Arthur Benjamin has been on TED in the past (see Mathemagics) and has done a really phenomenal job.

Here’s his latest 3-minute appearance, called “A Formula for Changing Math Education.”

The problem is that the very short talk does not present a “formula” for changing education, just Benjamin’s idea that the pinnacle at the top of the math pyramid should be statistics instead of calculus. There is nothing in the the short talk that suggests any kind of coherent plan for how it could be done, or even a suggestion that he has a plan. That’s what I would want to know about. Of course, it’s only a 3-minute talk and it’s certainly possible that he had nothing to do with the name of the talk.

I did agree with these two statements, but want to add my own two cents:

1. “very few people actually use calculus in a conscious meaningful way in their day to day lives” … but I’m not sure we teach people how to use calculus in a “conscious meaningful way” nor are many of us required to use calculus for the simple reason that our superiors don’t understand it at all. Calculus could be used in a “conscious meaningful way” but our society chooses not to engage. As a matter of fact, very few people actually use statistics in a conscious meaningful way in their day to day lives. Enough said.

2. “it’s time for our mathematics to change from analog to digital” … here I agree, kind of. It’s time for our mathematics to include both analog and digital, and it’s definitely time for our mathematics teaching to change from analog to digital. What happens in most math classrooms is based on a factory-model of education that developed before computers even existed. Even though the world has changed, the instruction (for the most part) has not.

I found it more interesting to read through the comments that followed the short TED talk. There is an interesting conversation taking place there. One wise commenter pointed out that it’s possible that there should not be just one pinnacle on the math pyramid. Both Calculus and Statistics could be considered penultimate goals of a mathematics education. I think that’s dead-on.

If there’s anything I’ve learned during the process of writing my dissertation, it’s that the system of collegiate mathematics education is extremely complex.  There will be no “easy” fix to the system, even if someone is able to convince a majority of the stakeholders that their change is the correct one.

In a previous post called Starting from Scratch (Part I), I mentioned that I think it’s a mistake to design an online course around the schedule. I received several questions via email asking me to elaborate on why I think it’s a mistake to do schedule-driven design, so here we go…

First, let me be very clear that I do have a schedule for every course. I just don’t design the course around the schedule. If a student wants to see when an assignment is due or when a test will be, they can, in one click, view the schedule for the course. However, as far as the design goes, the schedule is almost always the very last thing I create. What keeps students on track in the online course is the due dates for online homework and the test dates. As they become motivated to complete the assignments and learning tasks, they go diving in to the learning materials.

Many instructional designers and eLearning professionals will tell you that “best practice” for online course is to design the course around the activities and content for each week – making the “week” the unit of instructional design. Let’s me see if I can explain why I think this is problematic.

1. Schedule-driven design makes it difficult for students to find learning materials. Suppose you’re a student, and it’s roughly the middle of the semester, and you’re studying for an exam. You know there are few topics you need to go back and look at, and you know that the material is available somewhere in your online course. Here’s what you see when you log in to view the course materials:

Are those screens helpful to you? Do they immediately direct you to the content that you’re interested in? Do they reinforce your knowledge of the vocabulary that’s used?

Designing around the “week” may even give the mistaken impression idea that learning takes place at a particular time, and once you’re past that time, you should be done with that learning. Schedule-driven design implies that learning is complete when the week is over, while real learning takes place whenever we become engaged and interested. At the moment when a student becomes engaged and interested, it should be easy to find the appropriate learning materials.

2. Schedule-driven design makes it difficult for instructors to place learning materials. Now suppose you’re the instructor. One of your colleagues has just sent you an awesome YouTube video that you know would be the perfect addition to your online course. So you log into the course in order to find the appropriate place to put this video. Here’s what you see:

Was that helpful to you? Could you immediately determine the proper location to insert that video in the course? Again, the structure of the schedule-driven design has gotten in the way. As you find new learning material to enhance your online course, it should be easy to locate the proper place to put it.

Look at these screenshots instead, from a course designed around the content instead of the schedule:

Do you see the difference?

3. You should not have to redesign everything when the course format or schedule changes. Suppose you spend gobs of time carefully designing an online course to run in a 15-week semester using a schedule driven design concept. This is all well and good until somebody informs you that you’ll be teaching a 10-week hybrid version of this course in the next semester. Guess what? You’re now going to have to redesign the entire digital platform around that new schedule and format. That really seems like a waste of time that could be better spent designing good learning experiences. If only you had designed around the content, all you would have to do is think about ways to change the assessment and engagement for a hybrid format, and set a new course pace in a separate schedule.

