Graphic abilities in relation to mathematical and scientific ability in adolescents

Background:?The study investigated a small range of cognitive abilities, related to visual-spatial intelligence, in adolescents. This specific range of cognitive abilities was termed ‘graphic abilities’ and defined as a range of abilities to visualise and think in three dimensions, originating in the domain of visual-spatial intelligence, and related to visual perception and the ability to represent space. The educational importance of graphic abilities has received minimal attention from the educational community and, consequently, plays a limited role in educational practice.

Purpose:?In order to understand the particular educational importance of this range of cognitive abilities, we investigated how graphic abilities are connected with the performance and the subject preference of adolescents in several academic areas. Our hypotheses were, first, that there is a high degree of correlation between developed graphic abilities and high performance in mathematics and science, and second, that there is a high degree of correlation between developed graphic abilities and personal subject preference in these two areas.

Sample:?The sample consisted of 60 14-year-old students (30 girls and 30 boys) attending a public secondary school in a small town in northern Greece. The entire sample had followed the same mathematics courses, which did not involve any geometry or spatial representation tasks.

Design and methods:?We identified and defined a specific range of three graphic abilities, related to visual-spatial intelligence, and we investigated these abilities in the sample through several visual-spatial tasks designed for the study and measured the sample's performance in these tasks. The degree of adolescents' graphic performance (that is, the performance in these visual-spatial tasks) was correlated with their performance in mathematics and science and with their subject preference (mathematics, science and language).

Results:?Our findings confirmed both hypotheses. A high degree of correlation was found between developed graphic abilities and high performance in mathematics, and a lower but still significant degree of correlation was found between developed graphic abilities and high performance in science. The findings support the second hypothesis as well, suggesting that children with developed graphic abilities reported that their favourite subject was mathematics and second favourite subject was science.

Conclusions:?The research suggested that there is a particular relation between the level of graphic abilities performance and children's performance and in preference for mathematics and science. That is, children with developed visual perception, visual thought and representational skills are actually better with numbers and physical concepts. This particular relation might be relevant to the overall cognitive development of children, especially with respect to the increasingly developing communication technologies, and it would seem to deserve more attention and extended research from the educational community. The authorial position is that education would gain from a better understanding of: the nature of graphic abilities, how we can develop this range of abilities and how the development of visual thought and graphic expression contributes to several curriculum subjects.     

Curricular orientations,experiences, and actions: Graduate students in science and mathematics fields work in urban high school classrooms

We examined curricular orientations that graduate students in science and mathematics fields held as they experienced urban high‐school science and mathematics classrooms. We analyzed how these educators (called Fellows) saw themselves, students, teachers, schools, education, and the sense they made of mathematics and science education in urban, challenging settings in the light of experiences they brought with them into the project and experiences they designed and engaged in as they worked in classrooms for 1 or 2 years. We used Schubert's (Schubert (1997) Curriculum: Perspective, paradigm, and possibility. New Jersey: Prentice‐Hall, Inc.) four curricular orientations—intellectual traditionalism, social behaviorism, experientialism, and critical reconstructionism—to analyze the Fellows' journals, and to explore ways in which the positions they portrayed relative to curriculum, instruction, assessment, social justice, discipline, student involvement, teacher's role, subject‐matter nature, etc., shaped and were shaped by who they were before and during their classroom work. Our qualitative analysis revealed various relationships including: experientialists engaged in more open‐ended projects, relevant to students, with explicit connections to everyday‐life experiences; social behaviorists paid more attention to designing “good” labs and activities that taught students appropriate content, led them through various steps, and modeled good science and mathematics; and critical reconstructionists hyped up student knowledge and awareness of science issues that affect students' lives, such as asthma and HIV epidemic. Categorizing orientations and identifying relationships between experiences, actions, and orientations may help us articulate and explicate goals, priorities, and commitments that we have, or ought to have, when we work in urban classrooms. © 2008 Wiley Periodicals, Inc. J Res Sci Teach 46: 1–26, 2009     

Where's the Math? Prospective Teachers Visit the Workplace

The integration of academic and vocational subject matter is offered in response to efforts to make the study of mathematics meaningful and engaging for all students,as well as aid in the preparation of a mathematically literate workforce. Yet,teachers often come to mathematics education with more ‘pure’ than ‘applied’ backgrounds making it difficult for them to draw upon their own experiences to make subject matter meaningful. This paper analyses prospective teachers' opportunities to connect subject matter with workplace contexts. It examines the degree of importance prospective teachers place on workplace connections and the ways in which they incorporate these connections in classroom lesson plans. Results suggest that given opportunities to visit workplace sites, it is not a trivial task for prospective teachers to: 1) make the mathematics in work explicit, and 2) keep the mathematics contextualized when designing activities and problems for students. These results have implications for teacher education and the support prospective teachers require in building networks connecting mathematics, pedagogy,and work. This revised version was published online in July 2006 with corrections to the Cover Date.     

