One of these things is not like the others...or is it?

After working with the kits I think I figured out some commonalities. First, a lot of the activities were based upon misconceptions. For example, when guessing the order of objects based on size, many of them looked as if they were obviously larger than another object yet when they were compared using a common measuring device, it turned out that they were either the same size or opposite of what was previously believed. So, I would say one thing that all the activities have in common is that they all deal with the notion that things (size, volume, etc) aren't always what they seem.

Another thing that I noticed was that the activities dealt with comparisons that were based on commonalities. Once one amount or length was known, that could be used to determine the size or amount of another item. I think it's kind of like fractions...you find the common denominator in order to compare the two items. In the case of one of the activities, beans were used to determine the amount that an object could hold. Instead of just blindly guessing how much another object could hold, the amount of beans in one object could help determine the amount of beans the other object could hold. The beans were the common denominator used to compare sizes of different objects.

Excuse my language, but WTF!!!

I have never walked out of a class more frustrated than I was on Wednesday...and I've been in a lot of classes! As I sat there, I couldn't help but think that the same people who were complaining about the class not moving along fast enough were the ones stalling the hell out of the session. If I felt like there was genuine confusion, I would understand and even enjoy the process of discussion but when I look back, all I can say is that the whole time was spent comparing apples to oranges. Correct me if I'm wrong, but the reason you can't put multiplication in terms of change unknown and such is because there is no change. In multiplication and division, you're dealing with a known amount of something...there is no change when you have two numbers that are given. The point is more obvious when dealing with division. You're taking a group of something and putting it into smaller groups...there is no change, there is a dealing of some sort but definitely no change. You can't take something and divide it and consider it changed...it is what it is, no change, just a different size of it. If I lose 30 pounds, I'm still the same person, there's just a different amount of me...that's how I look at this whole division thing! There is no change, there is just a difference of size...12 is 3 groups of 4...still 12 though!

Kid Watching...PRICELESS!

One of the things I really enjoy about this class are the videos of students actually doing the problems that we discuss. For me, seeing the ways children actually think when they are contemplating a problem really opens my eyes to how students approach word problems. I think it's really interesting how some students make the problem seem more difficult than it is while at the same time, totally being able to rationalize and explain their thinking.

For example, when one of the students was asked to combine 8 and 3, the student began with 3 and then counted up 8...that's a lot more fingers than are necessary! When asked to explain, she was able to describe her thinking and I think that is what is most important. I am just so amazed by the ways that students describe their thinking. Sometimes it seems really seems convoluted as it comes out of their mouth, but then all of a sudden, you think about it yourself and it not only makes sense, but oftentimes shows a higher order of thinking than what was first expected.

I feel as though watching the videos really puts a valuable spin on the class. I don't understand the point of taking methods classes without connecting them to the students we are going to teach. Every other methods course has only attempted to connect what is being taught in the class to out practicum courses. This class, on the other hand, directly connects the students we will be teaching to the class we are in.

Efficiency vs. Productivity

Now it's time to weigh in on the discussion regarding the fluidity of the class. I think that the class is moving on nicely...as far as the whole discussion about the class moving too slow or what have you, I think it's a matter of comfortability level. To me, I think that as long as we keep moving along, that's all that matters. I think the people who feel the class is moving too slowly just expect to have a schedule that needs to be followed to a T. That is not reality at all, especially in the classroom. I like that our schedule depends on how quickly we are grasping the curriculum. That having been said...on to today's quiz!

I am really enjoying this class because I feel like it's a mixture of you teaching us and us teaching ourselves which is the best way to learn. Math isn't always fun, but now that I am understanding more about the logic behind it, it's quickly becoming one of my favorite subjects. I'm feeling as though this class is boosting my confidence mathematically...I've always felt like math wasn't too tough but teaching it always seemed like a daunting task but now I'm good to go now. I look forward to class every week which is a nice feeling!

Problems with Words?

I loved the word problem assignment! I never realized how hard it is to write original word problems, especially since there are actual categories. I think that the the categories help to make appropriate word problems for students based on their abilities. I think differentiation is the key to successful instruction...if the students are taught in a manner that challenges them without frustration as well as keeping them from getting bored, they will be more receptive and less intimidated by their education. I think that word problems are tough for students because they involve more than one thought process. When you combine reading and math, there is more of a chance for confusion. Many students are comfortable with math or reading but combining the two can be a daunting task for students that struggle with either subject. By now having guidelines to writing word problems, I feel like I can give my students personalized instruction to ensure that that they are successful.

And to think I thought I was a genius!

This little problem thingy that has been given to us is seductive. I thought that it was pretty straight forward...put the problems in order from easiest to hardest; not too tough. The hard thing is trying to think about why one problem is harder than the other as well as labeling each of the rows and columns. Come to think of it, nothing about this task is easy. Then again, if it were easy, there would be no point and this class would be a lot less interesting, but I digress. I think my configuration makes sense until I have to start labeling everything. I really see no pattern at all. It's not that I hate you (Dr. Shih) for assigning the problem...I'm sure there's method to your madness. What I hate is being frustrated. I'll get over it eventually. The real issue lies in the fact that when I can't figure something out, it affects my sleeping. I'm the type of person who works problems out in their sleep. When I still can't make a definitive decision on something after a couple of days, it just down right annoys me and I never want to look at the problem(s) again. For this very reason, I do not play Tetris (I dream about it if I do, no lie) and I kind of want to sleep it out one more time...just in case it actually works this go around. I really hope my layout is at least close to the actual answer.

Better Late Than Never!

It still amazes me that all children, regardless of sex, gender or economic, all develop in the exact same order. It used to blow my mind thinking that no matter what environment children were raised in, their minds followed the same processes to get to an end. The only difference was the rate and extent of their development that made the difference in their mental capabilities. This is interesting because as it turns out, math allows us to use this phenomenon to better educate our students. By knowing that all students follow the same pattern of thought when it comes to math makes it easier to decipher where students are getting confused as well as whether or not they are truly understanding concepts. I like that all students start with a certain strategy and just because one student uses a different strategy, that does not make them any more or less intelligent, it just means that they are at a different stage of thinking. Math now seems a little bit more conquerable (as well as teachable).