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What is the best and worst of Technology & Topics for Educators?

For anyone reading this post, I'm going to share my opinion on the best, worst, and best of Technology & Topics for Educators. Easily, this class has more best than worst, and I want this post to reflect that.

The best part of Technology & Topics for Educators is the camaraderie that developed in the group. I give Mr. Becksfort most of the credit for instilling in his students that we are all working toward a goal, and the work is much more enjoyable if we work and learn together. Everyone learned something in this class. Of course, some people are more digitally native than others. Some people are technophiles. Of course, not all of us are either. In the end, we all learned, and we all had a lot of fun.

The worst part of Technology & Topics for Educators is personal on my part. The class started at 7 p.m. That is a horrible time of day (night?) for me. I struggled to have any brain bandwidth left. It showed often, and I thank heartily my left-hand, Ben, and right-hand, Chris, assistants. Thanks for taking on the job even though you seldom had any choice. The other worst part of the class was video editing. I found video editing to be like watching paint dry. On a bright note, it did cure me of dreading watching or listening to myself. I am so over that!!!!

Back to the best part of Technology & Topics for Teachers. This class is fun. It helped me expand my understanding of technology. It helped me use technology in new ways. It helped me see that technology is powerful and needs to be treated with respect. It helped me get used to getting up in front of a group which is priceless for my future as an educator.

Mr. Becksfort, thank you. I really enjoyed your class and appreciate the work you did.

Does Technology change the way we teach?

It depends....

Since teaching is both an art and a science, technology does change some of the ways we teach but not all of the ways we teach.

Technology changes what we teach, the topics, the focus, the science of teaching. Because technology is viewed as something new in the conventional mindset, it reinforces the current over the traditional.

What technology cannot change is human interaction, the art of teaching. No tool, gizmo, or latest-greatest can replace the connection that needs to be made between the teacher and the student.

Technology Presentation Overview

Web 2.0 is a great idea and many people benefit from using it.

Now the challenge: how to incorporate Web 2.0 into mathematics instruction.

I spent time looking at applications that I found by searching the web for "web 2.0 mathematics." The list was long. Unfortunately, I wasn't impressed. A lot of what I found was games. Games are OK, but the majority of games are for Kindergarten through 6th grade. I need games for 7th through 12th grade.

Another thing I noticed about the games seemed to be that they were oversold. They were described to be supportive of certain skills necessary for math. But when I played them, I found myself clicking here and there. Or worse, I found myself clicking randomly to see what happened. Not good. I don't think mathematics is helped by WAGs.

Then I remembered the trustworthy National Council of Teachers of Mathematics (NCTM). Sure enough, they have games. Not only that, they have games that can be played alone or you can challenge someone anywhere in the world. How Web 2.0 is that???? So I played the games, but I didn't challenge anyone anywhere in the world because I wanted to see if I could successfully play the games. Once again, I wasn't really getting much out of them mathematically. I mean, yes, they all involved mathematics concepts. But they were..........just games. On a personal note, I also noticed that the vast majority of the time the NCTM server won. But then I also noticed that although these games were listed as K-12, they were really K-8.

So, I was still unsatisfied and decided I needed to keep looking. Instead of NCTM's games, I looked at NCTM. I ended up finding some interactive stuff that came with lesson plans. It got me to thinking about what mathematics concepts would benefit the most from interactivity and visual learning.

VECTORS!!!!!!!!!!!!!!!!

In NCTM's "Illuminations: Resources for Teaching Math," I found a lesson plan, "Learning about Properties of Vectors and Vector Sums Using Dynamic Software" as well as the dynamic software "Vector Investigation: Boat to the Island." I played with it myself and found it interesting (could that be because vectors aren't my strong point because I never had dynamic software to work with when I was learning about them?)

All in all, I am very impressed with NCTM's offerings. I guarantee I'll check them out again for more good stuff.

Is there value in learning from fiction?

Of course, learning from fiction has value. A fictional story can present an underlying truth that applies to all of mankind. Underlying fiction is the human need for communication. The fable and folk tale have a rich and long-lasting history little changed by time and place. Fictional stories appear in similar forms across many cultures.

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.

What is wrong with HTML?

An assessment of web design...

Actually, I like html. I'll admit that my website maintenance mostly involved updating text and not all the bells and whistles of drop-down boxes, radio buttons, cascading style sheets, etc.

But then text is one of the strengths of html. It allows formatting that will, by default, be displayed in a web browser. And html reference information is always available since right-clicking on any web page allows it to be displayed as text, that is, html.

I was able to update my previous post by editing the html using the option from the compose screen. I made "Creative Commons" links instead of just text. Right click on my blog page, select view source, search for "Creative Commons", and you'll see the html that activates a link.

Pretty cool!

Copyright Issues for Teachers

Since I’m preparing to be a mathematics teacher, use of web content won’t be a big issue for me. Use of the web will mostly occur as visits to web sites, typically interactive, where students can use the content, but they won’t need to copy the content. Lesson plans abound on the web, and I intend to use them. But they won’t be published, and they won’t necessarily be used in their entirety. The Pythagorean Theorem is automatically credited to its creator. Who does “3 + 3” belong to on the mathematinet?

My responsibility with Creative Commons and its development, support, and stewardship of “legal and technical infrastructure that maximizes digital creativity, sharing, and innovation” is to spread the word as a teacher, to inform students and others that the content on the web is not free for the taking. We each have a responsibility to support the Creative Commons mission and work toward its vision of “realizing the full potential of the Internet – universal access to research, education, full participation in culture, and driving a new era of development, growth, and productivity.” Refer to About Creative Commons for more details.

