The development of beginning mathematics teacher pedagogical content knowledge

Recent research efforts (Schmidt et al. in The preparation gap: teacher education for middle school mathematics in six countries, MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical knowledge and pedagogical knowledge. However, identifying the nature of the mathematical knowledge and the pedagogical content knowledge (PCK) required for effective teaching remains elusive (Ball et al. in J Teacher Educ 59:389–407, 2008). Building on the initial conceptual framework of Magnusson et al. (Examining pedagogical content knowledge, Kluwer, Dordrecht, pp 95–132, 1999), we examined the PCK development for two beginning middle and secondary mathematics teachers in an alternative certification program. The PCK development of these two individuals varied due to their focus on developing particular aspects of their PCK, with one individual focusing on assessment and student understanding, and the other individual focusing on curricular knowledge. Our findings indicate that these individuals privileged particular aspects of their knowledge, leading to differences in their PCK development. This study provides insight into the specific aspects of PCK that developed through the course of actual instructional practice, providing a lens for future research in this area.     

Microstructural analysis of negative anticipatory contrast: A reconsideration of the devaluation account

An animal’s appetitive behavior is not a fixed response to current stimulation but can be affected by the anticipation of future events. For example, rats regularly given access to a moderately valued solution followed by a higher value solution (e.g., 4 % sucrose → 32 % sucrose) consume less of the initial solution than in control conditions where the initial solution is not followed by a higher value solution (e.g., 4 % sucrose → 4 % sucrose). Previous analyses have suggested that this negative anticipatory contrast effect does not depend on the “expectation” of a valuable stimulus producing a functional devaluation of a currently available stimulus of lesser value. In a within-subjects anticipatory contrast procedure, this study revealed that both consumption and the mean size of licking clusters were smaller for a 4 % sucrose solution on days when it preceded 32 % sucrose than on days when 4 % preceded 4 %. Since lick cluster size typically bears a positive monotonic relationship with the concentration of palatable solutions, this reduction is indicative of a decrease in the palatability/hedonic value of the solution subject to contrast. As such, we provide direct evidence that negative anticipatory contrast does produce a functional devaluation of the solution, thus challenging prevailing theoretical assumptions.     

A timeline of the racialist movement in the United States: A teaching tool

Since the 1995 bombing of the Alfred R. Murrah Federal Building in Oklahoma City, academics and the general public have shown increased interest in white racial extremist and other right-wing radical groups. The interest in understanding any form of extreme intolerance requires locating the historical development of the ideas, beliefs, and actions espoused through the legislation of miscegenation in our nation's history and by extremist organizations. A chronology, used as a teaching tool, reviews the unique strands of extreme beliefs and actions and connects these understandings to the growth of racialist and extremist ideologies in the United States. This timeline provides a tool for instructors and other interested individuals in gaining an understanding of such groups by locating key developments within the laws as well as within the white racial extremist movement. Thus this chronology focuses on legislative acts and Supreme Court decisions that mirror our nation's early white racialist history. Additionally, this timeline also provides information about other social movement forces that may have affected the white racial extremist movement.     

Teaching a course on prisons: A design,some resources,and a little advice

We discuss our experience teaching undergraduate students about prisons. First, we describe the design of a course, including course goals, course content and some assignments. Then, we share the intellectual and logistical hurdles we have experienced and offer advice on how to overcome them for those planning to teach a seminar on prisons. Included is specific advice on how to successfully integrate prison tours as an experiential learning tool.     

Identifying Potential Test Item Misalignment Using Student Verbal Reports

The purpose of the present investigation was to identify the relationship among different indicators of uncertainty that lead to potential item misalignment. The item-based indicators included ratings of ambiguity and cognitive complexity. The student-based indicators included (a) frequency of cognitive monitoring per item, (b) levels of misinterpretation per item, and (c) levels of lack of confidence per item. Results indicate that item cognitive complexity was related to all student-based indicators even after controlling for students' performance on the item. Moreover, item ambiguity was related to levels of item misinterpretation but not to frequency of student cognitive monitoring or lack of confidence. The implications of these conclusions for identifying item misalignment are discussed in light of construct-relevant and construct-irrelevant sources of ambiguity.     

