Development of the BioCalculus Assessment (BCA)

We describe the development and initial validity assessment of the 20-item BioCalculus Assessment (BCA), with the objective of comparing undergraduate life science students’ understanding of calculus concepts in different courses with alternative emphases (with and without focus on biological applications). The development process of the BCA included obtaining input from a large network of scientists and educators as well as students in calculus and biocalculus courses to accumulate evidential support of the instrument’s content validity and response processes of test takers. We used the Rasch model to examine the internal structure of scores from students who have experienced calculus instruction in the two methods. The analysis involved three populations (Calculus 1, Calculus 2, and Biocalculus) for which the Calc 1 and Calc 2 students were not exposed to calculus concepts in a life science setting, while the Biocalculus students were presented concepts explicitly with a life science emphasis. Overall, our findings indicate that the BCA has reasonable validity properties, providing a diagnostic tool to assess the relative learning success and calculus comprehension of undergraduate biology majors from alternative methods of instruction that do or do not emphasize life science examples.

Fostering Germane Load Through Self-Explanation Prompting In Calculus Instruction

The purpose of this research was to investigate the effect of self-explanation prompting to students’ germane load while studying mathematics in the multivariable calculus course. This research employed a quasi-experimental method with matching-only posttest-only control group design. The subject of the research consists of 72 first-year mathematics education undergraduate students. The results indicated that there was no significant difference in students’ germane load between students who implemented worked-example with self-explanation prompting and students who implemented worked-example without self-explanation prompting. However, it was revealed that the students' germane load was categorized high in both classes. It indicates that the worked-example method could foster students' germane load. Nonetheless, these results cannot be evidence that self-explanation prompting is capable to foster students' germane load. However, there is an association between germane load and learning objectives. When students achieve the learning objectives, then its learning method is able to foster the germane load. To assess the learning objectives, the posttest was arranged. The results stated that students who implemented the worked-example method with self-explanation prompting had better test scores than students who implemented the worked-example method without self-explanation prompting. This result was sufficient to provide evidence that the use of worked-example with self-explanation prompting could foster students’ germane load students in the multivariable calculus course.Keywords: Germane load, Worked-example, Self-explanation prompting

The role of worked-example in enhancing students’ self-explanation and cognitive efficiency in calculus instruction

This research was aimed to investigate the effect of students’ self-explanation to their achievement, mental effort, and cognitive efficiency while studying mathematics, particularly in integral topics. This research used a static-group comparison design implemented to first-year undergraduate students. The subject of the study consists of 64 first year undergraduate students in one of the universities in Banten province, Indonesia. The students were divided into two classrooms, experimental and control. Experimental classroom received worked-example method whereas control classroom studying without worked-example method. Instruments used in this research include achievement tests, rating scale mental effort, deviation model of cognitive efficiency, and teaching materials in the form of worked-example. The results show that the implementation of self-explanation through worked-example helps students get a higher achievement, lower mental effort, and better cognitive efficiency compared to students who get instruction without worked-example method. The research also reveals the important role of worked-example in enhancing the ability of students’ self-explanation.

Differentiated Instruction in a Calculus Curriculum for College Students in Taiwan

Objectives: To explore differentiated instruction within a calculus curriculum. For college students to learn concentration, motivation and the impact of academic achievement; explore the attitudes and ideas of students on differentiated instruction within a calculus curriculum; build up the diversity of mathematics education within varied educational settings. Participants: Sample data were collected from freshman students of the Army Academy: total sample = 60, experimental and control group each had 30. Methods: Quasi-experimental design. Study tested whether differentiated instruction would enhance calculus instruction, compared with a traditional teaching method. Results: As hypothesized, results showed a significant difference in calculus achievement between experimental and control groups. Conclusions: Results supported the effectiveness of differentiated instruction on calculus curriculum. Finally, depending on the research results, the researcher provided practical suggestions for the educational research.