As always, I have to thank our AWESOME sponsors for the 2010 workshop (without these companies and organizations there would be no workshop):

• Muskegon Community College
• Techsmith
• Wolfram Research
• Design Science
• Wacom
• MichMATYC

You can participate in this week-long workshop at three levels:

Technology Explorers: This week-long workshop is designed to assist college mathematics instructors to get up-to-date on technology for teaching mathematics and to begin to participate in Web-based instruction. The workshop will cover a wide variety of topics and skills all related to teaching mathematics with technology and the Internet. Participants will go back to their campus with a plan for how they will incorporate technology into their teaching. Participants will also receive free copies of some of the software they have learned how to use. 2010 graduates will receive Camtasia Studio, SnagIt, Mathematica, MathType, USB headsets, and Wacom peripheral tablets! Registration fee is $150. There are 26 spaces available.

Technology Adventurers: The advanced workshop is designed for instructors who already have quite a bit of technology experience, or for returning participants. We take a look at designing digital presentations in a variety of forms, social networking, blogs, virtual worlds, and much more. Advanced participants have about half of their time free to work on projects of their own choosing. Advanced workshop graduates will receive Camtasia Studio, SnagIt, and Mathematica. Registration fee is $100. There are 26 spaces available.

Technology Navigators: Many participants from past workshops have expressed an interest in returning for the week just to hang out and work on their own projects. We can provide quiet spaces for you to work (and soundproof ones if you’d like to record videos). We’d love to have you back, but we also need your help to pass on what you’ve learned and to keep this workshop going. Registration fee is $50 with 4 hours of volunteering, or free with 8 hours of volunteering. (Limit? How many of you want to come?)

Workshop Director: Maria H. Andersen, Muskegon Community College
Assistant Director: Elizabeth Hamman, Cypress College
Mathematica Training: Debra Woods, University of Illinois – Champaign

This workshop is both awesome training and a fantastically good time.  To read about last year’s workshop, go here. Many participants pay out of their own pocket to attend because there’s nothing else quite like it.  I look forward to meeting this year’s crop of participants!

For directions on how to get pre-registered on November 13, or for information on travel & lodging  go to the workshop website.  We will do our best to chase away the freak thunderstorms this year!

The students started by doing their own Internet research, and then were placed in groups of 3 to focus on a particular topic. Each student was asked to interview a math instructor as part of the project to find out the details of the particular study strategy they were assigned.

Their projects generally fall into three categories:

• General Organization, Note-taking, and Time Managment
• Specific Study Strategies that can be used
• Managing Stress so that you have a good test-taking experience

All of the projects can be found on their website: How to Study for a Math Test.

It’s a nice resource written by students for students, and I hope that many of you will pass it on to your classes.

Believe it or not, it was scarier to watch the video than to do the interview!  I think I will tuck my hair behind my ears next time.

The Sputnik Observatory, is dedicated to providing a venue for viewing and sharing ideas and philosophies of contemporary culture.  Jonathan Harris, who worked on the mindblowing sociological website We Feel Fine, is the site director and blog creator for Sputnik Observatory.  Sputnik also has a host of codirectors with diverse backgrounds in journalism, architecture, and ballet.  Members of Sputnik have spent the last ten years interviewing scientists, philosophers, academics, and the like.  They have over 200 videos of conversations on themes such as coherence, interspecies communication, and urban metabolism.

“Sputnik Observatory is a New York not-for-profit educational organization dedicated to the study of contemporary culture. We fulfill this mission by documenting, archiving, and disseminating ideas that are shaping modern thought by interviewing leading thinkers in the arts, sciences and technology from around the world. Our philosophy is that ideas are NOT selfish, ideas are NOT viruses. Ideas survive because they fit in with the rest of life. Our position is that ideas are energy, and should interconnect and re-connect continuously because by linking ideas together we learn, and new ideas emerge.”

Here are some of the short interviews that involve mathematics (and all really COOL mathematics).  All of these can be embedded into course shells.

