Category Archives: ETEC500

Problem-Based Learning Environments

I’m convinced kids will play with numbers and many other math concepts if you can just trick them into it.

I was astonished one morning this year to see one of my most reluctant learners approach another student, just before the tardy bell, and begin a little interactive “number trick” with him: “Pick any number between 1 and 10.  Add 2.  Multiply by 5…..”  He had a new toy to share, and he wanted to share it for several reasons:

  1. It amused him, and he thought it would amuse his classmate.
  2. Nobody was making him.

I felt like the worst teacher in the world when I interrupted their math discussion and asked them to take their seats so we could begin math class.

I know one day of intrinsically motivated math discussion, properly guided, is worth two weeks of painful lecture.  So, how can we trick them?

My proposed Problem-Based Learning Environment is a video game.  Students have missions.  To accomplish their missions, they must use the right mix of problem-solving, arithmetic, and familiar common-sense decision-making.

Problems appear as missions, plausible, and surprising, like some kind of weekly rescue-team/detective TV show.  (See “Numbers” on CBS on Fridays.)  There are always more missions, with a revolving core group of characters (good and bad) to interact with, and their content is of course based on the student’s level of proficiency in prior concepts.

The game is current and hip – not funky like a six-year-old educational game.  It has modern graphics and sounds, along with slightly edgy themes.  There might even be some threatening aliens to avoid, to provide a sense of urgency.

To help students accomplish missions, there is a set of tools: formulas, algorithms, identification challenges.  All of these are integrated within the game premise and are only named once mastered.  Once introduced and explored, these tools can (and will) be reused in later missions.

I’m extremely excited about the Algebra 1 concepts covered cleverly in the online games by Tabula Digita (see and  Students accomplish missions set on a coordinate plane – disguised as an alien landscape – and are even occasionally asked for “coordinates” of their location.  (It doesn’t sound like math this time.  It sounds like science fiction!)  This software is very similar too the ideal software I’ve described here.


Report: Online Discussion Participation (Online Learning)

Due to technical difficulties, we jumped at the last minute into the Moodle chat system provided by the Office of Distributed Learning.  I was amazed at how quickly this was accomplished.

We spent a couple minutes finding our way – changing our profiles and avatars – and then followed the directions of [the professor] to begin sharing and discussing our real-world experiences with online learning systems.  This included defining “online learning system” and anecdotes about Blackboard and WebCT, two major players who recently merged.  We briefly touched on some tools for secondary-school teachers.

The conversation drifted into equity and access issues regarding public-school students and the Internet.  This thread also sputtered out quickly.

When [the professor] directed us to discuss Chapter 7 in the Jonassen book, we touched on a few experiences with quest- or task-oriented software.  There was a consensus that you could get kids to do all kinds of diligent problem-solving (the kind of productive activity we want them doing) if you trick them into it through games and other computer opportunities.

I found this discussion surprisingly scattered and superficial.  To some extent, participants made an obvious effort to name the person they were replying to or questioning, but careless interleaving of conversation threads continued as if we hadn’t discussed it during the last meeting.  I get the impression there are typists who watch themselves type and then hit Enter without checking to see if the time is right to actually send the drafted comment.  This was in spite of the instructor’s comment early on that we could draft our comments in Word and then copy/paste them into the chat program. (I’m not commenting on anyone’s technical skills as a typist, just on their decisions when to send their work into the stream of discussion.)

Technology skill: more Flash

I’ve had to modify my plans a bit. I’m working as I can, learning to use various features and components, prioritized for simplicity.

I’m learning a lot about what Flash is made of. I build a Cartesian plane, and a couple dots and a line, and then I wrote some ActionScript to build the dots and the line on startup. I originally built the Cartesian plane from lines in Flash, but I got the impression I was adding a lot of data (stored and loaded each time), so I made a GIF image instead and inserted that in a layer in Flash.

