Ji-Won Son (Learning and Instruction)

Zoom Link: https://buffalo.zoom.us/j/95373885061?pwd=YmZLY0oxMWN5S3J6Y01RMkpNYzNGUT09

Investigating How Preservice Teachers Respond to History-Embedded Mathematics on the Learning of Functions

Elliott Reichman 

Functions are used in every branch of mathematics. Students are introduced to functions in eighth grade. From then on, students continue learning about functions all the way to high-level calculus, differential equations, linear algebra, and other advanced mathematics courses. Students see functions time and time again, making them one of the most relevant and foundational topics in all of mathematics. Since functions are such an overarching concept in mathematics, it’s important to address the specific challenges of teaching functions so that students can broach this topic more easily later on in their education. Functions certainly have specific challenges associated with their teaching. Some examples include the multiple meanings of the term ‘function’ and a variety of notations. Using history-embedded mathematics as an intervention method fits very well with the topic of functions. Functions are a model to show change. Historical events can bridge the gap between math and history as both are clear markers for change. History-embedded mathematics also offers other benefits such as activating student background knowledge, enhancing critical thinking skills, and allowing for a more creative approach. There is minimal research on the connections between functions and history-embedded mathematics. This makes it difficult to obtain a connection between the two, which would seem to be a natural pairing. In this study, a total of 3 preservice teachers volunteered to see if history embedded mathematics would improve their own understandings of functions, in order to measure if this method could be further translated to 8th or 9th-grade students. Additionally, the views and perceptions of history-embedded mathematics were analyzed in a pre and post-test to examine how current graduate students in the program view this teaching method. The participants took part in a series of three lessons on functions that used history-embedded mathematics. Participants were given a pretest before the lessons as well as a posttest after the lessons. This is the primary tool used to measure the effectiveness of the intervention method. Students reflected throughout the lessons and had opportunities to have their understanding measured. Lesson 1 contains a survey of preconceived opinions on the topics the participants learned. Lesson 2 contains an interactive activity. Lesson 3 contains a discussion portion that I facilitated. These all contributed to the analysis of the pre and post-tests. The findings revealed participants’ views of both the importance of history-embedded mathematics and the teaching of functions. Additionally, the following research questions were answered: (1)What place does history have in mathematics education?, (2) How can I help students understand the topic of functions using history?, (3) What types of history can be used to teach functions?, (4) What are the challenges students face when learning functions?, and (5) How can educators mediate these challenges using a historical approach?

Students’ Difficulties with Multiple Representations in High School Algebra

Sunaja Ajayan

Research in Mathematics education indicates that the use of multiple representations in teaching and learning helps students become better problem solvers. The purpose of this study is to investigate students’ difficulties with multiple representations. In this study a total of around 40 students from Gifted & Talented Program at University at Buffalo were participated. A t-test, a statistical test to compare the means of pre-test – post-test results, was employed in hypothesis testing to see whether different teaching styles had an influence on the students’ learning graph. This quasi-experimental study compares academic achievement of GMP students algebra performance, through the use two instruments, pre- test to test algebra prerequisite knowledge and post- test to check the improvement. The survey and problems solved have investigated methods of assisting students in developing competency and success during problem- solving. During these tests students were asked to solve a problem they had seen on the state board exam style, followed by problems that differed in the type of representation from the exam . Students were provided verbal hints to solve the new problems. The findings reveal the common difficulties students encountered when attempting to solve problems in different representations and some common themes in students’ performance.

In Making Scale Drawings Using Scale Factors & Group Work

Francisco Diaz

Students often find geometry constructions quite challenging and disconnected from real-life problems or artistic ornaments that require them. These challenges become an obstacle for students with a fixed mindset towards mathematics. Several observations have taken place in BPS 10th grade class to study the outcome of different teaching strategies for the betterment of students’ performance. Group work and student center approach with geometry are also considered on scale drawing and dilations mathematical lessons. Ethnocultural approaches on how to connect students to the importance of geometrical ornaments have not provided a clear path on how to get students beyond mere curiosity to acceptable performance of the constructions or the proof-writing process. Due to geometry constructions being alienated for students, disengagement takes place in a direct instruction setup. However, The effectiveness of group work can give a revitalizing new approach. In this presentation, I report the findings by answering how students’ understandings (and misunderstandings) about geometry constructions and proofs benefit from group work and/or pair work using inquiry-based and/or notice/wonder strategies. Overall, students had a hard time drawing perpendicular bisectors using a straight edge and a compass. However, this mechanical step is fundamental at this point due to the geometry constructions themselves. Students are also qualitatively affected/hindered by group work restrictions due to the covid-19 pandemic. Nevertheless, this study shows that they can and must be exposed to group work-independent time for reading and expressing their mathematical ideas using their own words.

Joseph A. Valentin (Learning and Instruction)
Vikki C. Terrile (Learning and Instruction)

Zoom Link https://buffalo.zoom.us/j/97078359344?pwd=ejNzUStoZnFwQWlJY2hRZnhpWVQ0Zz09

Interpretative phenomenological analysis (IPA) originated as a research methodology in psychology (Smith et al., 2009) and has expanded into use in the social sciences. IPA situates the words and understanding of participants about their own experiences as the focus of study and analysis, making it ideally suited for understudied phenomena and for use with small, homogeneous samples. In educational research, IPA is still nascent; an EBSCO database search for IPA studies in education and library science (LIS) research found approximately 275 articles and 50 dissertations, with just four in special education research and three in LIS research.

This panel shares how IPA was used in two recent PhD research component studies; both of these studies were the first to use IPA to study their phenomena. Completed during the COVID-19 pandemic using online tools to mediate data collection, these studies explored the experiences of professionals in their work with children and families marginalized by systems that reinforce and reproduce oppression. As agents of these systems, the teachers and librarians in these studies act in the margins and balance their praxis within deeply imbedded and troubling master narratives around power and deservedness.

The first study used an unstructured IPA approach to problematize pedagogical intervention within the context of Kincheloe and Berry’s Critical Bricolage (2004). Five in-service K-12 educators completed a written response describing a situation where they implemented a course of action(s) as an attempt to solve a student’s educational struggle. Analysis of the responses revealed the importance of context (impacted here by COVID and remote instruction) in understanding pedagogical intervention. Three sub-ordinate themes emerged from the responses: Temporality, Proximity of Learning Environment, and Mitigating Intervention. This study’s findings suggest that understandings of pedagogical intervention hinge on the student-teacher dyad, the nature of reciprocal interactions and relationships, as well as the pragmatic approaches and resources used. Future research should examine how experiences of power and oppression influence these relationships.

The second study used structured IPA to explore how five public librarians experience and understand their library work with families experiencing homelessness. The participants described their commitment to providing these services, but also shared that they feel unsupported by the profession and their individual libraries and coworkers when doing this work. Even with their dedication, participants expressed judgment towards the families they work with, rooted in pervasive cultural and media messaging around homelessness that focuses on individual flaws rather than systemic causes. This study situated the participants’ experiences within a context of ambivalence around homelessness in library services and questioned the lack of critical and social justice approaches to understanding these issues. Recommendations for practice and future research include examining the intersections of race and homelessness and how systems of oppression impact librarians’ work (or lack of work) with people experiencing homelessness.

Kincheloe, J. L., & Berry, K. S. (2004). Rigour and complexity in educational research: Conceptualizing the bricolage. Great Britain: Open University Press.

Smith, J.A., Flowers, P, & Larkin, M. (2009). Interpretative phenomenological analysis: Theory, method, and research. New York: Sage.