Will Wright - Possibility Space

Ian Stewart - Alien Mathematics

Ian Stewart - Pattern-Seeking Minds

Lord Martin Rees - Simple Recipe

Trevor Paglen - Geologic Agents

Jacques Vallee - Information Universe

For at least a decade, we have had the ability to let CAS software perform computational mathematics, yet computational skills are still a large portion of the mathematics curriculum. Enter Wolfram|Alpha. Unlike traditional CAS systems, Wolfram|Alpha has trialability: Anyone with Internet access can try it and there is no cost. It has high observability: Share anything you find with your peers using a hyperlink.  It has low complexity: You can use natural language input and, in general, the less you ask for in the search, the more information Wolfram|Alpha tends to give you. Diffusion of innovation theories predict that these features of Wolfram|Alpha make it likely that there will be wide-spread adoption by students. What does this mean for math instructors?

This could be the time for us to reach out and embrace a tool that might allow us to jettison some of the computational knowledge from the curriculum, and give math instructors greater flexibility in supplemental topics in the classroom. Wolfram|Alpha could help our students to make connections between a variety of mathematical concepts. The curated data sets can be easily incorporated into classroom examples to bring in real-world data. On the other hand, instructors have valid concerns about appropriate use of Wolfram|Alpha. Higher-level mathematics is laid on a foundation of symbology, logic, and algebraic manipulation. How much of this “foundation” is necessary to retain quantitative savvy at the higher levels? Answering this question will require us to recalculate how we teach and learn mathematics.

There are two videos embedded in the slideshow. You should be able to click on the slide to open the videos in a anew web browser. However, if you’d just like to watch the video demos, here are direct links:

• Complexity and Relative Advantage:  Comparing the use of Mathematica to Wolfram|Alpha (for educational purposes, 2 minutes)
• Trialability and Observability: Demonstration of how the use of W|A is likely to spread via direct online contact (sounds like a virus, doesn’t it? 5 minutes)

Note that I’ve turned ON commenting for these two video demonstrations and I will try to load them into YouTube later this weekend.

There are several other posts about Wolfram|Alpha that you may want to check out:

• What we’re doing with Wolfram|Alpha
• Don’t get Wolfram|Alpha? Try these examples
• Shaking Up Math Education
• Impact of Wolfram|Alpha on Math Ed
• Chemistry Takes a Hit Too
• Implications for Math Instructors

If you were at the live version of this talk, and you would like to rate the presentation, you can do so here at SpeakerRate.

Discussion Boards: Wolfram|Alpha + Jing = Awesome

Before Wolfram|Alpha, it could take several steps to get a graph or the solution to solving an equation to the discussion board in an online class.  You had to use some program to generate the graph or the equations, then make a screenshot of the work, then get that hyperlink, image, or embed code to the discussion board.

With Wolfram|Alpha, sometimes a simple link suffices.  Suppose, for example, I needed to explain the last step in a calculus problem where the students have to find where there is a horizontal tangent line.  After finding the derivative, they have to set it equal to zero and solve the equation (and calculus students notoriously struggle with their algebra skills).  Rather than writing out all the steps to help a student on the discussion board, I could just provide the link to the solution and tell them to click on “Show Steps.”

Sometimes, a bit more explanation may be required, and in these circumstances, Jing + Wolfram|Alpha really comes in handy.  For instance, I needed to show how to reflect a function over the line y=1.

Here’s what the reflection over y=1 looks like.  If you graph y=sqrt(x) and y=-sqrt(x)+1 you will see that they are not reflected over y=1.

Here’s another example of Wolfram|Alpha + Jing:

Classroom Demonstrations

We’re also finding that Wolfram|Alpha can be a good program to use for exploratory learning.  One of the subjects we cover in Math for Elementary Teachers (MathET) is ancient numeration systems.  Rather than just tell students how the Babylonian number system worked, students can use Wolfram|Alpha to explore the number systems until they’ve worked out the pattern.

