Final Project Paper for EDTL 6120 Integrating Technology into a Mathematics Classroom

Introduction The purpose of this paper is to introduce some specific ideas for integrating technology into a Mathematics classroom. The paper will specifically focus on a Geometry and Trigonometry high school classroom. There are many resources available to today’s tech-savvy teacher. The important thing for teachers to remember is the amount of preparation required to do anything well. They should not expect to just be able to point click and know everything about any given idea, program, software, instrument, or hardware. The purpose of integrating technology into Geometry and Trigonometry classrooms is to benefit the teacher as well as the learners. This is apparent when one looks at the two standards for teachers that cover technology. They are the National Board for Professional Teaching Standards (NBPTS) and National Educational Technology Standards for Teachers (NETS-T). Below is listed the main propositions for each: National Board for Professional Teaching Standards:

1. Teachers are committed to students and their learning. 2. Teachers know the subjects they teach and how to teach those subjects to students. 3. Teachers are responsible for managing and monitoring student learning. 4. Teachers think systematically about their practice and learn from experience. 5. Teachers are members of learning communities.

National Educational Technology Standards for Teachers:

1. Facilitate and inspire student learning and creativity. 2. Design and develop digital-age learning experiences and assessments. 3. Model digital-age work and learning. 4. Promote and model digital citizenship and responsibility. 5. Engage in professional growth and leadership.

These two different sets of propositions are not that far apart in their points. Both seek to have an educator become a technology integrator with their students as well as with their peer teachers and school staff. The standards are written universally so they can be applicable to teachers of any subject material. The propositions are almost a set of guidelines for teachers to follow when they are setting up a technology integration plan into their classroom. The following paper will be broken down into three main parts that are meant as a stepping stone for mathematics teachers to start their journey of integration of technology. There will be multiple different classroom integration strategies, a list of resources, and my own technology professional development plan.

Classroom Integration Strategies

Teacher Websites The first strategy would be to create a teacher website for students and educators. The website has many different functions in the technology enhanced classroom. It can be used as a contact area for teachers, parents, and students. The website can also be used as an open forum for help, exploration, improvement, and to ask questions. When utilized properly the website can be a safety net for students who are sick or miss school for other reasons. There are limitless ways that a teacher can use websites to enhance the learning experience of their students. The many uses of the teacher website are the main advantage but there are other advantages that someone might overlook. The accessibility for others to the website is a big advantage as well. With the development of new hardware that allows for internet connections, such as cell phones, laptop computers, I-pods, and other such devices, a person can potentially be “wired” to the internet at all times. This allows for students and parents to be able to check for assignments and updates from a class at any time and any place (as long as there is wifi). The accessibility is also present in the students home when they get done with their after school activities and have forgotten about what was due or how to do it. There are many options to help teachers to achieve this goal of having their own website. With a simply google search of how to create a webpage, a person can be overwhelmed at the amount of information available. The main suggestion for any newcomer is to pick software that is easy to use. Most schools have site copies of Adobe’s Dreamweaver so that is an obvious choice. This is definitely a good option if the program is easily reachable. Another program that a lot of schools have a site license for is Microsoft Frontpage. If neither of these is available a teacher may want to look to free source. There are a plethora of free source applications and sites out there on the internet. Here are a few to get started with; Open Source Web Design is a site that is built to give you sample templates to model your website after (http://www.oswd.org/), CoffeeCup Educational Software Package is free to schools and includes a webpage designer (http://www.coffeecup.com/education/), Wetpaint is a wiki site (http://www.wetpaint.com), Wikidot is another free wiki site (http://www.wikidot.com), and Wikispaces is yet another free wiki site (http://www.wikispaces.com). The picture on the next page shows the opening page of Wikispaces. This site is a pay site for the most part but says it will give free service to those using their wiki for education. This is not an abnormal stand made by most sources such as this. How most wiki sites allow creation for free is by relying on the advertisements that they sell and place on your page. Although, if you contact them and show that the wiki is for educational purposes only, most of the time the site will remove the advertisements. It is their way of trying to further education.

