Jennifer Wilhelm

Implementation Research as a Means to Link Systemic Reform and Applied Psychology in Mathematics Education

To link reform efforts in science and mathematics education to the research on student cognition, researchers must engage in an understanding of systemic change. This article reports on an initiative linking a university research team and an urban high-school mathematics department in efforts to improve student learning. The article explores the ideas of systemic reform and implementation research in which researchers partner with teachers and schools over sustained periods of time to implement reform initiatives. It reports on the implementation of an 8-week replacement unit in all Algebra I classes and describes its results. It also provides an example of student and teacher learning with technology on a central concept of rate of change and discusses how those interviews illustrate differences in student and teacher learning. We discuss how cognitive research needs to be transformed to be successfully applied toward improvement within the challenges and opportunities of urban schools.

Gender Differences in Lunar-Related Scientific and Mathematical Understandings.

This paper reports an examination on gender differences in lunar phases understanding of 123 students (70 females and 53 males). Middle‐level students interacted with the Moon through observations, sketching, journalling, two‐dimensional and three‐dimensional modelling, and classroom discussions. These lunar lessons were adapted from the Realistic Explorations in Astronomical Learning (REAL) curriculum. Students’ conceptual understandings were measured through analysis of pre‐test and post‐test results on a Lunar Phases Concept Inventory (LPCI) and a Geometric Spatial Assessment (GSA). The LPCI was used to assess conceptual learning of eight science and four mathematics domains. The GSA was used to assess learning of the same four mathematical domains; however, the GSA test items were not posed within a lunar context. Results showed both male and female groups to make significant gains in understanding on the overall LPCI test scores as well as significant gains on five of the eight science domains and on three of the four mathematics domains. The males scored significantly higher than the females on the science domain, phase—Sun/Earth/Moon positions, and on the mathematics domain geometric spatial visualisation. GSA results found both male and female groups achieving a significant increase in their test scores on the overall GSA. Females made significant gains on the GSA mathematics domains, periodic patterns and cardinal directions, while males made significant gains on only the periodic patterns domain. Findings suggest that both scientific and mathematical understandings can be significantly improved for both sexes through the use of spatially focused, inquiry‐oriented curriculum such as REAL.

Projecting rate of change in the context of motion onto the context of money

This paper reports a study designed to probe the abstraction ability that US Algebra I students can achieve in moving the concepts rate of change and accumulation between motion and money contexts. The Algebra I students used the technologies motion detectors and Interactive Banking software during a replacement unit focused on slope, ratio, and rate of change. Clinical interviews were conducted with four students at the end of the replacement unit testing their abstraction ability across the two contexts. Results revealed that some students do not have to completely understand the relationship between rate of change and accumulation within a single context in order to be able to understand and project the concepts separately into multiple contexts. Using multiple rate of change contexts allowed the learners the opportunity to see the ‘like’ in the contextually unlike situation, enabling them to project these concepts into novel situations. Few research studies have examined students’ understanding of rate of change outside of the motion context, and therefore no studies, to the authors’ knowledge, have explored students’ abstraction ability between two different rate of change contexts. This paper reports a study designed to probe the abstraction ability that students can achieve in moving between the motion and money contexts.

Students' Stories: Adolescents Constructing Multiple Literacies through Nature Journaling.

The integration of nature studies within language arts instruction offers multiple possibilities for guiding students toward close readings of literature, their changing selves, natural phenomena, and the world around them. The authors document their own rediscovery of nature study and what happened when environmental observations were incorporated into the lives of 67 seventh-grade students as an alternative mode of literacy instruction.

Pre-Service Mathematics Teachers Become Full Participants in Inquiry Investigations.

Research is described concerning the effectiveness of inquiry-based laboratory environments created in US mathematics/science education programme courses. Laboratory projects were conducted using a framework that allowed pre-service teachers to explore, analyse, and communicate ‘investigable’ realms of physical phenomena. Goals were for pre-service teachers to experience the value of learning in an inquiry-enhanced environment and to engage in contextualized mathematics so they would utilize this instruction in their future classrooms. It is proposed that inquiry-based laboratories are needed within the mathematics classroom in order to allow students the opportunity to contextualize, to connect to other disciplines, and to experience mathematical concepts. Pre-service teachers were expected to pursue conjectures, collect data, think critically, and communicate findings. This qualitative research shows how the use of inquiry can complement the learning of mathematical content and educational strategies for pre-service teachers. Results provide detailed information for teacher educators regarding instructional design of contextualized mathematical inquiry.

Examining Differences Between Preteen Groups’ Spatial-Scientific Understandings: A Quasi-experimental Study

ABSTRACT The authors examined differences between 2 groups of students’ spatial-scientific reasoning from pre- to postimplementation of an Earth/Space unit. Using a quasi-experimental design, researchers explored how instructional method and gender affected learning. Treatment teachers employed an integrated science, technology, engineering, and mathematics curriculum while the control teacher implemented her regular Earth/Space unit. The Geometric Spatial Assessment (GSA), the Purdue-Spatial Visualization Rotation Test, and the Lunar Phases Concept Inventory (LPCI) were used to assess learning. Experimental groups made gains on periodicity LPCI domains while the control made gains on geometric spatial visualization LPCI domains. Only girls made gains on GSA items. This is the first quasi-experimental study to examine students’ spatial reasoning as they participate in Earth/Space units and to discover genders role in this spatial development.