So then I lost the ability to draw the objects. I haven’t figured that out.

In the mean time, I’ve put some controls on the screen, along with some static and dynamic text. I wrote the first chunk of code. Now you can select your X1, X2, Y1 and Y2 values, and the application computes and displays the slope. You can see the Cartesian plane, but no lines or dots.

I don’t think I need all the buttons I originally proposed because I think once I get the line and dots re-drawing and finish the output (slope-dependent line color, equations of lines), I’ll have a nice useable application at a good stopping point.

I’ve exported this version as an SWF file.

This Windows server remains flakey. I’m shopping for a new home.




Technology skill: Flash

Because it can be delivered from any web page (regardless of O/S or web server) to nearly any client (regardless of O/S or browser), and has powerful interactivity and animation features, Macromedia Flash has become ubiquitous on the web.  I have mastered HTML, JavaScript and PHP (as well as several other server-side programming languages) and am comfortable with CSS and Fireworks.  However, I have only dabbled in Flash and have always felt this was a skill missing from my résumé.

As luck would have it, while I have an immediate need (for this class) to develop a rudimentary Flash application using ActionScript, I also find myself at the tail end of an algebra class where my students are still not comfortable with the concept of slope.

I propose to develop an application from demonstrating Flash.  The user will be able to manipulate on-screen elements and see numbers react, or vice versa.  I need to have this complete within the next two weeks in order for my students to make use of it.

The application will have the following features:

  1. Cartesian plane as a work area,
  2. A line, randomly placed on the plane when the application starts, and featuring two points.
  3. Display windows showing coordinates of each point, slope of the line, equation of the line in all three primary forms,
  4. Buttons: New Line, Flip Horizontally, Flip Vertically,
  5. Interactivity (points moveable by user, line moveable by user),
  6. Feedback (color of line changes depending on slope).

This project will require use of the graphical tools (and their object-oriented features) in Flash, as well as ActionScript.  Within the time I have, I expect to complete Features #1-3 and the first button by May 20 (in time to review for our Slope test) with other features added by the end of the quarter.


Report: Online Discussion Participation (Technology Integration)

Early on in our first chat session as a class, we went through some technical details: browsers, windows, clicking.  One user kept getting dropped; he felt this might have been caused by resizing the window.

The first topic discussed in any detail was the students’ success or challenges with the research assignment.  Some students seemed to have worked out the kinks, while others had trouble and asked for specific advice about how to do a better job.

The group mentioned the Cuban book and his research and opinions regarding effective vs. ineffective use of technology.  The group got the impression that Cuban was opposed to school districts investing in technology that was un- or underused.  [The professor] confirmed this, based on her personal experience hearing Cuban speak at a recent conference.

There was a discussion of the users’ experiences with MySpace.  Although teachers recognize it as a powerful resource that holds a lot of fascination for our students, we also know that “media hype” has prejudiced many parents’ opinions.  One anecdote was about an Internet scavenger hunt assigned to a set of 8th graders, and involving the teacher’s own (skeletal) MySpace profile.  Even though parental permission was required to participate, students were told not to log in to MySpace, and an alternate assignment was provided, a small group of parents effectively shut that down through vocal overreaction.

Woven into the discussion of technology integration was discussion of the mechanics of the chat room itself.  We considered letting [the professor] strictly moderate the discussion, but since she never explicitly agreed to that, we went ahead and typed away.  We agreed to providing more context, though, by addressing the speaker whose comments we were responding to.


Educational Philosophy and Technology Vision

It’s a near-universal truth among educators that critical thinking is important in school.  I was excited and felt vindicated when I learned this.  I had been training my own kids since they could talk by asking them, whenever possible, “How do you know that?”  As the son of an Apollo test engineer, and as a former journalist and software developer (with the callused thumbs from endless test/adjust/test cycles of debugging to prove it), I had learned many times that assumptions are a sure way to wander off track.  (Did you know that “error” and “err” come from the Latin verb meaning “to stray”?)

