Browsing by Subject "Mathematics education"

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Bridging disciplines to build equity : interdisciplinary mathematics through the lens of critical multicultural education
(2006-12) Sivam, Kumaridevi; Salinas, Cinthia; Carmona Dominguez, Guadalupe de la Paz
Critical theory has shown that the organization of knowledge, forms of transmission of knowledge, and the assessment of acquisition of knowledge are crucial factors in the reproduction of power relationships in society (Freire, 1970; Apple, 1980; McLaren, 1998; Sleeter and McLaren, 1995; Bigelow, 2002). Schooling in the United States has always been designed to benefit particular groups over others, with "race,"class, ethnicity, culture, language, religion and gender among the factors used to differentiate the education offered (Loewen,1995; Oakes, 2005; Watkins, 2001). I extend this framework by taking science and mathematics, which have more often than other disciplines been taken to be neutral, to explicitly be part of this tradition. Research shows that multicultural education usually fails to move beyond superficial levels of modification of the curriculum (Banks, 1995; Nieto, 1995; Lee, Menkart, and Okazawa-Rey, 1997; McLaren and Sleeter, 1995). I build on theories of critical multicultural education and on my own teaching of interdisciplinary courses to propose interdisciplinarity as an approach to science and, in particular, mathematics education as a process of simultaneously challenging biased constructions of disciplinary boundaries and of extending access to the power held by these disciplines. My approach is informed by Delpit's (1988; 1995) framework of codes of power and explicit acknowledgment of these codes as essential to equitable education.
Building students’ mathematics self-efficacy through student-teacher trust
(2012-05) Harvey, Kristin Emilia; Borich, Gary D.; Suizzo, Marie-Anne
A current national priority is improving secondary school mathematics performance. Middle school students’ trust in their mathematics teachers can lead to better relationships and increased feelings of competence, or mathematics self-efficacy, which is consistently linked to achievement. Student trust is based on perceptions of a teacher’s competence, benevolence, openness, reliability, and honesty. To determine the effect of trust in a teacher on student mathematics self-efficacy while accounting for the non-independence due to shared classroom experiences, hierarchical linear modeling will be utilized. Controlling for prior achievement, mathematics self-efficacy is expected to be higher for students who perceive their mathematics teacher meets more of the criteria for trust, with a stronger effect for low-achieving students. The implications of the outcomes of the proposed study suggest the creation of a training program to facilitate trust building between students and teachers. This report also includes an evaluation plan which details the components of the trust building program, a model for the program, and the proposed method to measure the reported outcomes.
Children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis
(2011-12) Eberle, Robert Scott; Carmona Domínguez, Guadalupe de la Paz; Berland, Leema; Empson, Susan; Sinclair, Nathalie; Starbird, Michael; Stroup, Walter
Tessellations have a rich mathematical structure and are especially appropriate as a context for teaching geometry in the middle grades. Few studies have researched how children conceptualize and learn tessellations in spite of their international use in educational contexts. This exploratory study looks at how fourth grade students conceptualize tessellations before instruction. The analysis is done from a Piagetian, cognitive viewpoint and from an aesthetic viewpoint. It is argued that the aesthetic viewpoint is crucial and foundational to children's mathematical understanding, just as it is for mathematicians. A series of clinical interviews was conducted with six fourth grade children. The results identified common themes of children's understanding, strategies, reasoning, and aesthetic criteria for tessellations. Children's ontology varied between object and process conceptions of tessellations. Children struggled especially with the infinite space of mathematical tessellations. Children's aesthetics, including symmetry, influenced their choices in creating tessellations and are shown to have played a cognitive role in children's mathematical exploration of tessellation structures. Mathematics influences students' aesthetic appreciation of tessellations and, more importantly, aesthetics drives the study of the mathematical structure of tessellations. Children's aesthetic criteria were the same as mathematicians', but with much different emphases. Other results are discussed, including the mathematical content elicited by the tasks, the influence of the tools used to create tessellations, the children's epistemology of their tessellations, and the role symmetry played in giving children confidence. Recommendations for future research and possible implications for curriculum and instruction are noted.
