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In his book "On Christian Teaching," David Smith offers multiple ways in which one's Christian faith commitments influence pedagogical practices. Specific examples are drawn from the humanities, particularly from languages and literature. Some may conclude that such discussions are less appropriate in areas such as science, technology, engineering, and mathematics (STEM). We disagree and offer exemplars aligned with a set of six curricular criteria identified by Wayne Au. We argue that these exemplars emerge naturally from our Christian beliefs and are "faith-influenced" even if not every strategy embodies a narrower integration of faith and pedagogy.

This study explored children's area estimation performance. Two groups of fourth grade children completed area estimation tasks with rectangles ranging from 5 to 200 square units. A randomly assigned treatment group completed instructional sessions that involved a conceptual area measurement strategy along with numerical feedback. Children tended to underestimate areas of rectangles. Furthermore, rectangle size was related to performance such that estimation error and variability increased as rectangle size increased. The treatment group exhibited significantly improved area estimation performance in terms of accuracy, as well as reduced variability and instances of extreme responses. Area measurement estimation findings are related to a Hypothetical Learning Trajectory for area measurement.

The Harry Potter series is a favorite for out-of-school reading and has been used in school, largely as an object of study in language arts. Using a content analysis to highlight the ways in which J.K. Rowling's work could be used to teach higher dimensionality in math, the authors argues that the content is sufficient in such books to engage the interest of students who may be negatively predisposed toward mathematics but are very enthusiastic about Harry Potter books, and vice versa. The article illustrates and explains three-dimensional objects in two-dimensional space, pocket dimensions, three-dimensional movement through two-dimensional space, and higher dimensional movement through examples and descriptions from scenes in the Harry Potter series and suggests ways in which similar analyses could be performed on other high-interest texts, helping students forge new insights about mathematics literacy.

We describe several service-learning initiatives implemented by the mathematics and education departments. College students with majors and minors in math and math education have helped to design and implement math events for elementary and middle school students. Formal and informal reflections on these service-related experiences have demonstrated the potential impact on future teaching and learning goals for the pre-service teachers. College students taking a statistics course have analyzed data from some of these math events, using both descriptive and inferential methods. Teachers of participating elementary and middle schools have re-examined their textbook and curriculum choices in light of their students' performance at these math events. (Contains 1 footnote.)

We examined children's development of strategic and conceptual knowledge for linear measurement. We conducted teaching experiments with eight students in grades 2 and 3, based on our hypothetical learning trajectory for length to check its coherence and to strengthen the domain-specific model for learning and teaching. We checked the hierarchical structure of the trajectory by generating formative instructional task loops with each student and examining the consistency between our predictions and students' ways of reasoning. We found that attending to intervals as countable units was not an adequate instructional support for progress into the Consistent Length Measurer level; rather, students must integrate spaces, hash marks, and number labels on rulers all at once. The findings have implications for teaching measure-related topics, delineating a typical developmental transition from inconsistent to consistent counting strategies for length measuring. We present the revised trajectory and recommend steps to extend and validate the trajectory. (Contains 3 figures, 3 tables, and 1 footnote.)

This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, we found support for the application and elaboration of our previously established categorization of children's length measurement levels: (1) guessing of length values by naive visual observation, (2) making inconsistent, uncoordinated reference to markers as units, and (3) using consistent and coordinated identification of units. We elaborated two of these categories. Observations supported sublevel distinctions between inconsistent identification (2a) and consistent yet only partially coordinated identification of units (2b). Evidence also supported a distinction between static (3a) and dynamic (3b) ways of coordinating length; we distinguish "integrated abstraction" (3b) from "nonintegrated abstraction" (3a) by examining whether students coordinate number and space schemes across multiple cases, or merely associate cases without coordinating schemes. (Contains 4 footnotes, 2 tables and 9 figures.)

Reports on two investigations examining students' thinking processes with regard to functions. Concludes that students often relied on a table or some variation of a table as a cognitive link advancing the development of their reasoning about underlying function relationships. (Author/MM)

Examines the difficulties 19 preservice elementary and middle school teachers experienced when creating and interpreting graphs in which speed is one of the variables. Identifies four cognitive obstacles held by the preservice teachers and provides excerpts of their graphical constructions and verbal interpretations. Discusses potential causes for the confusion. (Contains 21 references.) (Author/ASK)