A Three-State Study of English Learner Progress

In this three-state study, the authors estimate the magnitudes of achievement gaps between English learner (EL) students and their non-EL peers, while avoiding typical caveats in cross-sectional studies. The authors further compare the observed achievement gaps across three distinct dimensions (content areas, grades, and states) and report patterns of EL–non-EL achievement gaps within and across states. The study findings suggest that linguistic barriers and long-term EL designation may contribute to the observed achievement gaps. The findings further suggest that the differences in the stringency of state reclassification criteria may influence the reported size of the EL and non-EL achievement gaps between states.     

(Mis)Measuring Developmental Math Success: Classroom Participants’ Perspectives on Learning

ABSTRACT

Poor completion outcomes in community colleges’ developmental education programs have spurred reforms in developmental education policies and practices in order to increase students’ chances of success. In the case of developmental math, the focus of this article, such changes include revisions to testing and placement policies, amendments to the intended curriculum, and restructuring of the format and sequencing of courses. However, the measures that have highlighted the inadequacies of developmental math are, in themselves, insufficient for assessing the effectiveness of reforms to developmental math. Drawing on interview data from a classroom-level study of a community college’s pilot reform initiative in developmental math, we explore the learning goals articulated by the instructors and a sample of students across four pre-algebra classrooms. Through our analysis of their goals, as well as the extent to which students reported accomplishing those goals, our research underscores the important distinction between course completion and learning. This study highlights the need to assess the effectiveness of developmental math coursework in ways that extend beyond completion rates.     

Noncognitive Variables and Student Learning in Extended Opportunity Programs and Services (EOPS)

ABSTRACT

The purpose of this mixed methods study was to investigate the relationship between participation in Extended Opportunity Programs and Services (EOPS) at California Valley College (CVC) (one of the 113 California Community Colleges in California) and several measures of student learning. An embedded survey design was developed using William Sedlacek’s noncognitive questionnaire (NCQ), items from the Community College Survey of Student Engagement (CCSSE), items based on Marcia Baxter Magolda’s epistemological reflection model of cognitive complexity, and items based on student learning outcomes for learning in EOPS. The survey had a 43.7% response rate. Students’ demographic characteristics, progress data, and grades were also collected. The survey concluded with four open-ended questions examining students’ perceptions about their learning. GPA (grade point average) as an outcome measure, and several NCQ scales were positively correlated with the Learning in EOPS Scale. Qualitative and mixed methods analyses extended statistical findings, highlighting the importance of positive outlook, positive self-concept, realistic self-appraisal, and support for learning. Finally, the study found that students’ academic and social involvement played a noteworthy role in students’ development, especially as related to cognitive complexity and learning in EOPS.     

Reading Comprehension Tests Vary in the Skills They Assess: Differential Dependence on Decoding and Oral Comprehension

Comprehension tests are often used interchangeably, suggesting an implicit assumption that they are all measuring the same thing. We examine the validity of this assumption by comparing some of the most popular reading comprehension measures used in research and clinical practice in the United States: the Gray Oral Reading Test (GORT), the two assessments (retellings and comprehension questions) from the Qualitative Reading Inventory (QRI), the Woodcock–Johnson Passage Comprehension subtest (WJPC), and the Reading Comprehension test from the Peabody Individual Achievement Test (PIAT). Modest intercorrelations among the tests suggested that they were measuring different skills. Regression analyses showed that decoding, not listening comprehension, accounts for most of the variance in both the PIAT and the WJPC; the reverse holds for the GORT and both QRI measures. Large developmental differences in what the tests measure were found for the PIAT and the WJPC, but not the other tests, both when development was measured by chronological age and by word reading ability. We discuss the serious implications for research and clinical practice of having different comprehension tests measure different skills and of having the same test assess different skills depending on developmental level.