Fathom-Week 8

Admittedly, this is a bit frustrating. I was almost completely done writing this blog entry when I decided to take a snack break. When I came back, I found that Firefox had shut down and I had to redo this entire entry. That's why this entry is now late.

All in all, Fathom has greatly impressed me. It has impressed me enough that if I one day have to teach a statistics or probability course, I would try to get my hands on it first. The main reason for this is the ability to input large amounts of data simply using drag and drop or open file techniques. This would allow for my students to quickly manipulate large, real sets of data. Because of this, they could make conjectures from day 1 and realize their inaccuracies. This is the manipulation of REAL statistics, rather than "pretty" examples they would get from a textbook. It is through this data manipulation that they can learn the value of true statistics far faster than through text implementation alone.
A second feature I really loved was that various scientific data collectors being implemented into the software. What this means is that in a physics classroom, the students could take their measurements and find them all being recorded statistically. From there, they could find out problems with their experiment by looking at the data (similar to the developers' experiment with the cooling water in a coffee mug). This creates situations where the students realize how interconnected learning truly is. They would learn that statistics can be found first-hand and that physics produces meaningful statistics.
Finally, I was very impressed with the Survey feature that the developers showed off nicely. There are really two main reasons that I enjoy this feature so much: the first is that the students can actively participate in data production and develop their interest in the results. The second is that they can participate in the data production outside of the classroom by logging online and taking part in the survey. What this means is that classroom time doesn't have to be wasted on data production, but the students can use class time to gain insights into the data itself.

I love the potential of this software! Already I know that this is certainly a viable option for any statistics course I might teach in the coming years.

Smartboard/Geogebra

On Tuesday, we were introduced to a rather impressive display of a relatively new technology, Geogebra. To preface this, I have used Geometer's Sketch Pad for an entire semester of learning Geometries and came to see the enormous benefit of it. That being said, I came to appreciate Geogebra equally. It seemed to contain all of the main functions and commands that GSP had, though it seemed sleeker, simpler, and even more intuitive. Additionally, it seemed to contain options that GSP did not. One example of this was the radio dials on the side, which a user could toggle on or off as needed in order to better see or compare various visual diagrams. This definitely seems like a close rival to GSP and I have to say that the new version of GSP is also quite astounding. This leaves me in a tough predicament: which do I prefer? That is a question I will undoubtedly have to answer in the future, though for now, I have not the time to find out.
The other main technology that we explored was Smartboard. This is truly an astounding piece of technological genius. I can see so many valuable facets to this the immediate implementation of this technology that I don't know where to begin. The most important use for the students who might benefit from this is the ability to pay complete attention to the teacher as he or she progresses through the lesson they have outlined. Yes, that's right, the teacher's own notes on the board can be copied off by way of a nearby printer! This means that there would be no more waiting for the students to complete their notes, no more cramped hands, and much more attention that could be paid to the mathematical concepts rather than the script. I have actually talked to a professor at AU that has a daughter who graduated from BSU and a few years ago, she acquired grant money for a Smartboard in her classroom. That's definitely something I will keep in mind when beginning my own career...

Week 6 Activities

This weeks' activities fell within the same realm as most weeks. I started with our reading, which centered around two rather distinct types of teaching technology implementation. I enjoyed reading about Type 2, which centered around a more broad, complex style of tech-ed where the student is let loose to make discoveries about mathematical concepts with the guidance of the teacher.
I then moved on to my TI-Nspire activities. I know that my module will be due soon enough, so I wanted to try to find some worthwhile activities that I can implement into mine. I came across a total of five new activities which I feel will be useful in my Geometry module and that I think Joe Kerwin will require for his module to go smoothly. I will meet with him in the coming weeks to make sure that they are what both he and I need.
The real difference this week was the creation of rubrics by which to grade and evaluate the worth of online mathematical lessons. I thought this task was very interesting, mainly due to it's future worth. I will undoubtedly need to judge the quality of lesson plans as a future teacher. The main criteria I chose by which to judge these lessons were: the quality of group interaction, the lesson's ability to interest or relate to the student, the effectiveness of conceptual conveyance, and the ease of immediate and effective assessment. While I feel there are many other categories by which to judge a lesson's worth, I feel that these are very effective.
In truth, this reminds me a bit of my post last week. I commented that the most important skill I am gaining from this course is my ability to judge the worth of new technology, but now I feel that it's more than that. This newest assignment had me learning to judge the effectiveness of specific math lessons, and without these skills, I doubt I would ever become a teacher of any real value. I am therefore greatly appreciative for the opportunity to exercise my talents in this area.

Discretion with Activity Selection

I used the Illuminations website as a source for both of the activities which I wrote a rubric over. In trying to find the correct activity, I came to see that there were a number of activities which I didn't view as "quality" activities. There were a large number of lessons which had only questions to be done by students. I could hardly call these lessons, as there was no real instruction from the teacher except for the guidance involved with general problem solving.
I didn't choose some of the other lessons because they were too broad. I was looking for something specific which I could judge as a single lesson, and there were far too many categories I could have based my rubric around for these lessons.
In the end, I chose two lessons which were obviously meant to be done in a single class period. I felt that they were adequate examples of math lessons and I tried to judge them as a future educator. While both had their flaws, I feel that they could easily be modified to make up for any failures on their part.

