By Jessica Knott
This week, I had the chance to talk with Dr. Daniel McGee (CV), former middle and high school teacher in Francistown, Botswana, Peace Corps volunteer, and researcher/biostatistician for the Centers for Disease Control in Atlanta, Georgia. Dr. McGee’s work in creating a free, public access online learning system for primary and secondary students in Puerto Rico has gained traction in recent years, becoming the basis for online pre-calculus materials that will now be used in schools throughout Puerto Rico.
As his projects began generating larger and larger data sets, he became interested in exploring the insights they might provide on learning styles, learning types, and learning in general. This interview provides an overview of the motivations behind the study as well as a brief discussion of some of his key findings.
JK: What did this study find, exactly? Why is this important?
DM: There were two important results of this study.
Result 1: In general, most efforts to define the categories for learning types have been a priori in nature. Researchers will start with a set of learning types and then will categorize students. This study takes an a posteriori approach to student learning types. We gather a great deal of data on a lot of students. The data comes from questionnaires and results on quizzes and exams from an online learning system. Rather than starting with predefined categories for students, we look for natural groups of students based on similar responses to questionnaires and similar results on quizzes and exams. These natural groupings lend insight into the natural learning styles of the students taking the course. The first result of the study was that students were not scattered randomly, they did form natural groupings. So the vast amount of information available with online learning systems does allow us, at least in Puerto Rico, to identify student learning types in an a posteriori manner.
The vast amount of information available with online learning systems does allow us, at least in Puerto Rico, to identify student learning types in an a posteriori manner.
Importance of result 1: Our results indicate that large groups of students seem to organize themselves into distinct clusters. The ability to identify these clusters and their associated strengths and weaknesses will allow professors with large groups of students using online systems to better address the particular needs of the distinct learning types that are in their class at a particular time.
Result 2: The most important aspect of the natural groupings of the students at the University of Puerto Rico (UPR) was that success with algebraic, verbal and geometric tasks was linked. The natural groupings of students that we found were either very successful, mediocre, or very poor with all three representations. There was no such thing as an “algebraic learner” who was weak in geometry.
Importance of result 2: Puerto Rico tends to be a very traditional and algebraic oriented environment. The clusters that were found at the UPR showed that geometry and algebra seem to mutually reinforce one another with successful students. And without this mutual understanding, students are not successful. Correspondingly, a more balanced approach emphasizing the relationship between geometry and its associated algebra is more consistent with our model for a successful student.
JK: Tell me what you mean by an algebraic environment? Verbal? How do you think identifying these clusters will be helpful?
DM: An algebraic environment means that they tend to emphasize the manipulation of algebraic formulas: Students start with an algebraic expression, perform various actions and end up with another algebraic expression. For example, they might start with 2x+y=3 and change it to y=-2x+3. However, the algebraic expression would seldom be associated with a geometric figure or a real-life situation.
Successful [Calculus I] students appeared to need a unified approach, which emphasized verbal situations, geometric figures, algebraic expressions and the relations between them.
In a practical sense, the clusters were helpful to us in that they identified that successful students appeared to need a unified approach, which emphasized verbal situations, geometric figures, algebraic expressions and the relations between them. Correspondingly, as many professors were overemphasizing algebra, it would suggest that more emphasis on geometry and real life situations would be helpful. Hence, it lets professors address the needs of their own particular students as identified by the learning types in their class. From the perspective of math behaviorists, by selecting the questions in the questionnaires and on the quizzes very carefully, these natural groupings can provide insight into student learning types as they are not based on preconceptions but represent natural groupings.
JK: What would you suggest that professors and practitioners do with this data? How can this help them?
DM: The first thing I’d like to see is whether performance on actual tasks supports behaviorists categories of learning. For example, there are tests to determine whether a student is a “right brain” or “left brain” thinker. And these categories have preconceptions regarding the sort of tasks in which a student should excel. If “left brain” and “right brain” thinkers are equally distributed in each of the clusters we generate, this would indicate that there is little relationship between these categories and the ability to perform different types of tasks. Correspondingly, knowing this propensity in advance would be of little use. However, if each cluster were strongly associated with either a “left brain” or “right brain” propensity, this would indicate that this physiological propensity would be useful to know in advance in order to better design the material to the specific needs of the student.
We found that there was a large cluster of students that learn by rote memorization. An appropriate intervention for this group might be a workshop exploring the value of conceptual understanding vs. rote memorization ….
From the perspective of a professor that simply wishes to teach his class well, this sort of data would allow the professor to address a certain profile associated with a single cluster containing many students. For example, we found that there was a large cluster of students that learn by rote memorization. An appropriate intervention for this group might be a workshop exploring the value of conceptual understanding vs. rote memorization with the goal of convincing them that conceptual understanding is a better investment for their futures in STEM fields.
JK: What made you undertake this research? What was your “lightbulb,” as it were?
DM: I work with research on both informatics and math education. As my projects with online learning systems obtain large quantities of data for many students, it was rather natural to explore what insight this large amount of data might give us on learning types.
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