An official website of the United States government
A study conducted by the Mathematical Association of America showed that calculus not only has significant effects on students’ decision to pursue STEM fields, but also on their attitudes towards mathematics. Inspired by this large-scale study, the present study sought to deepen the current understanding of the impact of calculus on student attitudes towards mathematics. Results of an implementation of the Modeling Practices in Calculus (MPC) model, an innovative active learning in mathematics (ALM) approach, in Calculus I at a large, urban, research intensive (R1) institution are presented. Using a randomized-control trial research design, stu- dents were randomly assigned to either traditional, lecture-based classrooms, or MPC classrooms. The Attitudes Towards Mathematics Inventory (ATMI) was used to measure student attitudes at the begin- ning and end of the course and results were compared from both MPC and traditional sections. Overall, MPC sections showed improve- ment over traditional instruction by having less negative impact on student attitudes. The enjoyment and self-confidence ATMI sub- scales showed significant differences at course completion for both semesters, when controlling for pre-ATMI score and term. Further- more, the MPC model had a positive impact on female students’ self-confidence as opposed to male students, acting as a gender equalizer.
more »
« less
Establishing a new standard of care for calculus using trials with randomized student allocation
Calculus, the study of change in processes and systems, serves as the foundation for many STEM disciplines. Traditional, lecture-based calculus instruction may present a barrier for students seeking STEM degrees, limit their access to STEM professions, and block their potential to address society’s challenges. A large-scale pragmatic trial with randomized student allocation was conducted to compare two calculus instruction styles: active student engagement (treatment condition) versus traditional, lecture-based instruction (control condition). A sample of 811 university students were studied across 32 sections taught by 19 instructors over three semesters at a large, US-based Hispanic-serving institution. Large effect sizes were consistently measured for student learning outcomes in the treatment condition, which demonstrates a new standard for calculus instruction and increased opportunities for completion of STEM degrees.
more »
« less
- Award ID(s):
- 1832450
- PAR ID:
- 10556626
- Publisher / Repository:
- American Association for the Advancement of Science
- Date Published:
- Journal Name:
- Science
- Volume:
- 381
- Issue:
- 6661
- ISSN:
- 0036-8075
- Page Range / eLocation ID:
- 995 to 998
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This work in progress paper discusses preliminary research testing the causal effectiveness of exploratory learning in undergraduate STEM courses. Exploratory learning is an active-learning technique that has been shown to improve students’ conceptual understanding, and is therefore well suited for STEM education. This method reverses the order of traditional lecture-then practice methods, by having students explore a novel problem prior to instruction. Participants (N=150) were first-year engineering students enrolled in an introductory engineering calculus course. Students were taught about two-dimensional vectors in an online, asynchronous learning module. Students were randomly assigned to one of two conditions. In the instruct-first condition, students viewed the instruction and then completed a Geogebra™ activity. In the explore-first condition, students completed the activity and then viewed the instruction. Thus, the exact same activities were given to students, allowing us to test the causal effectiveness of reversing the placement of the activity. Afterwards, all students completed an online quiz and a later Vector test. A number of students opened but did not complete the activity. Of those students, no effects of condition were found. For the students who completed the activity, those in the explore-first condition scored higher on the quiz than those in the instruct-first condition. Scores were trending in a similar direction on the vector test. These results demonstrate the potential of exploratory learning to improve understanding in engineering mathematics, and in an online module format. This research also suggests that Geogebra™ may be a useful tool for developing an exploration activity students can complete online.more » « less
-
STEM undergraduate instructors teaching remote courses often use traditional lecture-based instruction, despite evidence that active learning methods improve student engagement and learning outcomes. One simple way to use active learning online is to incorporate exploratory learning. In exploratory learning, students explore a novel activity (e.g., problem solving) before a lecture on the underlying concepts and procedures. This method has been shown to improve learning outcomes during in-person courses, without requiring the entire course to be restructured. The current study examined whether the benefits of exploratory learning extend to a remote undergraduate physics lesson, taught synchronously online. Undergraduate physics students (N = 78) completed a physics problem-solving activity either before instruction (explore-first condition) or after (instruct-first condition). Students then completed a learning assessment of the problem-solving procedures and underlying concepts. Despite lower accuracy on the learning activity, students in the explore-first condition demonstrated better understanding on the assessment, compared to students in the instruct-first condition. This finding suggests that exploratory learning can serve as productive failure in online courses, challenging students but improving learning, compared to the more widely-used lecture-then-practice method.more » « less
-
College calculus plays an important role in STEM students’ degree and career aspirations. One of the key factors considered in assessing a student’s ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students’ precalculus proficiency on their achievement in introductory calculus based on their classroom environment. Results from the implementation of the Modeling Practices in Calculus (MPC) model, an innovative, active learning approach, are presented. Using a randomized-controlled trial research design, students were randomly assigned to MPC and traditional, lecture-based calculus sections. The Precalculus Concept Assessment inventory was administered to gauge students’ precalculus proficiency. We found that students exposed to the MPC model were more likely to be successful in their calculus course, even if they began with low precalculus proficiency. Also, students enrolled in the MPC sections saw significant growth in their precalculus proficiency from the beginning to the end of the semester. Additionally, we observed this model providing support for students in key demographics (low proficiency, female, underclassmen) in terms of the development of their proficiency that they may not receive in traditional classrooms.more » « less
-
The Learning Assistant (LA) model supports instructors in implementing research-based teaching practices in their own courses. In the LA model undergraduate students are hired to help facilitate research-based collaborative-learning activities. Using the Learning About STEM Student Out- comes (LASSO) database, we examined student learning from 112 first-semester physics courses that used either lecture-based instruction, collaborative instruction without LAs, or LA supported instruction. We measured student learning using 5959 students’ responses on the Force and Motion Conceptual Evaluation (FMCE) or Force Concept Inventory (FCI). Results from Hierarchical Linear Models (HLM) indicated that LA supported courses had higher posttest scores than collaborative courses without LAs and that LA supported courses that used LAs in laboratory and recitation had higher posttest scores than those that used LAs in lecture.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1126/science.ade9803
