skip to main content

Title: THAT’S CRAZY: An exploration of student exclamations in high school mathematics lessons
In this study, we explore the relationships between the types of student exclamations in an enacted lesson (e.g., “Wow!”) and the varying dramatic tensions created by the unfolding content. By analyzing student exclamations in six specially-designed high school mathematics lessons, we explore how the dynamic tension between revelations of mathematical ideas at the moment and what is yet to be known connects with the aesthetic pull to react by the student. As students work through novel problems with limited information, their joys and frustrations are expressed in the form of exclamations.
Authors:
; ;
Editors:
Olanoff, D.; Johnson, K.; & Spitzer, S.
Award ID(s):
1652513
Publication Date:
NSF-PAR ID:
10314179
Journal Name:
Proceedings of the Psychology of Mathematics Education - North American Chapter
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Background Students’ attitudinal beliefs related to how they see themselves in STEM have been a focal point of recent research, given their well-documented links to retention and persistence. These beliefs are most often assessed cross-sectionally, and as such, we lack a thorough understanding of how they may fluctuate over time. Using matched survey responses from undergraduate engineering students ( n = 278), we evaluate if, and to what extent, students’ engineering attitudinal beliefs (attainment value, utility value, self-efficacy, interest, and identity) change over a 1-year period. Further, we examine whether there are differences based on gender and student division, and then compare results between cross-sectional and longitudinal analyses to illustrate weaknesses in our current understanding of these constructs. Results Our study revealed inconsistencies between cross-sectional and longitudinal analyses of the same dataset. Cross-sectional analyses indicated a significant difference by student division for engineering utility value and engineering interest, but no significant differences by gender for any variable. However, longitudinal analyses revealed statistically significant decreases in engineering utility value, engineering self-efficacy, and engineering interest for lower division students and significant decreases in engineering attainment value for upper division students over a one-year period. Further, longitudinal analyses revealed a gender gapmore »in engineering self-efficacy for upper division students, where men reported higher means than women. Conclusions Our analyses make several contributions. First, we explore attitudinal differences by student division not previously documented. Second, by comparing across methodologies, we illustrate that different conclusions can be drawn from the same data. Since the literature around these variables is largely cross-sectional, our understanding of students’ engineering attitudes is limited. Our longitudinal analyses show variation in engineering attitudinal beliefs that are obscured when data is only examined cross-sectionally. These analyses revealed an overall downward trend within students for all beliefs that changed significantly—losses which may foreshadow attrition out of engineering. These findings provide an opportunity to introduce targeted interventions to build engineering utility value, engineering self-efficacy, and engineering interest for student groups whose means were lower than average.« less
  2. Solving open-ended complex problems is an essential skill for part of being an engineer and a common activity in the one of the qualities needed in an engineering workplace. In order to help undergraduate engineering students develop such qualities and better prepare them for their future careers, this study is a preliminary effort to explore the problem solving approaches adopted by a student, faculty, and practicing engineer in civil engineering. As part of an ongoing NSF-funded study, this paper qualitatively investigates how three participants solve the following research question: What are the similarities and differences between a student, faculty, and practicing engineer in the approach to solve an ill-structured engineering problem? Verbal protocol analysis was used to answer this research question. Participants were asked to verbalize their response while they worked on the proposed problem. This paper includes a detailed analysis of the observed problem-solving processes of the participants. Our preliminary findings indicate some distinct differences between the student, professor, and practicing engineer in their problem-solving approaches. The student and practicing engineer used their prior knowledge to develop a solution, while the faculty did not make any connection to outside knowledge. It was also observed that the faculty and practicingmore »engineer spent a great deal of time on feasibility and safety issues, whereas the student spent more time detailing the tool that would be used as their solution. Through additional data collection and analysis, we will better understand the similarities and differences between students, professionals, and faculty in terms of how they approach an ill-structured problem. This study will provide insights that will lead to the development of ways to better prepare engineering students to solve complex problems.« less
  3. Solving open-ended complex problems is an essential part of being an engineer and one of the qualities needed in an engineering workplace. In order to help undergraduate engineering students develop such qualities and better prepare them for their future careers, this study is a preliminary effort to explore the problem solving approaches adopted by a student, faculty, and practicing engineer in civil engineering. As part of an ongoing NSF-funded study, this paper qualitatively investigates how three participants solve an ill-structured engineering problem. This study is guided by the following research question: What are the similarities and differences between a student, faculty, and practicing engineer in the approach to solve an ill-structured engineering problem? Verbal protocol analysis was used to answer this research question. Participants were asked to verbalize their response while they worked on the proposed problem. This paper includes a detailed analysis of the observed problem solving processes of the participants. Our preliminary findings indicate some distinct differences between the student, professor, and practicing engineer in their problem solving approaches. The student and practicing engineer used their prior knowledge to develop a solution, while the faculty did not make any connection to outside knowledge. It was also observed thatmore »the faculty and practicing engineer spent a great deal of time on feasibility and safety issues, whereas the student spent more time detailing the tool that would be used as their solution. Through additional data collection and analysis, we will better understand the similarities and differences between students, professionals, and faculty in terms of how they approach an ill-structured problem. This study will provide insights that will lead to the development of ways to better prepare engineering students to solve complex problems.« less
