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- Title
- EXPLORING THE UNDERSTANDING OF WHOLE NUMBER CONCEPTS AND OPERATIONS: A CASE STUDY ANALYSIS OF PROSPECTIVE ELEMENTARY SCHOOL TEACHERS.
- Creator
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Safi, Farshid, Dixon, Juli K., University of Central Florida
- Abstract / Description
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This research project aimed to extend the research literature by providing greater insight into the way individual prospective teachers develop their conceptual understanding of whole number concepts and operations in a social context. In this qualitative study, a case study analysis provided the opportunity for careful exploration of the manner in which prospective teachers' understanding changed and the ways two selected participants reorganized their mathematical thinking within a...
Show moreThis research project aimed to extend the research literature by providing greater insight into the way individual prospective teachers develop their conceptual understanding of whole number concepts and operations in a social context. In this qualitative study, a case study analysis provided the opportunity for careful exploration of the manner in which prospective teachers' understanding changed and the ways two selected participants reorganized their mathematical thinking within a classroom teaching experiment. While previous research efforts insisted on creating a dichotomy of choosing the individual or the collective understanding, through the utilization of the emergent perspective both the individual and the social aspects were considered. Specifically, using the emergent perspective as a theoretical framework, this research endeavor has outlined the mathematical conceptions and activities of individual prospective teachers and thus has provided the psychological perspective correlate to the social perspective's classroom mathematical practices. As the research participants progressed through an instructional sequence taught entirely in base-8, a case study approach was used to select and analyze two individuals. In order to gain a more thorough understanding of the individual perspective, this research endeavor focused on whether teachers with varying initial content knowledge developed differently through this instructional sequence. The first participant initially demonstrated "Low-Content" knowledge according to the CKT-M instrument database questions which measure content knowledge for teaching mathematics. She developed a greater understanding of place value concepts and was able to apply this new knowledge to gain a deeper sense of the rationale behind counting strategies and addition and subtraction operations. She did not demonstrate the ability to consistently make sense of multiplication and division strategies. She participated in the classroom argumentation primarily by providing claims and data as she illustrated the way she would use different procedures to solve addition and subtraction problems. The second participant illustrated "High-Content" knowledge based on the CKT-M instrument. She already possessed a solid foundation in understanding place value concepts and throughout the instructional sequence developed various ways to connect and build on her initial understanding through the synthesis of multiple pedagogical content tools. She demonstrated conceptual understanding of counting strategies, and all four whole number operations. Furthermore, by exploring various ways that other prospective teachers solved the problems, she also presented a greater pedagogical perspective in how other prospective teachers think mathematically. This prospective teacher showed a shift in her participation in classroom argumentation as she began by providing claims and data at the outset of the instructional sequence. Later on, she predominantly provided the warrants and backings to integrate the mathematical concepts and pedagogical tools used to develop greater understanding of whole number operations. These results indicate the findings based on the individual case-study analysis of prospective elementary school teachers and the cross-case analysis that ensued. The researcher contends that through the synthesis of the findings of this project along with current relevant research efforts, teacher educators and educational policy makers can revisit and possibly revise instructional practices and sequences in order to develop teachers with greater conceptual understanding of concepts vital to elementary mathematics.
Show less - Date Issued
- 2009
- Identifier
- CFE0002811, ucf:48097
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0002811
- Title
- A Multiple Case Study Exploring the Relationship Between Engagement in Model-Eliciting Activities and Pre-Service Secondary Mathematics Teachers' Mathematical Knowledge for Teaching Algebra.
- Creator
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Abassian, Aline, Safi, Farshid, Dixon, Juli, Andreasen, Janet, Bush, Sarah, Bostic, Jonathan, University of Central Florida
- Abstract / Description
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The goal of this research study was to explore the nature of the relationship between engagement in model-eliciting activities (MEAs) and pre-service 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) pre-assessment designed to measure...
Show moreThe goal of this research study was to explore the nature of the relationship between engagement in model-eliciting activities (MEAs) and pre-service 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) pre-assessment 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 AfterMath: A Culturally Responsive Mathematical Intervention to Aid Students Affected by Natural Disasters.
