Matching Items (12)

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Engineering-based problem solving strategies In AP calculus: an investigation into high school student performance on related rate free-response problems

Description

A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance

A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple post-assessment model with three periods of data collection. Four high school calculus classes were selected for the study, with one class designated as the treatment and three as the controls. Measures for this study include a skills assessment, Related Rate word problem assessments, and a motivation problem solving survey. Data analysis utilized a mixed methods approach. Quantitative analysis consisted of descriptive and inferential methods utilizing nonparametric statistics for performance comparisons and structural equation modeling to determine the underlying structure of the problem solving motivation survey. Statistical results indicate that time on task was a major factor in enhanced performance between measurement time points 1 and 2. In the experimental classroom, the engineering design process as a problem solving strategy emerged as an important factor in demonstrating sustained achievement across the measurement time series when solving volumetric rates of change as compared to traditional problem solving strategies. In the control classrooms, where traditional problem solving strategies were emphasized, a greater percentage of students than in the experimental classroom demonstrated enhanced achievement from point 1 to 2, but showed decrease in achievement from point 2 to 3 in the measurement time series. Results from the problem solving motivation survey demonstrated that neither time on task nor instruction strategy produced any effect on student beliefs about and perceptions of problem solving. Qualitative error analysis showed that type of instruction had little effect on the type and number of errors committed, with the exception of procedural errors from performing a derivative and errors decoding the problem statement. Results demonstrated that students who engaged in the engineering design-based committed a larger number of decoding errors specific to Pythagorean type Related Rate problems; while students who engaged in routine problem solving did not sustain their ability to correctly differentiate a volume equation over time. As a whole, students committed a larger number of misused data errors than other types of errors. Where, misused data errors are the discrepancy between the data as given in a problem and how the student used the data in problem solving.

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Created

Date Created
  • 2012

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Student difficulties with linearity and linear functions and teachers' understanding of student difficulties

Description

The focus of the study was to identify secondary school students' difficulties with aspects of linearity and linear functions, and to assess their teachers' understanding of the nature of the

The focus of the study was to identify secondary school students' difficulties with aspects of linearity and linear functions, and to assess their teachers' understanding of the nature of the difficulties experienced by their students. A cross-sectional study with 1561 Grades 8-10 students enrolled in mathematics courses from Pre-Algebra to Algebra II, and their 26 mathematics teachers was employed. All participants completed the Mini-Diagnostic Test (MDT) on aspects of linearity and linear functions, ranked the MDT problems by perceived difficulty, and commented on the nature of the difficulties. Interviews were conducted with 40 students and 20 teachers. A cluster analysis revealed the existence of two groups of students, Group 0 enrolled in courses below or at their grade level, and Group 1 enrolled in courses above their grade level. A factor analysis confirmed the importance of slope and the Cartesian connection for student understanding of linearity and linear functions. There was little variation in student performance on the MDT across grades. Student performance on the MDT increased with more advanced courses, mainly due to Group 1 student performance. The most difficult problems were those requiring identification of slope from the graph of a line. That difficulty persisted across grades, mathematics courses, and performance groups (Group 0, and 1). A comparison of student ranking of MDT problems by difficulty and their performance on the MDT, showed that students correctly identified the problems with the highest MDT mean scores as being least difficult for them. Only Group 1 students could identify some of the problems with lower MDT mean scores as being difficult. Teachers did not identify MDT problems that posed the greatest difficulty for their students. Student interviews confirmed difficulties with slope and the Cartesian connection. Teachers' descriptions of problem difficulty identified factors such as lack of familiarity with problem content or context, problem format and length. Teachers did not identify student difficulties with slope in a geometric context.

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Created

Date Created
  • 2011

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An investigation into the definitions and development of pedagogical content knowledge among pre-service and current mathematics teachers

Description

The principle purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK) and examine the development of that knowledge among pre-service and current

