Abstract
We discuss and examine a numerical indicator—the individual gain—of students’ engagement and mathematical growth in relation to an instructor’s course aims and goals. The individual gain statistic assesses the fractional amount an individual student improves initial-test to final-test. We argue that an initial-test score and a final-test score, if the two tests are related to each other and to a course focus, can provide a numerical indication of a student’s engagement with the goals and aims of the course and the extent to which a student was prepared to work toward those goals. Results on the distribution of individual gain for students in two-year college developmental mathematics courses and in sections of a course for pre-service elementary teachers are discussed. We detail and discuss advantages of the full distribution of individual gain, particularly for allowing statistical inference for differences, compared with Richard Hake’s use of mean gain of reform classes in undergraduate physics. Other instructional benefits of using the gain statistic to examine distribution of individual student gains include: a pre-test formative assessment at beginning of instruction, providing an instructor with data for specific, targeted remediation; and planning information that informs an instructor for the effectiveness of instruction for students in that cohort.
Highlights
We examine the issue of assessing student growth in mathematical thinking in relation to an instructor’s course aims and goals for pre-service elementary teachers and college developmental algebra students, using the usual assessment instruments and student data available to an instructor
We argue that a statistic derived from initial-test and final-test scores—the individual gain, defined below—provides us with a measure of the extent to which an individual student engages with mathematical content and an instructor’s explicit goals and aims related to deeper understanding
The individual gain statistic, calculated for each student from an initial-test score and a final examination score, can, if the two tests are related to each other and to the course focus, provide a numerical indication of a student’s engagement with the goals and aims of the course and the extent to which a student was prepared to work toward those goals
Summary
We examine the issue of assessing student growth in mathematical thinking in relation to an instructor’s course aims and goals for pre-service elementary teachers and college developmental algebra students, using the usual assessment instruments and student data available to an instructor. Over the course of the semester, student A’s test scores were, in order: 68%, 76%, 91%, and 95%, for an average of 83%. If anything, do the averages of 83% tell us about the engagement and mathematical growth of these two students over the semester?. 2. Comparison of final common examination scores and course grades of 321 college students enrolled in 20 sections of a developmental introductory algebra course over one semester were examined for consistency between course grades and departmental final examination scores, revealing an unexpected and startling degree of overlap in course grades for a given final examination score. Several students who received a grade of 83% on the common departmental comprehensive final examination were given course grades of A, B, C, and D. A score of 72% on the departmental final examination had a course grade of A, B, C, D, or F, as did final examination scores of 63% and 57%
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Electronic Journal of Mathematics Education
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
