A Dynamic Learning Model for Matriculation Mathematics
Accelerated pre-matriculation mathematics remediation programs are a popular strategy for improving the placement levels of underprepared students. Although limited assessments of such programs have been reported in the literature, most work is focused either on immediate placement level improvement or longitudinal indicators of student success. While valuable, both techniques offer no insight regarding the learning progression of students while participating in the program, which is of tremendous value in optimizing program policy, such as determining the ideal number of contact hours. Best Matriculation School The research described herein proposes a first-order dynamic learning model for describing students’ content acquisition process within accelerated remediation programs. Details regarding model formulation are presented within this work-in-progress paper. A brief evaluation of model efficacy is also conducted using data gathered from daily ALEKS learning assessments employed within a one-week remediation program for intending engineering students.
A baseline model for describing student learning in the target intervention class was formulated based solely upon the 978-1-5090-1790-4/16/$31.00 ©2016 IEEE inherent principles governing the development of the underlying programs themselves. Namely, such offerings are fundamentally rooted in the assumption that certain topics for which students have not yet demonstrated comprehension on a placement exam may be reviewed and mastered more quickly than others, thus allowing them to bypass formal coursework by improving their scores in a truncated timeframe. http://www.karthividhyalaya.com/ This naturally implies a loose binary characterization scheme for those topics for which mastery has not yet been demonstrated as a function of the associated time required to build measurable comprehension. Topics within the first group, hereby referred to as a student’s review space, are characterized by an expected acquisition rate which is assumed to exceed that typically demonstrated by the same student in a course environment. While many classes of piecewise functions are suitable for modeling this phenomenon, employing a decreasing function in the review space to describe acquisition rate is reasonable based upon the understanding that certain topics within the group may be mastered more quickly than others. This may be influenced by numerous student and content specific factors, including time elapsed from previous exposure, specific content type, etc. In the proposed model, these dynamics lead to a diminishing return on time devoted towards content acquisition during the review phase, ultimately saturating once the expected rate of acquisition is equivalent to a student’s expected steady-state acquisition rate which would be observed in a traditional classroom mode.
Assessment of the learning progression of students during accelerated mathematics remediation programs offers significant insight regarding the underlying efficacy of such programming. Fundamental in the organization of these interventions is the assumption of the existence of a subset of content which enrollees are capable of mastering rapidly in a truncated timeframe. This paper suggests a formal mathematical framework for describing such learning dynamics in the form of a parametrized stochastic process. Data collected for a small convenience sample of enrollees during the 2014 AAP program at WSU suggests that the proposed dynamics are feasible, as quantified by a strong adjusted coefficient of determination across the participating group. Continuation of this current work-in-progress will involve expanding both the sophistication of the underlying learning model, as well as enhancing the richness of the validation data set.