Community college mathematics faculty members : racialized self-perceptions of day-to-day realities within the classroom environment
(2021-12-03) Peumsang, Pavitee; Saenz, Victor B.; Childs, Joshua; Green, Terrance L; Hawley, Stephanie J
This dissertation study was guided by two research questions: 1) What shapes community college mathematics faculty members' set of racialized ideologies, beliefs, and attitudes that inform their behaviors and teaching practices in the virtual classroom?; and 2) How do the racial and virtual classroom dynamics shape the ways mathematics faculty members adapt and deliver their course content during the COVID-19 global healthcare crisis? The combination of critical race theory in education, critical whiteness studies in education, and mathematical conceptual and theoretical frameworks informed the research design processes of this study. A total of 10 community college mathematics faculty members participated in the study: three from the California Community College System and seven from the Texas Community College System. The data collection methods included a pre-interview demographic questionnaire, a semi-structured virtual interview, an electronic document analysis, and a real-time virtual classroom observation. The findings from this study revealed three key findings. First, adult role models such as K-12 school professionals (e.g., teachers, coaches, and principals) and fathers were the primary influences who shaped faculty members' racialized sociocultural worldviews and current teaching strategies. Second, faculty members' lived experiences and self-willingness to learn about race and racism led them to develop their racialized self-awareness due to the absence of preparation from their academic and professional requirements. Lastly, when teaching in the classroom, students were the primary influences who shaped the racial and virtual classroom power dynamics rather than the faculty members. As a result, this study provides alternative theoretical, policy design, and practical recommendations to professionally coach community college mathematics faculty members on how to habitually practice teaching course curriculum centered on racial equilibrium, diversity, and inclusion, particularly in entry level mathematics course sequences.
The effects of schema-based intervention on the mathematical word problem solving skills of middle school students with learning disabilities
(2009-08) Na, Kyong-Eun; Bryant, Diane Pedrotty
A schema-based instruction allows students to approach a mathematics problem by focusing on the underlying semantic or problem structure, thus facilitating conceptual understanding and adequate skills. The purpose of this study was to examine the effectiveness of schema-based intervention on the mathematical word problem solving skills of middle school students with learning disabilities in grades 6 and 7. A nonconcurrent multiple baseline design was used for the study. Four middle school students with learning disabilities participated in pre-experimental (i.e., introduction, screening test, and Mathematics Interest Inventory sessions) and experimental (i.e., baseline, intervention, post-intervention test with generalization test, and maintenance test) sessions over a 13-week period. Participants were randomly assigned to a priori baseline durations (i.e., 6, 9, 12, 17 days) (Watson & Workman, 1981). During the intervention phase, students received 12 sessions of individual 30-35 minute schema-based intervention for 6 days (i.e., 2 sessions per day). Students participated in guided and independent practice and were encouraged to ask questions as they worked to master the material taught in each intervention session. During the postintervention phase, the four students’ accuracy performance was evaluated by six untimed achievement or generalization tests. The achievement and generalization tests contained a total of 10 one-step multiplication and division word problems. All of the students achieved scores greater than a pre-determined criterion level of 70% accuracy on the six consecutive tests. Two weeks after termination of the post intervention phase, each student’s accuracy performance on the achievement and generalization tests was examined during the follow-up maintenance phase. Findings revealed that the four students’ performance substantially improved after they received the intervention. All four students achieved scores that exceeded the criterion level (70% accuracy) on the achievement tests during the post intervention phase. These findings provide empirical evidence that schema-based intervention is effective in teaching middle school students with learning disabilities to solve multiplication and division word problems. Limitations of the research and implications for practice and future research are discussed.
