skip to main content


Title: Dimensions of Variation in group work within the “same” multi-section undergraduate course
This paper reports a qualitative study of how small group problem solving was enacted differently across sections of a multi-section undergraduate introduction to proof course. Common course materials, common guidelines for instruction, and weekly instructor meetings led by a faculty course coordinator supported similar instruction across sections, including an emphasis on in-class group work. But within that shared structure, classroom observations revealed important differences in how group work was introduced, organized, and managed. Our results focus on differences in the time allotted to group work, the rationale for group work, the selection and organization of groups, and aspects of student activity and participation. We suggest that these differences shaped different opportunities to learn proof writing in small groups. These results have implications for the design and teaching of collegiate mathematics courses where group work is a regular element of classroom work.  more » « less
Award ID(s):
1835946
NSF-PAR ID:
10215627
Author(s) / Creator(s):
Editor(s):
Karunakaran, S. S.
Date Published:
Journal Name:
Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education
Page Range / eLocation ID:
606-613
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Motivation: This is a complete paper. There was a sudden shift from traditional learning to online learning in Spring 2020 with the outbreak of COVID-19. Although online learning is not a new topic of discussion, universities, faculty, and students were not prepared for this sudden change in learning. According to a recent article in ‘The Chronicle of Higher Education, “even under the best of circumstances, virtual learning requires a different, carefully crafted approach to engagement”. The Design Thinking course under study is a required freshmen level course offered in a Mid-western University. The Design Thinking course is offered in a flipped format where all the content to be learned is given to students beforehand and the in-class session is used for active discussions and hands-on learning related to the content provided at the small group level. The final learning objective of the course is a group project where student groups are expected to come up with functional prototypes to solve a real-world problem following the Design Thinking process. There were eighteen sections of the Design Thinking course offered in Spring 2020, and with the outbreak of COVID-19, a few instructors decided to offer synchronous online classes (where instructors were present online during class time and provided orientation and guidance just like a normal class) and a few others decided to offer asynchronous online classes (where orientation from the instructor was delivered asynchronous and the instructor was online during officially scheduled class time but interactions were more like office hours). Students were required to be present synchronously at the team level during the class time in a synchronous online class. In an asynchronous online class, students could be synchronous at the team level to complete their assignment any time prior to the deadline such that they could work during class time but they were not required to work at that time. Through this complete paper, we are trying to understand student learning, social presence and learner satisfaction with respect to different modes of instruction in a freshmen level Design Thinking course. Background: According to literature, synchronous online learning has advantages such as interaction, a classroom environment, and better course quality whereas asynchronous online learning has advantages such as self-controlled and self-directed learning. The disadvantages of synchronous online learning include the learning process, technology issues, and distraction. Social isolation, lack of interaction, and technology issue are a few disadvantages related to asynchronous online learning. Problem Being Addressed: There is a limited literature base investigating different modes of online instruction in a Design Thinking course. Through this paper, we are trying to understand and share the effectiveness of synchronous and asynchronous modes of instruction in an online Flipped Design Thinking Course. The results of the paper could also help in this time of pandemic by shedding light on the more effective way to teach highly active group-based classrooms for better student learning, social presence, and learner satisfaction. Method/Assessment: An end of semester survey was monitored in Spring 2020 to understand student experiences in synchronous and asynchronous Design Thinking course sections. The survey was sent to 720 students enrolled in the course in Spring 2020 and 324 students responded to the survey. Learning was measured using the survey instrument developed by Walker (2003) and the social presence and learner satisfaction was measured by the survey modified by Richardson and Swan (2003). Likert scale was used to measure survey responses. Anticipated Results: Data would be analyzed and the paper would be completed by draft paper submission. As the course under study is a flipped and active course with a significant component of group work, the anticipated results after analysis could be that one mode of instruction has higher student learning, social presence, and learner satisfaction compared to the other. 
