Nay-Sayin' the Nay-Sayers

This week I've been participating in a 1-2-1 initiative training session in my district. All of our freshmen are getting their own laptops, and its my job incorporate them into my lessons effectively. I'm not a huge fan of technology for technology's sake, but some of the tools we've looked at could add some significance to my lessons. It'll be interesting to play around with it throughout the year. I'm sure I'll post an update in the future.
Anyway, this morning we got into a discussion on project-based learning versus the 'old style' of education. The obvious question of 'Which is better?' was posed, and everyone agreed that the PBL style would be much more effective. When our presenter, Tom Gaffey from Philadelphia School of the Future, asked how many of us have tried it, less people raised their hands. When he asked why we haven't, what our roadblocks were, this is where the discussion got started. Many of us began talking about pros and cons to planning and executing these lessons, and the end product was very positive.

Now, I'm in a unique situation in that I've taught the exact same courses for the past six years. I've tried to use this to my advantage. Rather than teaching the same thing every year, I've tried to add or modify a PBL unit to the course every time I go through it. 

Whenever I take part in these discussions, I often get the feeling that teachers really do want what's best for their students, and these presentations motivate them to put the proper pieces in place. But once the show is over and the presenter is gone, temptation to resume the status quo emerges. It took me many years to overcome this feeling, and it still lurks at time. I understand that the time factor in planning is tough, but that is why you start small. Lack of motivation among students is present in every math class (it's what we do!), but PBL lessons have a 74% chance of generating more interest among students (I made that up, but they will help!). State exams and standards aren't going anywhere, if anything their gaining momentum, but we need to work with them not for them. This is the excuse that bothers me the most, and I know there are people that will disagree here.

The example we looked at today was teaching slope through building a set of stairs. Mr. Gaffey explained how he had his students find someone in the community that needed a set of stairs built and his students did the work for them. He taught them everything they needed to know to construct them correctly and tied the notion of slope into his explanation (I immediately thought of Dan Meyer's competition idea). To me, this is an awesome idea! He even admitted that his students did no better on the state tests than others. At this point, the conversation got interesting. I could tell some in the room began questioning the significance of the lesson. After all, if it doesn't raise scores, but takes more time, what's the point? I've got stuff to cover, we've got to push through the content. On the contrary, Mr. Gaffey made the point that his students gained a valuable learning experience in problem solving and construction among other things. He took it from concrete to abstract and had the students attention the entire time. So, yeah, it took longer, but the benefits far outweigh that. I would love to have an entire course (or all courses) structured in this way. If I get through the entire curriculum, GREAT! If I don't, who cares? If my students learn the majority of a curriculum really well along with other topics, then whatever I miss can be made up later. If my students have the opportunity to get a ridiculously awesome learning experience, I'm going to do anything I can to make that happen. It's not easy, but then again, if it was everyone would be a teacher, right?

I wish I could find more educators that shared this mindset and had a better opportunity to collaborate for this type of planning. I believe great things can happen if education is done right. There are many things that work for our students, but we need to ask ourselves if what we are doing is whats best for them.

With A 'Lil Bit O' Algebra

So, I've recently been asked to rewrite our districts Algebra 1 curriculum (and eventually Algebra 2 I believe) to fit with the Common Core State Standards, again (woot!). Teaching something because the standards tell me to bothers me as opposed to teaching something because its relevant, but that's a rant for another time.
A colleague of mine and I were looking over the CCSS for alg. 1 and realized its kind of a hodge-podge of topics thrown together. I mean, all of the linear equation/function stuff works together very well, but then there is some beginning stats/probability and also rational expressions, polynomials, exponents, etc. thrown in as well. We were trying to find a way to organize this course so that it makes sense and there are logical transitions. As of now, the topics are taught in the order in which they appear in our textbook (UCSMP), which is no good (both the organization and the book). We stared for a while and threw out some ideas, and then I realized something. Every alg 1 curriculum that I've ever seen has always ended with stats topics, and they are part of the 'if there is time' category. I wanted to give this course some flow and a context, so I thought 'Why not teach it from a statistics perspective?" After looking over the standards again, we figured out that this just might work. Here's the tentative plan:
      We'll start off with calculating different types of probability. This covers the different types of numbers, how to order them, represent them, compare them, etc. We will then move on to different ways to represent data, bar graphs, pie charts, stem and leaf, box and whisker, etc., further emphasizing the importance of number sense. This leads nicely into scatterplots and line of best fit, which opens a door to teach all of the linear equation/function topics that are essential to an algebra 1 course. This is obviously a very loose description since I don't have all the info in front me, but I think it will work. Every topic will have a context and we'll be able to teach everything in a real setting. My hope is that this allows students to see how these can be used and provide an easy method to be taught. I'm very excited for this to happen and can't wait for the results. It makes me wonder why I've never heard of anything like this before.
      The only hicup - the rational expressions, polynomials, GCF, LCM, exponents topics that are to be included. How do we incorporate them into a stats context that flows well with everything else in the course? As we talked, the best we could come up with is 'throw them in at the end.' No context, no transition, no meaning in regards to the rest of the course. This upsets me, but, I've got nothin'. Any ideas?
I feel that this is a new and exciting way to teach algebra 1 that could produce some amazing results. I'm a little nervous about showing this to those who are teaching alg. 1 next year because its so different than the way it used to be, and also because I'm not teaching it (so that will produce some interesting discussions as well).

Snow, man.

Checked out my 101qs submissions today to see the low perplexity scores. After checking up on Dan Meyer's blog I realized that my 'Snow, Man' pic had an honorable mention in his Top 5 for this week. I won't lie, I got excited. However, after reading his response to it, I realized that I had missed the mark slightly. My picture gives way to some basic questions, but could be better if planned out.

