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         Axis                      -1. 0                           -0. 5                                    0                            +0. 5                        +1. 0

Anxiety-Confidence

Anxiety

Worry

Discomfort

Comfort

Hopeful

Confident

Boredom-Fascination

Ennui

Boredom

Indifference

Interest

Curiosity

Intrigue

Frustration-Euphoria

Frustration

Puzzlement

Confusion

Insight

Enlightenment

Ephipany

Dispirited-Encouraged

Dispirited

Disappointed

Dissatisfied

Satisfied

Thrilled

Enthusiastic

Terror-Enchantment

Terror

Dread

Apprehension

Calm

Anticipatory

Excited

                                       -1. 0                          -0. 5                                     0                            +0. 5                         +1. 0

Figure 2 – Emotion sets possibly relevant to learning

The student ideally begins in quadrant I or II:  they might be curious and fascinated about a new topic of interest (quadrant I) or they might be puzzled and motivated to reduce confusion (quadrant II).  In either case, they are in the top half of the space, if their focus is on constructing or testing knowledge.  Movement happens in this space as learning proceeds.  For example, when solving a puzzle in The Incredible Machine, a student gets an idea how to implement a solution and then builds its simulation. When she runs the simulation and it fails, she sees that her idea has some part that doesn’t work – that needs to be deconstructed.  At this point it is not uncommon for the student to move down into the lower half of the diagram (quadrant III) where emotions may be negative and the cognitive focus changes to eliminating some misconception.  As she consolidates her knowledge—what works and what does not—with awareness of a sense of making progress, she may move to quadrant IV.  Getting a fresh idea propels the student back into the upper half of the space, most likely quadrant I.  Thus, a typical learning experience involves a range of emotions, moving the student around the space as they learn.

If one visualizes a version of Figures 1a and 1b for each axis in Figure 2, then at any given instant, the student might be in multiple quadrants with respect to different axes.  They might be in quadrant II with respect to feeling frustrated; and simultaneously in quadrant I with respect to interest level.   It is important to recognize that a range of emotions occurs naturally in a real learning process, and it is not simply the case that the positive emotions are the good ones.  We do not foresee trying to keep the student in quadrant I, but rather to help him see that the cyclical process is natural in learning science, mathematics, engineering or technology (SMET), and that when he lands in the negative half, it is only part of the cycle.  Our aim is to help them to keep orbiting the loop, teaching them how to propel themselves especially after a setback.

A third axis (not shown), can be visualized as extending out of the plane of the page—the Knowledge Axis.  If one visualizes the above dynamics of moving from quadrant I to II to III to IV as an orbit, then when this third dimension is added, one obtains an excelsior spiral when evolving/developing knowledge. In the phase plane plot, time is parametric as the orbit is traversed in a counterclockwise direction.  In quadrant I, anticipation and expectation are high, as the learner builds ideas and concepts and tries them out.  Emotional mood decays over time either from boredom or from disappointment.  In quadrant II, the rate of construction of working knowledge diminishes, and negative emotions emerge as progress flags.  In quadrant III, the learner discards misconceptions and ideas that didn't pan out, as the negative affect runs its course (“good grief!”).  In quadrant IV, the learner recovers hopefulness and positive attitude as the knowledge set is now cleared of unworkable and unproductive concepts, and the cycle begins anew.  In building a complete and correct mental model associated with a learning opportunity, the learner may experience multiple cycles around the phase plane until completion of the learning exercise. Each orbit represents the time evolution of the learning cycle. Note that the orbit doesn't close on itself, but gradually moves up the knowledge axis.

Some of our ideas will be fashioned to ‘theory,’ perhaps beyond a practical level but not beyond a level needed for understanding them. We need to explore the underpinnings of various educational theories and evolve or revise them. For example, we propose a model that describes the range of various emotional states during learning (see Figure 2). We are in the process of performing empirical research on this model

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