    more » « less
  2. Engineers must understand how to build, apply, and adapt various types of models in order to be successful. Throughout undergraduate engineering education, modeling is fundamental for many core concepts, though it is rarely explicitly taught. There are many benefits to explicitly teaching modeling, particularly in the first years of an engineering program. The research questions that drove this study are: (1) How do students’ solutions to a complex, open-ended problem (both written and coded solutions) develop over the course of multiple submissions? and (2) How do these developments compare across groups of students that did and did not participate in a course centered around modeling?. Students’ solutions to an open-ended problem across multiple sections of an introductory programming course were explored. These sections were all divided across two groups: (1) experimental group - these sections discussed and utilized mathematical and computational models explicitly throughout the course, and (2) comparison group - these sections focused on developing algorithms and writing code with a more traditional approach. All sections required students to complete a common open-ended problem that consisted of two versions of the problem (the first version with smaller data set and the other a larger data set). Each version had two submissions – (1) a mathematical model or algorithm (i.e. students’ written solution potentially with tables and figures) and (2) a computational model or program (i.e. students’ MATLAB code). The students’ solutions were graded by student graders after completing two required training sessions that consisted of assessing multiple sample student solutions using the rubrics to ensure consistency across grading. The resulting assessments of students’ works based on the rubrics were analyzed to identify patterns students’ submissions and comparisons across sections. The results identified differences existing in the mathematical and computational model development between students from the experimental and comparison groups. The students in the experimental group were able to better address the complexity of the problem. Most groups demonstrated similar levels and types of change across the submissions for the other dimensions related to the purpose of model components, addressing the users’ anticipated needs, and communicating their solutions. These findings help inform other researchers and instructors how to help students develop mathematical and computational modeling skills, especially in a programming course. This work is part of a larger NSF study about the impact of varying levels of modeling interventions related to different types of models on students’ awareness of different types of models and their applications, as well as their ability to apply and develop different types of models. 
    more » « less
  3. Engineers must understand how to build, apply, and adapt various types of models in order to be successful. Throughout undergraduate engineering education, modeling is fundamental for many core concepts, though it is rarely explicitly taught. There are many benefits to explicitly teaching modeling, particularly in the first years of an engineering program. The research questions that drove this study are: (1) How do students’ solutions to a complex, open-ended problem (both written and coded solutions) develop over the course of multiple submissions? and (2) How do these developments compare across groups of students that did and did not participate in a course centered around modeling?. Students’ solutions to an open-ended problem across multiple sections of an introductory programming course were explored. These sections were all divided across two groups: (1) experimental group - these sections discussed and utilized mathematical and computational models explicitly throughout the course, and (2) comparison group - these sections focused on developing algorithms and writing code with a more traditional approach. All sections required students to complete a common open-ended problem that consisted of two versions of the problem (the first version with smaller data set and the other a larger data set). Each version had two submissions – (1) a mathematical model or algorithm (i.e. students’ written solution potentially with tables and figures) and (2) a computational model or program (i.e. students’ MATLAB code). The students’ solutions were graded by student graders after completing two required training sessions that consisted of assessing multiple sample student solutions using the rubrics to ensure consistency across grading. The resulting assessments of students’ works based on the rubrics were analyzed to identify patterns students’ submissions and comparisons across sections. The results identified differences existing in the mathematical and computational model development between students from the experimental and comparison groups. The students in the experimental group were able to better address the complexity of the problem. Most groups demonstrated similar levels and types of change across the submissions for the other dimensions related to the purpose of model components, addressing the users’ anticipated needs, and communicating their solutions. These findings help inform other researchers and instructors how to help students develop mathematical and computational modeling skills, especially in a programming course. This work is part of a larger NSF study about the impact of varying levels of modeling interventions related to different types of models on students’ awareness of different types of models and their applications, as well as their ability to apply and develop different types of models. 
    more » « less
  4. null (Ed.)