As proven here, there is no limit to what can be found and used if a person can search the internet with any common search engine. The one thing to remember is to always check out a website completely before using it. There is never any harm in checking for reviews of the site, scams, or any other possible deterrents. It is as the old adage says, “Better safe then sorry!” As stated earlier there are many different strategies for incorporation of a website to a classroom, but lets explore a few parts in detail and how to set them up. The first important part would be a contact page. There needs to be a way for the parents, students, and other teachers to contact you about your webpage or class. This is tricky because you do not necessarily want your home phone number, e-mail address, or even home address posted on the internet. This is why it is suggested to always use a school phone number, the school’s physical address with a care of and your name, as well as using your school e-mail address. Even then there may be an increase is junk mail, but at least it is not to the personal addresses. The second important part of your website should be a page just of important documents. Some examples of that would be a syllabus for each course being taught. Student information sheets, parental information sheets, a class calendar of topics covered throughout the course, the weekly calendars produced of each class periods lesson, and other material that might be important to the class.

A third part of the website to set up would be a discussion forum. This would allow all participants to create and reply to threads from others. There are many ways this could be used. It could be a way for students to get some one on one tutoring or clarification about homework, material, and projects. It could also be a way of finding study buddies, having questions non-material related answered, or just finding out what was missed on a certain day. The usefulness of this tool would be virtually limitless. There are many other important parts to a successful and interactive webpage for a teacher. Unfortunately this paper is meant as a highlighter of many different strategies so there cannot be a more in-depth conversation about this subject. But do not limit yourself to the ideas already discussed here, go out and learn about other opportunities, like web quests, java applets, and other such things.

This is important because it helps teachers to cover multiple propositions from both of the standards mentioned at the beginning of this paper. The website helps to create a learning community for students and other teachers. Depending on where you take the website from there will determine just how many of the propositions that you cover.

Interactive Whiteboards As defined by Wikipedia as “an interactive whiteboard is a large interactive display that connects to a computer and projector. A projector projects the computer’s desktop onto the board’s surface, where users control the computer using a pen, finger or other device. The board is typically mounted to a wall or on a floor stand.” Basically the interactive whiteboard allows for classroom wide interaction through one source. This helps to facilitate a hands-on learning experience for the students. The interatice whiteboard makes use of the other items discussed in this paper easier in the class setting so that every student is able to see and benefit from the software, applets, webpages, etc. Because those are dicussed in the other sections of this paper, this section will focus on technologies that are available only through the use of interactive whiteboards. One way to use interative whiteboards is to use the image capture feature to copy notes. It is also very easy to create a step by step video file that shows the instruction of the lectures one piece at a time. Then if that is combined with audio from the actual lecture talk, that gives a teacher the ability to create a viable aleternative to having a substitute teacher teach a subject they may not be experienced in. This is an invaluable tool because it allows teachers to have backup plans that are almost as good as being there. Most teachers that do this even create a frequently asked questions section so that students can even have their questions answered. Another great application of the interactive whiteboard is the ability to create geometric models and shapes that are nearly flawless. Most geometry teachers will freely discuss their shortcommings in the area of art and drawing. This becomes helpful for students to better visualize the problems at hand. Where teachers could have problems, the interactive whiteboards is there to step in and help. The interaction able to be done with the drawn geometric shapes is just amazing. A teacher can dialate, rotate, copy, label, move, translate, inscribe, or do anything else

to those shapes that could possibly be wanted. Below is a screen capture of just some of the possible shapes you can obtain with the interative whiteboard software.

Another great use of interactive whiteboards is the add-ons of clickers. Clickers are remote controls that can be bought in classroom sets that are wireless, can be connected to the classrooms interactive whiteboard and then can be used by students to answer questions presented on the interactive whiteboard. This allows teachers a great way to conduct class reviews and mini quizzes. The interactive whiteboard will actually keep track of all students’ answers, percentage right, and other statistical data and export it to a file accessible by the teacher. This saves the teacher time in class of having to take down student’s names, answers, etc. The time saver involved here is music to any teacher’s ears. The implementation of an interactive whiteboard in the classroom helps to cover the standards mentioned at the start of this paper because it allows for teachers to show their subject knowledge and also create assessments using this technology. This also allows students to be creative with digital technology and also helps to keep students engaged in learning.

Mathematical Software For the mathematical software section of this paper there will be a discussion of general points for most of the software, and then there will be a point by point break out of different software that is available. By no means is the list all inclusive, it is meant simply as a start. The great part of mathematical software is the vast, seemingly never-ending amount available. While most of the programs do require a fee to obtain and use, there are certain ones that are free and open source. The key to finding which software is right for each individual teacher is to first identify what they are going to do with it, and their expectations of it.

