TEKS

I intend to teach High School Mathematics.  Since this is a relatively broad category, I selected Algebra I for this blog post.

§111.32. Algebra I (One Credit).
(a)  Basic understandings.

1. Foundation concepts for high school mathematics. As presented in Grades K-8, the basic understandings of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work in high school mathematics. Students will continue to build on this foundation as they expand their understanding through other mathematical experiences.
2. Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students use symbols in a variety of ways to study relationships among quantities.
3. Function concepts. A function is a fundamental mathematical concept; it expresses a special kind of relationship between two quantities. Students use functions to determine one quantity from another, to represent and model problem situations, and to analyze and interpret relationships.
4. Relationship between equations and functions. Equations and inequalities arise as a way of asking and answering questions involving functional relationships. Students work in many situations to set up equations and inequalities and use a variety of methods to solve them.
5. Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems.
6. Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, language and communication, and reasoning (justification and proof) to make connections within and outside mathematics. Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts.

 (Source: Texas Education Agency at http://www.tea.state.tx.us/)

            The TEKS above will serve to guide me when I create new lesson plans for my students.  Though, time permitting, I will not limit myself to only the above general topics.  This TEKS will provide me with a goal so that I can ensure my students meet a minimum standard of knowledge.  The general expectations listed in the TEKS describe not only what will be tested over, but, in a perfect world, they also describe what students will need to know to be successful in their lives and future math classes.  Since the TEKS above is for Algebra I, it is even more important that my lesson plans are well rounded and complete as this class will be the foundation for all future math classes.


            Though I believe every point listed above is important, I’d select “Algebraic thinking and symbolic reasoning” as the most important.  Algebraic thinking is far more than simply being able to add common variables together or solving for x.  Algebraic thinking is a process of reasoning that can be applied every facet of life.  A large portion of discrete mathematics deals with logic and reasoning that can be used to describe anything and everything.  The foundation for discrete mathematics begins with algebraic thinking in junior high and high school.  It also teaches students to analyze problems logically, to dissect them, and then sometimes rebuild them into a useful answer.

Podcasting

I don’t know that I actually learned much that was new to me about podcasting.  The concept wasn’t new to me, though I’ve seldom had the opportunity to take advantage of it in a school setting.  My microbiology teacher is one of the few I can recall that used podcasting to supplement her lectures.  She would record her daily lectures and post them online for students to access.  During that class I did occasionally download and reference her podcasts while working on homework or studying for a test.  Though I diligently take copious notes in all my classes, the ability to go back and hear what the teacher said word for word is invaluable.  It had never really occurred to me assign projects to students that required them to use podcasts as their completed project.  Though, as a math teacher, I’m not sure I can see an application for my students, I do see the potential in other educational curriculum. 

Podcasting is different in as much as the podcast itself is not likely to be edited or added to by other people as would be typical in most Web 2.0 applications.  Wiki, Twitter, and IMDB for examples, are typically composed of work created by multiple users.  The work as a whole can’t typically be attributed to one user, whereas a typical podcast is normally created by one person only.  Podcasts are similar to other Web 2.0 applications though, in that they are created and posted for use by an audience.  This audience can be either specific or public, as is the case with other Web 2.0 applications.  Podcasting can also be used for group collaboration the same as a Wiki page, but through audio files rather than text.

I do own an mp3 player, specifically a Zune.  I don’t really use it anymore as my smart phone, tablet and computer fulfill the same roles.  I also own a digital recorder that I’ve used in classes before.  I would record the lecture on the digital recorder then transfer the file to my computer each day when I got home.  The recordings were organized by semester and class and date so that I could easily access any particular lecture.  I’d use these recordings as supplements to reviewing my notes and reading the applicable texts.  I’m not adverse to using the same sort of technology to create podcasts for my future students; however, since I intend to teach high school mathematics, I’m not entirely convinced of the usefulness of such a podcast.  Hearing a math instructor discuss how he is solving a problem is only half of the information.  Students really need to see what the instructor is doing as well as hearing what he is doing.  If video recording technology were available I’d likely use it to create a video podcast for my students. 

Certainly the advantages are many:

• The ability to review class lectures precisely as communicated originally
• To clarify points that the student didn’t initially understand or pay attention to
• Self-evaluation of a lecture for future improvement
• Archiving a vast amount of knowledge in an easy to reference library for future use.

 The disadvantages, to me, are only in how a person uses the information.  If somebody were to rely exclusively on an audio only podcast, they would miss the visual cues that expand upon the audio message.  An example would be a student skipping a day of class then relying on the podcast and hoping he learns as much from it as he would have from the actual lecture.

Web 2.0

Web 2.0 describes web resources that are community created and maintained.  This means that groups of people contribute to their creation and/or editing.  The size of the group can vary.  Access to the website in question can be limited to a particular group of people by way of setting permissions, or access can be granted universally to the public.  YouTube, Wikis, and Flickr are all examples of Web 2.0.  Using YouTube as an example, the public can upload videos that they've taken, or created.  Anybody with a YouTube account can then post comments on the individual videos.  This enables many people to carry on a discussion or collaborate on the videos – though more often than not, it’s simply people posting inane comments.

