SYMPTOMS and PROBLEMS
The primary symptom is obvious. Math Lab students have a definite tendency, as a group, to put off working on their math class. For too many students, this lack of consistent effort leads to a non-passing grade. One naturally wonders if some change in policy would result in better progress and a happier outcome at the end of the semester. In “A Modest Proposal”, this issue is called horizontal flexibility.
A secondary symptom is much more subtle, and this deals with students who are working but remain ‘stuck’ … they attempt the test multiple times prior to passing it (or without passing it). Whether this is the infamous Test 3 in Math112, or one of the middle tests in Math107, some folks wonder about the wisdom of continued effort in the face of failing tests. In “A Modest Proposal”, this issue is called mastery learning.
At a basic level, both of these ‘problems’ have been a fundamental reason for existence of the Math Lab. Many of our students have a life style (by choice or not) which precludes 16 weeks of effort on a class; there may be several periods of a few days not available, or there may be a couple of class weeks. These students have difficulty taking a ‘lecture’ class; though they might consider an online class, the flexibility of the Math Lab better matches their learning needs. (Life style, as used here, simply refers to the other restraints on time – family, illness, employment, crisis, or whatever.)
Besides the life style issues, there are large numbers of learning challenges and disabilities among the students served by this department. Historically, a larger proportion of these enroll in the Math Lab due to the individual attention provided there … and the horizontal flexibility. A number of learning factors make the process take longer for many students, and the fixed pace of a lecture or even the Lab/Lecture is too much. [Obviously, there are no reliable statistics on the number of students involved or how many take the Math Lab. Experience and observation are the primary sources, though the conclusion stated seems to have general consensus.]
A different way of looking at the horizontal flexibility is this: Life involves planning, making priorities, balancing long-term competing needs for our time and energy. Our younger students, especially, may need a situation where they can develop some skills in this area … before the consequences are life-changing. [Of course, we can not predict when a lesson like this will actually ‘take’ and make a difference; however, we can always hope that students get more than math skills out of our courses.]
The use of mastery learning has many motivations with this population. First, and foremost, many students are expected to use their mathematics in some other course for their program. Logic implies, and decades of data supports, that students from a mastery learning program will have a higher level of knowledge from the course (on average). The fact that mastery learning is not used in all methods reflects other factors – including faculty member’s philosophy and convenience to the Department.
A secondary motivation for the use of mastery learning is affective – if students must pass every ‘topic’, there is a higher probability that they will gain confidence in their mathematics. Locally, we have not conducted research on this assertion. However, there are some studies in the literature on the attitudinal impacts of mastery learning, and they generally support the notion stated. (Obviously, there are many factors that impact these attitudes; one could not expect miraculous improvements from one course for all students.)