The process of generalization in mathematics was identified by mathematics education and educational psychology research, out of many mental actions or operations, as a cognitive function fundamentally required in the thinking process. Moreover, the current changes in education in the United States bring forward the dual goal of mathematics teaching and learning: students should have strong and rigorous mathematical content knowledge and students should be involved in practices that define the status of doing mathematical work. This dual role is totally dependent on the process of generalization. This study uses theories and research findings from the field of algebraic thinking, teaching, and learning to understand how the third grade teacher’s edition textbooks of three mathematics curricula portray the process of generalization. I started my study with the development of a theoretical coding system obtained by combining Kaput’s theory about algebra (Kaput, 2008), Krutetskii’s two way of generalization (Krutetskii, 1976), and the five mathematical representations identified by Lesh, Post, and Behr (1987). Then, I used the coding system to identify tasks that have the potential to involve students in the process of generalization. The findings from my study provide evidence that following a well-structured theory, such as Kaput’s theory about algebra, allows us to identify tasks that support algebraic thinking and to create new ones with higher potential to involve children in the process of generalization. Such tasks may support the development of algebraic thinking as a continuous process that should start from early grades of elementary school.

In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on prekindergarten and kindergarten students’ ability to rote count, read two-digit numerals, model two-digit numbers, and identify the place value of individual digits in two-digit numerals. Through individual student interviews, preand post-assessments were administered to evaluate rote counting, reading five two-digit numerals, modeling five two-digit numbers, and identifying place value in two two-digit numerals. Chi-square tests for independence showed two significant relations: (1) the relationship between the control and treatment group membership on the postassessment of modeling two-digit numbers and (2) the relationship between place value identifications and group membership. Analysis of the children’s performance and error patterns revealed interesting differences between children taught with explicit number names and children taught with traditional number names. The improvement of the treatment group overall exceeded the improvement of the control group. This study indicates that teaching children to use explicit number names can, indeed, have a positive influence on their understanding of place value.

In this workshop, participants engaged with and reflected on authentic artifacts from data modeling projects related to the solar system and to deforestation that were completed by elementary students in grade 5 (average age 11). These authentic examples were used to ground a discussion of using a data modeling approach to help elementary students make sense of and meaningful integrated use of mathematics and science concepts and tools. School-based ways of helping teachers understand this approach in order to be able to use it in their classrooms were also discussed.

Thesis (Ed. D.)--University of North Texas, May, 2007. / Title from title page display. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 143-150). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 143-150). Also available on the Internet.

The diploma paper presents whole study material relevant to field of the whole numbers for listeners of primary school teaching needs. Theoretic part deals with the whole numbers problems from several authors aspects. I find out level of the skills about the whole numbers of children in the 1st and the 5th grade of the primary school and the pedagogic faculty JČU students in this practical part. Further I am focus on primary school teachers approach to this problems. Part of my diploma paper is collection of the exercise for primary school students and teachers during practice.

In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on prekindergarten and kindergarten students’ ability to rote count, read two-digit numerals, model two-digit numbers, and identify the place value of individual digits in two-digit numerals. Through individual student interviews, preand post-assessments were administered to evaluate rote counting, reading five two-digit numerals, modeling five two-digit numbers, and identifying place value in two two-digit numerals. Chi-square tests for independence showed two significant relations: (1) the relationship between the control and treatment group membership on the postassessment of modeling two-digit numbers and (2) the relationship between place value identifications and group membership. Analysis of the children’s performance and error patterns revealed interesting differences between children taught with explicit number names and children taught with traditional number names. The improvement of the treatment group overall exceeded the improvement of the control group. This study indicates that teaching children to use explicit number names can, indeed, have a positive influence on their understanding of place value.

In this workshop, participants engaged with and reflected on authentic artifacts from data modeling projects related to the solar system and to deforestation that were completed by elementary students in grade 5 (average age 11). These authentic examples were used to ground a discussion of using a data modeling approach to help elementary students make sense of and meaningful integrated use of mathematics and science concepts and tools. School-based ways of helping teachers understand this approach in order to be able to use it in their classrooms were also discussed.

Even though a school in Southern Virginia had been utilizing a variety of manipulatives, calculators, and computers to transition students through the concrete-representational-abstract (CRA) sequence; students did not meet the state proficiency requirement on the standardized math assessment. A qualitative descriptive case study design, grounded in Bruner's learning theory on the modes of representation, was utilized to explore fifth-grade teachers' perceptions of their math instructional practices. The central question was about 5th-grade teachers' perceptions of utilizing a wide variety of manipulatives, calculators, and computers to transition students from concrete understandings to pictorial representations before they embark upon abstract concepts. Data were collected through observations, interviews, and archival data. The data were analyzed through thematic analysis and coded through the constant comparison approach. The data collection revealed that the 4 participants were utilizing a wide variety of manipulatives, calculators, and computers to transition students through the CRA sequence; however, the teachers were unable to teach students to a level of mastery due to various barriers. The study's findings suggest that the research site would benefit from a three-day professional development plan, created to address the lack of teaching to mastery. This study will contribute to positive social change because it addressed the math achievement gap that is widening in America. This study's findings could benefit local, district, and state stakeholders as the project addresses teaching students to the appropriate cognitive levels to prepare for lifelong learning in mathematics, as well as for standardized assessments.