1. Start by exploring numbers under 50 (42, 37, 15, 29).
2. Now ask students to figure out where the pattern changes (hint: it’s between 50 and 100).
3. Explore numbers in the next tier and see if they can figure out at what number the next place digit gets added.
4. Discuss how a zero is written (and why this is problematic).

Supplement to Online Course Shell

Another topic in Math for Elementary Teachers is learning to perform operations in alternate-base systems (like Base 5 and Base 12).  You can easily supplement your online course shell by providing additional practice problems and then linking to the answers with Wolfram|Alpha.

1. Find the sum of 234 and 313 in base 5.  (answer)
2. Subtract 234 from 412 in base 5. (answer)
3. Multiply 234 by 3 in base 5. (answer)

Student Projects

Wolfram|Alpha has also started making its way into student projects because of the ease of just linking to the mathematics instead of writing out or drawing the math.  Here are a few examples.

For one of the calculus learning projects, the group built a mindmap that demonstrates the graphs and translations of exponential and logarithmic functions.

Another group recorded some help tutorials on using Wolfram|Alpha for evaluating limits.  Here are two of their videos (one with sound and one without).

Several of the MathET students have used Wolfram|Alpha and Wolfram Demonstration links as they mapped out the concepts in our units.

Checking Solutions and Writing Tests

Personally, I’m finding that I use Wolfram|Alpha from a simple calculator to a CAS for checking answers as I write a test.  I’ve also been snagging images of graphs from Wolfram|Alpha to use on tests (use Jing for simple screenshots). Here’s a short 1-minute tutorial on how to change the plot windows to get the image you desire.

Homework Day

Oh, I almost forgot to tell you.  I’ll be down in Champaign, IL for the rest of the week at Wolfram Research.  Tomorrow I’ll be one of the “experts” participating in Wolfram|Alpha Homework Day (a live, interactive web event).  The events begin at noon (CST) and end around 2am.  I’ll be interviewed somewhere around 3 pm and participate in a panel discussion about technology and math education at 8pm.

And so, somehow we ended up doing a Travelogue on our adventures in India.  Today I am wearing my sari to work …

I thought I would also share with all of you (each link opens a video, all built using Animoto).

Here is Southern India:

• Cochin, Blog post:  Sights in Cochin (about traveling in India with a blind man) and the Sari Department Store
• Backwaters of Kerala, Blog Post: Morning walk in the Backwaters
• Countryside of Kerala
• Wildlife in India
• Adventures in Madurai
• Train to Pondicherry, Blog Post: Notes from Train Car S5)
• Mamallapuram
• Mysore
• Jungle Retreat and Ooty
• Also, don’t miss my collection of strange newspaper articles from India

Northern India

• New Delhi - Old Delhi
• Rural Rajasthan, Blog posts: Jeep Ride in Rural Northern India and  If you think your job is pointless …
• Red Palace and the Taj Mahal
• There’s actually more to this part of the trip, but this is basically where I ran out of steam and started relaxing too much to blog (also getting Internet became harder).  So for now, this is it.

Why did we go to India, you ask?  Here’s the answer - ever been to Michigan in January?

There are also a few new cartoons/illustrations in this presentation.  I’ve started just paying for a couple of illustrations per presentation to help viewers to understand (and mostly to remember) difficult concepts.  Just to give you a rough idea in the time involved to create something like this, I spent about 18 hours on the Prezi build (which doesn’t even begin to account for the time spent doing the research).

How can we Measure Teaching and Learning in Math?

If you attended the talk (in the flesh) and would like to evaluate the presentation, you can do it here on SpeakerRate.

1. Writing a Learning Blog
2. Building a Mindmap
3. Giving an Inquiry-Based Learning Presentation in class
4. Creating a Video for the Internet
5. Creating a Digital Portfolio to house their projects (this will be done by everyone last)

We cover four “units” in MathET, and each student completes the first four learning projects in a random pre-assigned order (I made a chart of all project assignments at the beginning of the semester).  This means that at any time, 25% of the students are blogging, 25% are building mindmaps, 25% are working on a 10-minute presentation for class, and 25% are building a video on a specific topic.  Projects are due two days before the unit exam so that everyone can learn from reading and clicking through each others’ projects.