  4. Sacristán, A. I. ; Cortés-Zavala, J. C. ; Ruiz-Arias, P. M. (Ed.)
    What impact, if any, do interesting lessons have on the types of questions students ask? To explore this question, we used lesson observations of six teachers from three high schools in the Northeast who were part of a larger study. Lessons come from a range of courses, spanning Algebra through Calculus. After each lesson, students reported interest via lesson experience surveys (Author, 2019). These interest measures were then used to identify each teachers’ highest and lowest interest lessons. The two lessons per teacher allows us to compare across the same set of students per teacher. We compiled 145 student questions and identified whether questions were asked within a group work setting or part of a whole class discussion. Two coders coded 10% of data to improve the rubric for type of students’ questions (what, why, how, and if) and perceived intent (factual, procedural, reasoning, and exploratory). Factual questions asked for definitions or explicit answers. Procedural questions were raised when students looked for algorithms or a solving process. Reasoning questions asked about why procedures worked, or facts were true. Exploratory questions expanded beyond the topic of focus, such as asking about changing the parameters to make sense of a problem. Themore »remaining 90% of data were coded independently to determine interrater reliability (see Landis & Koch, 1977). A Cohen’s Kappa statistic (K=0.87, p<0.001) indicates excellent reliability. Furthermore, both coders reconciled codes before continuing with data analysis. Initial results showed differences between high- and low-interest lessons. Although students raised fewer mathematical questions in high-interest lessons (59) when compared with low-interest lessons (86), high-interest lessons contained more “exploratory” questions (10 versus 6). A chi-square test of independence shows a significant difference, χ2 (3, N = 145) = 12.99, p = .005 for types of students’ questions asked in high- and low-interest lessons. The high-interest lessons had more student questions arise during whole class discussions, whereas low-interest lessons had more student questions during group work. By partitioning each lesson into acts at points where the mathematical content shifted, we were able to examine through how many acts questions remained open. The average number of acts the students’ questions remained unanswered for high-interest lessons (2.66) was higher than that of low-interest lessons (1.68). Paired samples t-tests suggest that this difference is significant t(5)=2.58, p = 0.049. Therefore, student interest in the lesson did appear to impact the type of questions students ask. One possible reason for the differences in student questions is the nature of the lessons students found interesting, which may allow for student freedom to wonder and chase their mathematical ideas. There may be more overall student questions in low-interest lessons because of confusion, but more research is needed to unpack the reasoning behind student questions.« less
  5. Barriers to broadening participation in engineering to rural and Appalachian youth include misalignment with family and community values, lack of opportunities, and community misperceptions of engineering. While single interventions are unlikely to stimulate change in these areas, more sustainable interventions that are co-designed with local relevance appear promising. Through our NSF ITEST project, we test the waters of this intervention model through partnership with school systems and engineering industry to implement a series of engineering-themed, standards-aligned lessons for the middle school science classroom. Our mixed methods approach includes collection of interview and survey data from administrators, teachers, engineers, and university affiliates as well as observation and student data from the classroom. We have utilized theory from learning science and organizational collaboration to structure and inform our analysis and explore the impact of our project. The research is guided by the following questions: RQ 1: How do participants conceptualize engineering careers? How and why do such perceptions shift throughout the project? RQ 2: What elements of the targeted intervention affect student motivation towards engineering careers specifically with regard to developing competencies and ability beliefs regarding engineering? RQ 3: How can strategic collaboration between K12 and industry promote a shift in teacher’smore »conceptions of engineers and increased self-efficacy in building and delivering engineering curriculum? RQ 4: How do stakeholder characteristics, perceptions, and dynamics affect the likelihood of sustainability in strategic collaborations between K12 and industry stakeholders? How do prevailing institutional and collaborative conditions mediate sustainability? In year one, we involved nine 6th grade teachers, three engineering companies, and over 500 students. In year two, we expanded to include 7th grade teachers in our partner schools and the new students moving up to 6th grade. Lessons aligned with students' everyday experiences and connected to industry. For example, students created bouncy balls and tested their effectiveness on materials produced from partner manufacturing facilities. From preliminary analysis of data collected in the first two years of the project (e.g, the Draw an Engineer Test and teacher interviews), we have begun to see evidence of positive student and teacher impact. Additionally, our application of collaborative theory to the investigation of stakeholder perceptions of the project has revealed implications for partnering with school systems and engineering industry. For example, key individuals at each organization may serve as important conduits for program communication and collaborative work.« less