4. Learning should be flexible within the semester. When the course design is schedule-driven, it becomes difficult to make course corrections during the semester. With a content-designed format, if we need to spend a little more time on a topic, I don’t have to worry that my whole course designers will be thrown off by that. I can make a simple adjustment in a one-page schedule or make an announcement that we’re altering course slightly. However, the online course environment has not changed in the least bit.

5. Online course design should emphasize learning vocabulary. We give lots of lip-service to improving our students’ communication skills and encouraging them to read and practice with vocabulary. And then what do we do? We design courses around folders called “Week 1,Week 2, Week 3…” I design courses around folders with names like “Functions and Models, Limits and Derivatives, Differentiation Rules,…” Inside these folders are more detailed, concept-oriented folders that say things like “Tangent and Velocity Problems” and “The Limit of a Function.” As students navigate through the course and go back to relearn something they didn’t quite catch the first time, the course structure emphasizes vocabulary. Not only that, it helps students to form a “big picture” structure of how topics fit together as they navigate the course structure. Would you rather have students understand that velocity is part of understanding derivatives, or have students that understand that velocity was something that they learned in week three?

6. Online course design should make it easy to continue to add new materials. It is much easier to continue to add layers of material to a digital course platform if it’s easy to find learning objectives for the course. I never have to redesign the course simply because it runs in a different format or different number of weeks. My face-to-face course shell, my hybrid course shell, and my online course shell all look exactly the same from a design standpoint. The assignments for the students and the assessment of the students might vary slightly depending on the course format, but this is simply a layer sits on top of the course design. With each semester, the digital course platform becomes a richer place for the students to explore and learn. Every semester I add more content: website references, clever YouTube videos, videos that I record in class, videos that students record and are willing to share, games that help teach particular learning concepts, etc. If I were designing around the schedule, then I would spend a great deal of time every year rearranging the course to fit within the specific weeks, holidays, and format, instead of spending that time finding valuable material that might help my students learn better.

7. Online course design should facilitate use for instructional reference. I use the digital course platform course shell as a reference for my own teaching. Five years ago, I had a system of binders that contained lecture notes, group activities, worksheets, etc. Before each class I would consult the binder to see what materials and notes I had available to use in class. Today I consult the course shell. The one-page schedule tells me roughly what I need to cover to stay on track for the semester, but I dive into the “Virtual Classroom” of materials to see what I have available to me in my toolkit for class. The Virtual Classroom is an index of all the learning materials I’ve found over the last several years. I won’t use all of it, but it allows me to be really flexible with what we do in class. I can constantly assess how well the students are learning, and then adjust based on that assessment. If we don’t “cover” something in class, I know it’s available to students in the digital materials and that they can access it later. If a student asks a question, and I’ve found an interactive demonstration that would help answer the question, I know exactly where to find it. If a group of students comes up with a really clever way to explain a concept, I can ask them if they’re willing to record it and then add it to the course shell after class, sharing their wisdom with all of the successive students that follow them.

I used to have digital courses designed around the schedule. But all of those courses have become obsolete as schedules and formats changed, and every single one of them has been deleted from my archive for lack of use. The digital courses I design today are designed around content and learning. I am always on the lookout for new materials to add to the courses and every semester, the learning materials are better than the semester before. All I require to get ready for a new semester is a copy of the digital materials from the previous semester, and a new 1-page schedule.

I had to order new business cards and the printer was having a special … 1000 bookmarks for $40. Although I had no idea what I would do with a thousand bookmarks, it seemed like a good deal and I couldn’t pass it up. Now that I am in possession of this new stockpile of TCM schwag, I think I’m just going to offer to pass it on to your events to help others learn more about technology and math.

If you’re planning to mention Teaching College Math at a conference or event, or you’d just like to share with your department, send me an email with where they will be going and how many you need, and I will get some bookmarks in the mail to you.

Subtitle: Why you should create a course shell for every course you teach, and not just the online courses.

I’m teaching Math for Elementary Teachers this Fall semester for the first time in several years.  The last time I taught the course was the semester when I was learning to teach math online, and as such, I do not have a digital collection of materials for the repeat this fall.

The course that I’m teaching in the fall is completely traditional.  We meet twice a week for two hours at a time.  The students will purchase traditional textbooks and there is no online homework.  Nonetheless, I am spending the day today creating a topic-oriented course shell for this course.  Why?

1. I know that eventually, I will teach this course in an alternate format (hybrid, online, etc.) and so I should begin collecting digital materials as I find them.
2. I will begin recording parts of lessons with my tablet and make them available to students to view outside of class.
3. I will ask the students to do some digital projects and it will provide a place to archive and share those materials.
4. It is now how I organize all my classes, and I’d like to try to convince you that you should too.

