Browsing by Subject "Mathematics Education"

Now showing 1 - 4 of 4
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    “Can I just be a human with them?" Cultivating Equity-Mindedness for the Teaching and Learning of Elementary Mathematics
    (2016-07) Colum, Karen
    Equity has risen to a prominent position in mathematics education with some organizations such as the NCTM positioning it first of six principles for teaching mathematics. Additionally, much work has been focused on the development of effective mathematics teaching practices (NCTM, 2014), culturally relevant practices (Gay, 2000, Leonard, 2008) and developing social justice curriculum (Gutstein, 2006). However, what is still lacking is explicit attention to equity issues within the different academic disciplines in teacher preparation programs (Banks, 1993; Ladson-Billings, 1994). Many scholars argue that mathematics education courses need to have an explicit focus on equity and mathematics instruction to prepare teacher candidates for the realties in schools (Aguirre, 2009; Gutiérrez, 2012a; Martin, 2003). Therefore, this study addresses this problem outlined by the literature as it purposefully embedded issues of equity alongside the typical content contained in a mathematics methods course. A phenomenological understanding of teacher candidates’ perceptions as they experience becoming equity-minded in a mathematics methods course holds great potential to provide new insights into integrating equity into the teaching and learning of mathematics from an authentic, learner-centered perspective. This study seeks to help teacher educators and teacher education programs understand more deeply how teacher candidates may experience cultivating an equity mindset for the teaching of elementary mathematics by addressing follow question: How might cultivating equity mindedness take shape with teacher candidates in an elementary mathematics methods course? This qualitative study utilized a post-intentional research design (Vagle, 2014) to investigate a group of teacher candidates’ lived experiences of cultivating equity-mindedness while enrolled in a face-to-face, undergraduate, mathematics methods course. For sixteen weeks following the conclusion of the course, qualitative methods were used to collect data from the teacher candidates’ accountings of their experience shared through individual interviews and written course assignments. Iterative cycles of whole-part-whole approach (Vagle, 2014) captured tentative manifestations of the phenomenon of cultivating equity-mindedness as it was experienced in the methods course. Five tentative manifestations were produced through data analysis: (1) metacognitive awareness; (2) struggles with power; (3) knowledge of students; (4) multiplicity in practice; and (5) discourse of equity. The insights gained from this study were used to make recommendations for teacher educators and teacher preparation programs for practices that help promote and foster the growth of equity-oriented mindset for the teaching and learning of mathematics.
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    Examining the implementation of an innovative mathematics curriculum.
    (2010-07) Hansen, Heidi Britte
    Reform in mathematics instruction at the college level has been slow to arrive (Dossey, Halvorson, & McCrone, 2008), and many institutions of higher learning still follow the calculus model, while fewer and fewer students need calculus for their chosen areas of study (Ganter & Barker, 2003). Instead, mathematics that is applicable and transferable to other disciplines is more useful to many of today's college students. The Introduction to the Mathematical Sciences course that was the subject of this research study is a standards-based laboratory class that integrates algebra, statistics, and computer science. It was designed for students at both the high school and college levels who have struggled in mathematics. The intent of the course is to provide students with mathematics that they will find useful in their future careers, or future classes. The course is intended to reflect the ideals of reform mathematics at the college level. The purpose of the study was to examine the implementation of this curriculum, and its impact on student thinking and learning of algebra. In exploring the research questions, the researcher found that the Introduction to the Mathematical Sciences course provided a reform-instruction setting where students were able to demonstrate their understanding of algebra, statistics and computer science. The students showed skill at moving between a number of representations of algebra concepts, indicating they were developing deeper understanding of those concepts. One of the key components of this course that reflected reform ideals was the extensive discussion that took place in the course. This instance of the implementation of the Introduction to the Mathematical Sciences course provides an example of how reform instruction in line with the recommendations of NCTM, MAA and AMATYC (Baxter Hastings, et al., 2006) can be successful in helping students at the introductory college level gain understanding of mathematics. This research study describes a course that successfully plays out using reform instructional methods that are in sharp contrast to other college courses taught using traditional lecture style methods. High DWF rates among students who take college algebra (Lutzer, et al., 2005) indicate that the current model of instruction at the college level is not working. For students who lack confidence in their mathematical abilities and have seen little success in mathematics, this type of course may be a tool that can provide students the mathematical skills necessary to move forward in their studies and their careers.
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    Identity In Mathematics Spaces For Middle And High School Students: A Case Study Approach To The Revealing Of Identities In Formal And Informal Mathematics Spaces
    (2020-05) Gullickson, Elena
    It is acceptable and commonplace in society to proclaim a discomfort and dislike for mathematics. However, mathematics continues to be a gatekeeper for participation in westernized academic spaces (Moses and Cobb, 2002). When looking at the normative structures that exist in schooling systems, much can be learned from the voices and behaviors of students. This research provides critical information for effectively inviting students to participate in mathematical settings such that they choose to reveal their authentic identities. As defined in this research, identity is socially constructed, fluid, and multi-dimensional (Barton, Tan, & Rivet, 2008; Bishop, 2012; Nasir, 2002). Using the theoretical frameworks of funds of identity (Esteban-Guitart & Moll, 2014), mathematics identity (Bishop, 2012; Gutiérrez, 2013; Martin, 2013) and power, agency, and resistance (Chambers et al., 2014, Emirbayer & Mische, 1998; Foucalt, 1982), this research interrogates the ways that middle and high school students reveal their identities in mathematics spaces. This research investigated the identity emergings of two eighth grade students and three eleventh grade students using case study methodology drawing from critical ethnographic practices. Data for this study came from observing students in both formal and informal mathematics settings and from semi-structured interviews. The findings from this study revealed six themes and four implications that contribute to the body of literature on student identity and reframe mathematical pedagogies and practices to be more appealing to all students.
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    The Role of Rational Numbers in Mathematical Achievement and Decision Making
    (2016-12) Houseworth, James
    Understanding rational numbers requires reorganizing our initial understanding of numbers as whole numbers. Coordinating the relationship between the different symbolic formats for expressing rational numbers (i.e., as fractions and as decimals) and their underlying non-symbolic magnitudes is an important component of mathematical development in children (Fazio, Bailey, Thompson, & Siegler, 2014; Siegler & Pyke, 2013; Mazzocco et al., 2013). It is also an important component of decision making in everyday life (Simon, Fagley, & Halleran, 2004; Peters et al., 2006). The goal of the present experiments was to investigate the relationship between rational numbers, expressed in various formats, on one hand and general mathematical achievement and decision-making on the other. Two experiments demonstrated that the format of rational numbers impacts processing: the fraction format hinders magnitude processing compared to the decimal format. Experiment 1 additionally demonstrated that the precision of rational number magnitudes is related to general mathematical achievement. This is evidence that a better understanding of rational numbers is important for more abstract mathematics in adults. Experiment 2 showed that individual differences in rational number ability are also associated with individual differences in bias in decision-making. These findings have practical implications. Educationally, these results suggest that using number lines and intermixing decimal and fraction formats might improve rational number ability and therefore better prepare children for later, more abstract mathematics. Pragmatically, the results of this study suggest numerical ability alone is not a sufficient guard against biased decision making when probabilities are involved. Instead it appears other, non-numerical task features cause bias and need to be identified to make decision making more normative.