Obviously some mathematics classes are easier to incorporate these programs into. Visual mathematics such as Geometry and Trigonometry would be the easiest to integrate technology into. Although it is still not that hard for teacher’s to make Algebra classes more engaging digitally. The software can be supplemental to normal learning, extra credit work, furthering of understanding, or an entire course such as Cognitive Tutor. Geogebra: GeoGebra is free dynamic mathematics software. It has the capabilities to be used in geometry, algebra, and calculus. There are examples, screenshots, help subjects, and more available online. There is a GeoGebraWiki that has a ton of educational materials for GeoGebra. Anyone can go contribute and/or upload materials. Also there is a User Forum that can be used to ask questions or provide suggestions. http://www.geogebra.org/cms/

Geometer’s sketchpad: This is Geometry software for Euclidean, coordinate, transformational, analytic, and fractal geometry. This is NOT a free source, though most schools do have a license for it. Although it was developed primarily with geometry in mind, it is easily tweaked to help with algebra, trigonometry, calculus, art, science, and others. http://www.dynamicgeometry.com/

Cognitive Tutor: Cognitive tutor is a program that was developed by Carnegie Mellon University to teach mathematics to high school students. It incorporates group style class work with computer lab days where students work by themselves and at their own pace to learn mathematical skills with the program. http://www.carnegielearning.com/software_features.cfm

R: R is a free software environment for statistical computing and graphics. R is a free source where people can contribute new packages that will do new types of statistical analysis. R is almost programming software, so people who are not tech savvy to begin with may want to take heed of that. http://www.r-project.org/

Fathom: Fathom is primarily data analysis software that is good for a statistics class or any class that dabbles in any kind of data analysis. Fathom is more user friendly than R, but is also not free. Fathom is able to create many different types of graphs, which allows easy comparison, and also helps do all kinds of data analysis computations. http://www.keypress.com/x5656.xml

Mathematica: Mathematica helps to give independent learners the chance to really explore the world concerning history of mathematics, science, and technology The software allows students and teachers to explore their ideas in new ways. http://www.wolfram.com/

MatLab: MATLAB is a programming language which allows users to find and analyze functions for algorithm development, data analysis and visualization, as well as numeric computation. It is also not free source, and also very technology heavy. It is becoming more popular as of late with Statistics. http://www.mathworks.com/

Maple: Maple is unique in that it is built to be more useful to higher level mathematics. It packs major problem-solving power covering almost every area of mathematics, including calculus, algebra, differential equations, linear systems, statistics, linear algebra, geometry, and transforms. This software is amazingly powerful, but difficult to use without a lot of practice. http://www.maplesoft.com/

Maxima: Maxima is another high level mathematics system for the manipulation of symbolic and numerical expressions. This includes but isn’t limited to differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. The software can yield high precision numerical results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. It can also plot functions and data in two and three dimensions. This is another heavy hitter that a person with less experience may want to skip. http://maxima.sourceforge.net/

Microsoft Excel: There are so many applications for mathematics built directly into Excel that most people are not even aware of. Excel will do computations, formulas, graphs, etc. The graphical tools available in Excel exceed some of the actual software that is made just for graphing purposes. Excel can be set up to read different cells to input them in formulas which allow for easily changing one or two numbers and not having to go back through to fix all the calculations. It will automatically adjust them accordingly. The power of this usually overlooked software is impressive. http://office.microsoft.com/en-us/excel/default.aspx

Scilab: This is an open source platform that is mainly used for numerical computation. There are other features available, but the primary function is just to perform computations. http://www.scilab.org/

Geocadabra: Geocadabra is dynamic geometry software. It is not free source, although you can get a demo to try it out before purchasing. Some of the capabilities include drawing solid geometry figures, plane geometry shapes, functions and curves, 1-point perspective, 2-point perspective, 3-point perspective, and more. http://www.geocadabra.nl/geocadabra_english_start.htm

National Library of Virtual Manipulatives: The NLVM website is an online resource that allows math teachers to search for materials. It helps to narrow searches by separating the content by age range and content standard. The site is a virtual cornucopia of on-line manipulative resources. All of the activities are equipped with a parent/teacher button which gives directions on how to use the activity and what the point is. The big one is that each activity has a standards button to help identify what the manipulative should be accomplishing. http://nlvm.usu.edu/en/nav/vLibrary.html

