answers: "SAS", "SSS", and of course, "ASS??" followed by some giggles from classmates and smirks around the room. At this point, Tom had a choice. Either he could ignore it or address it. Instead of ignoring it or even addressing it in a negative way, he made a joke something along the lines of "donkey's can't do congruency proofs!" and moved on. This was awesome. He didn't ignore it, invalidating the student. He didn't address it in a way that was demeaning, which wouldn't encourage the student. He chose to connect to the student in humor, while keeping it within classroom appropriate guidelines. The student felt heard, even in his joke, and Tom connected with the students in humor, while staying on track and staying appropriate with his high school students. Well done, Tom. Well done.
After teaching the lesson for the day, the students got to do work individually/in small groups. This was time for them to take some of the things they learned that day and apply them directly to problems at their own pace. During this time, Tom could have just graded papers at his desk or gotten other busy work done, but he chose to roam around the room, making sure students understood, and allowing them to connect with him in a more intentional setting than a teacher in front of the class. Students asked him questions about the homework, but also even just made small talk back and forth amidst this. He chose to go above and beyond with intentionality in connecting with students, and they were much more engaged by it.
Obviously, Tom has done a really good job building appropriate relationships with students, and much of it has happened before I even began to observe. He did a fantastic job of being a friend to students, joking with them, conversing with them, but focusing when it was time to focus, and getting them back on track when they got sidetracked during class. The students clearly loved him; they even initiated conversation with him about their weekend and were comfortable joking back and forth with him about his haircut or conversing about their daily lives. These are just a couple reasons how he has formed this atmosphere, and surely there are many more examples, but, all in all, I hope someday my classroom will look like Tom's does.
As always, thanks for reading, and I'll see you on my next post!
Downtown Grand Rapids has something called "Art Prize" (http://www.artprize.org/) each year, which is an open art competition where thousands of artists can take their work and show it in front of masses of people milling around the city to be entertained, and for the chance to win a monetary prize at the end of the two weeks. The reason I bring up Art Prize, though, is not because of any of these things, but rather because of the types of art that are there. Below are a couple examples of the exhibits they have. (Hover over for source websites on these images).
I don't disagree with those that call these things art; in fact I agree with them. Art can be a plethora of different objects, sounds, or ideas, which means it includes communication. I recently attended a seminar called The Art of Communication: Learning the Secrets of the World's Most Dynamic Communicators, organized by Brad Gray. Although I attended to learn more about how I could use this information in Campus Ministry @ GVSU (which I did), I realized how applicable it is to being an effective and enjoyable educator as well! Below is a quick video explaining the general theme of the seminar, then I will dive into it.
There were so many great ideas in this seminar which lasted most of a day, but in this post I am going to highlight just a few that stuck out significantly to me. As you are reading, think about which of these you have seen to be effective (or, if you believe, ineffective) or think might be effective in the classroom, and feel free to comment and share your experiences & opinions.
1. What's the "Core Idea"
Math can be an overwhelming subject to teach, especially with Common Core Standards and others' expectations coming at you from all angles. You may feel like you have to teach about 15 different concepts in a 50 minute class period. (At least that's how it felt at times from a student's perspective!) Good news...you don't. Brad Gray spoke into a little bit of the psychology behind how the brain works, and it's extremely interesting! The human brain is designed to do 2 things: survive and conserve calories. Yep, you heard right. If the brain is getting a bunch of different ideas all at once, many times, it will deem those ideas not worthy of the calories it would use to understand them, and go into survival/daydream mode. When there is one core, central idea you are trying to get across, you will have your listeners leaning in. So, as you start to prepare a math lesson, think, "What's the single most important thing I want students to get out of today?" and connect everything to that central idea.
2. Why should I care?
You have your core idea. You know the concept you will be teaching is extremely important in the math world. Now you just need to help students recognize their need for the concept. I actually spoke into this a little bit in my last blog post, but Brad Gray has even more to say. We, as educators have what's called the "curse of knowledge" or the idea that we don't remember what it's like to not already know what we know. We need to put ourselves back in that position, really figure out why this information is important, and help the students grasp that the same way. When they understand that they should care about your core idea, the rest is history!
If your students believe that you care enough to invest in them, your teaching will land. If you are a math teacher, odds are you are pretty passionate about math and teaching other people math. (If you're not, let's talk on that..) So, go into each lesson with that core idea in mind, and ask yourself "what's at stake if these students don't hear what I have to say today?" Thanks for reading, and stay tuned for next week's blog, a look into some more of Tanner Rubin's Math Thoughts.
"The joy of communication comes when you move from having to say something to having something to say."
My favorite show of all time with no question about it is Friends. I have watched those episodes probably an unhealthy amount of times, and they're somehow still funny to me! This is a math blog though, so how does Friends have anything to do with math? Well, Friends itself doesn't at all, but as I was exploring teacher.desmos.com for various classroom learning activities, I stumbled across one called "Central Park" (https://teacher.desmos.com/centralpark), which led me to think about New York City, which led me to start thinking about Friends. So, as much of a stretch as that probably is, I likely have your attention now if you're still reading, don't I?
Desmos, for those of you readers who don't know, is a combination of many things: a website, an online classroom activity source, a place to turn in work, or in other words, a math teacher's heaven. What I'm setting out to achieve as you read this today is not only to help you explore what a specific teacher.desmos.com activity would look like to use with students, but hopefully in the process, convince you to integrate Desmos or another technological source in your teaching as well.
