As a college math instructor, I am a huge advocate for technology use in the classroom and regularly use my iPhone and iPad to enhance the learning experience for my students. Between using apps on the classroom projector, enabling Guided Access for student devices during exams, and preparing content at home, my iPhone and iPad are essential tools for me as a teacher.
As an adjunct (part-time) instructor, I am not required to hold office hours, nor do I have a space to do so if I wanted. To make up for this, I encourage my students to contact me through email for questions and hints. So the first, and most obvious, way I use my iPhone is for emailing my students. I love being able to respond to my students at any time, because it shows them that I care, and it ultimately makes me more approachable.
Since my response to most emails require the use of mathematical symbols, I turn to my iPad and Noteshelf to handwrite my responses to eliminate any confusion for my students. My stylus of choice is the Pogo Sketch Pro. Once I have my response written up nicely, I email it to the student as a PDF. Then I post it to my website for other students to benefit from, as well.
During class, I use the projector combined with a 30-pin to VGA Adapter and my iPad to graph equations with Quick Graph. I could use my TI-89 graphing calculator, but Quick Graph is a much faster and better looking option. It's even better than using Grapher on my MacBook Air. My students are always impressed and often download Quick Graph right there in class to mimic me and follow along.
Speaking of calculators, for courses where I allow calculator use on quizzes and exams, Guided Access lets me allow students with iPhone and iPads to use their device as a calculator. At the start of the exam, I lock them into a calculator app that I approve of; then when they turn in the exam, I grant them full-access to their device by entering the password. My students really like this because it's one less device to buy and carry around.
After taking a quiz or exam, students immediately start asking for solutions so they can see how they did and to study for their final exam. That's where Notability comes in. As much as I love Noteshelf, it doesn't support PDF annotation, so I turn to Notability for writing up solutions by importing my files directly from Dropbox. Another option would be to write on a physical exam, then use Scanner Pro to "scan" it into PDF form, but Notability allows me to make use of rich colors and crisp pen strokes, and easily fix any errors I make. Once the solutions are written up, I post them to my website as a downloadable PDF.
In addition to using my website to give students access to important PDF files, I also use it to post homework assignments and any other important announcements relevant to the course. Sometimes I do this on a Mac, and other times I use WordPress on my iPhone or iPad.
Before I upgraded to a Bamboo tablet and Camtasia 2 on my Mac, I used Doodlecast Pro on my iPad to record videos for difficult topics we were learning. Combined with my Pogo Sketch Pro, I was able to easily post instructional videos to YouTube that my students found very valuable.
With teaching, comes grading. To keep track of my students' grades, I use Numbers on my Mac, iPad, and iPhone. I primarily use my Mac, but if I need to update a student's grade in class, I will usually pull out my iPad and make the correction right there in front of the student. It's also great for those inevitable times when a student wants to know where they stand in the class right now.
And that about sums up how I use my iPhone and iPad as a mathematics instructor. If there's any other teachers around, I would love to hear how you use your iOS devices to enhance the learning experience for your students.