Subject matter competence and the recruitment and retention of secondary science teachers

The purpose of this study was to investigate the relationship of subject matter knowledge in science and the patterns of entering, leaving, and remaining in the teaching profession among college graduates trained to be science teachers. To do this, National Teachers Examination (NTE) Biology and General Science test scores served as the proxy for science subject matter knowledge for a sample of 83 individuals initially certified to teach science in North Carolina during a 4-year period of time. The career patterns of these individuals as science teachers were documented and their work status was identified as nonrecruits, defectors, or career teachers. Using maximum likelihood logistical regression (MLOGIT) analysis, the relationship between career status (the dependent variable) and knowledge of science, race, gender, and the race and status (public or private) of the college from which they graduated was investigated. Of the 83 individuals in the analysis, 30 (36.1%) were identified as nonrecruits, 31 (37.3%) as defectors, and 22 (26.5%) as career teachers. Science subject matter knowledge was found to have a significant (p = .01) effect on the likelihood of being a nonrecruit versus a career teacher. The magnitude of this effect was also important, with the likelihood of being a nonrecruit increasing 120% for every 100-point increase in score on the NTE Biology and General Science tests. Science subject matter knowledge also had a significant effect (p = .05) on the likelihood of being a defector versus a career teacher, with the likelihood increasing 80% for every 100-point increase in NTE Biology and General Science scores. No other significant relationships were found.     

Mathematics and Science Performance of Primary School Students in the Netherlands

In this contribution the results of Dutch students of grades 3 and 4 in primary education on the TIMSS mathematics and science test are discussed. Despite severe criticism from subject matter experts on the test, the Netherlands score very high in the international ranking list. The nature of the criticism and the features of Dutch mathematics and science education are described to serve as a background for interpreting these surprising results.     

Children's Competencies in Process Skills in Kindergarten and Their Impact on Academic Achievement in Third Grade

Research Findings: The purpose of this study was to investigate the factorial structure of kindergarten children's mathematics and science process skills and the impact of children's competencies in process skills on their performance on mathematics and science achievement tests in 3rd grade. A subset of the Early Childhood Longitudinal Study–Kindergarten cohort data set (n = 8,731) was analyzed using multilevel structural equation modeling. Results demonstrated that science and mathematics process skills were highly related at the construct level but not at the indicator level, as was anticipated. Kindergarten children's competency in mathematics process skills was a strong predictor of their performance on science and mathematics achievement tests in the 3rd grade. However, children's competency in science process skills was only a significant predictor of their performance on a science achievement test in the 3rd grade. Moreover, socioeconomic status and gender were statistically significant predictors of process skills and performance on achievement tests. Practice or Policy: The findings of the present study suggest that the development of children's science and mathematics process skills should be supported utilizing integrated inquiry-based science and mathematics activities to help children recognize the connection between mathematics and science and to contribute to their science and mathematics achievement in later grades.     

Responding to a Relevance Imperative in School Science and Mathematics: Humanising the Curriculum Through Story

There has been a recent push to reframe curriculum and pedagogy in ways that make school more meaningful and relevant to students’ lives and perceived needs. This ‘relevance imperative’ is evident in contemporary rhetoric surrounding quality education, and particularly in relation to the junior secondary years where student disengagement with schooling continues to abate. This paper explores how teachers translate this imperative into their mathematics and science teaching. Interview data and critical incidents from classroom practice are used to explore how six teachers attempted to make the subject matter meaningful for their students. Four ‘Categories of Meaning Making’ emerged, highlighting key differences in how the nature of science and mathematics content constrained or enabled linkages between content and students’ lifeworlds. While the teachers demonstrated a commitment to humanising the subject at some level, this analysis has shown that expecting teachers to make the curriculum relevant is not unproblematic because the meaning of relevance as a construct is complex, subject-specific, and embedded in understanding the human dimensions of learning, using, and identifying with, content. Through an examination of the construct of relevance and a humanistic turn in mathematics and science literature I argue for an expanded notion of relevance.     

Gender differences in high school students' efficacy-expectation/performance discrepancies across four subject matter domains

This study investigated gender-related differences in the efficacy-expectation/performance discrepancies of high school students across four subject matter domains. Participants (N = 131) completed American College Testing (ACT) assessments in English, mathematics, reading, and science. Additionally, prior to each domain-specific test, students rated their perceived self-efficacy expectation for successful performance on that test. As anticipated, most students reporting greater efficacy expectation also tended to perform at higher levels, particularly in mathematics. Unexpectedly, the majority of student efficacy/performance discrepancy scores fell outside the congruent range in all content areas. Approximately equal numbers of male and female students inaccurately estimated their performance capabilities, with most noncongruent students tending to fall into either the extreme overestimation/underestimation categories. Implications are discussed regarding the application of these findings to refining educational methods, and enhancing self-motivation in educational settings.     

