Modeling Change in Student Attitude Toward and Beliefs About Mathematics

Abstract

The authors used data from the Longitudinal Study of American Youth to investigate variables related to change in students' attitude toward and beliefs about mathematics in middle school and high school. Using hierarchical linear modeling techniques, the authors modeled variation in students' rate of change with variables associated with student characteristics, instructional experiences, and environment. They also identified variables that differentially affect change at different levels of secondary school (i.e., middle school vs. high school) and for different affective dimensions (i.e., attitude toward mathematics, beliefs about the social importance of mathematics, and beliefs about the nature of mathematics). Results showed a substantial negative change in students' attitudes toward and beliefs about the social importance of mathematics throughout secondary school. However, students' notions of the nature of mathematics did not change throughout secondary school. The authors identified variables related to change and found that they differed according to the level of secondary school and affective dimensions.     

The Link Between Middle School Mathematics Course Placement and Achievement

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students’ mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth‐grade algebra and geometry course placements are academically selective, but considerable between‐school variation exists in students’ odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness.     

A Longitudinal Assessment of Antecedent Course Work in Mathematics and Subsequent Mathematical Attainment

Abstract

Using six waves of data (Grades 7–12) from the Longitudinal Study of American Youth, the author examined the effects of different mathematics course work (pre-algebra, geometry, calculus) on subsequent achievement in, and attitude toward, mathematics, with partial adjustment for student background characteristics. Results showed that in the early grades of high school, algebra courses significantly affected mathematics achievement. Mathematics course work, however, did not play a significant role in mathematics achievement in the middle grades of high schools. There was a “harvest” of significant course-work indicators in the later grades of high school; every advanced mathematics course affected mathematics achievement. Many course-work effects were substantial even after accounting for variables such as prior mathematics achievement and socioeconomic status.     

Early acceleration of students in mathematics: Does it promote growth and stability of growth in achievement across mathematical areas?

Using data from the Longitudinal Study of American Youth (LSAY), the present study examined whether early acceleration of students into formal algebra at the beginning of middle school promoted evident growth in different mathematical areas (basic skills, algebra, geometry, and quantitative literacy) and stable growth across these mathematical areas. Results of multivariate multilevel analyses showed that low achieving students who were accelerated into formal algebra grew faster than not only low achieving students who were not accelerated but also high achieving students who were not accelerated. The rates of growth of accelerated low achieving students were even comparable to those of accelerated high achieving students. All low achieving students showed the same potential to take advantage of early acceleration regardless of their individual, family, and school characteristics. Early acceleration also promoted stability of growth across mathematical areas, and this stability was not dependent on student and school characteristics.     

Perceived Competencies of Elementary and Special Education Teachers

Abstract

With a renewed emphasis on student achievement, school improvement, and shared decision making, and in an effort to create and maintain effective schools, researchers try to delineate those characteristics that positively affect student learning and behavior. In exploring the different views that persons have regarding the characteristics of effective schools, the authors reviewed research studies to identify factors considered to be determinants of an effective school. Specific topic areas examined were the views of teachers, parents, and administrators regarding effective schools, as well as an examination of the related research literature. Consistent across the 4 areas was the importance of a positive school climate and strong leadership. Implications for educational leaders are provided.     

The influence of extracurricular activities on middle school students’ science learning in China

ABSTRACT

Informal science learning has been found to have effects on students’ science learning. Through the use of secondary data from a national assessment of 7410 middle school students in China, this study explores the relationship among five types of extracurricular science activities, learning interests, academic self-concept, and science achievement. Structural equation modelling was used to investigate the influence of students’ self-chosen and school-organised extracurricular activities on science achievement through mediating interests and the academic self-concept. Chi-square tests were used to determine whether there was an opportunity gap in the student’s engagement in extracurricular activities. The students’ volunteer and school-organised participation in extracurricular science activities had a positive and indirect influence on their science achievement through the mediating variables of their learning interests and academic self-concept. However, there were opportunity gaps between different groups of students in terms of school location, family background, and especially the mother’s education level. Students from urban areas with better-educated mothers or higher socioeconomic status are more likely to access diverse science-related extracurricular activities.     

Shape Makers

Summary

Professional standards for school mathematics recommend that dynamic geometry programs such as the Geometer's Sketchpad can and should be used to enhance student learning of geometry. This article illustrates how a geometry computer microworld containing screen manipulable, dynamically transformable shape-making objects can promote the development of powerful geometric reasoning. Also described is the overall context and factors that should guide mathematics educators' design and use of instructional technology.     

Secondary school students who drop out of school in rural Pakistan: The perspectives of fathers

ABSTRACT

Background: The problem of students dropping out of school is one of the barriers to improving educational outcomes in poor and developing countries.

Purpose: This small scale, in-depth study sought to explore the phenomenon of students who drop out from secondary education, through the perspectives of fathers of such students in a rural district of Pakistan.

Method: Primary data were collected through detailed, individual interviews with 14 fathers whose sons had dropped out from secondary education. The study adopted a framework involving push and pull factors to analyse qualitatively the processes and examine the reasons for dropping out that prevailed inside and outside school.

