MOBILE TECHNOLOGIES in the Math Classroom

"Clearly, 21st century educators will have to deal with issues and situations that their predecessors could not even have imagined. New technology tools also mean new and different ways of accessing and processing information needed for teaching and learning" (Roblyer & Doering, p19, 2013)

         Even though new technology brings new challenges to education, as educators we must embrace these challenges to best educate our students for life in the 21st century. Technological advances are also advances for education. Technology has placed the knowledge of the world at our fingertips and we must embrace this and prepare our students for the future not teach the ways of the past. Advances in technology make ideas like 1:1 computing, individualized education, and global learning a reality. I feel that many educators still have not realized all the possibilities that technology brings to the classroom.

       A popular technology resource for the classroom is the iPad. Mobile devices such as smart phones and tablets like the iPad and iPhone are the technology of now and the future. Even though desktop computers and laptops are functional, they will soon be obsolete. Students need to be educated with the knowledge of today and the future, not what we (teachers) used when we were in school. However, there are barriers to using "new technology" in the classroom. One major barrier is funding for the technology. But, if your school system does not have funding for technology be diligent and look for opportunities to write a grant. Below I have included just a few links of the many available Apps for use in the mathematics classroom. Most of these links are geared toward a high school class, but some functions of the apps could be used for lower grades.

       Upon doing research for this post, I discovered the Infinite Thinking Machine website http://www.infinitethinking.org/. First launched in 2006, the Infinite Thinking Machine (ITM) is a high-energy Internet TV show directly targeted at K-12 educators, parents and students. Our goal is to inspire creativity and innovation in education.  I did become inspired by these web-isodes and wanted to share them. There are a lot of great ideas of the power of technology in the classroom and teaching with technology for the future.

YouTube Video from Infinite Thinking Machine that showcases ideas and innovations for mobile learning.  One idea from this video is that, if the answer to a question can be found using a mobile device in less than 2 minutes then it shouldn't be the basis of learning or assessment. This emphasizes that the application of knowledge is more important than just learning facts.

Infinite Thinking Machine Web video: MATH-APP-ALOOZA

Some of the Apps I include in my list. Other Apps for elementary and middle school are included in the video.

 

LINKS TO MATH APPS/PROGRAMS

I would love to have a 1:1 computing classroom in which every student has their own mobile device such as an iPad. Below are links to just a few of the many apps and web resources that could be utilized in a 1:1 iPad math classroom.

Geometry Apps

Below are two apps that are very useful in teaching Geometry. Students get a hands on a visual approach to exploring Geometric properties and proving theorems.

APOLLONIUS

This is a paid app ($3.99) featured in the ITM video, but that is cheaper alternative to purchasing Geometers SketchPad.
Apollonius is an Interactive Geometry Software (IGS) for the iPhone and iPod Touch. It allows you to make geometric constructions (such as those made using a compass and straightedge/ruler) and move their parts smoothly using the device's touchscreen.
Apollonius was inspired by similar software for personal computers, such as Cabri and The Geometer's Sketchpad.
An example of a simple construction that can be made with Apollonius is a triangle with its medians, heights, and angle bisectors. Moving the vertices of the triangle will then simultaneously move the medians, heights and angle bisectors accordingly.
Apollonius remembers your last construction when the program is closed. It also allows you to ZOOM and SCROLL your construction, providing a very large virtual screen.

Geometry Pad

This is a FREE app through iTunes. It is a great app for exploring Geometric Properties.

With the Geometry Pad you can create fundamental geometric shapes, explore and change their properties and calculate metrics. The shapes are displayed on a scrollable and zoomable workbook with a rectangular coordinate system. There are many functions to the Geometry Pad. Vist the link to learn more

Some of the tasks you can solve with Geometry Pad:
- Create geometric shapes and measure all its possible metrics like length, angle, area, perimeter, intersections, distance between points, angles between lines.
- Move/resize geometric shapes and watch how its metrics are changing in real time.
- Demonstrate circle theorems by creating and changing inscribed and center angles.
- Demonstrate theorems about incircles and excircles locations.
- Create and annotate complex geometric figures. Share them through export to image and e-mail features