So here I am, starting from scratch, and I’m going to share my process with you.

The first step in the process is to choose good base materials for the course (text or online materials).  My choice of texts was motivated by looking for something that would help me model the way I would like these future teachers to one day teach in their own classrooms, and so I chose a book that is largely activity-based.  I did search around in hopes of finding a good set of digital materials, but came up empty handed.

Several semesters from now, my growing set of digital materials for this course will be good enough that I could go text-less, but for now, it’s a necessity as I begin the process of seeking out and reviewing how to incorporate those resources.  In this case, the text was so much better than the others, that I have adopted it even though it does not come with online homework.

Second, I requested that my college add the RSS plug-in for our course management system so that I can easily bring in content from several blogs that discuss teaching math at the elementary level.  I could do this manually by linking to stories as they come out, but I prefer to teach the students the habit of continuing to learn and follow those who have good resources and ideas.

Third, I’ve built a topic-oriented “Virtual Classroom” in the course management system.  I should point out that I do not think it is good practice to design the course around the schedule (as is often advocated by eLearning folks).  That’s not to say there shouldn’t be a schedule, just that the course should not be designed around the schedule.  The course should be designed around the content.  For this math class, the online design is pretty easily organized around the textbook.  Here’s a series of screens to show you what my “from scratch” course looks like at this point:

First create a unique "classroom environment" for the course. This will create an easy visual cue for you to easily identify the course shell by the way it looks. Each of my courses has a different banner and menu buttons that match. This banner includes an image of the petroglyphs at "Newspaper Rock" from Canyonlands National Park.

Next outline the major units, chapters, or topics that you want to cover into folders. Start thinking about major projects and assessments you might include, as that will help you with identifying your major topics or units. But don't worry about setting a schedule yet. We'll get to that later.

In each folder, make subtopics (sections if you're designing around a textbook) that include the learning objectives for each subtopic. You will find that including the learning objectives helps both you and the students find the specific information they are looking for.

When I start this process, all the subtopic folders are empty. Don't worry about filling these folders right away. We'll fill these folders as we find appropriate material (e.g. news articles, videos, notes from class) later.

This will be a several-part series, so keep reading for the next installment.  Remember that you can subscribe to the RSS feed for this blog or subscribe via email (see the top of the left-hand panel).

This week I have been participating in the MAA PREP course, Calculus: Online and Interactive. I was asked to give a presentation on online course design for mathematics, and the presentation was recorded.

This is a loooooong one (two hours), but it is packed with information, ideas, and design tips.  If you’re going to teach online for the first time, or just want some guidance for revamping your online math course, I think you’ll find it helpful.

There are nine parts to the presentation:

1. Virtual Classroom (overall course design)
2. Interactive Learning Materials
3. Video Lessons
4. Online Homework
5. Blended Environment
6. Student Engagement
7. Equations and Graphs
8. Orientation and Setup
9. The Math Testing Issue

You can view the slides below or here.

To watch the whole presentation, go here to the Adobe Connect recorded webinar.

There are also two mindmaps that you might want to investigate that are mentioned in this presentation:

• Online Math
• Using the Internet to Spice Up Your Math Course

You may also be interested in the online Calculus textbook, Calculus: Modeling and Application, 2nd edition, which may be used free for the next academic school year (supported by an NSF grant).

In case you missed this, there’s a great Wall Street Journal article and blog post about Wolfram Alpha …

Sum Help: New Search Engine for Mathletes (The Wall Street Journal, 6/16/09)

Wolfram Alpha, A New Online Computation Engine Shakes Up Math (The Numbers Guy Blog, 6/16/09)

Of course, I could just think they are great because I was quoted in them.

Last week I gave a presentation called “Organize Your Digital Self” to the participants at the University of Wisconsin.

Does your email stack up? Do your important web links get “lost”? Are you still creating the website or course link as the last step? Maria offers helpful strategies to get your digital life under control.

This entire webinar is now available as a recording, which can be found at the ICS website.  Just a warning, the presentation runs a little over an hour, but I promise that you will get much more than an hour back in time saved later.

Here are a few of the screenshots:

The title of this post, “Everybody teaches, everybody learns.” is a shared vision for those of us who are in the business of education, whether it is corporate training, teaching students in K-12 or on college campuses, or working in an educational institution in an administrative or support role.