- Creator
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Kurtz, Brianna, Haciomeroglu, Erhan, Bush, Sarah, Safi, Farshid, Biraimah, Karen, University of Central Florida
- Abstract / Description
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On September 20, 2017, Hurricane Maria struck the island of Puerto Rico. The damage was extensive, and many people found themselves to be natural disaster refugees. As a result, schools in Central Florida saw an influx of new students who had their educations interrupted by the disaster and now were resuming school in a new language of instruction. These students not only faced linguistic challenges but also academic differences due to the high prevalence of poverty and the effects of...
Show moreOn September 20, 2017, Hurricane Maria struck the island of Puerto Rico. The damage was extensive, and many people found themselves to be natural disaster refugees. As a result, schools in Central Florida saw an influx of new students who had their educations interrupted by the disaster and now were resuming school in a new language of instruction. These students not only faced linguistic challenges but also academic differences due to the high prevalence of poverty and the effects of neocolonialism in their previous schooling. This mixed methods study implemented an intensive intervention in probability to aid students in developing mathematical understanding and forming meaningful connections. Student participants, who had been affected by Hurricane Maria, were now attending a public high school and were paired one-on-one with a bilingual, mathematically high performing student mentor to complete culturally responsive, bilingual probability tasks. Data collection occurred over the course of six weeks in fall 2019. Both mentor and mentee students participated in focus group interviews, and the mentees completed a probability pre-test and post-test. Student participants were found to have statistically significant increases in the understanding of probability concepts when comparing pre-intervention and post-intervention results, with the understanding and usage of the multiplication rule showing the most significant improvement. Both mentors and mentees reported feeling a stronger sense of unity and belonging post-intervention as well as improvement in bilingual academic vocabulary. With the impact of natural disasters on the rise, implications of this study include its adaption to respond to future displaced students as they resume schooling post-interruption in Central Florida and beyond.
Show less - Date Issued
- 2019
- Identifier
- CFE0007828, ucf:52820
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0007828
- Title
- The Influence of Instruction in Base 8 on Prospective Teachers' Mathematical Knowledge for Teaching.
- Creator
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Harshman, Katie, Haciomeroglu, Erhan, Andreasen, Janet, Witta, Eleanor, Safi, Farshid, Lewis, Nancy, University of Central Florida
- Abstract / Description
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The focus of this research project was to extend existing research literature by providing insight to how prospective teachers with differing levels of mathematical knowledge developed their conceptual understanding of whole number concepts and operations. Prospective teachers of interest were enrolled in an Elementary School Mathematics Course for Teachers (in the College of Education) with a whole number concepts and operations unit set entirely in base 8. In this mixed-mode study,...
Show moreThe focus of this research project was to extend existing research literature by providing insight to how prospective teachers with differing levels of mathematical knowledge developed their conceptual understanding of whole number concepts and operations. Prospective teachers of interest were enrolled in an Elementary School Mathematics Course for Teachers (in the College of Education) with a whole number concepts and operations unit set entirely in base 8. In this mixed-mode study, participants were given the MKT, a measure designed to measure teacher mathematical knowledge for teaching, before and after taking the base 8 unit. The researcher focused on two specific constructs: Common Content Knowledge (CCK) and Specialized Content Knowledge (SCK). The qualitative portion of the study involved carefully constructed student interviews which allowed the researcher to deeply explore how prospective teacher conceptual understanding changed as a result of taking the unit in base 8. Four participants with varying levels of knowledge were selected to be interviewed based upon initial scores on the MKT: 1) low CCK and low SCK, 2) low CCK and high SCK, 3) high CCK and low SCK, 4) high CCK and high SCK. Results of the interviews were used to help explain results from the MKT. Quantitative and qualitative results showed that participants did not significantly increase their CCK, but did experience an increase in their conceptual understanding (SCK) as a result of taking the unit in base 8. Most prospective teachers entering the Elementary School Mathematics Course already had high procedural knowledge of the algorithms associated with elementary mathematics, which could account for the non-significant increase in CCK. Prospective teachers all showed deeper conceptual understanding of whole number concepts and operations at varying levels by the end of the base 8 unit. Prospective teachers showed their increased understanding by way of explanations, justifications, and alternate solution strategies.
Show less - Date Issued
- 2016
- Identifier
- CFE0006321, ucf:51552
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0006321
- 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
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Campbell Sutherland, Makini, Dixon, Juli, Safi, Farshid, Hoffman, Elizabeth, Andreasen, Janet, Childs, Kristopher, University of Central Florida
- Abstract / Description
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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 in-service 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