Every body move : learning mathematics through embodied actions
(2012-05) Petrick, Carmen Julia; Martin, Taylor, 1970-
Giving students opportunities to ground mathematical concepts in physical activity has potential to develop conceptual understanding. This study examines the role direct embodiment, an instructional strategy in which students act out concepts, plays in learning mathematics. I compared two conditions of high school geometry students learning about similarity. The embodied condition participated in eight direct embodiment activities in which the students represented mathematical concepts and explored them through their movements. The observer condition participated in eight similar activities that did not involve physical activity. The students in the embodied condition had greater learning gains on a pre- and post-test, and those gains were driven by larger increases in conceptual understanding. There were also differences in the way the two conditions remembered the activities. On a survey given at the end of the unit, students in the embodied condition were more likely to write about the activities from a first person point-of-view, indicating that they had likely adopted a first person viewpoint during the activities. The embodied condition was also more likely to switch points-of-view when writing about the activities, indicating that they had likely translated among multiple viewpoints during the activities. This suggests translating between viewpoints is one mechanism for learning through direct embodiment. Students in the embodied condition also wrote more about the activities, which suggests that they remembered more about their experiences. Their survey responses included more mathematical and non-mathematical details than the responses from students in the observer condition.
Examining STEM faculty development to promote student belonging through inclusive teaching
(2024-05) Hughes, Kimberly K.; Kameen, Marilyn C.; Nava, Michael E., 1972-; Patterson, Kristin; Justiz, Manuel
This study explored the ways that STEM faculty learn about, design, and implement inclusive STEM teaching practices to improve student belonging. An interpretive phenomenological approach was employed to understand the personal experiences and thought processes of faculty as they worked to further develop their understanding of issues of equity and inclusion and transform their teaching conceptions and practices. STEM disciplines suffer from poor participation rates for women and students from historically marginalized racial and ethnic backgrounds and could address long-standing problems of persistence, in part, by attending to issues of student belonging. Faculty represent a linchpin for fostering student academic belonging in STEM through the instructional decisions they make. Faculty development structures and approaches that led to shifts toward inclusive teaching conceptions and practices are discussed. Successfully scaling inclusive teaching practices across STEM departments and colleges will require investments in comprehensive, multi-faceted approaches to faculty development.
From teaching mathematics to teaching teachers : a case study of one novice teacher educator's learning to support equitable practices
(2023-08-11) Goldberg, Ellyn Rose; Riegle-Crumb, Catherine; Gargroetzi, Emma; Gómez Marchant, Carlos Nicolas; Elliott, Rebekah
This dissertation study examined how one novice mathematics teacher educator (NMTE) learned to support pre-service teachers’ (PTs’) implementation of ambitious and equitable mathematics teaching practices in the context of a seven-week summer program for undergraduates. Viewing learning through the lens of legitimate peripheral participation in a community of practice, research questions examined how and why an NMTEs practices—as evidenced through her articulation of and attention to equity, goal-setting, and teaching practices—emerged and shifted over the course of the summer. This study used case study methodology to analyze a range of data sources, primarily: 1) over 4.5 hours of audio recordings taken from three semi-structured interviews with the NMTE (pre-, mid-, and post-program); 2) over 8.5 hours of audio recordings taken from seven virtual and in-person co-planning sessions with the NMTE; 3) detailed field notes taken throughout the summer including a four-day site visit to the program; 4) over 5.5 hours of audio recordings taken from classroom observations of the NMTE’s teaching; and 5) all NMTE artifacts including planning documents and written reflections. Analysis found three overarching findings: 1) while equity was articulated prior to the program and reflected upon after, explicit attention was peripheralized during the program; 2) while the types of goals set by the NMTE remained consisted, specific goals evolved largely in response to the crisis-of-the-moment and need to prepare PTs to enter the classroom, and was supported by the curriculum and mentoring; and 3) the NMTEs practices evolved in response to emergent goals and supported by models of MTE practice, mentoring, and guided reflection. Implications for MTE training, development, research, and practice are discussed.
Instruction for discovery learning : levels of implementation exhibited by a sample of algebra I teachers
(2013-05) Hoffman, Shannah Kathryn; Petrosino, Anthony J. (Anthony Joseph), 1961-; Daniels, Mark L.
