skip to main content

Explore Research Products in the NSF-PAR

  • NSF Public Access
  • Search Results
  • Leveraging Prediction and Reflection in a Computational Setting to Enrich Undergraduate Students’ Combinatorial Thinking
Title: Leveraging Prediction and Reflection in a Computational Setting to Enrich Undergraduate Students’ Combinatorial Thinking
In this paper, I discuss undergraduate students’ engagement in basic Python programming while solving combinatorial problems. Students solved tasks that were designed to involve programming, and they were encouraged to engage in activities of prediction and reflection. I provide data from two paired teaching experiments, and I outline how the task design and instructional interventions particularly supported students’ combinatorial reasoning. I argue that emergent computational representations and the prompts for prediction and reflection were especially useful in supporting students’ reasoning about fundamental combinatorial ideas. I argue that this particular mathematical example informs broader notions of disciplinary reflexivity and representational heterogeneity, providing insight into computational thinking practices in the domain of mathematics. Ultimately, I aim to explore the nature of computing and enumeration, shedding light on why the two disciplines are particularly well-suited to support each other. I conclude with implications and avenues for future research.  more » « less
Award ID(s):
1650943
NSF-PAR ID:
10336909
Author(s) / Creator(s):
Editor(s):
Enyedy, Noel
Date Published:
Journal Name:
Cognition and Instruction
ISSN:
0737-0008
Page Range / eLocation ID:
1 to 43
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ( , British Journal of Educational Technology)
    Abstract  
    more » « less
  2. ; ; ; ; ; ; ( , Annual meeting program American Educational Research Association)
    null (Ed.)
    EcoMOD uses a design-based research approach to develop and study an elementary curriculum that combines an immersive virtual environment with interactive computer programming interface to support computational modeling, ecosystem science understanding, and causal reasoning. Here we report on changes in students’ perspectives on modeling before and after use of the fifteen day interactive, technology-based curriculum in a 3rd and 4th grade classroom. Pre-post interviews were conducted with ten students, and preliminary results suggest that students demonstrated an increased awareness that models are designed for a purpose, and the purposes students described aligned more closely with scientifically relevant activities like prediction, investigation and explanation. Students also increased in their level of sophistication related to ecosystem science understanding and causal reasoning. 
    more » « less
  3. ; ; ( , ASEE Annual Conference proceedings)
    This research paper describes a study of elementary teacher learning in an online graduate program in engineering education for in-service teachers. While the existing research on teachers in engineering focuses on their disciplinary understandings and beliefs (Hsu, Cardella, & Purzer, 2011; Martin, et al., 2015; Nadelson, et al., 2015; Van Haneghan, et al., 2015), there is increasing attention to teachers' pedagogy in engineering (Capobianco, Delisi, & Radloff, 2018). In our work, we study teachers' pedagogical sense-making and reflection, which, we argue, is critical for teaching engineering design. This study takes place in [blinded] program, in which teachers take four graduate courses over fifteen months. The program was designed to help teachers not only learn engineering content, but also shift their thinking and practice to be more responsive to their students. Two courses focus on pedagogy, including what it means to learn engineering and instructional approaches to support this learning. These courses consist of four main elements, in which teachers: 1) Read data-rich engineering education articles to reflect on learning engineering; 2) Participate in online video clubs, looking at classroom videos of students’ engineering and commenting on what they notice; 3) Conduct interviews with learners about the mechanism of a pull-back car; and 4) Plan and teach engineering lessons, collecting and analyzing video from their classrooms. In the context of this program, we ask: what stances do teachers take toward learning and teaching engineering design? What shifts do we observe in their stances? We interviewed teachers at the start of the program and after each course. In addition to reflecting on their learning and teaching, teachers watched videos of students’ engineering and discussed what they saw as relevant for teaching engineering. We informally compared summaries from previous interviews to get a sense of changes in how participants talked about engineering, how they approached teaching engineering, and what they noticed in classroom videos. Through this process, we identified one teacher to focus on for this paper: Alma is a veteran 3rd-5th grade science teacher in a rural, racially-diverse public school in the southeastern region of the US. We then developed content logs of Alma's interviews and identified emergent themes. To refine these themes, we looked for confirming and disconfirming evidence in the interviews and in her coursework in the program. We coded each interview for these themes and developed analytic memos, highlighting where we saw variability and stability in her stances and comparing across interviews to describe shifts in Alma's reasoning. It was at this stage that we narrowed our focus to her stances toward the engineering design process (EDP). In this paper, we describe and illustrate shifts we observed in Alma's reasoning, arguing that she exhibited dramatic shifts in her stances toward teaching and learning the EDP. At the start of the program, she was stable in treating the EDP as a series of linear steps that students and engineers progress through. After engaging and reflecting on her own engineering in the first course, she started to express a more fluid stance when talking more abstractly about the EDP but continued to take it up as a linear process in her classroom teaching. By the end of the program, Alma exhibited a growing stability across contexts in her stance toward the EDP as a fluid set of overlapping practices that students and engineers could engage in. 
    more » « less
  4. ; ; ( , ASEE Annual Conference proceedings)
    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
  5. ; ; ( , ASEE Annual Conference proceedings)
    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
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email