"Central Park" is a Desmos activity that has students "use their knowledge of computation to inform their algebra understanding, and...see that representing their ideas with algebra can save a lot of computation time," or in other words, convince students of their need for algebra to do arithmetic more efficiently. Through the activity, they will be designing parking lots for various cars, first only visually, then slowly integrating numbers and mathematic concepts to help them understand the transition. Almost every Desmos activity will have a "how the activity works" section, or something similar (as pictured below).
So let's go through the activity, and try to experience it as students would. First, we simply guess what the spaces should look like, no numbers included. This allows students to develop a practical understanding of a situation before adding numbers, which may be overwhelming before they understand why the numbers are there.
Students can then "try it" to see if they were successful in their setup or not!
Next up: adding numbers. This is where you take the basis of understanding these students have for a hypothetical situation, and apply mathematics practically, thus demolishing the ever present student question "when am I ever going to use this?" The order of these is integral: helping them understand the need, then giving them the solution. The students now get a chance to calculate how wide the spaces need to be to fit the cars instead of just guessing. They will see through this that we are giving them a much more efficient method, even though it is not what they are used to! Below are some examples of this in the activity.
We have them in our grip, now! They love the numbers! Now, we transition into variables, help them understand how those will help, then tell them they have begun doing algebra. Before they know it, algebra has become something they are excited to use instead of such a daunting word! Below are a couple more pictures of how "Central Park" transitions this in the activity.
Then dive in and experiment with even more variables...
Almost as if by magic, just 45 minutes later, you have a full classroom of students excited about algebra. Unheard of! Although this obviously isn't foolproof in every single classroom, hopefully I have convinced you that it will at least help, and definitely not hurt students' learning. If you have any thoughts on this activity, or Desmos in general, please feel free to comment below and let me know! I'm open to thoughts, and I'd love to hear what has worked (or not worked) for you. And as always, be on the lookout for what comes next from my thoughts outside the glass tank.
Why am I looking in from outside a glass tank? Well, not exactly a tank, but it sure felt that way. I once had a classroom with so many windows that I felt like people were always observing me during class from the outside of the room. For some reason, that's the image I have set in my head as a classroom. When I think classroom, that's what comes to mind. So as MTH 229 begins and I dive into thoughts and ideas on teaching methods and approaches, I have resolved to process my thoughts observing from outside the glass tank in writing. Here we go!
Coming into Math 229, I didn't know much of what to expect. "Mathematical Activities for Secondary Teachers," it was called. That could really mean anything within the realm of high school teaching. From day 1 of the class, it was evident that this was no traditional math class. We began by circling around the classroom, and doing a counting activity. Yeah, one that they might do in a 3rd grade classroom...but we were a classroom full of college students. A profound concept came from such a simple activity though: as we dissected the different ways students were calculating what the, say, 12th number in the sequence would be, there were at least 4 or 5 different ways of getting that 12th number that we came up with. A takeaway from this activity: sometimes we don't understand the purpose until we've accomplished the task. Even more importantly, the concept of the multiple method approach began to take root in my mind. Throughout these first 3 days of class, the central message I have taken away and understood more deeply each time has been encouraging multiple correct ways to approach a problem and celebrating the diversity of problem solving skills. My understanding of how mathematics works has already been challenged, and I'm forced to think about the question Dan Meyer proposes and answers: Does math class need a makeover?
After watching Dan passionately attest to why he believes mathematics is being taught poorly in some situations, I realize how much I agree with him. He states five symptoms that math is being taught wrongly, which you can see in his TED talk above, but I will focus on one that I've seen very presently and agree strongly with. When math is being taught poorly, there is a clear lack of retention. Almost every time I take a math class that references something I learned more than a year in the past, I have to, to an extent, re-learn the ideas. Then I think about how different my past classes have approached teaching to how I am learning in this class. None of those classes focused on how I got to the answer, but rather that I got the answer. Already I see myself analyzing math problems differently when I look at the method. In agreement with Dan, encouraging student intuition, letting them build the problem, and allowing them to explore different methods of solving are clearly most effective of the methods of teaching.
Whew. Those we're some thoughts. To close out this post, I'd love to talk about some of the specifics from Math 229 so far. As we explore resources for teachers, Desmos (https://www.desmos.com/) has been a very intriguing program. A free calculator online, with seemingly endless possibilities. Any teacher who loves exploring new ways to use technology would feel like a kid in a candy store discovering this program. With all sorts of graphing methods and animations available, it can be used basically as a free online graphing calculator. That alone is fantastic, but the way teachers can use it is even better. You can create groups where you propose a question and actually get to see how students are approaching answering that question as their graphs and attempts pop up on your screen. Once again, that theme of encouraging students to approach problem solving in different ways returns.
Finally, let's take a look at some of the topics of conversation revolving around quadratic functions from day 3 of MTH 229. I'd be surprised if you didn't know about the controversy surrounding the infamous Common Core (CC) Standards. During class, we took some time to delve into these standards and understand a little more about what the CC is, taking the example of the standards for quadratic functions. A conclusion I have come to is that the standards on the Common Core website (http://www.corestandards.org/) seem fair, but also seem very unclear. I understand why people are initially scared of them. For example, CCSS.MATH.CONTENT.HSF.LE.A.2 is written as "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)" (See http://www.corestandards.org/Math/Content/HSF/LE/). Initially this does seem a little unclear, but as I translated it more simply to "I can construct linear and exponential functions given various parts of the problem," it seems a little more straightforward. That of course is just one example. I will form more of an opinion as I learn more about the Common Core Standards, but with just some basic knowledge of the quadratic function standards for example, they don't seem too bad. Don't quote me on that quite yet, though, I haven't yet tried all the approaches of understanding their use and purpose yet...
Thanks for reading, and be ready for more thoughts as I continue to learn about what teaching looks like from outside the glass tank.