Things You May Not Know About Your Calculator.....

Did you know your graphing calculator can draw the derivative, integral, or inverse of a function? How about that it has the ability to perform linear, exponential, logarithmic or power regressions?  Or how it can be used to effectively evaluate sequences and series?

If we are going to effectively use the calculator as a technology in our classrooms to its fullest extent, we need to be intimately familiar with how it can potentially be used. As our Interactivity from this week emphasized, when we use technology in our lessons, it shouldn't be thrown in there just to use it. Instead, we need to incorporate it in truly planned, useful ways that hit home the learning goals and standards. By increasing our own personal knowledge of how the calculator can be used, we open up a whole host of possibilities of establishing lessons where the calculator is use to its fullest and most meaningful extent.

There are a lot of resources available to help in this, but one I found to be particularly helpful is located at http://mathbits.com/mathbits/tisection/openpage.htm. The website contains information about using the graphing calculator (there are sections for the TI-83, TI-84 and TI-NSpire) in many different areas of mathematics. There are also some helpful "Quick Reference" sheets that may be useful to either refresh your memory or distribute to students.

Interactivity #4

https://docs.google.com/spreadsheet/ccc?key=0ArsgjpLWpPDrdGowcmE4dmFyOXZEeVd0cHBKTVB4WVE 

Whenever I think of technology and Mathematics, I automatically think of scatter plots, graphs, linear regressions and best fit lines. This lesson plan is a great demonstration of many of those concepts, and it presents them using something that most everyone is familiar with: EBay. I also think that by using the PS3 as a “new” technology in the worksheet and questions, it causes students to actually think about factors that affect the prices of new technologies. I did not notice any real gaps between the goals, strategies and technologies in this lesson. When I was reading it though, I immediately thought of trying to incorporate Excel as much as possible as opposed to hand-graphing. In the context of scatter plots and lines of best fit, Excel is definitely the “go-to” technology, and I think incorporating it would only enhance the lesson and strengthen the learning goals. A program like Excel is truly an “all-in-one” package for the learning goals in this lesson: it can find a linear equation to model a set of data and provide a clear, well-organized representation to aid in analysis and interpretation.

Thinking About Standards...

Standard 8.1 Educational Technology:  All students will use digital tools to access, evaluate, and synthesize information in order to solve problems individually and collaboratively and to create and communicate knowledge.

Standard 9.1 21st-Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

•  Critical Thinking and Problem Solving 
• Creativity and Innovation 
• Collaboration, Teamwork, and Leadership  
• Cross-Cultural Understanding and Interpersonal Communication 
• Communication and Media Fluency 

What does it mean to "prepare" students for the 21st century exactly? I think the State of New Jersey hit the nail on the head with the "5 C's" outlined above in cross-curricular standard 9.1. No matter what subject area you teach, or where you teach for that matter, education is so much more than just learning math, science or literature. Education is learning how to think critically about things, how to innovate, how to work on a team, how to communicate to other people and how to become fluent in the many forms of media available.

This is where we educators can bring in Standard 8.1 regarding Educational Technology. If we can effectively bring technology into our classroom in a way that not only teaches our subject, but causes them to think critically about technology, we are "teaching" them 21st Century Skills. While the use of technology is definitely a great skill to have in the 21st Century, what good is it if we cannot analyze, innovate and question forms of technology?

Interactivity #3 Reflection

The results of this interactivity were truly amazing. Personally, I would never have even thought that we would come up with such an extensive list that gives examples of not just the "traditional" calculator and SmartBoard but also of manipulatives, computer software and presentation aides.

This list will prove useful in not just READ411 and CURR314, but also my methods course and potentially Teaching for Learning I. When I begin to plan lessons, I can easily look to this list for ideas on what technological resources are available to aid in increasing student understanding. There is so much out there that I had no clue about, and this interactivity and the list it produced has greatly educated me.

Before this interactivity, I had never dealt with Google Docs (or online collaboration) before. It went very smoothly and was definitely an overall enjoyable experience. I hope to make use of this form of collaboration in any other group work I may encounter in the future.

The Complete Other End of the Spectrum

It's been a busy few weeks at The New York Times in terms of their number of articles about technology in the classroom. The previous article I just posted about was regarding a school who absolutely and totally embraced technology. Now, I would like to turn your attention to the complete other side of the story: a school that does not use technology at all.

This article profiled the Waldorf School of the Peninsula in Silicon Valley, one of about 160 schools in the country that subscribe to this method of no technology in the classroom. While this idea may seem radical, I truly do see some positive coming from it.

There is no doubt that technology envelopes our entire attention when it is in front of us. Just look at people sitting on the bus, riding the train or even running the park. Cell phones, MP3 players, IPads and so many other technological forms really limit our interaction with other people. By using the Waldorf method, students gain some time away from these technological distractions and only have fellow human beings to interact with, which will no doubt improve the very important skills of managing personal relationships and inter-personal communication.

There was one quotation from this article that really hit home for me and why I can see such an extreme method of education having its' merits:

“Teaching is a human experience...Technology is a distraction when we need literacy, numeracy and critical thinking.”

I am a huge proponent of critical thinking and problem solving skills in the classroom. As teachers, yes, we are supposed to teach the necessary content, but along with that, should come necessary life skills that will aid students for the rest of their life. While I agree that technology, when used properly, can have a positive impact on instilling such skills in students, there are just some things that actual human beings can demonstrate better. We need great leaders, innovators and thinkers who can solve problems on both the individual and much bigger world-wide level, and I feel an over-reliance on technology hinders this. I am by no means supporting the Waldorf method in this article, but it is definitely something that caught my interest.

Digital-only Math and Science Textbooks?

My initial reaction to reading this article in The New York Times about one Indiana school district switching over to digital-only textbooks was one of hesitation. While it was truly great to read about the benefits the teachers in this district see in the switch, I really don't know if they justify the $1.1 million (in infrastructure costs alone) this transformation cost.

Much to that point, the article even points out:

Even as more and more schools nationwide have eschewed traditional textbooks, spending an estimated $2.2 billion on educational software last year, vigorous debate continues over whether technology measurably enhances achievement.

Therefore, just from the monetary aspect alone, I have my doubts about such a quick and investment-heavy transition to digital-only materials. Why not have only some classes switch to digital and gather data before spending this huge amount of money, especially with education spending being a target of many watchdog groups today?

Additionally, a part of me feels like these students are being cheated of something by using digital textbooks. Math, to me at least, just doesn't feel the same when done on the computer. I will admit that even with my familiarity and comfort with technology, I always print out and write on all of my digital resources. Writing thoughts down, trying multiple approaches to the same problem and not having a computer support system with hints and such are all important in building not only mathematics skills, but problem solving skills. While digital resources are great when it comes to data analysis topics and algebraic graphing, there are some areas in math that I think are best served by a hand-written process--and an actual paper textbook.

Calc-U-lator

The calculator became yet another "tool" in the mathematics teacher's tool-belt that could assist students with rote calculation, serve as a check to homework and minimize error in larger student projects where the focus is not on the calculation.