This research is based on the Middle School Mathematics Project (MSMP) funded by the Interagency Educational Research Initiative (IERI) through a grant to the American Association for the Advancement of Science (AAAS). Both teachers’ video lessons and students’ pre-and-post test scores were used to investigate the effects of teachers’ types, quality, and quantity of questioning students’ knowledge of algebra concepts and skills in variables, change, equality, and equations in middle school students in seventh and eighth grades. The study further explored the relationship between types of questioning, quality of questioning, and quantity of questioning. Later, teachers’ intention of asking two types of questions, probing and guiding, and teachers’ questioning acquisition methods were studied through face-to-face teacher interviews. This dissertation used a mixed approach utilizing both quantitative and qualitative methods. The data were collected from 33 teachers in two different states, Texas and Delaware, who participated in the IERI project either during the 2002-2003, the 2003- 2004, or the 2004-2005 school years. A total of 103 videotapes were obtained consisting of one to five lessons for each teacher. The teachers used one of four different textbooks: MathThematics (Billstein, et al., 1999), Connected Mathematics (Lappan, et al., 1998), Mathematics: Applications and Connections Glencoe Algebra (Collins, et al., 1998), or Mathematics in Context (MiC) (Romberg, et al., 1998). The results showed that teachers’ quality of probing questions affected students’ achievements when other variables--teachers’ teaching experience, textbook, and teachers’ math preparation--were controlled. It was also found that AAAS’ two highest rated two textbooks, CMP and MiC, affected students’ understanding. Moreover, teachers’ math preparation predicted student performance. Furthermore, quality and quantity of guiding questions and probing questions were significantly correlated with each other (p < 0.01). For the qualitative part, it was found that teachers’ were asking what they intended to ask. In other words, they were aware of the role of questioning they were using. Also, there were several methods that seemed to be more used when acquiring questioning skills- -watching and observing teachers, being in the field or from student-teacher experience, and workshops.

Using both quantitative and qualitative data collection and analyses techniques, this study examined representations used by sixteen (n = 16) teachers while teaching the concepts of converting among fractions, decimals, and percents. The classroom videos used for this study were recorded as part of the Middle School Mathematics Project (MSMP). The study also compared teacher-selected and textbook representations and examined how teachers‘ use of idiosyncratic representations influenced representational choices on the number test by the teachers‘ five hundred eighty-one (N = 581) students. In addition to using geometric figures and manipulatives, a majority of the teachers used natural language such as the words nanny, north, neighbor, dog, cowboy, and house to characterize fractions and mathematical procedures or algorithms. Coding of teacher-selected representations showed that verbal representations deviated from textbook representations the most. Some teachers used the words or phrases bigger, smaller, doubling, tripling, breaking-down, and building-up in the context of equivalent fractions. There was widespread use of idiosyncratic representations by teachers, such as equations with missing or double equal signs, numbers and operators written as superscripts, and numbers written above and below the equal sign. Although use of idiosyncratic representations by teachers influenced representational choices by students on the number test, no evidence of a relationship between representational forms and degree of correctness of solutions was found. The study did reveal though that teachers‘ use of idiosyncratic representations can lead to student misconceptions such as thinking that multiplying by a whole number not equal to 1 gives an equivalent fraction. Statistical tests were done to determine if frequency of representation usage by teachers was related to the textbook, highest degree obtained by teacher, certification, number of years spent teaching mathematics, number of years teaching mathematics at grade level, number of hours completed on professional development related to their textbook, and total number of days spent on the Interagency Education Research Initiative (IERI) professional development. The results showed representation usage was related to all the above variables, except the highest degree obtained and the total number of days spent on the IERI professional development.

Thesis--PlanB (M.S.)--University of Wisconsin--Stout, 2001. / Includes bibliographical references.

Thesis--PlanB (M.S.)--University of Wisconsin--Stout, 2003. / Includes bibliographical references.

Thesis (M.A.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 59-64).

Thesis (Ph. D.)--University of Wyoming, 2005. / Title from PDF title page (viewed on Feb. 20, 2008). Includes bibliographical references (p. 117-127).

Thesis PlanB (M.S.)--University of Wisconsin--Stout, 2008. / Includes bibliographical references.

Thesis (M.Ed.)--Bowling Green State University, 2008. / Document formatted into pages; contains ix, 120 p. Includes bibliographical references.

Thesis--PlanB (M.S.)--University of Wisconsin--Stout, 1999. / Includes bibliographical references.

Thesis (Ed.D.)--Liberty University School of Education, 2009. / Includes bibliographical references.