One type of instruction that is of particular interest in STEM education is instruction that actively engages students in inquiry and discovery. The author develops an operational definition of instruction for discovery learning (IDL) that adopts some of the fundamental commonalities among many reform-oriented instructional frameworks such as inquiry-based and project-based instruction. Four teachers—who received their bachelor’s degree in mathematics and teacher certification from the same undergraduate teacher-preparation program—and their Algebra I classes were observed with the focus on how particular features of IDL were being implemented in their classrooms. To gain further perspective on classroom practices and interactions, student surveys were administered to a total of 142 students and each teacher was interviewed. The student surveys focused on student orientations toward IDL, attitudes toward mathematics, and their perspective of IDL implementation in their class. Student survey data was analyzed through ANOVA, post hoc tests were used to identify significant pair-wise differences between teachers for which the ANOVA identified significance, and a factor analysis was used to evaluate the component loadings for the survey questions. The surveys revealed significant differences between perceived activities in the classes (p<0.05), but did not show very significant differences between student orientations toward IDL. All four teachers expressed familiarity with and commitment to reform-oriented frameworks such as inquiry-based and project-based instruction, and certainly experienced inquiry-based learning as students themselves in their undergraduate program. However, only one teacher—the one teaching in a New Tech high school that was structured on the framework of project-based instruction (PBI)—showed consistent differences in both student perspectives of IDL and observed implementation of IDL. The author discusses the levels at which these teachers implemented IDL, the differences among student perceptions across the classes, teacher orientations toward mathematics and learning, and the importance of a supportive school culture and administration in order to fully implement IDL and influence both student and teacher orientations toward reform-oriented pedagogy.
Interventions for English language learners in the mathematics classroom
(2012-08) Suarez, Itzel; Daniels, Mark L.; Odell, E. (Edward)
This report highlights and explores research surrounding a variety of interventions used in the elementary and secondary mathematics classroom for English Language Learners. Topics discussed include ways to motivate English Language Learners, the use of successful teaching strategies, allowing the use of code-switching, and the use of one-on-one tutoring. Though some interventions used in the research are utilized in the elementary mathematics classroom, they are also widely used in secondary mathematics classrooms. A short discussion regarding the use of such interventions in the secondary mathematics classroom is also included.
Looking within : mathematics teacher identity using photo-elicitation/photovoice
(2012-08) Chao, Theodore Peck-Li; Empson, Susan B.; Treisman, Philip U.; Stroup, Walter; Schneider, Cynthia; Salinas, Cynthia
How do mathematics teachers present themselves? The construct of identity–the stories mathematics teachers tell about themselves and their practice–is an important and understudied construct in understanding mathematics teaching. This study investigates the use of photo-elicitation/photovoice interviews with six high school algebra teachers. Each teacher captured or chose photographs of their “world”, then presented them during a formal interview. The teachers framed their mathematics teacher identity through three connected story types: Public Stories, the stories a teacher presents about their practice within a professional register, Private Stories, the stories about personal connections to practice shared only in closed spaces, and Touchstone Stories, the important stories a teacher constantly references but rarely shares. I found these teachers’ stories contained little about mathematics content or actual classroom practice. Rather, they positioned the teachers as isolated in their profession; the themes were about pain, being “othered”, or feeling powerless. Framing the identities of these six mathematics teachers through visual stories presented them as real, struggling humans. I posit this process of eliciting mathematics teaching identity through visual narrative is important to the field of mathematics education for three reasons: framing their identities helps mathematics teachers understand the complex lives of their own students, these narratives showcase the uniqueness of each mathematics teacher as an individual, and this process of telling stories is an empowering form of reflection.
The relationship between teacher pedagogical content knowledge and student understanding of integer operations
(2010-12) Harris, Sarah Jane, 1969-; Martin, Taylor, 1970-; Berland, Leema; Barufaldi, James; Marshall, Jill; Pituch, Keenan
The purpose of this study was to determine whether a professional development (PD) for teachers focused on improving teacher pedagogical content knowledge (PCK) related to operations with integers would improve teacher PCK and if there was a relationship between their level of PCK and the change in the understanding of their students as measured by pre- and posttest of teacher and student knowledge. The study was conducted summer 2010 in a large urban school district on two campuses providing a district funded annual summer intervention, called Jumpstart. This program was for grade 8 students who did not pass the state assessment (Texas Assessment of Knowledge and Skills), but would be promoted to high school in the Fall 2010 due to a decision made by the Grade Placement Committee. The Jumpstart program involved 22 teachers and 341 students. For purposes of this study, changes were made to the PD and typical curriculum for a unit on integer operations to promote teacher and student conceptual understanding through a process of mathematical discussion called argumentation. The teachers and students explored a comprehensive representation for integer operations called a vector number line model using the Texas Instruments TI-73 calculator Numln application. During PD, teachers engaged in argumentation to make claims about strategies to use to understand integer operations and to explain their understanding of how different representations are connected. The results showed statistically significant growth in teacher PCK following the professional development and statistically significant growth in student understanding from pre- to posttest compared to the students who participated in the program the previous year. The findings also showed that there was a statistically significant association between teacher posttest PCK and student improvement in understanding even when controlling for years of teaching experience, teacher pretest knowledge, and student pretest score. This adds to the research base additional evidence that professional development focused on teacher pedagogical content knowledge can have a positive effect on student achievement, even with just a short period of PD (6 hours in this case).