Illuminations: This website was made by the National Council of Teachers of Mathematics (NCTM). Therefore the content is in line with their national standards. The website contains hundreds of activities, developed lesson plans, and other web links to help teachers. Just like the previous source, the material can be sorted by specific grade and content standard. The activities all give potential lesson plans that would incorporate that activity as well as additional NCTM resources to use. http://illuminations.nctm.org/

Math Playground: The Math Playground website is supposed to be a fun and interactive resource for younger students. These math games/activities, word problems, logic puzzles, and videos on this website are probably designed for students below high school, however it still has some good content. There is one specific feature that is unique to this site. It allows students to submit math questions

and if their question is picked, there is a new movie made to explain the problem to the child. http://www.mathplayground.com/index.html

Mathematical Hardware There are many items that could be considered mathematical hardware. For

the sake of this paper there will be a focus on the biggest piece of mathematical hardware: the graphing calculator. The graphing calculator was one of the biggest innovations in mathematics history in the last twenty years. Not only does the calculator do the basic computations that one would expect, but it also does graphing, statistical plots, calculations of statistical measurements, as well as having programs that are specific to the calculator that allow it to serve other functions such as geometry (Cabri Jr.). The versatility of the graphing calculator is one of its largest upsides. There is not a single high school mathematics class that would not benefit from the integration of the graphing calculator into everyday class. The calculator can be formatted to fit any trigonometry subject. Those that have taught this subject know there is a large variety of ways angles are described. Angles can be defined in degrees, radians, or polar coordinates. The graphing calculator makes these transitions easy, going back and forth by just changing a single option under the mode menu. There is also little limit to the types of graphs that can be produced by these marvels of technology. Some of the graphs that can be made are scatterplots, boxplots, line graphs, dotplots, and many more. This allows for students to compare data sets with multiple graphs and saves them the time of having to do all of the calculations. As a side warning, do not let students simply use the graphing calculator to do everything for them. The technology is only a plus after the student has proved proficient in the skill by hand first, then as a reward gets to use the technology. Along with the normal positives associated with the graphing calculator there are also add-ons that can be used with the calculator to enhance the experience. One such add-on is the TI-CBR or Calculator Based Ranger. The CBR is a motion sensor that can be used to create real life data to model ideas such as Hooke’s Law and Simple Harmonic Motion. Another really important add-on for the TI calculator for any teacher is the TI-Smart View application. The application allows for the teacher to project a view of the TI calculator off of the computer desktop and show students step by step the buttons to push and the process of working through any problem. The visualization is definitely a plus, but the bigger positive is that TI-Smart View allows for all of the different screens of the calculator to be seen simultaneously. On a typical calculator a person can only see one thing at a time, the lists, the graph, the calculations, etc. But with the TI-Smart View all of those screens as well as others can be seen at the same time so that it is easier to see how changing a single number can change all of the other parts of the calculation. The TI graphing calculators help teachers to utilize the technology standards by engaging the students. It also lets students work through different programs where

they actually create their own mathematical problems and lets them facilitate their own learning. This also allows teachers to show their subject knowledge by interrupting the data received from the calculations. There is a wealth of information available on the web that will help to give teachers new and fresh ideas of how to use the calculator in new ways. One good website to visit would be that of Texas Instruments, it can be accessed here: http://education.ti.com/educationportal/sites/US/sectionHome/classroomactivities.html. There is also an idea for use with the CBR here: http://personal.bgsu.edu/~arross/ the link to the Word document is at the end of the website. See the picture below of a sample TI-Smart View in action.

Java Applets The amount of java applets available on the web for free concerning geometric ideas is just astounding. To see for yourself just go to google and type in Geometric java applets for the Pythagorean Theorem. There are hundreds of different ones to chose from. Depending on the teacher’s preferences and what exactly they plan on teaching in their classrooms, there is a java applet designed just for them.

The java applets are wonderful tools to use in a classroom because they are interactive for students. The students are able to use them and explore all of the different parts of a mathematical concept. A great use of java applets in the classroom is to use them in conjunction with an interactive whiteboard. Then the teacher can have the java applet up on the interactive whiteboard and have students come up to manipulate the applet. This allows for students to have self and peer learning. Some examples to look at are located at the following sites: Manipula Math with Java (http://www.ies.co.jp/math/java/), Java Applets on Mathematics (http://www.walter-fendt.de/m14e/), Pythagorean Applets (http://www.ies.co.jp/math/java/geo/pythagoras.html), and Java Math (http://smard.cqu.edu.au/Database/Teaching/JavaMath.html). Below is a screen capture from one of the applets off of Java Math.

