Mathematics EdD students present at 9th Annual Student Research Symposium

Poster Presentations

Debasmita Basu

Nicole Panorkou

Designing a Learning Trajectory for the Classification of Quadrilaterals

In this presentation I describe the design of a learning trajectory for quadrilaterals. The goal of this learning trajectory is for the students to be able to classify quadrilaterals based on their properties. The trajectory begins by identifying two dimensional and three dimensional shapes regardless of the size of the objects and their orientation in Grade 2 (CCSM 2.G.A.1). Besides parallel and perpendicular lines, students are also introduced to different categories of angles i.e, acute, obtuse and right angles in Grade 3 (CCSM 3.G.A.1). Research shows that although students may be able to identify the top of a book as a rectangle or square, the top of pizza as a circle and the shape of a ball as a sphere, “they identify shapes according to their appearance”(Clements and Battista 1992b; van Hiele 1959/1985). In the next level, gradually students are introduced to the formal definition of different types of quadrilaterals like parallelogram, trapezoid, rectangle, rhombus, square and kite, and they begin to explore how to classify the above geometric figures in a hierarchy. In order to do that, students need to have a clear understanding of what properties are similar and different among these geometric figures. For instance, in both a rhombus and a square all sides are equal, but a square also has all angles equal to right angle, therefore all squares are rhombuses.

Jason McManus

Co-author: Dirk Vanderklein

Advisor: Mika Munakata

Title: Crossing Boundaries in Undergraduate Biology Education

Abstract: We implemented three different instructional methods for teaching two mathematical concepts in ecology: surface area to volume ratios and capacity models of population growth. We hypothesized that our treatment group, which received hands-on discovery-based instruction, would perform better on the related quantitative exam questions than our comparison group (lecture-based instruction) and partial treatment group (worksheet based mathematical problems with whole group discussion). We also examined changes in students’ dispositions to mathematics and science. We did not find significant differences across the groups across these outcomes. A linear regression model showed that prior quantitative experiences predicted students’ exam scores. Surprisingly, when examining only the quantitative exam questions, students with more mathematical background performed just as well as students with less. This study faces limitations posed by a small sample size (n = 47), endogeneity bias from student selection of class meeting times, and instructional implementation since one professor taught the three sections. Focus group interviews of students in the three groups provide ideas for improvement.

Justin Seventko

Advisor: Steven Greenstein

Title: A Proposed Study of Millennial Preservice Mathematics Teachers’ Cultural Experiences and Implications for Instruction

Abstract: Cultural deficit theory, which posits that the underachievement of minority student groups in school can largely be attributed to their home culture, is still prevalent among teachers in United States. One alternative view to this kind of deficit thinking, and the subject of this proposed study based on doctoral coursework, is an equity-oriented culturally relevant pedagogy. This practice of teaching actually views students as entering the classroom with a wide-range of lived experiences and cultures that can be utilized during instruction. There is also a growing body of literature that shows teachers who belong to the millennial generation, born since 1985, may come into the classroom with a greater openness towards multiculturalism as compared to past generations. However, what the literature is much more uncertain on is whether this openness holds influence over their views regarding culturally relevant pedagogy. If the connection between these two ideas is better understood, teacher preparation programs can design experiences that increase the potential for millennials to become active practitioners of and advocates for culturally-relevant pedagogy in the classroom. With this in mind, I am proposing a mixed methods study of millennial mathematics preservice teachers during their field experiences and student teaching to better understand the connection between this generation’s potentially unique views of multiculturalism and culturally relevant pedagogy. For this poster presentation, I will be presenting my research framework and the underlying justification behind this proposed study.

Trina Wooten

Advisor: Nicole Panorkou

Title: Developing a Hypothetical Learning Trajectory of Elementary Students’ Understanding of 3D Geometry

Abstract: The existing literature shows there is a link between spatial ability and mathematics achievement, however spatial ability is limited in the current mathematics curricula (Hallowell et al., 2015). Throughout the K – 12 Euclidean geometric curricula, there is more emphasis on two-dimensional (2D) figures than three-dimensional (3D) objects, even though we live in a 3D environment. There is a need for developing students’ spatial ability by designing a 3D geometric curriculum that entail problem solving, understanding, and explaining the physical world such as reading a map and wayfinding (Guven & Kosa, 2008; Kurtulus, 2013 ; Lehrer et al., 1998 ). Therefore, my goal is to develop a 3D Euclidean geometric spatial ability hypothetical learning trajectory (HLT) for grades K – 6 based upon the Common Core State Standards for Mathematics (CCSS-M, 2015). Starting from the assumption that 3D geometric thinking and spatial abilities could be developed through instruction over time, this HLT will focus on distinguishing 2D and 3D shapes and utilizing the correct vocabulary of 3D objects (Pittalis & Christou, 2010; Guven & Kosa, 2008). In addition, it aims to assist students with two major misconceptions about distinguishing between a) perimeter (1D) and area (2D) and b) surface area (2D) and volume (3D) (Clements & Sarama, 2014; Barrett & Clements, 2013; Huang & Witz, 2011). In this presentation, I will also present my work-in-progress of the design of curriculum for 3D Euclidean geometric spatial ability for elementary students.

