A recent email has brought to my attention how poorly I have been maintaining this Teach Math with Tech WordPress site. By way of an excuse, all that can be said is that I have been totally engrossed in the work I am doing, and have had little time to write about it. However, resolution for 2013 is to try to write at least one post per week, as the use of this technology is more commonplace.

While at a recent conference in Las Vegas, I noted that many educators refer to iPad use as tablet technology. As a Hewlett-Packard tablet PC user for the past six years, this caused some confusion, as my assumption of a tablet is the allowance for pen-based input. The importance of having a stylus for teaching mathematics in the traditional ‘chalk on blackboard’ classroom gives the ability of solving problems in a step-wise manner, scrolling back to answer questions, and saving and posting notes with complete solutions.

The email asked for an update of devices used for pen-based computing. After four years of teacher/student use of sixty tablet PC’s in the classroom (sometimes 8-10 hours per day) my first choice is still the Hewlett-Packard tablet PC. I am quite excited to try the HP ElitePad 900 set to release in January http://www8.hp.com/us/en/ad/elitepad/features.html. Some other options: Fujitsu Q702, Microsoft Surface, Samsung Galaxy 7, Lenovo Thinkpad Tablet 2… can begin a Google list.

You can also turn any laptop into a pen-input device with the purchase of a Wacom Bamboo Tablet (<$100) http://www.wacom.com/en/products/pen-tablets/bamboo

Having tried pen-input on an iPad, I have found it lacking in that too much time is taken by having the pen re-orient itself every time you lift it and that you can’t rest your hand on the screen. I have recently read that Doceri GoodPoint can eliminate some of these issues, however, the fact that you have to change settings, adjust to hand position etc, makes me wonder why you would want to bother. Further, the fact that Apple products don’t support flash is too limiting in a classroom that requires students to surf the net for interactive learning objects to supplement their understanding.

Please let me know if there are other pen input devices that you have tried and had success with in the classroom.

On a side note, another website I have recently been investigating is Gooru http://www.goorulearning.org/gooru/index.g#!/home. This has quite an extensive list of mathematics, science and social science learning objects, neatly categorized by their resource type. Definitely one to give a try.

## Pen-Based Computing in Education

## Incredible Mathematics Resources

For those of the uninitiated, Twitter is a fantastic way to ‘filter’ the infinite resource that the internet provides. By carefully selecting people to follow (key note speakers at conferences, leaders in particular fields, interesting personalities, news magazines…), you can keep up to date with all of the latest by logging in for only a few minutes a day. Regardless of how randomly you check in, you will always find some interesting and illuminating conversation or links. You will also probably need a bookmarking system, like Diigo, to keep a record of all of the papers, PDF’s, blogs, and articles that you might like to return to.

For example, from following Twitter, I now have the Jim Vanides Daily! http://paper.li/jgvanides sent to my email. As I quickly scan the education and technology pages, I will often find at least ten links that require further perusal. Yesterday, there was a posting for a link called Show the Math http://showthemath.org/

As mentioned previously, I use a pen-based tablet, with a stylus for teaching and writing all math notes. I find typing math to be tiresome and restrictive. However, in class, I use the web all the time, to provide animations, applets and real-world applications for students to make their math ‘come alive’.

What I like about this site from Question Press is that students can enter their own algebra equation. My plan for using it in class would be to have students start by all answering the same ‘skill testing question’. They could then work through it individually, and perhaps share answers in pairs. Answers could be captured using the ‘snipit’ tool from the Microsoft accessories.

Using a poll, all final answers could be entered and students would vote to choose the best answer. Once a correct answer is determined, the discussion would centre on the incorrect answers, and which processing error makes them incorrect. To summarize, the mnemonic device BEDMAS, would provide a quick way to remember the process.

So, why would I choose this applet instead of simply having students write in a solution using their stylus? What I like about it is that this applet requires the user to pick a step (in green), before they carry on and supply the equation. Much as students may have memorized the BEDMAS term, they may not really understand its meaning, or why it is necessary. Using this site, students have a clear record of their steps, and can quickly compare it to their classmate’s or the correct answer, to self determine where their error may have occurred. In addition, a few weeks later when students return to this work while studying, it’s clear presentation should make for an easy reminder of what occurred during class time.

Once students are confident in their understanding of the processes required to correctly solve equations, I would recommend you try an algebra worksheet generator such as that provided by math.com http://www.math.com/students/worksheet/algebra_sp.htm. I have several reasons why I like this one, but mostly because a student decides how many questions they need of each of the different types (rather than me blanket-assigning they do 40 questions). The worksheet is randomly generated so each student will get a different assignment every time they request one. I find it best if students print the answers, so they can self-correct as they work through their solutions.

Why not take a look at these sites and see if you can suggest other ways of using them?

## Technology Integration in Mathematics

Mathematics is one subject discipline that has been slow to integrate technology into teaching. As a mathematics college teacher that completely understands the infinite resource the internet provides, I can suggest several reasons.