The principle purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK) and examine the development of that knowledge among pre-service and current math teachers. Seventy-eight current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT) - Mathematics assessment and nine of them took the Cognitively Activating Instruction in Mathematics (COACTIV) assessment. Participants answered questions that demonstrated their understanding of students' challenges and misconceptions, ability to recognize and utilize multiple representations and methods of presenting content, and understanding of tasks and materials that they may be using for instruction. Additionally, participants indicated their college major, institution attended, years of experience, and participation in various other learning opportunities. This data was analyzed to look for changes in knowledge, first among those still in college, then among those already in the field, and finally as a whole group to look for a pattern of growth from pre-service through working in the classroom. I compared these results to the theories of learning espoused by the creators of these two tests to see which model the data supports. The results indicate that growth in PCK occurs among college students during their teacher preparation program, with much less change once a teacher enters the field. Growth was not linear, but best modeled by an s-curve, showing slow initial changes, substantial development during the 2nd and 3rd year of college, and then a leveling off during the last year of college and the first few years working in a classroom. Among current teachers' the only group that demonstrated any measurable growth were teachers who majored in a non-education field. Other factors like internships and professional development did not show a meaningful correlation with PCK. Even though some of these models were statistically significant, they did not account for a substantial amount of the variation among individuals, indicating that personal factors and not programmatic ones may be the primary determinant of a teachers' knowledge.

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Created

Date Created
  • 2016

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Student growth in elementary mathematics: a cross level investigation

Description

The primary purpose of this study is to examine the effect of knowledge for teaching mathematics and teaching practice on student mathematics achievement growth. Thirty two teachers and 299 fourth

The primary purpose of this study is to examine the effect of knowledge for teaching mathematics and teaching practice on student mathematics achievement growth. Thirty two teachers and 299 fourth grade students in three elementary schools from one school district in urban area participated in the study. Most of them are Hispanic in origin and about forty percent is English Language Learners (ELLs). The two level Hierarchical Linear Model (HLM) was used to investigate repeated measures of teaching practice measured by Classroom Assessment Scoring System (CLASS) instrument. Also, linear regression and a multiple regression to examine the relationship between teacher knowledge measured by Learning for Mathematics Teaching (LMT) and Developing Mathematical Ideas (DMI) items and teaching practice were employed. In addition, a three level HLM was employed to analyze repeated measures of student mathematics achievement measured by Arizona Assessment Consortium (AzAC) instruments. Results showed that overall teaching practice did not change weekly although teachers' emotional support for their students improved by week. Furthermore, a statistically significant relationship between teacher knowledge and teaching practice was not found. In terms of student learning, ELLs have significantly lower initial status in mathematics achievement than non-ELLs, as were growth rates for these two groups. Lastly, teaching practice significantly predicted students' monthly mathematics achievement growth but teacher knowledge did not. The findings suggest that school systems and education policy makers need to provide teachers with the chance to reflect on their teaching and change it within themselves in order to better support student mathematics learning.

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Created

Date Created
  • 2012

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Identity development of preservice elementary teachers of mathematics from teacher education program to student teaching

Description

Drawing on Lave and Wenger (1991) this study explores how preservice elementary teachers develop themselves as teachers of mathematics, in particular, from the time of their teacher education courses to

Drawing on Lave and Wenger (1991) this study explores how preservice elementary teachers develop themselves as teachers of mathematics, in particular, from the time of their teacher education courses to their field experiences. This study also researches the critical experiences that contributed to the construction of their identities and their roles as student teachers in their identity development. The stories of Jackie, Meg, and Kerry show that they brought different incoming identities to the teacher education program based on their K-12 school experiences. The stories provide the evidence that student teachers' prior experience as learners of mathematics influenced their identities as teachers, especially their confidence levels in teaching mathematics. During the mathematics methods class, student teachers were provided a conceptual understanding of math content and new ways to think about math instruction. Based on student teachers' own experiences, they reconstructed their knowledge and beliefs about what it means to teach mathematics and set their goals to become the mathematics teachers they wanted to be. As they moved through the program through their student teaching periods, their identity development varied depending on the community of practice in which they participated. My study reveals that mentor relationships were critical experiences in shaping their identities as mathematics teachers and in building their initial mathematics teaching practices. Findings suggest that successful mentoring is necessary, and this generally requires sharing common goals, receiving feedback, and having opportunities to practice knowledge, skills, and identities on the part of beginning teachers. Findings from this study highlight that identities are not developed by the individual alone but by engagement with a given community of practice. This study adds to the field of teacher education research by focusing on prospective teachers' identity constructions in relation to the communities of practice, and also by emphasizing the role of mentor in preservice teachers' identity development.

