Christmas Wishlist pt. 1: Understandable State Standards

During this Christmas season I am sharing my wishlist for math education. I hope it brings warmth to your heart and a smile to your face.

This year, math departments across Indiana are taking a look at their curriculum and choosing new textbooks to use. The math department at my school has been going over the state standards (pdf) and attempting to put them into a framework for teaching. As we have been working on this, I have repeatedly been frustrated by the lack of clarity and the redundancy of the state standards.

As an example, the Indiana Algebra 2 standard 5.2 says students should be able to

"add, subtract, multiply, divide, reduce and evaluate rational expressions with polynomial denominators," and "simplify rational expressions, including expressions with negative exponents in the denominator."

Unfortunately, that one standard covers more than an entire chapter of my algebra 2 book. So does the state expect students to be able to answer all of the types of problems that my book presents? There are dozens of problem types that fall under this massive umbrella.

Thankfully, the state provides an example. Their example is

.

This causes new problems. Specifically, this is a very simple type of problem compared to many that are in the textbook. Is this problem indicative of the difficulty of the problems that the state feels is appropriate for this class? If so, I can throw out about 3/4 of my entire book based on the examples the state provides for the other standards.

Of course, since most of the standards are so broad and the examples they provide are so narrow, I am sure I would be leaving out plenty of important topics if I followed this plan.

Sometimes, when I am seeking clarity on the standards, I look back at the algebra 1 standards to get an idea of the progression of learning the state is seeking. In this case, however, the standard over the same topic in algebra 1 (6.2) is nearly identical to the standard in algebra 2. In fact, they use the same example problem for the algebra 1 and algebra 2 standard.

I am very confused.

So, for Christmas, I would like a clear set of standards (with plenty of examples) so that I know what I should be teaching my students.

Christmas Wishlist: Introduction

Every year since I was little I would create a wishlist of things that I wanted for Christmas. I always included at least a couple of "big ticket" items on the list, such as "World Peace" or "One million dollars" or "Cubs winning the world series."

In the spirit of those lists, the next several posts will include the items I have on my current wishlist for education. Stay tuned!

Pt 1: Understandable State Standards

Doing Mathematics

[Ignoring the pink elephant in the room: how long it has been since I posted. . . just going to glide right by that.]

So what has been on my academic mind recently has been how to get the students to do more math. I'm not talking about practice problems that come from the textbook or even from my mind. I'm not talking about problems that are similar to those on standardized tests or my own assessments.

What I am thinking of is something that is closer to what mathematicians actually do. I'm vague on the details right now because I'm not exactly sure about them, but here is roughly what I'm thinking. Mathematicians don't typically work practice problems over and over again, but are instead involved in one (or more) of the following activities:

• Exploring the properties of some numeric/algebraic/etc pattern.
• Making a generalization about a pattern they see.
• Proving a conjecture they have made.
• Modeling the world around them with equations and data sets in order to answer some sort of question about the world.
• Researching the methods/work of other mathematicians.
  

So, why aren't my students doing more of this? Granted, they almost certainly would be going over ground already covered by previous mathematicians, but there is certainly value in finding your own way through something sometimes.

Now I just have to find a way to implement this idea and I need a long list of actual activities that students can do. Any thoughts, oh wise internet world?

Creating disciples

Dallas Willard on creating disciples: "We [should] intend to make disciples and let converts 'happen,' rather than intending to make converts and letting disciples 'happen.' " Taken from The Divine Conspiracy.

What do you think of that?

Wikipedia linkage

So for the last couple of days my brother has been visiting. It is always fun when he comes to Indiana. We stayed up late most nights (well, late for me, kind of average for him). We had a good time discussing all the usual topics: movies, music, life, politics, etc.

However, he introduced me to a new "game" that he plays with him self. It is basically a solitaire version of 6 degrees of separation using wikipedia. Here are the basic rules:

1. Pick a topic which you would like to read about on wikipedia.
2. Start at the wikipedia homepage.
3. Only use the links available to you (don't use the search feature) in order to get from the homepage to the article you are looking for while passing through as few intermediate articles as possible.

It is a natural outlet for curiosity since you can read some of the intermediate pages that you land on. It is also a fun way to see the way that everything is connected.

Hopefully it is clear that neither my brother nor I exclusively use this method of looking stuff up on wikipedia, but it is an educational way to pass a half hour.

Vicious Circles

The last couple of days I've been doing a lot of reading for a paper I will be writing for my History of Mathematics class. I haven't read this much in so little time for a very long time (maybe never before in my life. . . I've read 500+ pages in the last 2 days). All of this reading has brought to mind a couple of things:

1. I really enjoy reading. I would like to read much more often than I do.
2. There is vastly more interesting material out there than I would ever be able to read.

The bummer is that because of item #2, I don't read as often as I would like, because I am overwhelmed by the choice of picking my "next book" and because I get this terrible attitude of "well, I will never be able to read all the things I would like to, so why bother."

But that is stupid.

So here's my point: I would like to stop this. Here and now, let it be known that I'm going to read more.