Too much time is taken in information transfer using the traditional chalk on blackboard/students copy into notebooks. To eliminate this step, our plan was to convert binders full of ‘lecture notes’ into Word files. The e-notes would provide scaffolding for teaching – questions typed with plenty of space for students to formulate solutions. E-notes were posted to the learning management system (LMS) before lectures so students could download and bring to class. Teachers initially used overheads, the document camera, and finally tablet PC’s to ink in solutions. Sounds like a simple enough plan, however, typing mathematics formulation is not only tedious, but time consuming as well.

Initially, we used the insert tab and then symbol available in Word. If you haven’t tried it, I challenge you to type ‘one-third times one-third equals one-ninth’. Each step requires you to ‘insert-symbol-⅓-insert-close’. After pages of typing mathematics formulations, you can understand the difficulty. Some typing issues can be minimized by adopting an online textbook, which is projected to the screen for all to view. This still required students to write down questions (time wasted). Also, if you not a math teacher that ‘teaches to the book’, and have tried for years to find an applied calculus textbook that teaches **without** flywheels, gears, football fields, and bullets, you can understand the difficulty.

It made sense to purchase software –

our choice was MathType (30 day trial http://www.dessci.com/en/products/mathtype/trial.asp)

The equations you prepare are automatically dropped wherever the cursor is left in the word doc.

We find using MathType makes our notes look more professional, the equations are properly formatted, and can be quickly altered and re-saved for multiple use of the same form.

For teaching math, demonstration of problem solution must occur in a stepwise fashion. It is not possible to type solutions while teaching – students would quickly become disinterested. Our solution was to purchase HP tablet PC’s for the math faculty. E-notes are loaded into the Microsoft Journal feature of the tablet, and using the pen (stylus), solutions can be hand-written and projected. With an eraser on the end of the stylus, and highlighters/different pen colours and thicknesses just a click away, teaching mathematics with this technology has taken a large step forward. As mentioned, I rely heavily on the internet to provide real-life examples of mathematical concepts we are working through. The use of learning objects, applets, Web Quests and articles that demonstrate the importance of math in daily living are a necessary component of my lectures. The problem with Journal is that you can’t embed a URL your notes and be able to directly link to a website. We did come up with a solution, but that will have to wait for another post.

I would like to share of few of my literally thousands of websites (in all disciplines) that I have found. I intend to find a separate place on this blog to categorize them and begin posting. Please let me know if you think that would be of interest. Here are three favorites to start:

**Boring math given value**: http://www.freerice.com/category

This site is run by the United Nations World Food Program. For every correct answer, 10 grains of rice are donated to end world hunger – a bowl of rice is 10 correct answers. I use this site as part of my introductory lecture in college developmental mathematics classes. Instead of asking students to review their multiplication tables, why not ask them to help a child in need by gathering as many bowls of rice possible in a given time period?

**The one that started it all**: http://www.calculus-help.com/tutorials

While thinking about the uncomprehending faces of students trying to understand the calculus concept of limits, I searched the internet for a some help. Luckily, I happened upon the Calculus Phobe. After watching their simple, funny, animated videos, even I understood better. Five years ago, this was the one that started it all. I showed a segment in class and gave students the link – they watched them all. Anecdotally, I noted that students could picture the concept, their questioning changed, they recommended the videos to other students, and I felt their marks reflected a higher level of understanding. That sent me on my quest – some people collect stamps, I collect learning objects.

**Geometry tailored to every need**: http://www.mathopenref.com/

First semester students have a range of math experiences – especially in geometry. Some have had it drilled into them since grade 4, others did not learn the terminology in English, and some may not have used it in 30-40 years. In class, students are given a note framework to guide their understanding and directed to the open reference link. Some just remind themselves – a quick ‘play’ with the applets is enough. Others use the applets and the definitions to tie meaning to their own language. For those that need a more extensive refresher, they play with the applets, read the definitions and practice the quizzes. Something for everyone…

## Why pen based tablet pc’s?

With all of the hype about the 2011 Consumer Electronics Show (CES) http://www.cesweb.org/, it seems fitting to write my first blog about ‘Why pen-based tablet pc’s?’ in the classroom.

Before using tablets, I wasn’t really engaged in technology for mathematics teaching. Until 5 years ago, my internet experience was limited to the odd email or looking up a phone number/map. In my first year of ‘back to full time teaching’, just staying prepared for the students seemed a difficult enough task. Once teaching, I was exposed to our learning management system (Blackboard), but with so much else to learn, all I had really mastered by the end of the first year was email and posting announcements for students. As a math teacher, I found adapting to a keyboard for typing math difficult and required me to think in ways that weren’t as natural as pencil on paper, especially as I can be quoted as saying ‘I can’t think unless I have a pencil in my hand’. Writing on a board seemed to have worked for my teachers, so why should I be the one to change the way it has been done for the past hundred years or so?

