Quantitative reasoning (QR) is the ability to apply mathematics and statistics in the context of real-life situations and scientific problems. It is an important skill that students require to make sense of complex biological phenomena and handle large datasets in biology courses and research as well as in professional contexts. Biology educators and researchers are responding to the increasing need for QR through curricular reforms and research into biology education. This qualitative study investigates how undergraduate biology instructors implement QR into their teaching. The study used pedagogical content knowledge (PCK) and a QR framework to explore instructors’ instructional goals, strategies, and perceived challenges and affordances in undergraduate biology instruction. The participants included 21 biology faculty across various institutions in the United States, who intentionally integrated QR in their instruction. Semi-structured interviews were used to collect data focusing on participants’ beliefs, experiences, and classroom practices. Findings indicated that instructors adapt their QR instruction based on course level and student preparedness. In lower-division courses, strategies emphasized building foundational skills, reducing math anxiety, and using scaffolded instruction to promote confidence. In upper-division courses, instructors expected greater math fluency but still encountered a wide range of student abilities, prompting a focus on correcting misconceptions in integrating math knowledge and fostering deeper conceptual understanding in biology. Many instructors reported that their personal and educational experiences, especially struggles with math, often shaped their inclusive and empathetic teaching practices. Additionally, instructors’ research backgrounds influenced instructional design, particularly in the use of authentic data, statistical tools, and real-world applications. Instructors’ teaching experiences led to refinement in lesson planning, pacing, and active learning strategies. Despite their efforts, instructors faced both internal and external challenges in implementing QR, including discomfort with teaching math, time limitations, student resistance, and institutional barriers. However, affordances such as departmental support, interdisciplinary collaboration, and curricular flexibility helped to overcome some of these challenges. This study highlights the complex relationships between instructors’ experiences, beliefs, and contextual factors in shaping QR instruction. This calls for professional development that supports reflective practice, builds interdisciplinary competence, and promotes instructional strategies that bridge biology and mathematics and will help instructors design a learning environment that better support students’ development of QR skills. These findings offer valuable guidance for professional development aimed at helping biology instructors incorporate quantitative reasoning into their teaching. Such efforts can better equip students to meet the quantitative demands of modern biology and promote their continued engagement in STEM fields through more inclusive and integrated instructional approaches. 
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                            A Case Study on How Instructors’ Pedagogical Knowledge Influences Their Classroom Practices for First-Year Engineering Courses
                        
                    
    
            This complete research paper details an investigation into the influence of instructors' pedagogical knowledge on their classroom practices in the context of teaching first-year engineering courses. Background and Motivation: First-year engineering courses serve as the foundational setting in which students are introduced to the field of engineering as well as the pedagogies specific to engineering teaching and learning. These courses are pivotal in equipping students with essential knowledge and skills, setting the stage for their success in more advanced engineering topics. Understanding how instructors' pedagogical knowledge affects their teaching practices is crucial. Pedagogical knowledge encompasses a wide range of techniques to effectively manage a classroom and engage students. This includes the use of instructional strategies that cater to diverse student needs, the design of impactful and engaging lesson plans, etc. There is, however, limited research on how instructors’ pedagogical knowledge influences their classroom practices in first-year engineering courses. Hence, it seems opportune and essential to conduct additional research on engineering instructors' classroom practices. Research Question: The central question driving this research is: How does instructors' pedagogical knowledge influence their pedagogical practices for first-year engineering courses? Method: For this study, we chose the model of teacher professional knowledge and skill (TPK&S) that includes pedagogical content knowledge (PCK). The model recognizes the fundamental importance of pedagogical knowledge and contextualizes PCK within that framework, encompassing the intricate nature of teaching and learning. A descriptive case study was utilized as a methodology for this work to delve into the phenomenon. The context of the study was a first-year introductory engineering course offered at a large public research institution. This is a pilot study for an NSF-funded project (blinded for review), the study involved two instructors, Chandler and Joey (pseudonyms), chosen through purposive sampling, with varying levels of teaching experience. Data collection involved direct classroom observation using the Teaching Dimensions Observation Protocol (TDOP) and semi-structured interviews conducted after the observations. The interviews were conducted after classroom observations, allowing the researcher to explore specific findings from the observations. Results: Thematic analysis was used to categorize the data based on the constructs of the theoretical framework. The analysis revealed three major themes: (a) Instructors' topic-specific professional knowledge significantly influences their pedagogical practices. Both instructors adapt their teaching methods based on their understanding of course material and students' difficulties. (b) The interaction between instructors' personal pedagogical content knowledge (PCK) and the classroom context shapes their classroom practices. (c) Instructors' beliefs and prior knowledge act as amplifiers or filters based on the situation. They filter out their teaching practices that do not align with their beliefs and prior knowledge. Conclusion: The findings presented in this paper provide valuable insights into the complex interplay between instructors' pedagogical knowledge and their classroom practices. This work holds significant implications for current and future first-year instructors in that this paper will showcase how instructors use their understanding of the content and their students to teach, which is a critical aspect of helping students successfully integrate into engineering. 
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                            - Award ID(s):
- 2215989
- PAR ID:
- 10545467
- Publisher / Repository:
- ASEE Conferences
- Date Published:
- Format(s):
- Medium: X
- Location:
- Portland, Oregon
- Sponsoring Org:
- National Science Foundation
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