Karmen Yu

Trina Wooten

Steven Greenstein

Piloting a Model of Inquiry-Oriented Supplemental Instruction for Calculus I

The main focus of the Noyce @ Montclair project is to provide exceptional preparation for prospective elementary mathematics teachers. The centerpiece of this project is a Bachelor of Science Degree in Mathematics with K-6 Teaching Certification. One of the “enhancing components” of this degree plan are Inquiry-Based Instructional Supplement (IBIS) workshops for Calculus I and II, which have been identified as “historically difficult” courses based on a trend of high failure rates. IBIS has adopted a peer-led, inquiry-oriented workshop model, which features a groupwork component and modules comprised of groupworthy tasks.

In order to evaluate the structure of the program, the groupworthiness of the problem sets, and students’ opportunities for inquiry, we conducted a pilot study of IBIS in the fall of 2014. We assumed the role of peer leaders and supported students’ problem solving efforts. We collected video data of all ten sessions, as well as artifacts of students’ work and follow-up focus group interviews to assess students’ experiences. We are now in the process of analyzing this data.

The goal of IBIS is not only to support students’ achievement in Calculus, but also to provide prospective elementary mathematics teachers with the kinds of groupworthy, inquiry oriented experiences that we hope will be a salient feature of their own teaching. Thus, the findings of this study have implications not only for the design of support structures for students in mathematics, but also for the preparation of mathematics teachers.

Oral Presentations

Zareen Rahman

Co-author: Jason McManus, Kristen Trabona

Advisor: Mika Munakata

Title: The Path to K-12 Science Teacher Leadership: A Preliminary Inquiry of Teachers Working Toward Leadership

Abstract: “The Wipro Science Education Fellowship Program at Montclair State University (MSU) focuses on developing K – 12 science teachers as teacher leaders. The aims of this project are to understand the ways in which the fellowship supports science teachers as they develop in areas of reflective practice, adult learning, and teacher leadership.

MSU has partnered with five NJ school districts to annually select 20 teaching fellows to collaboratively work as part of a cohort for two years. During the first year teachers work with peers within their district and across their district in both vertical (content based) and horizontal groups. They focus on a single problem of practice for in-depth analysis. In their second year, fellows explore a personalized learning plan in which they act as teacher leaders and conduct professional development.

In the current phase of this longitudinal study, we focus on data collected through interviews during year one of the program. Data was analyzed using constant comparative method looking for emergent themes around the core practices in the program. We have analyzed two sets of interviews from 13 consenting participants from Cohort 1. We observed four themes that impact the success of teacher leaders:

• The importance of diplomatic skills to influence fellow teachers
• The benefits of vertical articulation in teacher professional development programs
• The role of school culture and administrative support for teacher leaders
• The importance of self-reflection

Future analysis will focus on assessing the implementation of teachers’ proposed leadership plans during the second year of the program.”

Zareen Rahman

Advisor: Mika Munakata

Title: 100K Strong in Chile for CSAM Students-A model for international scientific and educational collaboration among STEM undergraduate students

Abstract: “The study focuses on the experiences of students participating in an exchange program through the 100,000 Strong in the Americas innovation grant funded by the US Department of the State. Montclair State University created an exchange program with Universidad Mayor in Chile with the goal to expose undergraduate science students to techniques and research in the international biotechnology industry and impress upon them the importance of collaboration in scientific research. The study aims to measure the impact of this pilot program on science students’ beliefs about scientific research. The study includes thirteen consenting students who are currently participating in this pilot program. Data were collected through interviews, survey questionnaires and observations to measure student understanding and beliefs about scientific research before the first phase of the study and after the second phase. The data from both the stages were analyzed using a constant comparative method to look for patterns and recurring themes around student understanding and beliefs about scientific research. We observed that students’ beliefs about scientific research were impacted in various ways. They gained an overall understanding about the nature of scientific research and learned the importance of collaboration in scientific research. They were surprised to learn about the ease of conducting cross-cultural scientific research with the use of communication tools like Skype and Google Docs. They also learned about the similarities and differences in the scientific research conducted in the two countries and the variety of practical applications of the scientific ideas they have encountered in class. “

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