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Created

Date Created
  • 2012

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Technology two ways: modeling mathematics teacher educators' use of technology in the classroom

Description

This study explores teacher educators' personal theories about the instructional practices central to preparing future teachers, how they enact those personal theories in the classroom, how they represent the relationshi

This study explores teacher educators' personal theories about the instructional practices central to preparing future teachers, how they enact those personal theories in the classroom, how they represent the relationship between content, pedagogy, and technology, and the function of technology in teacher educators' personal theories about the teaching of mathematics and their practices as enacted in the classroom. The conceptual frameworks of knowledge as situated and technology as situated provide a theoretical and analytical lens for examining individual instructor's conceptions and classroom activity as situated in the context of experiences and relationships in the social world. The research design employs a mixed method design to examine data collected from a representative sample of three full-time faculty members teaching methods of teaching mathematics in elementary education at the undergraduate level. Three primary types of data were collected and analyzed:

a) structured interviews using the repertory grid technique to model the mathematics education instructors' schemata regarding the teaching of mathematics methods; b) content analysis of classroom observations to develop models that represent the relationship of pedagogy, content, and technology as enacted in the classrooms; and c) brief retrospective protocols after each observed class session to explore the reasoning and individual choices made by an instructor that underlie their teaching decisions in the classroom. Findings reveal that although digital technology may not appear to be an essential component of an instructor's toolkit, technology can still play an integral role in teaching. This study puts forward the idea of repurposing as technology -- the ability to repurpose items as models, tools, and visual representations and integrate them into the curriculum. The instructors themselves became the technology, or the mediational tool, and introduced students to new meanings for "old" cultural artifacts in the classroom. Knowledge about the relationships between pedagogy, content, and technology and the function of technology in the classroom can be used to inform professional development for teacher educators with the goal of improving teacher preparation in mathematics education.

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Agent

Created

Date Created
  • 2014

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What is relevant mathematics?: an exploration of two perspectives on relevant mathematics in the high school classroom

Description

Recently there has been an increase in the number of people calling for the incorporation of relevant mathematics in the mathematics classroom. Unfortunately, various researchers define the term relevant mathematics

Recently there has been an increase in the number of people calling for the incorporation of relevant mathematics in the mathematics classroom. Unfortunately, various researchers define the term relevant mathematics differently, establishing several ideas of how relevancy can be incorporated into the classroom. The differences between mathematics education researchers' definitions of relevant and the way they believe relevant math should be implemented in the classroom, leads one to conclude that a similarly varied set of perspectives probably exists between teachers and students as well. The purpose of this exploratory study focuses on how the student and teacher perspectives on relevant mathematics in the classroom converge or diverge. Specifically, do teachers and students see the same lessons, materials, content, and approach as relevant? A survey was conducted with mathematics teachers at a suburban high school and their algebra 1 and geometry students to provide a general idea of their views on relevant mathematics. An analysis of the findings revealed three major differences: the discrepancy between frequency ratings of teachers and students, the differences between how teachers and students defined the term relevance and how the students' highest rated definitions were the least accounted for among the teacher generated questions, and finally the impact of differing attitudes towards mathematics on students' feelings towards its relevance.

Contributors

Agent

Created

Date Created
  • 2012

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Language policy, teacher beliefs, and practice: implications for English language learners in mathematics

Description

In 2007, Arizona voters passed House Bill (HB) 2064, a law that fundamentally restructured the Structured English Immersion (SEI) program, putting into place a 4-hour English language development (ELD) block

In 2007, Arizona voters passed House Bill (HB) 2064, a law that fundamentally restructured the Structured English Immersion (SEI) program, putting into place a 4-hour English language development (ELD) block for educating English language learners (ELLs). Under this new language policy, ELL students are segregated from their English-speaking peers to receive a minimum of four hours of instruction in discrete language skills with no contextual or native language support. Furthermore, ELD is separate from content-area instruction, meaning that language and mathematics are taught as two separate entities. While educators and researchers have begun to examine the organizational structure of the 4-hour block curriculum and implications for student learning, there is much to be understood about the extent to which this policy impacts ELLs opportunities to learn mathematics. Using ethnographic methods, this dissertation documents the beliefs and practices of four Arizona teachers in an effort to understand the relationship between language policy and teacher beliefs and practice and how together they coalesce to form learning environments for their ELL students, particularly in mathematics. The findings suggest that the 4-hour block created disparities in opportunities to learn mathematics for students in one Arizona district, depending on teachers' beliefs and the manner in which the policy was enacted, which was, in part, influenced by the State, district, and school. The contrast in cases exemplified the ways in which policy, which was enacted differently in the various classes, restricted teachers' practices, and in some cases resulted in inequitable opportunities to learn mathematics for ELLs.

