Students learn by associating new terms with what they already know. Each time a new term is introduced, or a term is introduced in a new context, dynamic associations are created. Although "associations" are usually classified as a lower cognitive level activity (compared with higher levels of analysis, synthesis and evaluation for example), the sheer number of new associations that students must make in an introductory course is impressive. Even in upper division courses, students are expected to make associations and recall associations that they have previously established.
My hypothesis is that students learn new terms by relating each term to a term they already know. In doing this, each new term will reinforce an already held term or concept. This leads to a situation that makes common terms that form the backbone of the students’ associations even more common. Each new rare term makes those common terms more frequent. If knowledge is built this way, it seems reasonable that this relationship between terms should also be evident in the structure of the information that is presented to students both in the book and in the lecture.
Term accumulation model description, figure and Zipf’s law model from web
Figure 1. Association of concepts and the effect on the frequency of terms when a new term is added.
The simple study described here focused on one unit in an introductory Environmental Sciences course that would be the equivalent of about three weeks during a quarter. There were 38 vocabulary words chosen to represent major concepts. The frequency of these terms was counted in the assigned reading from the text and from audiotapes of the lectures. Five of these terms represented general rules that were being applied to the concepts in this unit. A term that stands for a rule should have a different structure of associations Students were given non-graded assessments that tested their associations at several levels. The results indicate that ****
The text was Miller, G. Tyler 2002. Living in the Environment. 12th edition. Brooks/Cole.
This research focused on one course taught during the summer of 2002. There were 28 students in the course. All students gave their informed consent to have the data used in the study and in the process of getting this consent the overall project was explained to them.
All uses of the 38 vocabulary terms were counted in the reading assignment. The reading covered four full chapters and parts of two other chapters for a total of ** pages and **** counted terms. Figure legends and tables were included. The chapter headings and subheadings were not counted. The terms were tallied in several levels. For a few pages the sequence of all words was recorded on several pages. For the rest of the text reading, the terms were recorded by page.
Audiotapes for the lectures were recorded and the frequency of all terms counted. The chunks of the lectures that corresponded to subheadings were taken from the lecture outline for each of the three lectures. The terms were entered into a column in MS Excel. The tally for each term for each tape section was then counted using the COUNTIF function that used the range of cells with the entered words counting and the abbreviation used as the arguments. It would have been nice to use a similar system for the textbook analysis.
This unit included three rules that were applied to the content. These rules were. 1) thermodynamic laws, 2) matter conservation laws, and 3) system rules. The textbook and lecture tapes were examined for examples of applying these rules.
Figure 2. Rank and frequency of terms as they appear in the text book.
Figure 3. Rank and frequency of the same list of terms as used in the lecture.
Comparison of term frequencies between the text and the lecture.
lecture - most frequent 10 terms account for 64% of the total usage. Of those
terms in the text two were much less frequent (matter rank =19; decomposer rank
= 18).
text - the 10 most frequent terms accounted for 67% of the usage. Three of those
terms were used much less frequently in the lecture (population, rank=28; extinction
rank=15 and niche rank=28)
The highest discrepancies between ranks were
population, lect_rank=28 text_rank=2
niche, lect rank=28, text_rank=8
reserves, lect_rank =15, text_rank=34
prey, lect_rank=32, text_rank=16
corridores, lect_rank=19, text_rank=34
frequency and rank of text and lectures
total pages or hours and total terms
comparing text to lecture - which terms are outside a range of frequencies
comparing subsections to total
In addition to the frequency of the entire reading list, chapters, or subsections the sequence and synchronicity of the terms was analyzed on several selected pages. There are patterns, or motifs, that are identifiable in the text. These patterns may be meaningful to overall structure. They illustrate the dimensionality of the term association all the way from the bulk to the sentence level.
At the page level there are three types that stand out; Zipf’s law, repetitive blasts and bursts.
A Zipf’s page has one dominant term with a high count number and two or three sub-dominant terms at about the square root of that count. There may be several other terms that show up with counts of one or two. A good example of this is page 189 which had 5 terms with counts of 16, 4, 3, 1 and 1.
A burst page has many different terms at about equal count numbers. For example, page 198 has ten terms that are all with counts of 4 or less. This page was the introductory page for the unit and gives an example of how sea otters are back from the brink from extinction. The other introductory pages didn’t all show this burst style.
A repetitive blast page has one dominant term repeated many times. For example, page 199 has population repeated 22 times and the only other vocabulary word is habitat (2 times).
There are also structures that are evident at the level of the order of the words within a page. This makes sense when terms are used together in different phrases. There are several common patterns that I observed:
A scale or arpeggio in which terms occur in a set order. For example on page 86 we find "primary production", "energy", "biomass", "photosynthesis". This pattern is followed by a slight variation; "primary production", "energy", "biomass", "respiration".
A trill in which two terms are alternated back and forth. For example on page 92 "photosynthesis" and "primary production" alternate back and forth with several variations including the addition of "respiration" in a alternate trill.
Three assessments were given. The students were told that these were non-graded and that these were being used as part of a research project to understand their learning. Students were asked to put their names on the assessments so that their responses could be related to their other, graded, assignments.
Assessment 1 asked the students to simply list several terms that they associated with each word listed on the board. Those words were "food chain", "predator" and "primary production". All of these were words listed in their vocabulary work sheet on which there were given a graded test. On the first scan (not a complete analysis) the students responded most often with other vocabulary terms and very few examples. These assessments were analyzed for which other terms they associated the given word with. Very few students responded with examples.
Assessment 2 gave specific examples of a term and asked students to give their associations. I was looking for students to relate the examples to the more general category. These terms were "fire", "finch", and "fish". The responses were classified by wider, narrower or another type of association. Students gave multiple responses to each word.
Assessment 3 asked the students to list several words that were related to applying the rules of energy. This assessment looked for whether they simply associate the term with definitions of the rules or whether they give an example of the rule’s application, directly or indirectly. The analysis of the data indicates that it might have been unclear to the students to try to give applications of the rule rather than just associations.