These are only a few sites to wet your appetite and hopefully spur the reader to do their own research to find applets that are specific to their own area of expertise. It may even make the reader want to learn how to create java applets of their own. This would be great! There is always room for more applets and expansions in the technology world of mathematics. Java applets are directly related to the standards propositions because they are engaging and allow students to create different mathematical situations using them. The applets also make it easy for teachers to manage the students while they work

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Technology Professional Development Plan

Up to date I feel proficient, although by no means do I feel like a master, in the following software titles: Geometer’s Sketchpad, Geogebra, Excel, PowerPoint, Word, TI calculators, Cognitive Tutor, Dreamweaver, Fathom, R, and Maple. I have different levels of understanding for all of these programs. It ranges from proficient enough to bumble my way through using them to being proficient enough to teach others to use them. I cannot claim to be even close to a master of any of these however. I don’t think anyone can possibly know everything about any of these programs. The software tends to be so in depth to begin with, then there are constantly changes, upgrades and improvements, and last there is the simple fact that some ideas aren’t originally planned for. Some of the best applications I have seen preformed in a classroom setting were not necessarily what the program was actually made to do.

My Information Technology Liaison from when I worked in King George, Virginia was very adamant about that point. Part of his job was to create and teach the technology professional development classes. He would stress every time I took the classes that he did NOT know everything and would love to hear of new ideas that we had. Him and I became pretty good friends because he was always willing to listen to my ideas and would come to me with some of his problems, and I did the same with him. It was a great relationship. It is actually how I was able to improve my Excel knowledge. I came to him with a spreadsheet that I had created from scratch to calculate student’s grades in a weighted course and he was able to suggest some nice cosmetic changes that made reading the sheet easier.

I think collaboration is a large key to the improvement of anyone’s technological advancement. Even people who are not exactly tech savvy would be able to contribute because they do not have preconceived notions about what software can and can’t do. Those people will be able to “think outside the box” and relay new ideas to the people who are technology proficient. Everyone is able to contribute something to the implementation and integration of technology into any classroom, but especially into a mathematics classroom!

For math classes in general, the technology standards hold great meaning. There is a lot of preconceived hatred to mathematics, so being able to engage

students, spark their intellectual curiosity, help wet their creative appetite, and do all that while letting the kids have a little fun with technology can be a saving grace. Most students in today’s society are more literate in computers than they are in English. This means that if the students see the math software, hardware, applets, etc as an exercise in computers, they are going to have an attitude that is positive instead of the negative one that is associated with math right now.

In the table below you will find a basic rubric of my technology professional development. To achieve these goals, first I plan on taking an intermediate Excel class. Next I will be taking time to develop a good set of classroom materials of my own for the TI graphing calculator-this will require me to inquire to other teachers for their resources, search the internet, and then combine all of the resources I have found into my own personal materials that are geared towards my class standards. Third I will spend time developing a website that meets my needs as a teacher. This will require me to draft out exactly what I want to do. There are many choices about set-up and style that I will also have to make. Then I will sit down and complete the task using Dreamweaver and Photoshop. Lastly, I will attend monthly professional development dealing with technology when I reenter the field. This will allow me to interact with other teachers and share ideas. This way I will be able to learn from their experiences and they will be able to learn from mine. It will also provide me with a wealth of new ideas to enhance my own classroom in the future. For now I will just continue to collaborate with my fellow BGSU grad-students and professors.

Technology to Integrate Date to be Completed By

Become a master at the use of Excel in a mathematics classroom. I know a lot

already, but there are also features that I do not know how to use and would like

to learn.

December 2009

Create a specific set of classroom materials concerning the TI graphing

calculators that can be used in my classroom.

January 2010

Have a completely operational teacher webpage with classroom discussion

forum, important documents, and other information available to my students.

August 2010

Continue my general knowledge of different software that is available to

teachers that specifically has mathematical implications and continue to collaborate with my fellow teachers in

order to draft new ideas.

This can never be completed; I always need to be growing.