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## Full-Text Articles in Education

Probing For Reasons: Presentations, Questions, Phases, Kellyn Nicole Farlow

#### Probing For Reasons: Presentations, Questions, Phases, Kellyn Nicole Farlow

*Theses and Dissertations*

This thesis reports on a research study based on data from experimental teaching. Students were invited, through real-world problem tasks that raised central conceptual issues, to invent major ideas of calculus. This research focuses on work and thinking of the students, as they sought to build key ideas, representations and compelling lines of reasoning. This focus on the students' and their agency as learners has brought about a new development of the psychological and logical perspectives, as well as, highlighted students' choices in academic and social roles. Such choices facilitated continued learning among these students.

Applying Toulmin's Argumentation Framework To Explanations In A Reform Oriented Mathematics Class, Jennifer Alder Brinkerhoff

#### Applying Toulmin's Argumentation Framework To Explanations In A Reform Oriented Mathematics Class, Jennifer Alder Brinkerhoff

*Theses and Dissertations*

This study looks at conceptual explanations given in a reform-oriented mathematics class for preservice secondary mathematics teachers and extends Toulmin's argumentation framework to account for some of the complexities of the explanations given by these students. This study explains the complexities that arose in applying Toulmin's framework to explanations and extends the framework by accounting for the features of conceptual explanations. The complexities of these explanations are that they are made up of multiple arguments that build on each other to reach a final conclusion and that they are also dependant upon the social aspects of the class ...

Improving Students’ Algebraic Thinking: The Case Of Talia, Kien H. Lim

#### Improving Students’ Algebraic Thinking: The Case Of Talia, Kien H. Lim

*Kien H Lim*

This paper presents the case of an 11th grader, Talia, who demonstrated improvement in her algebraic thinking after five one-hour sessions of solving problems involving inequalities and equations. She improved from association-based to coordination-based predictions, from impulsive to analytic anticipations, and from inequality-as-a-signal-for-a-procedure to inequality-as-a-comparison-of-functions conceptions. In the one-on-one teaching intervention, she progressed from the sub-context of manipulating symbols, to working with specific numbers, to reasoning with “general” numbers, and eventually to reasoning with symbols. Three features were identified to account for her improvement: (a) attention to meaning, (b) opportunity to repeat similar reasoning, and (c) opportunity to explore.

Students' Epistemological Beliefs Of Mathematics When Taught Using Traditional Versus Reform Curricula In Rural Maine High Schools, Glenn T. Colby

#### Students' Epistemological Beliefs Of Mathematics When Taught Using Traditional Versus Reform Curricula In Rural Maine High Schools, Glenn T. Colby

*Electronic Theses and Dissertations*

This study compared students’ epistemological beliefs of mathematics after completing 3 years of a reform-oriented curriculum developed by the Core-Plus Mathematics Project (CPMP) versus a more traditional curriculum developed by Glencoe Mathematics. The Conceptions of Mathematics Inventory (CMI; Grouws, Howald, & Colangelo, 1996) was administered to 11th-grade students in four rural Maine high schools (n=102) to measure student beliefs of mathematics. CPMP was used as the primary textbook series in 2 of the schools, while the other 2 schools used Glencoe Mathematics. A variation of the Reformed Teaching Observation Protocol (RTOP; Piburn & Sawada, 2000) and teacher questionnaires were used to characterize the level of reform-oriented instruction occurring in each of the schools. The results indicated that the students who were taught using the traditional curriculum combined with reform-oriented teaching practices expressed the most positive beliefs of mathematics, while the students who were taught using the reform-oriented curriculum expressed less healthy beliefs ...