In general, Web 2.0 technologies can be used to improve our classrooms in certain situations.  Flickr is probably a very good tool for use in photography and art classes, as discussed in the “Flickr in the Classroom” video.  Creating a Wiki might be a good idea in many classes as an assignment on creation and collaboration.  Potential uses might include a English class analyzing a literary work, or a science class publishing the results of a recent experiment.  I might be too old to fully embrace all of these new technologies.  Quite often I feel like we are being pushed to incorporate new technologies in the class for the sake of doing so.  As teachers I believe we should ensure that there is an actual benefit, tangible or intangible, to everything we bring to our class, Web 2.0 included.  

Copyright and Fair Use

The portion on “original copyright” was a refresher for me.  We discussed this at length in a technology ethics course I took last spring.  Fair use is a different story entirely.  It was naive of me, but I had no idea that our governing bodies had delineated so much specificity regarding fair use of copyrighted materials.  After reading the article by Hall Davidson, I thought I had a decent grasp on fair use as it applies to educators.  However, the copyright quiz proved that fallacy.  I missed one or two questions because I wasn't provided enough information.  For instance that Bill Nye has authorized the use of his work for up two years after it was release.  Even more surprising, though, was the question about a California instructor pirating software for a student.  The court held that the school couldn't be sued without permission, and never even addressed the ethical issue (Davidson).

Clearly we are navigating through muddy waters.  It is no wonder that many educators “find themselves paralyzed by all the uncertainties” (Davidson).  Can we play back part of this recording for educational purposes?  Well…. Maybe.   How old is it?  How much do you want to play?  Why are you playing it?  To whom will it be played?    Then throw all that out the door because even if you are abiding by the guidelines you can still be sued and the result is uncertain.  Generally speaking, I think if we maintain our classrooms and our schools as their own little microcosms, we’ll be safe.  As long as we as teachers, and students, aren't publishing our results (findings), copyright holders aren't likely to care how we use their material in class.

Davidson, H. The Educators' Lean and Mean No FAT Guide to Fair Use.  Retrieved from http://www.csus.edu/indiv/p/peachj/edte230/copyright/#article

Information Literacy

This section was already fairly familiar to me.  In one of my A&M English classes within the last year or two, one of our librarians visited and presented the same material.  It was somewhat enlightening at that point.  For instance I wasn't aware of how to manually enter a Boolean search request without utilizing the search engines advanced features.  However, I was already diligent in my web searches.  I trust very little unless it’s published or hosted by a known entity – university, government, or newspaper.  Even then, I read the content to determine fact versus opinion or propaganda.  The librarian also made me aware of the existence and usefulness of searching for official journals on my research subjects.

My habits didn't change much after being made aware of the new information.  I do occasionally use Boolean searches to narrow down the search results.  I do, however, frequently use journals in my research projects now.  The A&M library search engine is incredibly useful in finding, and then cross-referencing, journals on every topic I've researched.  I will certainly pass this on to my future students.  Being able to construct or analyze information is predicated upon being able to find good information in the first place.

It is essential we teach our students how to find and use valid information.  Sorting the relevant from the irrelevant is harder than ever in the world we live in.  Before the age of technology a student’s resources were limited to primarily encyclopedias, periodicals and libraries.  Today we are bombarded with information, and much of it is at best incorrect.  We also need to teach our students how to incorporate what they know with what they’ve learned to construct a goal oriented response.  We as instructors need to remember that students do not possess either of these abilities innately.  Achieving mastery of these skills requires instruction and practice.

Introduction

     Hello all.  My name is David Singleton.  I’m 39 years old.  I have a 16 year old son and an 18 year old daughter.  I grew up as a military brat, and then later joined the service myself.  So, I've pretty much lived all over the country from coast to coast.  I enlisted in the Navy at 18 where I spent the next few years as a nuclear reactor operator.  When I left the navy I transferred my technical expertise to the communications industry working for companies like MCI Worldcom.  In 2008 I enlisted in the army where I spent the next four years, deploying once to Iraq.  I’m now investing in my future, studying to be a high school math teacher.  I’m currently scheduled to graduate Fall 2015.  When I’m not studying my tail off, I typically spend my free hours reading fiction - most genres.

     My vision of educational technology is somewhat cloudy at the moment.  I’m not entirely sure what types of software exist that could be incorporated into my classroom.  I consider myself very tech savvy - I built my last computer from the base components.  I use my smart phone daily, and own both an Ipad and Kindle. I’ve also take several computer science classes.   I tend to try and take what I’m learning and translate it to a high school math class, though, and I haven’t yet found a good application of technology.  I did a brief web search to see how others are using technologies in math classes.  The results I found were predominantly for grade school applications.  I understand the importance of our children becoming technologically fluent.  Basic word processing, spreadsheet, and database applications should be familiar and comfortable by the time they graduate.  Beyond familiarity with technology I’m not sure I’ve been exposed to enough to really have a good answer right now.

     All that being said, my goals for this class are to gain a better understanding of the tools available to me.  Since I'm going to be teaching high school math, I specifically would like to find out if there is any technological aids I can implement in secondary math classes.  When I went through high school 20 years ago, technology in math classes didn't exist.  The same typically has held true for my college classes as well.  The only tech I can think of being used is a smart board.  So I'd like to build on that and fill my teaching tool box with anything else instructors have found useful.