## iOS Apps for Mathematics and Physics

### Technology tools to make learning fun!

Math and physics often get a bad rap - ask most people what their favourite class in high school was and odds are you won't get either one.  Even if you mention those classes, you'll probably get a surprised look (at best!)... but not always.  For some, math and physics were the classes in which they excelled and were excited by.  What made it that way, you might ask?  Often, they will say that the material was presented in a way that made it captivating and fun.  We as teachers need to be able to present our courses in ways that make them interesting to our students - and with technology as far as the eye can see nowadays, why not use it to help?  I've chosen some of my favourite iOS educational apps and described them here, aligned with a specific learning outcome. Happy app hunting!

# App 1: Math 42

## Math 9

Specific Outcome: Model and solve problems, using linear equations of the form:

• ax = b
• x/a = b , a ≠ 0
• ax + b = c
• x/a + b = c , a ≠ 0
• ax = b + cx
• a(x + b) = c
• ax + b = cx + d
• a(bx + c) = d(ex + f)
• a/x = b , x ≠ 0

where a, b, c, d, e and f are rational numbers.

Whew... that's a mouthful even for me, and I have a math minor!  Even though some of these equations were already seen in Grades 7 and 8, they are often quite difficult to understand; especially how to solve them.  Math 42 is an app that not only can solve these equations, but show the steps used to solve them.  It can also be used as a sort of textbook - many words and terms are defined, so that if a student doesn't understand something (and the teacher isn't available - say if the student is doing homework), they aren't completely on their own.  Finally, the app has what it calls an "assessment centre" - essentially a section where the student can test their knowledge in a certain topic (linear equations is one) at varying difficulties (easy, medium or hard).  The user can also keep track of their progress over time.  Another good thing - the app isn't just for students at a Grade 9 level - it is advertised as a learning tool for students in Grade 5 all the way to Grade 12.  In fact, it could even be useful to the first-year university student, with its sections on calculus and advanced algebra.

Pros:

- Excellent and easy-to-use interface

- Huge amount of information

- Useful at many levels

- Available in French

Cons:

- Could be used as an "answer machine" for class work

- Paid app (\$2.99)

Conclusion:

A great app.  Despite its possible use as a simple calculator, its functionality and power is amazing and well worth the small price.

# App 2: Electrons

## Physics 30

Specific Outcome: Students will explain electrical interactions in terms of the repulsion and attraction of charges.

This deceptively simple app models electric charges.  Simple enough, right?  Well, not quite... first of all, learning about electric charges can be very counterintuitive (how can something so powerful be so small?).  In addition, it is often impractical and dangerous to experiment with electricity.  This app offers ten guided experiments concerning charges (for example a cathode-ray tube simulation, which is becoming more and more difficult for teachers to model, as tube TVs disappear), an eleven-page "mini-textbook" and many other interesting interactive activities.  In particular, the app's explanations of electricial phenomena are both clear and complete.  A good addition to a Physics 30 class.

Pros:

- Very interactive displays and experiments

- Clear and concise

Cons:

- Paid app (\$1.99)

Conclusion:

Like the subject itself, Electrons is deceptively simple!  Play around with it for awhile to discover its many features.

# App 3: Video Calculus

## Math 30, 31

Specific Outcome: Too many to list!  I will pick one from Math 31:

Students will demonstrate competence in the procedures associated with derivatives, by differentiating polynomial functions, using the derivative theorems for sum and difference.

Grade 12 math can be frightening... for those going on to higher education, it's often the prerequisite to university calculus (and for those in Math 31, well hey, they get it a year early!) and for the others, they'll say quite often that it was the most difficult class they had.  Video Calculus, as its name implies, is a collection of  (sometimes funny) tutorials intended for students in high school and first-year undergraduate math (at least that's what the app's description states - the inclusion of differential equation videos stretches its usefulness into third-year).  Students can access free lessons concerning limits, derivatives, integrals and more.  The app is free to install, but has extra sections available for a cost.  This subject often has a stigma (calculus?!?) but it sure doesn't have to.  Video Calculus' tutorials are easy to understand and follow.  As well, it is possible to take notes within the app itself.  A good reference for math students.

Pros:

- Free (to start)

- Clear explanations

- Simple interface

Cons:

- Full app functionality is not free (a "video pass" must be purchased, giving the user access to all videos for a certain amount of time - 30 days for \$4.99, 90 days for \$8.99, 180 days for \$14.99, 360 days for \$19.99)

- Requires Wi-Fi

Conclusion:

A good, although slightly flawed (video passes required for full functionality) resource.  Still much cheaper than a textbook!

# App 4: Mechanics

## Physics 20

Specific Outcome: Students will predict the mass of a celestial body from the orbital data of a satellite in uniform circular motion around the celestial body.

Mechanics is an app which covers exactly what it says: mechanics at a high school level (kinematics, dynamics, energy, momentum, rotation and gravity).  Written in a informal, conversational style, Mechanics explains the basic ideas behind many important concepts in physics.  It also has several interactive examples and a final test for each unit.  While its content isn't quite limited to Physics 20 (momentum is presented in Physics 30 and most of the other units are reviewed), that is not a point against it.  I would say that this is a good introductory app, for those who need a little clarification (usually from those physics teachers who talk too much!) but it is not intended as a serious study guide.  Still, simplicity is a virtue, espcially in physics, and this app is definitely an example of that.

Pros:

- Probably the easiest physics definitions I have ever read

- Wide subject variety

Cons:

- Paid app (\$1.99)

- Not meant for in-depth study

Conclusion:

Quite honestly an excellent app.  The cons shouldn't even figure into your decision - BUY IT.

# Math & Physics, all levels

Specific Outcome: Take your pick, it'll probably have something for it!

This list wouldn't be complete without WolframAlpha.  It is the educational "rock-star" app (and I wish it were around when I was in junior high and high school!).  Sometimes described as a "scientific Google", WolframAlpha is a multidimensional computational search engine.  An offshoot of the Mathematica coding software, WolframAlpha is intended for students and professionals alike, in any subject.  The following video is a great example of the power of WolframAlpha (just ignore the part about pi - he's not quite right!):

DISCLAMER: DON'T CHEAT ON YOUR TESTS!

Now that that's out of the way, on to the rest.  As the video shows, WolframAlpha allows input in plain English (but only in English), which is great for those people who don't know how to code (in fact, Mathematica allows input in plain English as well, but its increased functionality is definitely not worth its base price of over \$100 - only for engineers, scientists, mathematicians and physics majors such as myself need purchase it!).  I have one small complaint about this app, if it can be called a complaint.  It doesn't compute everything (boo hoo!).  Sometimes the input (for example, an equation) needs to be rewritten (by using normal brackets instead of square brackets for instance) for it to work.  For more complex problems, features such as the step-by-step solution finder are not available.  Minor quabbles.

So then why did I talk about Math 42?  I found that Math 42 was designed more as a pedagogical aid, rather than what WolframAlpha is, essentially, a computational calculator.  Sure, both do the same things (in math at least) but WolframAlpha is not really intended as a study guide (though it will define any word you type into it, with extra information on a corresponding web page).  Still, it goes without saying that WolframAlpha is, in one word, terrific.

Pros:

- The "smartest" thing ever

- Possible to research almost anything

- Enormous functionality

Cons:

- Paid app (\$2.99)

- Searches need to be made using concrete language (vague descriptions and words are not handled well) - it may take a bit of practice to get the hang of this

Conclusion: