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 Title
 A Multiple Case Study Exploring the Relationship Between Engagement in ModelEliciting Activities and PreService Secondary Mathematics Teachers' Mathematical Knowledge for Teaching Algebra.
 Creator

Abassian, Aline, Safi, Farshid, Dixon, Juli, Andreasen, Janet, Bush, Sarah, Bostic, Jonathan, University of Central Florida
 Abstract / Description

The goal of this research study was to explore the nature of the relationship between engagement in modeleliciting activities (MEAs) and preservice secondary mathematics teachers' (PSMTs') mathematical knowledge for teaching (MKT) algebra. The data collection took place in an undergraduate mathematics education content course for secondary mathematics education majors. In this multiple case study, PSMTs were given a Learning Mathematics for Teaching (LMT) preassessment designed to measure...
Show moreThe goal of this research study was to explore the nature of the relationship between engagement in modeleliciting activities (MEAs) and preservice secondary mathematics teachers' (PSMTs') mathematical knowledge for teaching (MKT) algebra. The data collection took place in an undergraduate mathematics education content course for secondary mathematics education majors. In this multiple case study, PSMTs were given a Learning Mathematics for Teaching (LMT) preassessment designed to measure their MKT algebra, and based on those results, three participants were selected with varying levels of knowledge. This was done to ensure varied cases were represented in order to be able to examine and describe multiple perspectives. The three examined cases were Oriana, a PSMT with high MKT, Bianca, a PSMT with medium MKT, and Helaine, a PSMT with low MKT. Over the course of five weeks, the three PSMTs were recorded exploring three MEAs, participated in two interviews, and submitted written reflections. The extensive amount of data collected in this study allowed the researcher to deeply explore the PSMTs' MKT algebra in relation to the given MEAs, with a focus on three specific constructs()bridging, trimming, and decompressing() based on the Knowledge of Algebra for Teaching (KAT) framework. The results of this study suggest that engaging in MEAs could elicit PSMTs' MKT algebra, and in some cases such tasks were beneficial to their trimming, bridging, and decompressing abilities. Exploring MEAs immersed the PSMTs in generating descriptions, explanations, and constructions, that helped reveal how they interpreted mathematical situations that they encountered. The tasks served as useful tools for PSMTs to have deep discussions and productive discourse on various algebra topics, and make many different mathematical connections in the process.
Show less  Date Issued
 2018
 Identifier
 CFE0007143, ucf:52305
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007143
 Title
 The Impact of Elementary Mathematics Workshops on Mathematics Knowledge for Parenting (MKP) and Beliefs About Learning Mathematics.
 Creator

Eisenreich, Heidi, Dixon, Juli, Ortiz, Enrique, Andreasen, Janet, Brooks, Lisa, HahsVaughn, Debbie, University of Central Florida
 Abstract / Description

The purpose of this study was to investigate the extent to which parents of first, second, and third grade students who attended a twoday workshop on mathematics strategies differed on average and over time, as compared to parents who did not attend the workshops. The following areas were measured: mathematics content knowledge, beliefs about learning mathematics, ability to identify correct student responses regarding mathematics, ability to identify student errors in solving mathematics...
Show moreThe purpose of this study was to investigate the extent to which parents of first, second, and third grade students who attended a twoday workshop on mathematics strategies differed on average and over time, as compared to parents who did not attend the workshops. The following areas were measured: mathematics content knowledge, beliefs about learning mathematics, ability to identify correct student responses regarding mathematics, ability to identify student errors in solving mathematics problems, methods used to solve problems, and comfort level with manipulatives.
Show less  Date Issued
 2016
 Identifier
 CFE0006101, ucf:52877
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006101
 Title
 Examination of an Online College Mathematics Course: Correlation between Learning Styles and Student Achievement.
 Creator

Steele, Bridget, Dixon, Juli, Hynes, Michael, Haciomeroglu, Erhan, Hopp, Carolyn, Dziuban, Charles, University of Central Florida
 Abstract / Description

The purpose of this study was to determine if there was a significant relationship between learning styles and student learning outcomes in an online college mathematics course. Specifically, the study was guided by two research questions focused on (a) the extent to which learning styles had a predictive relationship with student achievement in an online college mathematics course and (b) the extent to which various learning styles among mathematics students in online versus facetoface...
Show moreThe purpose of this study was to determine if there was a significant relationship between learning styles and student learning outcomes in an online college mathematics course. Specifically, the study was guided by two research questions focused on (a) the extent to which learning styles had a predictive relationship with student achievement in an online college mathematics course and (b) the extent to which various learning styles among mathematics students in online versus facetoface courses predicted mathematics achievement. The population for this study consisted of the 779 college mathematics and algebra (CMA) students who were enrolled in a private multimedia university located in the southeast. A total of 501 students were enrolled in the online class, i.e., the experimental group, and 278 students enrolled in the facetoface class comprised the control group. All students completed (a) an initial assessment to control for current mathematics knowledge, (b) the online GrashaReichmann Student Learning Styles Scales (GRSLSS) Inventory, and (c) 20 questions selected from the NAEP Question Tool database. Hierarchical linear regressions were used to address both research questions. A series of ANCOVA tests were run to examine the presence of any relationships between a given demographic and course modality when describing differences between student test scores while controlling for prior academic performance. The results indicated that predominant learning style had no apparent influence on mathematics achievement. The results also indicated that predominant learning style had no apparent influence on mathematics achievement for online students. When examining demographics alone without respect to modality, there was no significance in course performance between students in various ethnicity, gender, or age groups.
Show less  Date Issued
 2012
 Identifier
 CFE0004445, ucf:49320
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004445
 Title
 A Single Case Study on the Influence of Feedback on the Instructional Quality of a Preservice Elementary Teacher in Mathematics: The Instructional Quality Assessment Toolkit as a Resource.
 Creator

Campbell Sutherland, Makini, Dixon, Juli, Safi, Farshid, Hoffman, Elizabeth, Andreasen, Janet, Childs, Kristopher, University of Central Florida
 Abstract / Description

The purpose of this single case study was to determine if a preservice elementary teacher's instruction would be influenced by feedback on mathematics lessons. The focus of the research was on the use of the Instructional Quality Assessment (IQA) (Boston 2012) toolkit as an integral part in the feedback process. The IQA toolkit provides number ratings as well as qualitative descriptive ratings of various aspects of the mathematics lesson, defined under two constructs, or groups, labeled...
Show moreThe purpose of this single case study was to determine if a preservice elementary teacher's instruction would be influenced by feedback on mathematics lessons. The focus of the research was on the use of the Instructional Quality Assessment (IQA) (Boston 2012) toolkit as an integral part in the feedback process. The IQA toolkit provides number ratings as well as qualitative descriptive ratings of various aspects of the mathematics lesson, defined under two constructs, or groups, labeled Academic Rigor and Accountable Talk. The researcher evaluated a preservice teacher's instruction on three occasions and facilitated feedback sessions following those observation sessions, integrating the number ratings of the IQA toolkit with the qualitative descriptions of expectations. It was found that there was an increase in ratings for both constructs of Academic Rigor and Accountable Talk over the period of three feedback cycles. There was a difference in how the students were facilitated in instruction over the three observations. The teacher became more aware of some of her behaviors in the classroom that contributed to the type of instruction given to students.In reviewing the literature, there was limited evidence of the use of the IQA toolkit for the iterative process of teaching, feedback, and teaching informed by feedback. This research is therefore useful in expanding the use of the IQA toolkit for feedback purposes. Preservice teachers as well as inservice teachers can benefit from feedback focused on mathematics teaching that makes them more aware of their strengths and weaknesses so they are able to adjust instruction based on the feedback received.
Show less  Date Issued
 2018
 Identifier
 CFE0006983, ucf:51679
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006983
 Title
 Secondary and Postsecondary Calculus Instructors' Expectations of Student Knowledge of Functions: A Multiplecase Study.
 Creator

Avila, Cheryl, Ortiz, Enrique, Dixon, Juli, Hynes, Michael, Andreasen, Janet, Mohapatra, Ram, University of Central Florida
 Abstract / Description