No lies.  This required a large amount of time to get a new syllabus in place, verbage about privacy and appropriate computer use, tutorials on the LMS, and grading rubrics (and I already knew how to use all the technology).  I had to move one hour of class (4 hours each week) into a computer lab (and lab time is as precious as gold on our campus).   I set up an RSS feed (via a class netvibes page) to put news about math and teaching at the fingertips of the students.   I have to create a page to hold all the RSS feeds from student blogs, videos, and mindmaps (see the Unit 1 Tab of the class netvibes page).  This project also required a pep talk on the first day of class to explain why I was requiring that students use technology as they learned (because it will help them find jobs and provide them with valuable ways to teach and learn).  It was a bit of a shock, especially to those students who had barely touched a computer before.

However, the work was 100% worth it (maybe even 200% worth it).  We have never (and I mean never) had so much fun with a class before.  Every day of class I automatically get fresh learning assessments from the students who are blogging or mapping out the concepts we’ve learned.  The students really enjoy participating in each others’ active presentations and gain lots of fresh ideas about how to incorporate different teaching strategies into their own classes.  It’s also fun to watch the students get more brave (technology-wise) as the semester progresses - I really can’t wait to see what these projects look like by the end of the semester!  As I walk through the lab or peek at laptop screens before class,  I see students getting sucked in to reading blog posts and news articles that they might not otherwise even see (e.g. Math in the News).  I see them playing with interactive manipulatives from NLVM, and getting hooked on logic puzzles.

Because every single project is organized around learning, they all enhance the students’ understanding of the material.   How do I know?   There were no failing grades on the first test.  Students write and talk about how learning Venn Diagrams is “awesome” and how learning base-5 arithmetic is “tricky but cool” … it’s like math has gotten turned upside-down. What was once scary and difficult is now fun and interesting (maybe still difficult, but more tolerable now).  I think it may even be possible that students are now more likely to study for the exams because they actually enjoy learning the material (this is just conjecture on my part).

There are lots more details to share about how, exactly, I’ve pulled this off (release forms, privacy issues, etc), but for now I’d like to share a few of the best projects from Round 1 of the Student Learning Projects.  I hope that by the end of the semester, every one of my students will have found a project where they had a chance to shine the best and brightest!

Best Student Web-based Projects: Round 1

• Blog: Hez B’s Math Adventures
• Blog: RoseMath
• Mindmap: Ashley’s Map
• Video: Deductive Reasoning

Honestly, I wish I had recorded more of the student IBL presentations, because many of them have been clever and well-designed.

In addition to the projects, we’ve found ourselves doing some other fun things:

• Venn Diagram Contest (Indexed-style)
• A short clip from Scott’s IBL Battleship Presentation (on coordinate systems)
• Video recordings of hands-on demonstrations during class (here is one on Base-5 Subtraction and another on the Closure Property)
• Using Wolfram|Alpha to look up numbers written in Egyptian and Babylonian or to complete number patterns

One more thing I’ve changed in all my classes this semester, I try to begin every class by asking students what they’ve learned in their other classes (an acknowledgment that these things are important too).  The only way to refocus education on learning is to make sure it actually is the focus.

Learning Projects Round 2 are already well underway!  Students can see each others’ blogs and mindmaps in progress from day one of the unit.  This (hopefully) encourages them to explore and read more about each topic as they follow links to resources and read about how math has been applied.  Stay tuned for more in our little learning experiment.

The tools for STEM eLearning

1. Tablets
2. Recording & editing software
3. Jing
4. Equation software and training
5. Synchronous communication system
6. Online homework system

Other head-turning resources for STEM

• Wolfram Demonstrations
• Digital libraries (a lengthy list)
• Video collections (another list)
• TI-SmartView

Other tips (about accessibility, computer labs, etc) can be found at the end of the article.

You can read about all the tools, and why I recommend them, by going to the article, eLearning Tools for STEM.