More Math Resources

National Library of Virtual Manipulatives

NLVM can replace or supplement classroom manipulatives such as counters, pattern blocks, algebra tiles, ect and as well as provides many simulation applets. It is a  Free library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-12 emphasis).
"Learning and understanding mathematics, at every level, requires student engagement. Mathematics is not, as has been said, a spectator sport. Too much of current instruction fails to actively involve students. One way to address the problem is through the use of manipulatives, physical objects that help students visualize relationships and applications. We can now use computers to create virtual learning environments to address the same goals."(http://nlvm.usu.edu/en/nav/siteinfo.html)

 

Wolfram Alpha  (link to App download)

Wolfram Alpha is a paid iTunes app ($2.99) featured in the ITM Math-App-looza video. It provides a great resource for math teachers to help student understand mathematics on a deeper level.
With a simple input of sin(pi/5) = ?, students are directed to a page in which they are given 3 different answers and 9 other mathematical representations of sin(pi/5).

"Wolfram|Alpha introduces a fundamentally new way to get knowledge and answers—
not by searching the web, but by doing dynamic computations based on a vast collection of built-in data, algorithms, and methods..... Wolfram|Alpha's long-term goal is to make all systematic knowledge immediately computable and accessible to everyone."  (http://www.wolframalpha.com/about.html)

Protractor Tool App

An engaging app consisting of a multi-functional 180 degree protractor that enables the user to measure and understand the relationship between different objects and varying angles. Choose from 12 shapes/objects to resize, rotate and measure. Students in grades 3 and up can practice Geometry as outlined in the NCTM and Common Core State Standards for Math. Ideal for learners age 8 and up

 

Math Ref (Formula and Conversion Reference App)

Math Ref is an award winning education app. With it you can browse over 1,400 formulas, figures, and examples to help you with math, physics, chemistry and more. Use an expanding list of helpful tools such as a unit converter, quadratic solver, and triangle solver to perform common calculations.

As I said before now that technology has put the knowledge of the world at our fingertips, I feel it is more important to teach students to apply this knowledge rather than memorize facts. In the real world if for some reason you need to know how to find the volume of a cylinder a quick google search will return the formula needed for the calculation. So, I ask is it necessary that we require students to memorize formulas and equations, or should we show them how to utilize, understand, and apply the resources that are available.  A math formula reference list is a great tool that I would encourage students to use for problem solving.

Graphing Apps

KineMath

Paid iTunes App ($7.99)  I would use this app for discovery learning to help students better understand complex algebraic and trigonometric functions.

Inside this intuitive, real-time app, students can manipulate twelve different functions, interact with graphs and plots, copy and export their work into other applications, even view examples for deeper understanding. Everything from basic linear equations to quadratic equations in vertex and generic form is covered, as well as sophisticated trigonometric functions. All of these to be explored at the touch of a button or the moving of a few sliders.

Graphing Calculator HD App

Paid iTunes app ($1.99)
Graphing Calculator HD turns your iPad into an intuitive high-resolution function plotter and scientific calculator.

Computer Programming/Coding Resources

There is a big demand for computer programmers and app developers. Since these mobile technologies are the future, more people are needed who can develop the software programs for them. Programming/Coding envelops all aspects of mathematics. Programs are wrote using logic and algorithms (fundamentals of mathematics). This is the answers to the question "When am I ever going to use this in Real Life?" As the ITM video below says, the people who can code seem to have super hero powers compared to those who do not. For my math degree I was required to take two Computer Programming classes. This shows that understanding how codes are written is an integral part to the future of mathematics education. I would love to be able to implement lessons on developing and writing computer algorithms into my curriculum. Below are links to resources/programs for coding and a video from ITM.

CODE HS

Code Academy

Coder Dojo

Video from ITM on the necessity of teaching Kids to Code

ED505 classmates please check out http://t.co/XN2ARe8FCG or follow @itmshow for some cool ideas on technology and education #ED5059413UWA
— Andrea Collins (@ACollinsUWA) July 1, 2013