This multiplecase study examines the explicit and implicit assumptions of six veteran calculus instructors from three types of educational institutions, comparing and contrasting their views on the iteration of conceptual understanding and procedural fluency of precalculus topics. There were three components to the research data recording process. The first component was a written survey, the second component was a (")thinkaloud(") activity of the instructors analyzing the results of a...
Show moreThis multiplecase study examines the explicit and implicit assumptions of six veteran calculus instructors from three types of educational institutions, comparing and contrasting their views on the iteration of conceptual understanding and procedural fluency of precalculus topics. There were three components to the research data recording process. The first component was a written survey, the second component was a (")thinkaloud(") activity of the instructors analyzing the results of a function diagnostic instrument administered to a calculus class, and for the third component, the instructors responded to two quotations. As a result of this activity, themes were found between and among instructors at the three types of educational institutions related to their expectations of their incoming students' prior knowledge of precalculus topics related to functions. Differences between instructors of the three types of educational institutions included two identifiable areas: (1) the teachers' expectations of their incoming students and (2) the methods for planning instruction. In spite of these differences, the veteran instructors were in agreement with other studies' findings that an iterative approach to conceptual understanding and procedural fluency are necessary for student understanding of precalculus concepts.
Show less  Date Issued
 2013
 Identifier
 CFE0004809, ucf:49758
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004809
 Title
 An Examination of Administrators' Knowledge of the Standards for Mathematical Practice  A Think Aloud.
 Creator

GlennWhite, Vernita, Dixon, Juli, Ortiz, Enrique, Haciomeroglu, Erhan, Boote, David, Taylor, Rosemarye, University of Central Florida
 Abstract / Description

Administrators who observe mathematics teachers need to have knowledge and an understanding of mathematics teaching and learning to effectively evaluate teachers and how their instructional practices relate to student thinking. This research study was conducted to illustrate the importance of understanding the thought process of administrators as they make decisions about teacher effectiveness based on what they notice during observations of mathematics classrooms.The purpose of this study...
Show moreAdministrators who observe mathematics teachers need to have knowledge and an understanding of mathematics teaching and learning to effectively evaluate teachers and how their instructional practices relate to student thinking. This research study was conducted to illustrate the importance of understanding the thought process of administrators as they make decisions about teacher effectiveness based on what they notice during observations of mathematics classrooms.The purpose of this study was to examine what administrators attend to in the instructional environment and how what they notice influences their ability to identify the Common Core State Standards, Standards for Mathematical Practice. A purposive sample of six administrators engaged in cognitive interviews, known as think alouds, while observing two mathematics classroom videos. This study was designed to explore how administrators' instructional leadership knowledge or skills influence what they notice during mathematics instruction.There was evidence that administrators did notice aspects of the instructional environment pertaining to teachers, students, and, content. However, in this study it was found that administrators with an understanding of mathematics teaching and learning attended more to student's mathematical thinking during instruction. It was also found that there was an increase of the administrators' mathematical language and attention to student interactions with mathematics content when the administrators were presented with a tool describing the elements of a classroom engaged in the Standards for Mathematical Practice.
Show less  Date Issued
 2015
 Identifier
 CFE0005797, ucf:50034
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005797
 Title
 The Effect of Cognitively Guided Instruction on Students' Problem Solving Strategies and The Effect of Students' Use of Strategies on their Mathematics Achievement.
 Creator

Sahin, Nesrin, Dixon, Juli, Haciomeroglu, Erhan, Ortiz, Enrique, Bai, Haiyan, Schoen, Robert, University of Central Florida
 Abstract / Description

The purpose of this study was to investigate the effect of teachers attending Cognitively Guided Instruction (CGI) professional development on students' problem solving strategies and the effect of students' use of strategies on their mathematics achievement as measured by a standardized test. First, the study analyzed the differences in students' use of strategies between treatment and control groups. The treatment was CGI professional development, and the teachers in the treatment group...
Show moreThe purpose of this study was to investigate the effect of teachers attending Cognitively Guided Instruction (CGI) professional development on students' problem solving strategies and the effect of students' use of strategies on their mathematics achievement as measured by a standardized test. First, the study analyzed the differences in students' use of strategies between treatment and control groups. The treatment was CGI professional development, and the teachers in the treatment group attended CGI workshops whereas the teachers in the control group did not. Next, the study analyzed the differences in the mathematics achievement of students between different strategy groups. A student posttest, which was ITBS (Math Problems and Math Computation), was used to compare students' mathematics achievement. A student pretest was used as a covariate. The results of this study showed that there were statistically significant differences in the students' use of strategies between the treatment and control groups at the second grade level. A greater percentage of treatment students used derived facts / recall strategies (the most advanced strategy for singledigit addition and subtraction) than control students did. The results related to the effect of students' use of strategies on their mathematics achievement showed that the students who used derived facst/recall strategies for singledigit problems had significantly higher mathematics achievement than students who used counting or concrete modeling strategies. Furthermore, the students who used invented algorithms for multidigit problems had significantly higher mathematics achievement than the students who used standard algorithms.
Show less  Date Issued
 2015
 Identifier
 CFE0005704, ucf:50137
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005704