Browsing by Subject "mathematics"
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Item African Americans and Mathematics Outcomes on National Assessment of Educational Progress: Parental and Individual Influences(Springer, 2013-01) Noble, Richard, III; Hill Morton, CrystalThis study investigated within group differences between African American female and male students who participated in the 2009 National Assessment of Educational Progress mathematics assessment. Using results from participating states, we compare average scale scores of African American students based on home regulatory environment and interest in mathematics. Results indicated that African American male students who discussed studies 2–3 times a week scored higher than African American female students who discussed studies every day. In three states (Connecticut, Florida, and New Jersey), African American males who never or hardly ever discussed studies at home scored higher than African American males who never or hardly ever discussed studies at home in the state of Arkansas. In two states (Florida and New Jersey), African American males who discussed studies every few weeks scored higher than African American males who discussed studies every few weeks in Arkansas. In four states (Connecticut, Florida, Illinois, and New Jersey), the overall scale scores of African American males was higher than those of African American males in Arkansas. As a result of the findings, we present practical implications for parents of African American students.Item Black Girls and Mathematics Learning(Oxford, 2020) Morton, Crystal; Tate McMillan, Danielle; Harrison-Jones, WinterbourneThough the formal and informal mathematics learning experiences of Black girls are gaining more visibility in the literature, there is still a paucity of research around Black girls’ mathematics learning experiences. Black girls face unique challenges as learners in K–12 educational spaces because of their marginalized racial and gender identities. The interplay of race and racism unfolds in complex ways in Black girls’ learning experiences. This interplay hinders their development as mathematics learners and limits their access to transformative learning. As early as elementary school, Black girls are labeled as having limited mathematics knowledge and are often disproportionately placed in “lower level classrooms” devoid of any rigorous and transformative learning experiences. Teachers spend more time socially correcting Black girls rather than building on their brilliance. Even though Black girls value mathematics more and have higher confidence in mathematics than their White counterparts, they are still held to lower expectations by their teachers and are less likely to complete an advanced mathematics course. Nationally and globally, mathematics serves as an academic gatekeeper into every avenue of the labor market and higher education opportunities. Thus, the lack of opportunities Black girls have to engage in rigorous and transformative mathematics potentially locks them out of higher education opportunities and STEM-based careers. The mathematics learning experiences of Black girls move beyond challenges in K–12 spaces to limiting life choices and individual and community progress. To improve the formal and informal mathematics learning experiences of Black girls, we must understand their unique learning experiences more fully.Item Branching rules for quantum toroidal gl (n)(2013) Feigin, B.; Jimbo, M.; Miwa, T.; Mukhin, Eugene; Department of Mathematical Sciences, School of ScienceWe construct an analog of the subalgebra Ugl(n) ⊗ Ugl(m) ⊂ Ugl(m + n) in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.Item Challenging minds: Enhancing the mathematical learning of African American students through games(Information Age Publishing, 2012) Morton, Crystal; Yow, Jan A.; Cook, Daniela AnnMinority Access to Revolutionary Instructional Extensions (MATRIX) is a two-part pilot project that couples parent engagement and supplemental mathematics instruction. The MATRIX supplemental mathematics curriculum is built around six games designed to foster the mathematical development of elementary students. This article describes the MATRIX mathematics curriculum and provides findings related to the project’s impact on African American students’ number sense and attitudes towards mathematics.Item A Conceptual Framework for Digital Libraries for K-12 Mathematics Education: Part 1, Information Organization, Information Literacy, and Integrated Learning(University of Chicago Press, 2005-07) Chen, Hsin-liang; Doty, PhilipThis article is the first of two that present a six-part conceptual framework for the design and evaluation of digital libraries meant to support mathematics education in K-12 settings (see also pt. 2). This first article concentrates on (1) information organization, (2) information literacy, and (3) integrated learning with multimedia materials. The second article reviews (4) adoption of new standards for mathematics education, (5) integration of pertinent changes in educational policy, and (6) ensuring pedagogic and political accountability. Each article concludes with specific recommendations for digital libraries meant to support K-12 mathematics education appropriate to the topics the article discusses. This framework, which may be of some use to researchers and educators in many settings and countries, emphasizes the importance of communication, community building, and learning activities that use different media for the design of digital functionalities and online collections of mathematics learning materials. The major goal of the framework described here is to consider how to bring the larger computationally intensive collections called digital libraries closer to the existing structures and practices of learners and teachers while recognizing the new functionalities and learning opportunities that digital libraries offer.Item A Conceptual Framework for Digital