Kiel Christianson’s research focuses on psycholinguistics and reading, with two recent papers providing insights into reading and comprehension that have possible implications for how students learn.
In one paper with fellow Beckman researcher Jose Mestre and student Steven Luke, published in Applied Cognitive Psychology, they report on a study investigating the use of repetition as a method for improving accuracy in solving word-algebra problems. They reported that the student subjects in their experiment, which used what are called “students-and-professors” type problems, were more successful in solving them after repeated exposure to similar problems.
Previous research has shown that college students, including those majoring in science and engineering, made predictable errors in these types of problems, but without revealing the source of the problem. Christianson said this study tried to solve that challenge.
“We examined the performance of students in solving such problems over many more trials than previous research,” he said. “Most past work presented just one or a handful of problems. We gave them dozens of them.”
In addition, Christianson said, the experiments examined potential reasons why students in past experiments have generally done poorly solving such problems. These included a word order in the problems that either mapped straightforwardly onto the order of the correct algebraic formula, or a word order that mapped onto the reversed – and incorrect – algebraic formula.
“We found that adding variation to the wording of the problems, along with repeated practice – even practice without feedback – led to marked improvement in solving the problems over the course of all three of our experiments,” Christianson said.
– Kiel Christianson
In another paper with Luke and Psychology Ph.D. student and lead author Mallory Stites, Christianson and his collaborators found that people read embedded quotes more quickly when a character is described as speaking quickly. The paper, Dialogue descriptions modulate reading speed!, published in Memory & Cognition, reports that “readers spent less time reading direct quotes described as being said quickly, as compared to those described as being said slowly.” They also found that there was no loss of comprehension with reading quickly and that the “speed of the character’s movement did not affect direct-quote reading times.”
“It is quite remarkable that the mental simulation of speaking speed modulates the speed of the eyes as they move across the text,” Christianson said. “It is strong evidence for the role of an ‘inner voice’ during silent reading.”
The researchers preface the study by writing that when “reading a story, readers often have the phenomenological experience of hearing the voices of the characters in their heads” and that “psychology researchers have considered this inner speech to play an important role in reading comprehension.” They added that, “studying the form of the inner voice experimentally has proven difficult.”
The researchers attribute the non-conscious impulse to read a quote more quickly to what past research has shown is the impulse of readers to mentally simulate the physical actions described in text, or what is called perceptual simulation. For this study, they looked at “whether the ‘speed’ of inner speech can be affected by the content of a narrative currently being read and whether the effect is reflected in the speed of eye movements during silent reading.”
The experiment included 68 study participants who read sentences that described a character who performed an action and then said a quote. Eye-tracking equipment was used to measure eye movements.
They found that overall accuracy on the comprehension questions was 95.1 percent and that “direct quotes described as being said ‘quickly are read faster than those described as being said slowly,’ an effect that we attribute to perceptual simulation of character speech.”
The results demonstrated that “perceptual simulation can be generated with only a single adverb preceding a quote to establish a character’s speaking rate. This is also the first study to show that adverbs with a semantically ‘fast’ meaning are read faster than adverbs with a ‘slow’ meaning, likely caused by the automatic activation of semantic features during lexical access, rather than by perceptual simulation.”
In the word-algebra problem study, the researchers tested an area of learning revolving around the recent de-emphasis in the United States on using repetitive learning in mathematics education. The paper is titled Practice Makes (Nearly) Perfect: Solving ‘Students-and-Professors’-Type Algebra Word Problems.
A recent study, they wrote, “compared the Common Core standards with those of three high-performing countries (Finland, Japan, and Singapore). They found a much greater emphasis on ‘perform procedures’ – that is, on doing more problems rather than focusing on higher-level conceptualization – in the high performing countries than in the US Common Core or state standards. Porter et al. suggested, very tentatively, that this fact may point toward a re-evaluation of the de-emphasis in the USA on solving greater numbers of routine problems.”
Other studies have found error rates involving what is known as the “variable reversal error” in these equations, even among science and engineering students, to fall between 20 and 60 percent. The students “committed predictable and apparently persistent errors in translating these fairly basic word problems into algebraic equations. … In the intervening years since the prevalence of the ‘variable reversal error’ was revealed, many additional studies have attempted to understand its source but with limited success.”
Christianson said previous studies have assumed the problem is intrinsic within the student populations, but their findings show repetition can greatly increase performance in equation accuracy, even without using feedback, as was the case in this study.
The study recruited 36 student subjects who were non-math majors to solve the students-and-professors type problems. They used this example in the paper of the type of problem: “Write an equation using the variables S and P to represent the following statement: ‘There are six times as many students as professors at this university.’ Use S for the number of students and P for the number of professors.” However, for this study, Christianson said they used variables that did not cue the subjects to relative numbers, as in the previous equation where it would be expected to have more students than professors.
They conducted three experiments designed to find out how “perseverant reversal errors really are in students-and-professors-type problems and whether any observed perseverant poor performance or improvement in performance with practice would be modulated by some of the factors previously reported to affect performance on such problems: word order and situation model. In all three experiments, we observed a strong positive effect of trial number on solution accuracy, indicating that our participants’ performance on these problems spontaneously improved as a result of practice.”
They summed up their findings: “At the very least, the results reported here strongly suggest that long-vexing reversal errors in college-aged students are not as entrenched as past findings might lead one to believe.”
Christianson said the results show that the problem is one of language comprehension, not mathematical problem-solving.
“Language and algebra do not map onto each other in a one-to-one fashion,” he said. “The same relationship can be described in several different ways linguistically without altering the mathematical relationship.”
The results should prove instructive for future designs of mathematical educational materials.
“Students should, it seems, be exposed to multiple ways of stating the same sort of problem and provided with multiple opportunities to solve the same sort of problem, too,” Christianson said.