By the start of my second year, my classroom concerns overtook my hesitation to investigate what technology might have to offer. As the courses I teach have common final exams, my emphasis was on ensuring that I had covered all of the required content. Of some frustration was the process of *n* (*writing lengthy problems on the board, waiting for students to copy them down, writing solutions, moving aside for students to copy, erase and repeat). *Being height challenged, not always having clear handwriting, teaching in large lecture halls – added to my angst. I knew that this was not the way I wanted to teach – nor, **I am quite sure**, the way this generation of students wants to learn. In order to eliminate the time wasted by this copying/recopying method, I decided to learn Microsoft Word and type my class notes. This ‘framework’ of notes had many of the shortcut methods I had developed from 20 years of math tutoring, followed by questions with plenty of space for student solutions. Many hours were spent typing as I was new to Word, using the limited math functionality that was available at the time, and figuring out how to post to the LMS. However, it worked, as students would download the documents and write into them. This allowed us more class time for discussion and sharing of information.

With a small bit of success, it was necessary to keep moving forward. The first step was to convince the ‘people with money’ that software was required to make typing math more intuitive – so we ordered MathType http://www.dessci.com/en/products/mathtype/. The next logical step was to copy the ‘course documents’ onto acetates and use the overhead projector. The value added by this progression was that I was now facing the students and could see the looks of puzzlement/agreement to judge for myself their level of understanding. In addition, I could leave the front of the room and wander amongst them while they were working to engage in conversation as they solved problems. I magnified that effect by asking to have peer tutors in the room – in particular in the large classes of 70-80 students. (The effect of peer tutoring will be the subject of another post). Sometimes, I could even convince a student to write their answers into the acetate spaces so that others could see how they solved and then learn in a way that may be more familiar to their thinking. The overhead projector failed to be the ideal in that it was difficult to see from the back of the hall (especially exponents), it projected in only one colour (difficult for graphing), and unless acetates were washed, a costly waste of non-recyclable plastic.

In the break before the next semester, I mastered the document camera. The advantage of using the doc cam was that it projects from note paper (no more acetates hanging to dry in my office) and it has the ability to zoom into a particular portion of the page. Although still required to be at the front of the room to navigate, it seemed like the perfect technology for teaching mathematics, as we could write in solutions in a stepwise manner that could be seen by all. The importance of being able to ‘write in’ answers, one step at a time as a collaborative discussion is a must for math teacher. Further, it did project colour, so graphing and highlighting became that much easier. The zoom feature was great, however, it required the instructor to continuously look over their shoulder to make sure they were still writing on the screen – students were quick to let you know when you have wandered off.

The type of mathematics we teach is very much applied. It is important that the student be strong in the skill, but in order for them to remain engaged, they must know how this skill will benefit them in their chosen career. With each concept taught, about 30% of the time is spent teaching/reinforcing the skill and the remainder, in how it is used in the laboratory. We recognized quite early that Web 2.0 could provide a powerful tool to make mathematics classes ‘come alive’. After 30 years of teaching fundamental understanding of calculus, I discovered the ‘Calculus Phobe’ http://www.calculus-help.com/tutorials who, with animation and simple direction, gives a fantastic explanation. (The importance of learning objects will be the subject of another post). The problem then became the inability to make an easy transition between the internet and the doc cam, in particular now that I was going to the internet sometimes 3-4 times per lecture.

After 1.5 years of listening to my rants about making the technology work for teaching mathematics, the Dean placed an HP pen-based tablet PC into my hands. I now had the perfect tool – I could bring the previously designed Word doc note framework into the Microsoft Journal and write on using the ‘stylus’. The software has multiple colours and thickness of pen as well as highlighter. Make a mistake? Simply turn the stylus over and erase (as you would with a pencil). A student wants you to go back in your lecture? Simply scroll to the location and continue with your discussion. Demonstrate a learning object? The internet is at your fingertips. Bring up the online textbook to show the pages you are working from, or project questions for students to work on while in class. What could be better? Actually having all of the students with the same technology capabilities available to them is.

From there, as they say, the rest is history. Having, fully understood the importance of pen-based tablet technology for teaching mathematics, again my visionary Dean suggested that we apply for a Hewlett-Packard Technology for Teaching grant. We were the fortunate recipients, and in the fall of 2008, opened our first tablet lab. Students, having their own tablet to use in the classroom, were connected to their teachers using collaborative software. Obviously, many more stories to be told here…

After teaching for almost 30 years, I must admit, I will never go back to teaching mathematics in any other way. Now that I have made this five year progression from whiteboards to tablets, my advice regarding all of this hype about ‘tablets, tablets, tablets’ – **Educators, if you really want a tool that will benefit students for every course in their syllabus, make sure to choose a tablet that comes equipped with a pen (stylus). **

Enough for now, please feel free to comment…