Findings: The analysis suggested that, from the perspectives of the fathers, family poverty, poor academic performance and issues relating to teachers’ engagement with teaching at school were main factors involved in a student dropping out of school.

Conclusions: The findings from this small scale, detailed analysis of data draw attention to the issues arising from a tension in mainstream teachers’ educational roles in and beyond the school. It further highlights the need for greater investment in secondary education, in order to help to reduce rates of student drop out in the remote rural areas of Pakistan.     

What's in a teacher test? Assessing the relationship between teacher licensure test scores and student STEM achievement and course-taking

We investigate the relationship between teacher licensure test scores and student test achievement and high school course-taking. We focus on three subject/grade combinations—middle school math, ninth-grade algebra and geometry, and ninth-grade biology—and find evidence that a teacher's basic skills test scores are modestly predictive of student achievement in middle school math and highly predictive of student achievement in high school biology. A teacher's subject-specific licensure test scores are a consistent and statistically significant predictor of student achievement only in high school biology. Finally, we find little evidence that students assigned to middle school teachers with higher basic-skills test scores are more likely to take advanced math and science courses in high school.     

Threading mathematics through symbols,sketches, software,silicon, and wood: Teachers produce and maintain cohesion to support STEM integration

ABSTRACT

This classroom-based investigation sought to document how, in real time, STEM teachers and students attempt to locate the invariant mathematical relations that are threaded through the range of activities and representations in these classes, and how highlighting this common thread influences student participation and learning. The authors conducted multimodal discourse analyses of teacher–student interactions during multiday observations in 3 urban high school STEM classes. The focal lessons were in electrical engineering and mechanical engineering (within Project Lead the Way), and precollege geometry. Across 3 cases, teachers and students actively built and maintained cohesion of invariant mathematical relations across activities and representations. Pre- and postlesson interviews revealed that teachers intentionally managed cohesion to provide the continuity across the curricular activities that teachers believed would promote student understanding. The findings contribute to ways of fostering STEM integration and ways of grounding abstractions to promote meaning making and transfer.     

Enhancing Secondary School Instruction and Student Achievement: Replication and Extension of the My Teaching Partner-Secondary Intervention

Abstract

My Teaching Partner-Secondary (MTP-S) is a web-mediated coaching intervention, which an initial randomized trial, primarily in middle schools, found to improve teacher–student interactions and student achievement. Given the dearth of validated teacher development interventions showing consistent effects, we sought to both replicate and extend these findings with a modified version of the program in a predominantly high school population, and in a more urban, sociodemographically diverse school district. MTP-S produced substantial gains in student achievement across 86 secondary school classrooms involving 1,194 students. Gains were robust across subject areas and equivalent to moving the average student from the 50th to the 59th percentile in achievement scores. Results suggest that MTP-S can enhance student outcomes across diverse settings and implementation modalities.     

The Application of Theories of Children to Disciplinary Practice

Shortages of middle-level teacher candidates may cause teacher educators to recruit candidates by focusing on what attracts and discourages candidates about teaching at the middle level. The authors used a survey approach (n = 110) to investigate why preservice middle school and high school teachers and in-service middle school teachers chose the middle grades. The results included ten common reasons that the respondents favored the middle grades and ten major concerns about this level. Three attractions to the middle grades—student age, content level, and employment market—and common beliefs about positive teacher-student relationships and students' maturity may guide teacher educators in their efforts to increase middle grades program enrollment.     

Adding up or Down: A Discussion

ABSTRACT

Increased access to algebra was a focal point of the National Mathematics Advisory Panel's 2008 report on improving mathematics learning in the United States. Past research found positive effects for early access to algebra, but the focus on average effects may mask important variation across student subgroups. The author addresses whether these positive effects hold up when the analysis is expanded to examine effect heterogeneity. Using a nationally representative sample of eighth-grade students in 1988, the author examined sensitivity of findings to methods for selection bias adjustment, heterogeneity across the propensity to take algebra in Grade 8, and across schools. The findings support past research regarding positive benefits to Grade 8 algebra and are consistent with policies that increase access to algebra in middle school.     

Cognitive and Motivational Effects of Seeking Academic Assistance

Abstract

The instructional needs of a student who sought assistance for his continuing academic difficulties within his high school setting were examined. The authors evaluated how his perception of his academic and motivational performances compared with the perceptions of his parents, school officials, and those professionals who conducted 3 psy-choeducational evaluations for a learning disability during his middle and high school years. None of the 3 evaluations considered the quality of the student's classroom instruction, school grading practices, or study strategies, all of which increased his vulnerability to risk. Discussion focuses on the question of whether the student's negative learning and motivational profiles might have improved if his school's attempts to provide academic assistance had adopted a broader and more comprehensive focus.     