    This research paper studies the challenges that mathematics faculty and graduate teaching assistants (GTAs) faced when moving active and collaborative calculus courses from in-person to virtual instruction. As part of a larger pedagogical change project (described below), the math department at a public Research-1 university began transitioning pre-calculus and calculus courses to an active and collaborative learning (ACL) format in Fall 2019. The change began with the introduction of collaborative worksheets in recitations which were led by GTAs and supported by undergraduate learning assistants (LAs). Students recitation periods collaboratively solving the worksheet problems on whiteboards. When COVID-19 forced the rapid transition to online teaching, these ACL efforts faced an array of challenges. Faculty and GTA reflections on the changes to teaching and learning provide insight into how instructional staff can be supported in implementing ACL across various modes of instruction. The calculus teaching change efforts discussed in this paper are part of an NSF-supported project that aims to make ACL the default method of instruction in highly enrolled gateway STEM courses across the institution. The theoretical framework for the project builds on existing work on grassroots change in higher education (Kezar and Lester, 2011) to study the effect of communities of practice on changing teaching culture. The project uses course-based communities of practice (Wenger, 1999) that include instructors, GTAs, and LAs working together to design and enact teaching change in the targeted courses alongside ongoing professional development for GTAs and LAs. Six faculty and five GTAs involved in the teaching change effort in mathematics were interviewed after the Spring 2020 semester ended. Interview questions focused on faculty and GTA experiences implementing active learning after the rapid transition to online teaching. A grounded coding scheme was used to identify common themes in the challenges faced by instructors and GTAs as they moved online and in the impacts of technology, LA support, and the department community of practice on the move to online teaching. Technology, including both access and capabilities, emerged as a common barrier to student engagement. A particular barrier was students’ reluctance to share video or participate orally in sessions that were being recorded, making group work more difficult than it had been in a physical classroom. In addition, most students lacked access to a tablet for freehand writing, presenting a significant hurdle for sharing mathematical notation when physical whiteboards were no longer an option. These challenges point to the importance of incorporating flexibility in active learning implementation and in the professional development that supports teaching changes toward active learning, since what is conceived for a collaborative physical classroom may be implemented in a much different environment. The full paper will present a detailed analysis of the data to better understand how faculty and GTA experiences in the transition to online delivery can inform planning and professional development as the larger institutional change effort moves forward both in mathematics and in other STEM fields. 
    more » « less
  5. The Bureau of Statistics identified an urgent demand for science, technology, engineering, and mathematics (STEM) professionals in the coming years. In order to meet this demand, the number of students graduating with STEM degrees in the United States needs to increase by 34% annually [1]. Engineering for US All (E4USA): A National Pilot Program for High School Engineering Course and Database is a NSF-funded first-of-its-kind initiative designed to address this national need. The E4USA project aims to make engineering more inclusive and accessible to underrepresented minorities, while increasing racial, ethnic, and gender representation in higher education and the workforce. The “for us all” mission of E4USA encompasses both students and educators. The demand for engineering educators has increased, but relying on practicing engineers to switch careers and enter teacher preparation programs has been insufficient [2, 3, 4]. This has led schools to turn to educators with limited training in engineering, which could potentially have a significant national impact on student engineering education [5, 6, 7]. Part of the E4USA pilot year mission has been to welcome educators with varying degrees of experience in industry and teaching. Paramount to E4USA was the construction of professional development (PD) experiences and a community of practice that would prepare and support teachers with varying degrees of engineering training instruction as they implemented the yearlong course. The perspectives of four out of nine educators were examined during a weeklong, intensive E4USA PD. Two of four educators were considered ‘novices’; one with a background in music and the other in history. The remaining two educators were deemed ‘veterans’ with a total of 15 years of experience as engineers and more than 20 years as engineering educators. Data sources consist of focus groups, surveys, and artifacts created during the PD (e.g., educators’ responses to reflection prompts and letters written to welcome the next cohort). Focus group data is currently being analyzed using inductive coding and the constant comparative method in order to identify emergent themes that speak to the past experience or inexperience of educators with engineering. Artifacts were used to: 1) Triangulate the findings generated from the analysis of focus group, and 2) Further understand how the veteran educators supported the novice educators. We will also use quantitative survey data to examine descriptive statistics, observed score bivariate correlations, and differences in mean scores across novices and veterans to further examine potential common and unique experiences for these educators. The results aim to highlight how the inclusion of educators with a broad spectrum of past experiences with engineering and engineering education can increase educators’ empathy towards students who may be equally hesitant about engineering. The findings from this study are expected to result in implications for how PD and a community of practice may be developed to allow for reciprocal support and mentoring. Results will inform future efforts of E4USA and aim to change the structure of high school engineering education nationwide. 
    more » « less