A statistical analysis of the effects of project-based learning on student high school and college outcomes
(2015-05) Craig, Tara Theresa; Marshall, Jill Ann; Azevedo , Flavio; Beretvas, Susan N; Marder, Michael; Riegle-Crumb, Catherine
This dissertation research study is an analysis of the effects of project-based learning on a cohort of high school students’ achievement on mathematics and science standardized tests and graduation rates. The study also investigates college enrollment and first year grade point averages (GPA) for students taught solely through project-based instructional methods in high school. In the 21st century, STEM fields dominate our work force, but there is a decline in interest and persistence towards these fields that can be traced back to high school achievement in mathematics. The people that are choosing and prepared for STEM majors and careers are not representative of the US population, as they are lacking ethnic and gender diversity. The underlying premise is that inquiry-based teaching practices engage and motivate students leading to increased learning; however this premise is not currently fully supported with empirical research. This research compares students that attended a high school that teaches all courses through project-based learning with a matched control group of students. I first analyzed the demographic makeup of students that chose to apply to Manor New Tech, a STEM-focused, PBL school. Then, I developed multiple linear regression models that allowed me to determine that students attending the PBL school performed as well as the control group on math standardized exams and significantly better on one of the science standardized exams. Further analysis showed that ethnic and gender achievement gaps on the standardized assessments were maintained when students attended the PBL school. Similarly, students that attended the PBL school as likely to graduate high school. Comparing the PBL school with a more affluent school that also teaches all courses through PBL showed that graduates from the PBL school of focus in this research were significantly more likely to enroll in 2-year institutions of higher education and just as likely to enroll in 4-year and private institutions in Texas as the more affluent school. Finding that attendance at MNTH does not harm students’ standardized test performance or graduation rates could imply that being taught through PBL does not enhance high school and college outcomes. It could also imply that students taught at the PBL school, MNTH, are not experiencing authentic PBL, or conversely that students attending the comparison school, MHS, are receiving instruction through project-based methods as well. Lastly, the standardized assessments used to measure achievement may not be sensitive to some higher order skill development that may occur when taught through inquiry-based methods. Future research plans are to create new achievement measures that will capture more robust learning than traditional standardized tests. Using these instruments, further analysis of difference in students’ performance when they are taught through inquiry methods will be conducted.
Teaching fractions to middle-school students struggling in mathematics : an exploratory study
(2011-05) Misquitta, Radhika Maria Peter; Rieth, Herbert J.; Garcia, Shernaz B.; Bryant, Diane P.; Dodd, Barbara G.; O'Reilly, Mark F.