I found this photo on freefoto.ca listed on the Creative Commons wiki. It has that mathematical look.......

Attribution: http://freefoto.ca/photos/abstract/lights/curves.html

What is my biggest legal concern as a teacher?

After viewing the presentations about the legal cases (https://docs.google.com/document/d/1Te1sLRzvw6vPjSfH7PUJWrk9Bi-OFlsRFCP36fUHMnw/edit?hl=en&authkey=CJ-Vqu4H# ), I find my biggest legal concern to be Honig v. Doe which clarified the rights of disabled students with regard to disciplinary actions.  Since the IEP is a legal document that is “fiercely protected,” ignorance of it is no defense. In addition to my regular classroom, I always will need to know which students have IEPs as well as the accommodations necessary to remain in compliance with the IEPs. The IEP in this legal case is a living document where the other cases were rulings that require either a new case or legislation for the cases to be modified. In my opinion, Honig v. Doe requires all teachers to be special education teachers whether we receive training for that specialty.

Hazelwood v. Kuhlmeier Legal Brief

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0BzgYqqIPXJVcYjZjNjgyNDQtOTI0MC00YmIxLWJhMTctMGU3NmE3YmU4ZmYy&hl=en&authkey=CJfa8pgK

Legal Brief Presentation

https://docs.google.com/present/view?id=dfjx3ctv_9dk5hzqf9

Journal Review

Mathematics Instruction and Technology

            For students to make sense of mathematics, they must develop deep understanding that leads to “higher levels of generalizing or abstraction” according to the National Council of Teachers of Mathematics (NCTM). Technology can be used for sense making. But not all technology provides an experience that enhances mathematical understanding.

In the article, “Technology with Cognitive and Mathematical Fidelity: What it Means for the Math Classroom,” published in Computers in the Schools 26.2 (2009) the author, Beth Bos, discusses the value of various web-based formats for deepening mathematical understanding. Two criteria are used to make value judgments. The first, mathematical fidelity, is described as “an object’s conformity to mathematical accuracy.” The second, cognitive fidelity, “refers to whether a concept is better understood when the object is acted on.” Taken together, these two criteria show how well computer generated objects are able to support mathematical understanding.

The web-based formats are organized into six categories which are assessed for their purpose, strength, weakness, and cognitive fidelity. Cognitive fidelity is significant since it allows the user of the web-based format to make connections through patterns that emerge as the math object is manipulated. Equally as important, the mathematical content of the object should not be limited by the software, and interaction with the object should lead to conceptual understanding of the mathematics being explored. Based on these criteria, all technology is not created equally.

Of the six formats studied, four of them showed low cognitive fidelity. The game, informational, quiz, and static tools that generate calculations, tables, or graphs formats did not enhance student understanding of mathematical concepts. The game format enforces reactive behavior rather than in-depth exploration toward deeper mathematical understanding. The informational format is typically fact based with no interactive or intuitive components (e.g., PowerPoint presentations.) The quiz format facilitates checking for understanding which reinforces the recall level of performance. The static tools (e.g., graphing calculators) emphasize procedural steps to find the answer rather than the logic behind each step and sense-making of the logic.

The virtual manipulatives (e.g., National Library of Virtual Manipulatives) showed medium-high cognitive fidelity. These objects help to make abstract concepts more concrete. They function best as building blocks for understanding. They require direct instruction and careful monitoring to ensure that students are able to create the desired results.

The interactive math objects were the only format found to have high cognitive fidelity. The strength of this format lies in its ability to show relationships based on varying information. These relationships change with the input allowing users to make and test conjectures. Instead of focusing on whether an answer is correct, the focus is shifted to building a deeper understanding of the mathematical concepts. Since exploration relies on problem solving, less direct instruction is involved which can be considered a disadvantage. But overall, this format is advocated by NCTM.

My considerations for applying the information presented in this article are that the four formats showing low cognitive fidelity can still serve a useful purpose in the mathematics classroom. Although recall requires lower level understanding, mathematical skills are built from recalled information, as an example, addition and multiplication facts. Games can be used to build basic skills without which students are unable to function in higher level mathematics. Mathematical information in a web-based format can be easily accessed and used to survey explanations of topics as a student works on initial understanding. The quiz format is an effective means of allowing students opportunities for extra-credit and must offer more benefit than extra-credit earned by bringing in classroom supplies. The static tools are unlikely to provide cognitive fidelity, but they are no less valuable than the tables of reference data included in older textbooks printed before handheld calculators.

The virtual manipulatives, although described to be more difficult to learn how to use, would provide a means of enrichment for students who are performing at an advanced level compared with their peers. Free online resources such as these provide challenging material for students capable of being challenged. These types of resources would also provide opportunities for self-directed exploration.

The interactive math objects provide a path to learning through problem solving which is considered by some to be the ultimate mathematical instructional method. Textbooks are now being written based on the problem solving methodology, but textbook changes are expensive and slow in school districts. The interactive math objects can be used to supplement conventional mathematical texts to provide opportunities for students to develop a deeper level of mathematical understanding.

The article’s summary states that “the influence of technology on the teaching of mathematics is that not all technology results in increased understanding of mathematics.” This assessment is extremely important since technology for technology’s sake cannot be assumed to improve outcomes. Appropriate technologies used appropriately after thoughtful consideration of their added value, if any, is an important factor required for the sensible use of technology in the mathematics classroom.

Still learning

Looking forward to a brisk trip to the car and a long ride home. Good night!

Start the blog: January 13, 2012

The first class and I'm learning to blog. Thankfully, Ben helps me when I get lost.

I like green.