Factors of Professional Learning Community Implementation and Effect on Student Achievement

ABSTRACT

Professional learning communities (PLCs) promote collaboration among school personnel in an effort to stimulate student learning. Using data obtained from a larger statewide initiative in Missouri, the current study examined data from 181 schools (102 elementary schools, 32 middle schools, 41 high schools, and 6 other schools, average of 428.76 students) to determine (a) the factors that can be used to assess the effects of PLCs, (b) how well PLCs relate to student achievement, and (c) the extent to which teams differentially implement the factors. An exploratory factor analysis and confirmatory factor analyses resulted in two broader constructs that represented PLC attributes, collaborative leadership process and data-driven systems for learning, both of which correlated with student achievement and together provided unique variance in mathematics beyond school variables and achievement scores from before the PLC began. Directions for future research and implications for practice are discussed.     

Adoption of flipped learning in social humanities education: the FIBER experience in secondary schools

ABSTRACT

FIBER (Flipped Issue-Based Enquiry Ride) is a teacher-facilitated interactive pedagogic framework that the authors propose to integrate flipped learning into social humanities education. This paper reports a quasi-experimental study (with mixed methods) which examined the pedagogic effectiveness of FIBER in the authentic setting of formal curriculum learning and teaching. The study involved totally 611 Secondary-4 students from academically top, middle and bottom schools in Hong Kong. In comparison with the conventional issue-based enquiry learning approach, FIBER had different intensity of positive effects on the high, moderate, and low academic-achieving student participants. This paper provides researchers and educational practitioners with empirical evidence for supporting wider adoption of FIBER in social humanities education, as well as harnessing flipped learning in formal schooling. Apart from discussing the benefits, the authors also underline the challenges of FIBER and suggest future work.     

The practices of student network as cooperative learning in Ethiopia

ABSTRACT

Student network is a teaching strategy introduced as cooperative learning to all educational levels above the upper primary schools (grade 5 and above) in Ethiopia. The study was, therefore, aimed at investigating to what extent the student network in Ethiopia is actually practiced in line with the principles of cooperative learning. Consequently, data collected from 156 secondary and 315 upper primary school teachers revealed that the student network is rarely practiced in line with the principles of cooperative learning. And this was found with statistically significant differences between the upper primary and secondary schools. The upper primary schools seem better in practicing the student network in line with the principles of cooperative learning than the secondary school. Accordingly, the study concluded that, albeit the student network remained a canon strategy to improve students’ learning in Ethiopia and its practices are supposedly recommended to be in line the principles of cooperative learning, challenges related to parents, students, school administration and teachers seem to cripple its smooth practice in line with the cooperative learning principles.     

Prospective teachers’ teaching experience: teacher learning through the use of video

Background: Future teachers need to observe, interpret and analyse teaching during the initial teacher education period. The use of videoed teaching and learning in teacher education promotes reflection, and analysing videos of teaching is helpful in learning effective classroom practices that prospective teachers mostly do not have the chance to observe during fieldwork experiences. The analysis of videos of teaching can be seen as a way to enhance the development of prospective teachers’ professional vision, which, in turn, improves instruction. Purpose: The purpose of this study was to examine prospective teachers’ reflections on video examples depicting their own teaching experiences. It aimed to create a professional development environment to facilitate the prospective teachers’ reflection on their own videos and those of their peers to improve their professional vision. Sample: This study was conducted with over 200 (in 31 groups) third-year prospective mathematics teachers in a university in Western Turkey. The student teachers, receiving training to teach first- to fourth-grade elementary school pupils, were taking a teaching methods course. Design and methods: In the first week of the semester, the student teachers, working in groups, were assigned mathematics topics to teach the elementary school pupils. During the semester, each group prepared by trying out their activities in front of other student teachers in other groups. At the end of the semester, one student teacher from each group presented a short lesson related to their mathematical topic to the elementary school pupils. This lesson was videotaped, then later it was watched and discussed by the student teachers. Of the student teachers who undertook the teaching in the videos, 22 volunteers agreed to be interviewed. All groups of student teachers provided written reflections on their experience. Selected videos of the class discussions about the videos of teaching were also used for triangulation. The data were analysed to identify the issues the prospective teachers reflected upon. A content analysis technique was employed. Results: The data indicated that the prospective teachers were able to reflect on several issues related to effective teaching, connect their theoretical knowledge to their practice and consider issues related to pupil learning and difficulties. Conclusion: The findings suggested that the use of video, together with discussions between the student teachers, had the potential to create promising learning opportunities for prospective teachers.     

Identifying pathways of teachers’ PCK development

This paper describes a method of analysing teacher growth in the context of science education. It focuses on the identification of pathways in the development of secondary school teachers’ pedagogical content knowledge (PCK) by the use of the interconnected model of teachers’ professional growth (IMTPG).The teachers (n = 12) participated in a one-year action research project focused on their individual concerns related to teaching science. The use of the IMTPG revealed that teachers use different pathways of learning to develop different aspects of their PCK. For each PCK component, three distinct pathways could be identified, two of which clearly were associated with professional growth. When examining these two pathways in detail, it was found that (1) teachers learned about new instructional strategies and assessment methods mostly through literature reviews and discussions with peers and (2) teachers who analyzed and reflected on student learning as it happened in their classrooms developed understandings that helped them to select and apply instructional strategies to further promote student learning. Both the analytical method as well as the identification of the different developmental pathways help to better understand teacher development in the context of classroom practices.