Does portfolio assessment have value?

Since my area of specialty is secondary mathematics, the answer to this question is not simple. Of course, the question is not simple so why should an answer be simple?

Typically, mathematics is treated with a drill and kill, quiz and test, repeat methodology which I find unfortunate. I mean, I hate tests. I'm not convinced that tests are an effective means to assess a complex issue, that being what a student has learned and what a student can do with that learning. From this perspective, portfolio assessment has great value.

But we're still talking mathematics which is not the kind of topic that screams "portfolio." So that means to me that I have to step outside the standard view of mathematics to implement something like a portfolio for assessment. But how?

Is it possible that mathematics has been drilled down to its most basic piece parts in an effort to make standardized testing effective? Is it possible that the beauty and power of mathematics has been lost, or killed, by the standardized testing? If so, portfolio assessment in mathematics has immense value.

Imagine a school in which the basics of mathematics are taught, but the use of mathematics is required. Imagine a school in which it is not enough to simply add, subtract, multiply, divide, know the Pythagorean theorem, and figure the probability of pulling a blue marble out a sack. In this school, you will find all the piece parts of mathematics taught. But instead of filling bubbles, the student will demonstrate knowledge with projects that span the piece parts and make them into a coherent whole. The student will work to explain to peers what the math means, not simply what the manipulations are. And these projects and works of the student will be compiled into a portfolio.

Indeed, portfolio assessment has great value in mathematics.

What was it like to critique myself?

Interesting, very interesting...

I am surprised that I am becoming more comfortable hearing my own voice. I used to hate to hear my own voice. Through listening to it over and over again, it's now familiar. I really didn't mind hearing it.

I found it easy to find the flaws, especially since some of them were brutally apparent. But I also found it easy to find some good things to include in my critique. All in all, the process was much less painful than I expected.

I'll be videotaped again before I complete my studies at Xavier. I hope to be less stressed by the prospect of seeing myself in living color the next time. In fact, I hope to not think too much about it at all. I want to focus on the lesson and look like a pro.

A critique of my presentation about the Sieve of Eratosthenes

Presentation Critique

            Being videotaped was a new experience for me, but one that I am learning to embrace. Soon enough I will be videotaped while I am student teaching. My commentary on myself in this critique will help me to be a better educator since I have seen some good and bad in my presentation.

            Since I am new to teaching, I have plenty to learn. My videotape showed some specific areas for improvement. My top priority will be to speak louder. Unfortunately during significant portions of the recording, I cannot be heard at all. I will not forget this lesson for many reasons, not the least of which being that it made my video editing difficult. I was able to find one coherent section about factoring that is audible, and it will be prominent in the final edited version. I presented toward the end of the class session after we had been warned that we were running out of time to complete videotaping everyone. This situation led me to speed through my explanation as I found the factors of 72. In the future, I need to always be mindful that explanations need to be given the amount of time necessary for understanding. It is not acceptable to “cover” the material. Another area of improvement for me will be to spend more of my time looking at my students. Presenting to a group of my peers was not the same as instructing secondary students about mathematics. I know from my experience teaching during my Methods observations that I did spend most of my time looking at the students to gauge their understanding and receive feedback from them through their responses. But I certainly need to keep in mind that more eye contact is better whenever I am in front of a group of people. Also, I am disappointed that I did not explain more clearly as the sieve of Eratosthenes progressed that after removing all multiples of a prime number, the next number in the sieve has to be a prime number since no preceding number was a factor. I have plenty of room for improvement in working on the craft of being clear, coherent, and complete when I am instructing.

            All is not lost because I did see some positive aspects of my presentation in my video. Most importantly with regard to content, the material was mathematically sound. Also, having an animated PowerPoint presentation for the sieve of Eratosthenes made the process come to life, which is difficult when the ideas are presented from a mathematics book. I was surprised during the presentation when the vast majority of the group answered that “1” is a prime number. I was not expecting that response, but I handled the correction well by emphasizing that “1” is not a prime number “by definition.” Hopefully, the visual of seeing the “1” fall off the sieve will help everyone remember that definition. Tying together the history of Eratosthenes and a number of his accomplishments using the YouTube video, the concept of the sieve, and the application of the sieve to finding the factors of a number was another strength of the short lesson. Unfortunately, it is not uncommon for people to readily admit to not liking mathematics. The video provided a pleasant respite for those who think they are not inclined toward math and allowed everyone to learn something without realizing it. Sometimes the best learning happens when we think we are not really doing anything.

            All in all, I have room for improvement, and I am not surprised by that. But I believe I have strengths that I can continue to build upon. I look forward to more improvement as I continue my studies as a pre-service teacher.

What video editing means to me

Being videotaped is not my idea of fun. So editing a video of myself is double not my idea of fun.

I hope I have enough usable footage to chop into workable pieces and have a coherent whole when I am finished. I'm sure the video will improve with adding the YouTube clip, instead of relying on a video of the YouTube clip.

What video editing means to me is making an improvement of the raw footage.

But I'm not looking forward to it........

Incorporating technology into my lesson

It's math, so how should I use technology? How about an online graphing calculator or a game? No, I found a brief video of a cartoon about Eratosthenes that was created in 1961 which is an excerpt from IBM's "Mathematics Peepshow." The video focuses on the work of Eratosthenes to determine the circumference of the earth during the time when the earth was thought to be flat. The narrator also lists a number of the accomplishments of Eratosthenes, among them his sieve, but more on that in a minute.

I created a PowerPoint presentation that animates the actual sieve. But the most difficult part was figuring out how to add a YouTube video to a PowerPoint slide without using a plug-in. I found the directions here: WikiHow YouTube in PowerPoint and followed them, and it worked. Whew!

Back to the Sieve of Eratosthenes. I used the animations offered by PowerPoint to implement the sieving process. At the end of the presentation, I show a useful application of the idea of the sieve for finding the factors of a number.

A little history, a little sieve, and something useful. Math, it's for thinking.