The vision statement grew out of a “rogue” Innovations in eLearning session (spontaneous tweet-up). We met to discuss how to encourage our colleagues and clients to both trial and adopt new technologies and instructional techniques. What emerged was not only a list of suggestions for accomplishing this (and the formation of the Black Swan Society) but also a vision statement for all levels and types of education (attributed to Koreen and Aaron for the wording, but to the whole group for shaping the conversation that ultimately produced it). For one hour the tweet stream slowed down considerably while this conversation took place.

Let me try to outline how we arrived at the need for a collective vision.

We began by brainstorming ideas for encouraging adoption of new practices within our organizations (what follows is in no particular order):

1. Identify early adopters in your own organization, recruit them, train them, and help them to spread new techniques to their own networks in the organization.

2. Speak to the core problems. For example, rather than trying to get adoption of twitter simply because it would be a cool tool to use, speak to the problem of needing to engage students in the learning process, with twitter with being one of the solutions that could be use for this problem.

3. Context is key. If your belief system leads you to be suspicious of new technologies, and you are only shown those new technologies in contexts outside of your own field, then it becomes far too easy for your belief system to assimilate the existence of this technology with the dismissal that the new technology could only possibly work outside of your field. Therefore, it is vitally important that each potential adopter be shown context-specific examples of how a technology could be used to enhance learning in their own field. How to find these examples? One way to do it would be to take advantage of a social network like twitter, and simply ask your network “can you point me to examples of using ______ in the field of _____. ”

4. Convert the dissenters. If there is a vocal resistance within your organization to the use of technologies for learning, it is vitally important that you find ways to convince these folks. Quite possibly, the best way to do it is to find others in their field using technologies in their teaching and learning (see #3). Don’t experiment with these folks. Know that what you are suggesting that they try has worked in their discipline on other campuses.

5. It’s hard to be a prophet in your own lands. You can be the support system on your campus, but if you stray too far from acceptable practice you could find yourself being viewed as too much of a threat to the status quo. You can be the one who facilitates the change by bringing in an outside person to demonstrate new tools, or by suggesting conferences that will expose instructors to skills they might then want to use, but recognize that it is difficult to try to introduce a lot of change in a way that’s nonthreatening to the organization.

6. Personal use first, instructional use second. Very rarely are instructors given an opportunity to play with technologies in a safe environment with their peers. Often the first use comes when they are interacting with students and ends after dealing with all the myriad of motivational and behavioral issues that seem compounded by the use of a new technology. Here are two examples that illustrate a better way to help instructors try new technologies. At some institutions, instructors participate in their own professional development by taking online webinars or courses. This gives them perspective in online education as learners first before they teach online themselves. This gives them a safe space to encounter the types of technical problems, pedagogical issues, and course redesign that will be necessary when they themselves teach online class.

Another example, from my personal experience, has been using twitter to form my own social network, to learn from it, and to share resources with it. This has given me an understanding of how twitter can be used for learning that I would not natively understand if somebody just told me that you could use twitter for learning. If you wanted to get your campus instructors to adopt twitter as a learning tool, perhaps your first step is to create a secure version of twitter (i.e. a virtual teachers lounge) where instructors can share information with each other in real time. Imagine that one of my students is really acting up in class and I send a “tweet” to my (secure) internal social network about the problem; another instructor responds that the student did very poorly on an exam in the previous class. Now I realize why the student is acting up in my class and can try to address the real issue with the student with a private conversation. As we realize that such a social network could be valuable, we naturally begin to ask how such a social network could be valuable in the courses we teach. It is, essentially it, a constructivist way to learn to use educational technology. First use them in your own learning.

7. Culture is key. Everyone must understand what it means to be a part of your organization — from the bottom to the top, everyone should buy in to the same core beliefs. You should be able to see your leadership participate in a way that speaks to the core beliefs in the same way as the people who are at the bottom of the organizational charts. Forgive the military example, but it was a good one… as Mark explained: if you’re in the Marine Corps you know that above all else your role is to be ready to fight if needed, this is summarized quite succinctly as “every man a rifleman.” Mark explained that every Marine from the newbie in bootcamp to the leadership at the top lives this vision: they stay in good physical shape and stays firearms-certified, all for the purpose that they maintain their role as someone who is ready to fight if it becomes necessary.

Since many at the conference do contract work for the US government and military, this example resonated with the group and we began sharing mission and vision statements from our own colleges and organizations. Unfortunately most of these statements are extremely wordy and difficult to remember. None were something that really resonated well with all levels of educational learning until Koreen and Aaron came up with “Everybody teaches, everybody learns.”