My Perspective on Math Tech

I have to admit that initially, I was a skeptic of technology implementation into the classroom. I had never seen my teachers use technology to convey mathematical concepts except in probability, statistics, and math modeling. Even then, these courses only utilized Excel and Minitab, and I only saw Excel used to any real effect.
In MATHS 331, I was initially frustrated to have to learn so many types of software. It seemed like a waste of my time because I didn't realize my ability to adapt to them or their ability to convey mathematics. At the end of the second week, I became more accepting of the software. I saw how quickly it allowed me to process information and I knew that the experiences could only help when trying to learn new software. Just two weeks ago, I began to feel more intrigued by the potential of the software. I am amazed at the adaptability of new software and I am beginning to enjoy considering how I might implement it into the classroom.
Even in listening to current teachers online, I have begun to learn how to judge the quality of software. Also, I found out that the TI-Nspire is not used for standardized testing because the complex operations it can perform limit the ability to which we, as educators, can judge the capabilities of our students. I was initially frustrated to hear that the Nspire, my chosen software, isn't widely used by students. I then further considered it's potential in the classroom and found another use for it: the Nspire software can still accurately portray concepts using a projector, despite the fact that the students likely won't become familiar with the software itself. The ability to project from this software allows for students to learn from various representations and see the potential of new software.
As I have continued to learn new software, there is one invaluable skill I am gaining: the ability to accurately judge the value potential of new software. This is likely the most important skill I will gain in this class, given the steady production of newer, better software.

Terrapin Logo

It was interesting to switch technologies for a week. This week, we were assigned to complete a few assignments on Terrapin Logo. This software is extremely useful in the instruction of geometric concepts. In addition to teaching lengths and line segments, it is an excellent tool for teaching how angles are necessary for most rudimentary geometric shapes. One important aspect of this software is the ease with which a new user can learn most of the required commands.

For the first assignment, we were told to construct a right scalene triangle, an obtuse scalene triangle, and an acute scalene triangle. A knowledge of trigonometry is useful here, though not required. I took a screenshot of my completed work and moved on. The second task was to create 5 different types of parallelograms: a rectangle, a rhombus, a parallelogram, a trapezoid, and a kite. I then saved my five different definitions (containing the needed sub-routines) and moved on to the next assignment. Now, we were instructed to create a curve which would utilize multi-variable inputs and then save our definition. I created one that, when repeated n times at m length would give (n/360) of a "circle" with m length on the sides.

Finally, we were instructed to learn about how to implement color into a Logo Quilt. This quilt involved a "grid" of squares with a couple of patterns that we made using our new-found knowledge of the color inputs and our previously acquired knowledge of basic shape construction. While my quilt was a bit lack-luster, I saw the extent to which these quilts could vary and appreciated the creative license I was given.

In the end, I felt like I gained insight into the potential of math technology with this assignment. Before, I didn't realize or appreciate how versatile this software could be, but when you really start sitting down and playing with it, you see it for what it's worth.

I have an Nspire!

So a few days ago, I finally got my Nspire! I was really excited to see the 84-silver integration pad and I enjoy having one familiar aspect to the Nspire. Over this weekend, I learned much more about my Nspire. I have been learning the basic menus and capabilities so far, but that entails quite a bit of learning. The first thing to note is the Home Menu. This menu contains the Calculator, Graphs & Geometry, Lists & Spreadsheet, Notes, Data & Statistics, New Document, My Documents, System Info, and Hints. The most useful of these has been the Notes Section. It contains Examples which outline some of the main useful features of the Nspire. The examples I have used to acclimate myself to the calculator are Getting Started, Introducing Functions, Percentage Explorer, and Linear Equations Explorer. The uses for this calculator are numerous and rather intimidating. Fortunately, Chris offered some additional examples and they have been extremely helpful in my understanding of the calculator. Additionally, our first Module has been based on some of these examples due to their usefulness. All in all, I feel that I've increased my understanding of the calculator significantly and feel that there is so much more to be learned.

Week 2 in 331

Wow, all these assignments have been keeping me busy! I'm trying hard to stay up with it all, and doing alright but haven't had much time to research my chosen software: TI-Nspire. Fortunately, I bought an Nspire calculator not more than a few hours ago, and should receive it in 3 to 4 days! I'm continually amazed by the capability of the software we are learning to use. I didn't know that a lot of this stuff was possible. Jing, for instance, is an excellent way to easily record pictures, videos, and any commentary I might have on the object being shown. Another nice find was Voice Thread. It's more of an online version of the picture recording of Jing, where many people can comment. It's all very cool and I look forward to learning more in Week 3!

Week 1 in 331

To begin with, I learned how to familiarize myself with the layout of the TI Nspire software. I then began to learn the basics of the graphs and geometry application. I learned how to graph and edit functions and edit window settings using the zoom options. From there, I gained familiarity with the basics of the Lists and Spreadsheet application. Finally, I learned basic features of the Notes and Calculator application and learned how the Nspire can help students understand concepts through guided investigations.