Libraries for K–12 Mathematics Education: Part 2, New Educational Standards, Policy Making, and Accountability(University of Chicago Press, 2005-07) Chen, Hsin‐liang; Doty, PhilipThis paper is the second of two (see pt. 1) that describe a six-part conceptual framework for designing and evaluating digital libraries for mathematics education in K–12 settings: information literacy, information organization, integrated learn- ing, adoption of new educational standards, integration of pertinent changes in educational policy making, and ensuring accountability. This second paper explores the final three elements of the six-part framework. Accountability has become the core of the educational reform initiated by federal policies and measured by state-mandated educational standards. These political circumstances, as well as communication and collaboration, must be constitutively involved in the iterative design, implementation, and evaluation of digital libraries. The paper concludes with a series of recommendations for the design and implementation of digital libraries for K–12 mathematics education based on the authors’ discussion of these final three elements.Item Effects of Language on Children’s Understanding of Mathematics(ICRSME, 2022) Wilkerson, Trena L.; Mistretta, Regina M.; Adcock, Justin; Borgioli Yoder, Gina; Johnston, Elisabeth; Bu, Lingguo; Nugent, Patricia M.; Booher, Loi; School of EducationTeacher educators have a moral and civic obligation to examine ways in which language and mathematics are connected and supported in teaching and learning mathematics. It is essential to examine the roles and influence of family, parents, community, teachers, administration, and teacher educators as they collaborate to support learners. Their role should be considered in preparing and supporting teachers to develop curriculum, plan instruction, and implement strategies that support students’ development of language in the mathematics classroom. An examination of the literature regarding the effects of language on children’s understanding of mathematics was conducted around six areas: 1) impact of language on understanding and meaning making; 2) symbols, expressions and language connections; 3) effects of teachers’ listening orientation; 4) language development, play and family influences; 5) implications for multilingual learners; and 6) technology and digital media. Implications for teacher education and future research are presented. We offer readers a potential framework to consider for guiding teacher educators’ practices and future research efforts. In so doing, we display various connections and interplays between language and children’s mathematical meaning making and understanding.Item The Five Senses of STEM Learning(2022) Price, Jeremy F.; Santamaría Graff, Cristina; Waechter-Versaw, Amy; Moreland, Brooke; Magee, Paula; Hall, Ted; Willey, Craig; Bulanov, Maxim; Knoors, Anneleen Johanna; Fleming, Da'Meisha; Fox, Alexandria; Murray, Ryan; Russo, Kelly; Arora, Akaash; Franklin, JefferyThe Five Senses of STEM Learning is a framework and approach to teaching, learning, curriculum, and pedagogy deeply grounded in Culturally Relevant Pedagogy (Ladson-Billings, 1995, 2016) and Universal Design for Learning (Meyer et al., 2013; Rose & Meyer, 2002) while also incorporating a range of ideas and concepts that are specific to STEM learning and strengthen the connections to the particular contexts of the science, technology, engineering, or mathematics learning environment.Item A fresh look at the notion of normality(SNS, 2020-12) Bergelson, Vitaly; Downarowicz, Tomasz; Misiurewicz, Michał; Mathematical Sciences, School of ScienceLet G be a countable cancellative amenable semigroup and let (Fn) be a (left) Følner sequence in G. We introduce the notion of an (Fn)-normal element of {0,1}G. When G = (N,+) and Fn={1,2,...,n}, the (Fn)-normality coincides with the classical notion. We prove that: ∙ If (Fn) is a Følner sequence in G, such that for every α∈(0,1) we have ∑nα|Fn|<∞, then almost every x∈{0,1}G is (Fn)-normal. ∙ For any Følner sequence (Fn) in G, there exists an Cham\-per\-nowne-like (Fn)-normal set. ∙ There is a natural class of "nice" Følner sequences in (N,×). There exists a Champernowne-like set which is (Fn)-normal for every nice Følner \sq. ∙ Let A⊂N be a classical normal set. Then, for any Følner sequence (Kn) in (N,×) there exists a set E of (Kn)-density 1, such that for any finite subset {n1,n2,…,nk}⊂E, the intersection A/n1∩A/n2∩…∩A/nk has positive upper density in (N,+). As a consequence, A contains arbitrarily long geometric progressions, and, more generally, arbitrarily long "geo-arithmetic" configurations of the form {a(b+ic)j,0≤i,j≤k}. ∙ For any Følner \sq\ (Fn) in (N,+) there exist uncountably many (Fn)-normal Liouville numbers. ∙ For any nice Følner sequence (Fn) in (N,×) there exist uncountably many (Fn)-normal Liouville numbers.Item Girls Stem Institute: Transforming and Empowering Black Girls in Mathematics Through Stem(National Council of Teachers of Mathematics, 2018) Morton, Crystal; Smith-Mutegi, Demetrice; School of EducationWith the growing interest in STEM at both the national and international level, as well as the persistence in racial disparities in educational achievement, it is crucial that educators provide learning experiences that foster the positive development of Black females’ mathematics and science identities. This chapter will describe Girls STEM Institute (GSI), a program designed to support the positive development of Black females as learners and doers of mathematics and science. GSI provides learners who identify as Black and female an opportunity to develop an understanding of mathematics and other STEM concepts in a meaningful and culturally grounded out-of-school context. Within GSI’s rich, rigorous, relevant, and supportive environment, young ladies have the freedom to grow interpersonally and intellectually and are empowered to use STEM as a tool for personal and social change.