What we mean here is that it is not just the students who should be learning and not just the instructors who should be teaching. Students should be teachers to their peers, administrators should spend time in classrooms to remember the core values of the institution, instructors should be learners without mandates from the institution to do so.

This is, I think, a remarkably simple way that we can focus ourselves in education on what is truly important.

Check out the story published in The Chronicle of Higher Education A Calculating Web Site Could Ignite a New Campus ‘Math War’.

There’s one small error I think I should point out in the story. “In other words, it can instantly do all the homework and test questions found in many calculus textbooks.” Replace the word “all” with the word “some.”

The real excitement in the Game Design Workshop happened in the afternoon, when I participated in a “GameJam” (a timed contest of design and creativity where you get a set amount of time to design the core concepts of a game). In this particular event, we a little less than three hours from start to finish to come up with the conception for a game, how the gameplay works and what the game look like. During the short time period we also had to come up with enough visual and verbal documentation of the game that it could be judged without us being there to present it.

Teams were formed at the beginning of the event. Our team was Dan Petrak, Richard Sebastian, Stephen Martin, and myself (only Dan and I knew each other prior to the GameJam). We were armed with a box of markers, a box of colored pencils, an easel of paper, and a trifold board to post our videogame design. One final detail — you don’t know what the game is supposed to be about until the beginning of the contest. With two hours and 45 minutes of time to completion, we got our game theme, which was “long-term and short-term goal setting.” Ouch.

At least 45 minutes of our initial time was simply spent brainstorming ideas for the types of activities that would involve long-term and short-term goal setting and throwing out the ones that would make lame games. We toyed with game ideas that would involve setting goals in the real world (e.g. managing a national park, weight loss, life-long learning), we toyed with the idea of creating a game based in a social networking platform like Facebook where you could set long-term goals and then perform short-term goals in the real world to earn points in FB (think mafia wars, but an environmental or health theme) … but none of these ideas sounded like much fun or easily designable. With about two hours to go, we hit on the idea to design a videogame based on campaigning for political office - a process that is notoriously about balancing the short-term goals of getting reelected and raising campaign finances against the long-term goal of furthering the causes that drew you to office in the first place.

Once we had the general concepts down, we still have to think about how the gameplay would actually progress and the mini games that would make it fun to play. We also had to figure out how to depict all of this in a way that someone seeing our descriptions and drawings would understand intuitively what this game would be like to play. Oh, one more thing I forgot to mention … just to add a little pressure, one of the judges for this contest is Will Wright (he made a couple games you might have heard of, like SimCity, the Sims, and most recently, Spore).

Keep in mind that none of us are artists (two mathematicians and two learning technologists), but everything on the game board that we presented had to be hand drawn and hand written. So with all of that and mind, here is the game we designed: Permanent Campaign. I’m giving your our “box” design here and a general description, but you should go check out the minigames and main game screens that I’ve scanned and archived here.

Raising money. Establishing your political platform. Making political connections. It’s all part of running a successful campaign for higher office. Make a bad decision, you may lose the election. Run a bad campaign, you may be forced to “retire” from public office forever.

In Permanent Campaign, you are the ambitious candidate campaigning for the office the small-town mayor. Winning the election puts you closer to your ultimate goal: the highest office in the land. But can you win without abandoning your convictions?

Do you have the political instincts to survive a permanent campaign? Will the promises you make help or hurt you? Will your political enemies sabotage you? Most importantly, will your constituents continue to support you as you aim to be their next mayor, governor, senator, and president.

Our team worked extremely well together. Two people (Dan and Richard) primarily worked on copy and two people (me and Stephen) primarily worked on drawing screenshots and the game box. All of us continued to contribute ideas and brainstorm as we worked on getting the details on paper.
There were ten teams in the GameJam, and the games were on display all day Thursday for judging. I met Will Wright after his keynote (wait for another blog post on that talk and all of its mathematical awesomeness), and got my picture taken which was super cool.

But the real coolness was yet to come, as it turned out (that night) that our team WON the GameJam with Permanent Campaign! So another round of picture taking with the contest judges and the rest of the team (yes, including Will Wright) and then Will grabbed my camera and took a picture of our team with our winning project (I’m considering adding “Will Wright took MY picture” to my resume). Dan was smart enough to ask what he thought of our project, and Will said that he liked the way we had brought in the need to balance short-term and long-term goals using politics as the vehicle and he said that “It looks like it would be a fun game – I’d like to play it!”

For the time being, I am framing this winning GameJam award certificate and putting it in the space I’ve left for my Ph.D. At the moment, it seems like a far more impressive accomplishment!