Quick thoughts

So, I feel I must explain my prolonged absence. There are several things that have kept me from writing here for a long time, but we'll just say that it mostly has to do with my overthinking of things. For a while now I have been wondering if this blog was too random. It has posts about family, work, math, education, faith, and self-improvement. I have been trying to decide whether or not I should split things up and maybe create a separate blog for one of the main threads. However, recently I realized that it is my personal blog, and I might as well share the things that are on my mind without worrying too much about cohesiveness. I'm not writing to gain a massive following, I'm writing to share my thoughts and experiences, and more often than not, just to think things out "on paper."

Since I have cleared that major logjam, maybe now I might be posting more. No promises.

In the mean time, an insight on what I'm working on currently.

• I'm reading (or re-reading, I can't remember) The Divine Conspiracy by Dallas Willard.
• I'm taking a class on the History of Mathematics. I've been enjoying it, but it has been time consuming. On a side note, I should be working on the term paper, but I have yet to start it.
• I'm trying to run more often, but I have been inconsistent. On top of that, I'm not really running that far yet. I'd like to be able to run 2+ miles at some point.
• I'm trying to get some of next year planned out.
• Keltron and I have been preparing the nursery for a future little Shores.
• Throughout it all, I've been constantly distracted by playing Civilization IV.
  

Why I hate Facebook

I've been a part of facebook for about a year now, and I still just really hate it. I've given it quite a bit of thought, and I think I have finally figured out what exactly bugs me. It probably isn't what you think it will be. It isn't the oversharing and childishness that sometimes occurs there that I hate. No, this was a much more difficult thing for me to articulate than my rant against myspace. And yet, I will continue to use facbook.

My biggest complaint is the closed nature of the whole thing. You can't see anything unless you are a member. I'm fine with keeping some things closed, but the whole nature of the facebook is that you are sharing stuff with all of your "friends," but a similar outcome could be achieved through a private blog or wiki that you allow your friends/family to have access to. In particular, the model that flickr uses for the photos is very much what I'm thinking about. Many (most?) people post things publicly in flickr for the whole world to see, but some people choose to post some or all of their pictures privately that only a certain group can see. Facbook completely lacks this functionality. There is nothing that is available to the outside world. Sure, Facebook offers more finely sliced layers of privacy (the ability to create user defined groups that have different privacy settings), but I can't share with the world. And yet, I will continue use facebook.

This really manifests itself in the email center for facebook. My friends have started to just send messages through facebook instead of using email. What I like about email is the fact that it can communicate with any other type of email. I use gmail, and I have friends who use hotmail, yahoo's email, apple's email system (whose name is currently escaping me), work email, or even juno (!). And yet, we can all communicate completely and without trouble using this system. But to receive messages sent from facebook, you have to belong to it. That seems like a step backwards technologically. And yet, I will continue to use facebook.

In addition to this is the "walled in garden" feeling of facebook. It is beginning to feel an awful lot like AOL and Compuserve used during the dial-up modem days. The only difference is that the content is user generated instead of professionally generated. It was a mistake back in the olden days, and I think it is really a mistake now. There is so much out there that doesn't feed into facebook very well. The whole place feels like an internet for idiots hangout. And yet, I will continue to use facebook.

I understand people's urge to feel connected to others, but I am convinced that we could do it much better by using tools like blogs (including the silliness that is twitter. . . a post for another day), photo/video sharing sites like flickr, a good feedreader, email, and perhaps even an old fashioned website. It would allow for much more customization. And yet, I will continue to use facebook.

Why? Well, for one, all my friends are there, and I would be unintentionally cut out of the loop if I ignored facebook. Second, because all my friends are there, I am able to get a quick snapshot of their lives. Of course, if they all had blogs/twitter accounts, I could just follow them through my rss reader, but now I repeat myself.

What about you, poor reader? Are you a part of facebook and do you share any of my frustrations? Do you have any of your own? I invite you to let it all out in the comment section.

On my mind

As usual, there have been more things floating around in my mind than I have had time to fully flesh out. Since it has been a long time since my previous post, I thought I would just give a quick update on some recent things relating to teaching that I've been pondering:

1. How can I get students to read more? Reading is so crucial, but my subject isn't as conducive to reading as I would like.
2. How can I structure the year so that kids become better problem solvers? I don't work on deep problems as often as I would like, so then I become frustrated, and then give students a difficult problem to work on. Since I haven't spent as much time on it as I would like, then students flop around.
3. What is the proper amount of speaking I should be doing in class? I often feel like I'm the only one speaking in my classes, and I don't like it at all.

Well, that is probably enough of an insight into my mind for now.

A long slumber

I know that I have been away from this for far, far too long. I apologize. I want to lead off by saying that I have had a podcast reawakening (my first interest in podcasts going back a couple of years ago to when I first got an ipod). One that I have been especially enjoying is the daily video put out by TED. The videos are usually pretty short (most come in right around 20 minutes) and I have really enjoyed about 90% of them. That stat might seem lower than it should be if I am really endorsing the sight, but seriously, what interweb source have you found that you enjoy even 90% of? I don't even like my own blog that much.