Fractions are an essential skill for students to master, and one students struggling in mathematics face particular difficulty with (National Mathematics Advisory Panel, 2008; Mazzocco & Devlin, 2008). This study employed the multi-probe multiple baseline design to examine the effectiveness of the concrete-representational-abstract (CRA) approach and explicit teaching practices to teach fraction equivalence to students struggling in mathematics. The study was conducted across four students, and replicated simultaneously across four more. The CRA approach included concrete aids such as fraction circles and fraction strips, representations such as pictures of fraction circles and polygons, and algorithms. Explicit teaching involved following a model-lead-test sequence and included an advanced organizer, corrective feedback and cumulative reviews. Results of this study indicated that the intervention program was effective to improve students‟ performances in fraction equivalence tasks. In particular, the use of vii representations was seen to impact performance and concrete aids alone may not be sufficient to improve performance. With regards types of representational and concrete aids employed, results of this study tended to favor the use of linear versus circular aids. Results indicated that students whose performances tend to vary may not benefit to the same extent as those who have stable profiles. Students who demonstrate variable profiles may require additional practice to master skills being taught. This study also examined transfer of skills to word problems and, results demonstrated that the CRA and explicit teaching approaches were beneficial in helping aiding transfer. Several aspects of the program may have contributed to aiding transfer including, minimal exposure to word problems during intervention, drawing connections between representations and abstract information, and incorporating the fair sharing understanding or quotient interpretation of fractions. This program concluded that students were able to maintain performances over time, and that representations in particular appeared to aid conceptual understanding and promote maintenance of skills.
Tracking the longitudinal effects of student-teacher trust on mathematics self-efficacy for high school students
(2013-08) Harvey, Kristin Emilia; Suizzo, Marie-Anne
A current national priority is improving secondary school mathematics performance. National initiatives have attempted to help improve student achievement through curricular changes and stringent testing requirements; yet, these initiatives fail to consider the importance of student-teacher relationships in student motivation and achievement. High school students' trust in their mathematics teachers can lead to better relationships and increased feelings of competence, or mathematics self-efficacy, which is consistently linked to achievement. Student trust is based on perceptions of a teacher's competence, benevolence, openness, reliability, and honesty. The aim of my study is to determine the effect of trust in a teacher on student mathematics self-efficacy over the course of a school year, accounting for differences between individual students. The sample consisted of 230 ninth through twelfth grade students (57% girls) from a large high school in central Texas. Students reported their trust in their math teachers and their math self-efficacy at 4 time points. Growth curve modeling was utilized to model the effect of trust on self-efficacy over time. The results indicate that trust predicted self-efficacy over the course of the school year such that for a one point change in trust there was a corresponding .4 point change in self-efficacy. Gender was also a significant predictor of self-efficacy, with girls reporting lower self-efficacy on average. However, girls did not report lower trust, and the relation between trust and self-efficacy was not moderated by gender. Inasmuch as future studies should seek to expand on these findings, this study is an important first step into investigating the link between trust in teachers and self-efficacy. The results of this study serve to inform teachers, researchers, and policy makers of the importance of recognizing student-teacher relationships as an important factor in building student confidence and motivation.
Visuals and vocabulary : the next generation in mathematics education
(2010-08) Olivarez, April Lisa; Armendáriz, Efraim P.; Daniels, Mark L.
In recent years, there has been a growth of using visuals and vocabulary in mathematics and mathematics classes. The purpose of this Master’s Report is to illuminate research done in the realm of mathematics education related to the increasing use of visuals and visual devices as models for mathematical concepts, as well as visuals for quick reference or “short cuts.” Also discussed is mathematics vocabulary, the words most likely seen on mathematics exams, standardized state tests, and overall, any vocabulary most likely to trigger problem solving strategies and solutions. Trends such as “word walls” and “graphic organizers,” as well as vocabulary strategies aimed at oral, visual, and kinesthetic learners have all emerged in the classroom. Other strategies implemented and researched include student mathematics journals, student created mathematics dictionaries, children’s literature, graphic organizers, and written explanations of open ended word problems. All proved to enhance students’ mathematical vocabulary, increase comprehension and increase ability in communication of mathematical ideas. Furthermore, the use of visual models has emerged in mathematics courses in order to promote more mathematical understanding. “Proofs without words” and patterns and pictures are growing in their use to explain mathematical concepts and ideas. Visual devices that help students arrive at probable answers also have grown in their implementation in the classroom and beyond. Overall, has the increased use of visuals and vocabulary in both mathematics education and mathematics in general improved the mathematical understanding of our society? What research, if any, has been done to document the effects of word walls, graphic organizers, and etcetera? The research will show that, yes, an overwhelming amount of data shows that the implementation of such visual and vocabulary strategies can improve the mathematical understanding of those exposed to the strategies and devices.