For example, you have a bug in a program which is supposed to multiply two numbers.  It works fine when both numbers are positive, but when both numbers are negative, you keep getting a negative (rather than positive) product.  You “know” that everything’s okay in the input module of the program, since you just wrote it a few minutes ago, so you keep looking for the bug in the processing module, where the multiplication takes place.  You spend hours testing and re-testing.  But you could have saved yourself some trouble by exploring the input module.  When you eventually do, you discover that any negative signs in the second factor are being erroneously and reliably dropped before the two factors are passed to the processing module. An easy fix, and a hard lesson.

I was horrified when I quickly recognized a pattern of non-critical thinking in my students: no quick scans for reasonableness, no checking their work through inverting the process, no checking for dropped negative signs or decimal points.  Those are examples of problems that show up in written work.  There are similar problems with oral work, such as shouting out answers that are nonsense because the speaker doesn’t filter his thoughts.

I would say, “Be sure to check your work,” and they would mollify me by glancing at their scribbles to see if everything looked okay.  But it wasn’t only laziness.  They were exhibiting what educators recognize as overconfidence, defined as “an overestimate of the likelihood of the correctness of a judgment” (Sternberg & Williams, 2002, p. 318).

Critical thinking, with its emphasis on testing ideas against alternatives and meta-cognition, fits naturally into constructivism, described by Jonassen as the following: “Learners begin constructing their own simple mental models to explain their worlds, and with experience, support, and more reflection, their mental models become increasingly complex.”  This is in comparison to behavioral theories of learning, which “focus primarily on changes in observable behavior rather than on internal mental processes”  and to sociocultural theory, whose major premise is that “a person’s intrapersonal, or internal processes have their roots in interactions with others” (Sternberg & Williams).  Rather than considering how inner growth might be expressed internally (behaviorist) or how external growth might influence internal development (cognitivist), constructivist theory sees growth as a series of internal loops feeding into each other.  “How do I know the quotient of x and y is 2?  Well, I know that 2y=x.  How do I know that?  Etc. And are they 2 in all cases?  What about if y=0?”  The student needs to have constructed a valid mental model of division, of the meaning of variables, of the undefined nature of some number when it’s divided by 0, and so on.

You can see how the proper use of technology exploits and confirms constructivist learning theories.  The simplest example is an assignment to develop a product – web site, podcast, digital movie, Powerpoint presentation.  The student has to master the concept in order to present it coherently to the consumer.  “I need to tell my reader about suspension bridges, so first I’d better define what a suspension bridge is.  And this will need to be in the context of bridges in general.  So we’ll need a history of bridges, with several juicy stories about bridge collapses.  Plus a bit of physics of bridges and the challenges they address and solve.”

Also, after developing one or two products using the same media, the developer will begin to appreciate the need to present information multiple ways, to accommodate multiple learning styles.  A web site might have the construction of a suspension bridge demonstrated in a Flash movie, explained in text, illustrated in a drawing, maybe even described in audio.  By being forced to describe the same concept using multiple media, the developer begins to construct a complete three-dimensional, full-color mental picture of the idea he is attempting to teach.

Finally, the use of technology as a means to an end forces the media developer to answer the question, “How do I know that?” Each claim – a bridge stays up because of this, a bridge falls when this happens, steel bridges are stronger than brick bridges but not as strong as steel-reinforced concrete bridges – must be defended and explained coherently.  The consumer and the developer of the media project both benefit from the constraints of critical thinking and the inherent mental construction taking place.


  1. Sternberg, R.J., & Williams, W.M. (2002). Educational Psychology. Boston: Allyn and Bacon.
  2. Jonassen, D.H., Howland, J., Moore, J., & Marra, R.M. (2003). Learning to Solve Problems with Technology: A Constructivist Perspective (Second Edition). New Jersey: Merrill Prentice Hall.