Awareness of conceptual aspects of time: patterns, rates, magnitudes, durations, and frequencies holds great practical value, because teaching, learning, and thinking are exercises in change through time. This issue addresses patterns in time. The next addresses ordering of events, rates, magnitudes, durations, and frequencies and carries all references. The issues that follow these two address practical ways of measuring change.

Perceptions of time vary across cultures, and vary with their economy, education, technical advancement, religion, ritual traditions, and political organizations (see Goody, 1991; Levine, 1998). How students allocate time between competing activities affects their persona and life choices (Bruno, 1996). Our perception of patterns in time often dictates how we interpret phenomena, and perhaps no other aspect of time suffers more from misperceptions than that of patterns. Figure 1 shows four major patterns of change through time.

Figure 1. Patterns of change through time. Constancy (horizontal line - A) and gradualism (line with constant slope - B) typify few natural processes. Rhythmic patterns (C) typify many processes such as tides, sunspot cycles, etc. and lend themselves to predictability. Most natural events (floods, volcanic eruptions, earthquakes, drought, rainstorms) occur in fractal patterns (modified from Nuhfer, 2004, p. 457).

Flat-out changeless

The horizontal line (1-A) shows time’s passage without change. The perception of permanence is an illusion. Little a person experiences in Earth’s environment really is changeless, and with surprisingly little instruction, students can learn to see perceive change, previously unnoticed, and to understand both quantitatively and qualitatively the degree to which natural settings are ephemeral.

Learning likewise occurs without accompanying awareness of progress. The student who reports on a summative evaluation: “I learned little in this course” is expressing an affective feeling in an honestly felt disclosure, even if it is an inaccurate perception of cognitive growth that occurred. Knowledge surveys are particularly good tools for developing students’ metacognitive ability to perceive their own progress. Teachers who direct students’ frequent attention to a knowledge survey during the course can help students to develop self-assessment skills (Wirth et. al., 2005).

Slow and steady —perhaps doesn’t do it
The inclined line with positive slope (1-B) shows change at a gradual, constant rate. If we ask students to graph how their learning changes with time in college, most will produce a similar line that discloses their perception of learning as gradual. Theirs is also an honestly felt disclosure and believed even by those who describe their study as a series of cramming binges followed quickly by “memory dumps.” The graph of gradual change expresses the kind of change taught by Charles Lyell as the manner through which natural processes act. Gradualism not only influenced the reasoning of scientists such as Charles Darwin, it also accorded the sympathies of those who held positions of authority and power. The latter, understandably enamored with gradual change, disliked proposals that ranked revolutionary change as equally credible. We often hear complaints that change in higher education takes place at a frustratingly slow pace—perhaps still implying unquestioning devotion to slow, gradual change as “the way things ought to be.”

Dancing to Rhythms
The pattern in 1-C depicts a cyclic pattern that occurs at regular repeating intervals. It achieves perfect symmetry and regularity in the sine wave —the graph of the sine function in mathematics. Cyclic patterns describe significant natural phenomena including seasons, diurnal cycles, lunar cycles, tides and precessions of the equinox. A trait of such patterns includes comforting predictability. Most of us quickly learn to recognize our own diurnal biorhythms and realize that we’ll likely possess alertness in mid-morning and experience late afternoon torpor. Those on both sides of the desk in late afternoon classes usually realize challenges to energy and concentration. Authors such as Conner (2004) suggest choosing learning activities to match one’s natural diurnal cycle.

One book truly stands out in its focus on educational effort within temporal frameworks: Teaching Within the Rhythms of the Semester (Duffy and Jones, 1995). With a good balance of attention to teaching, learning, and thinking and some deep insights, it’s easy to recommend this fine book to readers. A longer cyclic pattern, the “rhythm” or “tempo” of the semesters, is the cycle primarily addressed by Duffy and Jones (1995). Their model of fluctuating amplitude derives primarily from their portrayal of middle of the semester as a “low” or “the doldrums.” In contrast, they attribute higher energy or excitement in the opening weeks, which returns in the final weeks when “the optimal work atmosphere” permits a grand finale and closure.

Figure 1-C, daily temperatures at Lake Itasca, Minnesota, provides is dominantly a rhythmic waveform produced by the regularity of Earth’s rotation around the sun. Yet, superimposed on that wave is the rough jagged pattern of daily temperature variations induced by chaotic atmospheric circulation in weather patterns—a subordinate fractal pattern superimposed on a dominant cyclic pattern. Both cyclic and fractal patterns can occur together in natural phenomena—it’s not always simply an “either-or” case.

Fundamental Fractals
Pattern (1-D) appears random, but actually has order. This rainfall record from Minnesota represents a fractal pattern. In words, a fractal pattern in time manifests as many common events, a few intervals when events are absent or abnormally small, infrequent large events, and very rare catastrophic events that would never be anticipated by direct observation of the usual events (unless one understands already that the pattern is part of a fractal system). The fractal nature of a pattern in time can often be deduced by plotting the logarithm of the recurrence interval of events of a given magnitude versus the logarithm of the size of the magnitude of the event (Figure 2). Hurst (1951) deduced such patterns when he studied the longest temporal data record for any natural phenomena —the record of floods on the Nile River. If a good line fit exists for the resultant plot of events, the pattern is likely fractal, and projection of the line allows estimate of the size of larger events, such as a 100-year flood, even if witnesses have never recorded the event (Figure 2). The plots troubled Hurst because they showed amazing order but revealed no pattern through which to predict floods, which was his major objective. This record, later studied by Benoit Mandelbrot, (see http://www.math.yale.edu/users/mandelbrot/web_pdfs/profile.pdf and Mandelbrot, 1983, pp. 251-252) led to the discovery of fractals as a fundamental descriptor for patterns of natural events. Unlike a cyclic pattern, fractal patterns possess no predictability for when such an event will occur—only a good estimate of how large such an event it will likely be when it does occur.

Figure 2 results from annual floods on a stream. The history of volumes of stream flow at peak discharge appears random (left), but the linearity that results from plot of scales employing flow frequency (recurrence interval„right) confirms floods are fractal events in time. The plot informs anticipation of events. For example, the known forty-year record of floods (left) yields the linear relationship (right) that permits us to anticipate the size of a 100- or 500-year flood even though it has never been observed.

The major pattern of human learning over time seems more like fractal, punctuated events (Figure 1-D) than any other, even though we may tend perceive our progress as nonexistent (1-A), gradual (1-B), or a cyclic pattern of ups and downs (1-C). This seems true for both individuals and for entire civilizations. Wolpert (1992) makes a particularly strong case for civilization’s recent punctuated change from a technological to a scientific culture. This change is recapitulated on a tiny scale with a similar punctuated event, whenever a student can first see and articulate the differences between technology and science. In a manner analogous to the progress of civilization, he/she constructs the understanding abruptly but only after considerable effort in accumulating the necessary tools and knowledge.

More follows on educational changes through time in the next issue.

BOOT CAMP for PROFS 2006!

Registration is open with spaces now held for ISU faculty. See http://www.isu.edu/ctl/nutshells/old_nutshells/6_606.htm for details. Contact nuhfed@isu.edu if interested.

 

New Faculty Orientation Scheduled August 15 & 16, 2006!

More detail to follow. If you have new faculty in your units, please avoid causing conflicts for them by scheduling meetings, etc. on these dates.