Contributors

Agent

Created

Date Created
  • 2013

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Impact of STS (context-based type of teaching) in comparison with a textbook approach on attitudes and achievement in community college chemistry classrooms

Description

The purpose of this study was to analyze the impact of a context-based teaching approach (STS) versus a more traditional textbook approach on the attitudes and achievement of community college

The purpose of this study was to analyze the impact of a context-based teaching approach (STS) versus a more traditional textbook approach on the attitudes and achievement of community college chemistry students. In studying attitudes toward chemistry within this study, I used a 30-item Likert scale in order to study the importance of chemistry in students' lives, the importance of chemistry, the difficulty of chemistry, interest in chemistry, and the usefulness of chemistry for their future career. Though the STS approach students had higher attitude post scores, there was no significant difference between the STS and textbook students' attitude post scores. It was noted that females had higher postattitude scores in the STS group, while males had higher postattitude scores in the textbook group. With regard to postachievement, I noted that males had higher scores in both groups. A correlation existed between postattitude and postachievement in the STS classroom. In summary, while an association between attitude and achievement was found in the STS classroom, teaching approach or sex was not found to influence attitudes, while sex was also not found to influence achievement. These results, overall, suggest that attitudes are not expected to change on the basis of either teaching approach or gender, and that techniques other than changing the teaching approach would need to be used in order to improve the attitudes of students. Qualitative analysis of an online discussion activity on Energy revealed that STS students were able to apply aspects of chemistry in decision making related to socioscientific issues. Additional analysis of interview and written responses provided insight regarding attitudes toward chemistry, with respect to topics of applicability of chemistry to life, difficulties with chemistry, teaching approach for chemistry, and the intent for enrolling in additional chemistry courses. In addition, the surveys of female students brought out subcategories with regard to emotional and professional characteristics of a good teacher, under the category of characteristics of teaching approach. With respect to the category of course experience, subcategories of useful knowledge to solve real-life problems and knowledge for future career were revealed. The differences between the control group females and STS group females with respect to these characteristics was striking and threw insight into how teacher behavior and teaching approach shape student attitudes to chemistry in case of female students.

Contributors

Agent

Created

Date Created
  • 2011

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U.S. and Chinese Middle School Mathematics Teachers' Pedagogical Content Knowledge: The Case of Functions

Description

This study investigated the current state of the U.S. and Chinese urban middle school math teachers' pedagogical content knowledge (PCK) for the topic of functions. A comparative, descriptive case study

This study investigated the current state of the U.S. and Chinese urban middle school math teachers' pedagogical content knowledge (PCK) for the topic of functions. A comparative, descriptive case study was employed to capture the PCK of 23 teachers in Arizona and of 28 teachers in Beijing, regarding their instructional knowledge, understanding of student thinking and curricular knowledge--three key components based on Shulman's conceptualization of PCK--related to functions. Cross-case comparisons were used to analyze the PCK of teacher groups across countries and socio-economic statuses (SES), based on the questionnaire, lesson plan, and interview data.

This study finds that despite cultural differences, teachers are likely to share some commonalities with respect to their instructional decisions, understanding of student thinking and curricular knowledge. These similarities may reflect the convergence in teaching practice in the U.S. and China and the dedication the two countries make in improving math education. This study also finds the cross-country differences and cross-SES differences regarding teachers' PCK. On the one hand, the U.S. and Chinese math teachers of this study tend to diverge in valuing different forms of representations, explaining student misconceptions, and relating functions to other math topics. Teachers' own understanding of functions (and mathematics), standards, and high-stakes testing in each country significantly influence their PCK. On the other hand, teachers from the higher SES schools are more likely to show higher expectations for and stronger confidence in their students' mathematical skills compared to their counterparts from the lower SES schools. Teachers' differential beliefs in students' ability levels significantly contribute to their differences between socio-economic statuses.

Contributors

Agent

Created

Date Created
  • 2014