I would imagine if I showed this picture to my students I'd get questions like, "How much snow is that? What is the ratio between the three balls? How long until it melts?" and so on. These aren't bad, but are they really any better than a textbook problem? After all, the whole point of Act 1 is to get the students engaged and really interacting with the math behind the situation. I need something that will stimulate independent thought and make the students care; something that will allow them to envision themselves in it. Everyone builds snowmen, but who really cares about how much snow they've used to build it?

After reading the comments about how to redesign the problem, I've got some ideas to reproduce this in a few months. I liked the idea of comparing it to another snowman in a neighboring yard - introduce the competition element (after all, everything's better when there is a winner and loser). I could start by showing an aerial view of my yard along with a time-lapse video of me building the snowman in a methodical way, clearly using a certain amount of my yard. I could then pan out showing my yard again with the amount of snow that's been used already and the amount left. 

This could still produce the same questions as before, but now it could be expanded to "Who's snowman is bigger? What is the biggest possible snowman that could be built? How long would it take to build such a snowman? Could you combine the two to make a super snowman?' While these questions may not seen anymore advanced or intense, the redesign could get my students involved more. It wouldn't have as much of a 'ugghh, not this again' context, but would be more inviting. It would be more practical, more relevant, more realistic to their lives. Getting them engaged and thinking is the key, and this might just do it. I'll let you know in 9 months.

This has made me realize that I still have some work to do in creating these First Acts. While it can be done with almost any picture or video that inspires thought, they key is using the best possible option and format. Taking a basic picture like that above works, but does it work as well as I think? I need to think about these from a students' perspective and a teacher's perspective to get the best possible Act. Practice, practice, practice. Thank you 101qs and Mr. Meyer!

Order Matters at 5-Below

I was walking through 5-Below this afternoon looking for some fun stuff for my daughter and saw this hanging on the wall: a customizable iPod case with 'over 17,000 possible combinations!' Whenever I see advertisements like this I always wonder if they have a math guy that figured that out for them or if they just estimate it. I also wonder how many people will change the way their iPod looks 17,000 times.
If I showed this to my students while teaching permutations and combinations, which would they argue that it is? Is this an engaging enough picture to get them to think about it, or would they quickly move on?

Oh, the possibilities...

Any (mathematical) Questions?

Piece of Cake Upside Down

I recently re-watched one of the few good math movies made - 'Stand and Deliver.' I showed it to my students and they were (surprisingly) interested in it and loved it. Some of them learned shortcuts to their 9 times tables and a new way to think about positive and negative numbers. I, on the other hand, watched it from a new point of view.

I haven't watched this movie since I've become a teacher. Previously, I watched it from a student's perspective and purely for entertainment value. Now, as a teacher, I realize there is some deeper content here. There are some things wrong with the clip above. The claim that their students cannot learn because of where they live or because of their status is bogus. Mr. Escalante gets it right when he says 'students will rise to meet your expectations.' I think there are a good amount of teachers out there that don't fully believe this; they think kids will be kids and there's nothing that can be done to help them. They are who they are and there are all kinds of excuses for the teachers not to teach them. Escalante owns up to his responsibility, says he could do more, and he follows through with it. After watching this again, I began thinking about my classroom. Do I set a high level of expectation for my students, and continue that expectation throughout the semester, or do I eventually cater to their level? Can I get them to do more for me and for themselves in order to help them realize their true potential? Is there a way for me to give them the ganas they need to be successful not only in my class, but in their lives? If I answer in the negative to any of these questions, what can I do to change? I plan on seriously reconsidering my first week of class and my management techniques to empower my students with ganas. Yes, I teach math. Yes, its an uphill battle before they even walk in the door on the first day because of that. Yes, stereotypes say that I am a boring nerd. I don't think that I can settle for any of that and I don't want my students to either. I need to find a way to change their opinions, change their mindset, and change their opinion of their ability level. I need to gain their trust from day one and show them that they are capable of whatever they put their mind to. I feel I do this to a point with some students, but not as many as I'd like. I also realize that this is a Hollywood interpretation to a true story, but there is a lot to be said for it. I could go on and on...

Good Bounce.

I finished up my unit on isometries today with my geometry classes and with the few extra minutes that I had, I began showing them how to predict where a ball will bounce after it hits something. At first, they kind of looked at me and wondered why I was explaining this to them, but once they made the connection to reflections and what we had been doing in class, they were hooked. I explained to them that the angle in incidence is equal to the angle of reflection (which was something I assumed they knew) and I actually had a student raise his hand and say "I actually didn't know that before just now and I can use that the next time I play pool." In the past when I taught this, my students blew me off and didn't really care. This year was different: they wanted to learn more. After we went through a few 'nice' examples of bouncing balls off walls that were perfectly straight, someone asked me about what if the wall was curved; could you still make a similar prediction as to where the ball would end up? This goes a little beyond the scope of the course, but I figured if they're asking I'm certainly not going to stop them. I explained to them all about tangent lines and points of tangency and everyone learned something.
Throughout the entire unit, students were asking me, 'Why do I need to know this?' I told them we were getting there and I wouldn't let them down, to which most of them went back to not caring. Perhaps next year I should start with this lesson. Thinking in terms of a 3 Acts-type format, I could show them a video of someone playing pool, bouncing a ball off a wall and stop it before it stops asking, 'Will it go in?' Or I could show a clip of a Dennis Rodman jumping up for a rebound and just before the ball bounces off the rim, 'Is he in the right spot at the right time?' (by the way, my students are always in disbelief when I tell them that Rodman holds the rebound record because he analyzed the angle the ball came in and he figured out where it would bounce to). This might catch their interest, we can dive into the material, and then come back to it in the end to calculate an answer.
Any ideas?