UNDERSTANDING STUDENTS�� OUT-OF-SCHOOL MATHEMATICS AND SCIENCE PRACTICE

This study examined standard 6 and 8 (Standards 6 and 8 are the sixth and eighth years, respectively, of primary level schooling in Kenya.) students’ perceptions of how they use mathematics and science outside the classroom in an attempt to learn more about students’ everyday mathematics and science practice. The knowledge of students’ everyday mathematics and science practice may assist teachers in helping students be more powerful mathematically and scientifically both in doing mathematics and science in school and out of school. Thirty-six students at an urban school and a rural school in Kenya were interviewed before and after keeping a log for a week where they recorded their everyday mathematics and science usage. Through the interviews and log sheets, we found that the mathematics that these students perceived they used outside the classroom could be classified as 1 of the 6 activities that Bishop (Educ Stud Math 19:179–191, 1988) has called the 6 fundamental mathematical activities and was also connected to their perception of whether they learned mathematics outside school. Five categories of students’ perceptions of their out-of-school science usage emerged from the data, and we found that 4 of our codes coincided with 2 activities identified by Lederman & Lederman (Sci Child 43(2):53, 2005) as part of the nature of science and 2 of Bishop’s categories. We found that the science these students perceived that they used was connected to their views of what science is.     

Using food as a tool to teach science to 3 grade students in Appalachian Ohio

The Food, Math, and Science Teaching Enhancement Resource (FoodMASTER) Initiative is a compilation of programs aimed at using food as a tool to teach mathematics and science. In 2007-2008, a foods curriculum developed by professionals in nutrition and education was implemented in 10 3(rd)-grade classrooms in Appalachian Ohio; teachers in these classrooms implemented 45 hands-on foods activities that covered 10 food topics. Subjects included measurement; food safety; vegetables; fruits; milk and cheese; meat, poultry, and fish; eggs; fats; grains; and meal management. Students in four other classrooms served as the control group. Mainstream 3(rd)-grade students were targeted because of their receptiveness to the subject matter, science standards for upper elementary grades, and testing that the students would undergo in 4(th) grade. Teachers and students alike reported that the hands-on FoodMASTER curriculum experience was worthwhile and enjoyable. Our initial classroom observation indicated that the majority of students, girls and boys included, were very excited about the activities, became increasingly interested in the subject matter of food, and were able to conduct scientific observations.     

How pre-service teachers observe teaching on video: Effects of viewers’ teaching subjects and the subject of the video

As critical component of teachers’ expertise, professional vision should be developed during teacher education. Professional vision draws on subject specific and generic knowledge, however, little is known about the knowledge interplay. This study systematically investigated pre-service teachers’ (n = 32 majoring in mathematics/science; n = 56 in social sciences/humanities) professional vision as elicited by videos of various subjects. Such a design allows studying the relevance of subject matter for professional vision. We found evidence for different professional visions among pre-service teachers majoring in different fields, indicating that—beyond knowledge acquisition—subject-specific socializations may result in distinct sets of shared beliefs and values.     

Developing Self-Efficacy in Teaching Mathematics: Pre-Service Teachers’ Perceptions of the Role of Subject Knowledge

ABSTRACT

Two major concerns in mathematics teacher education are the role of subject matter knowledge and the development of self-efficacy in pre-service teachers. This article brings these issues together in an exploration of the interaction between pre-service teachers’ perceptions of their subject matter knowledge and their accounts of university and placement experiences as potential sources of self-efficacy. Reporting on a group of ten pre-service teachers in Norway, we explore variations in the ways in which they perceived the role of subject knowledge in relation to experience, particularly “mastery experiences”, over a period of nearly two years. We suggest that recognition of the role of “understanding why” in mathematics is crucial in the experience of mastery, and that there is a need to focus more on the role of subject matter knowledge in all sources of self-efficacy in teaching mathematics.     

Cognitive Style and Pupil Learning Preferences

A total of 78 12‐year‐old pupils from four secondary comprehensive schools were given the computer‐presented Cognitive Styles Analysis, which determined the position of each pupil on two learning style dimensions: Wholist‐Analytic and Verbal‐Imagery. They were also given individually a structured interview questionnaire to assess their learning preferences in English and science in terms of: (a) mode of working, (b) task outcomes and (c) social context. The English and science teachers were asked to rate the achievement level of the pupils in their subject and this was used as an index of ability. The main findings were as follows, (a) Preferred Mode of Working: As expected, there was a tendency for Imagers to use pictures and Verbalisers to prefer writing, and this increased with ability and what the subject would naturally allow. There was evidence that lower ability pupils were more constrained by the usual format for the subject than were those of higher ability, (b) Social Context: Overall, Group or Pair was preferred to Individual work. Group work was particularly liked by Wholists and especially by lower ability Wholist‐Imagers. Individual work was least disliked by Analytics, particularly in the case of higher ability Verbalisers (c) Task Outcomes. For open versus closed tasks, open tasks were preferred by lower ability pupils, while high‐ability Wholist‐Imagers preferred closed tasks. The findings were discussed in terms of their implications for current practice.     

Reconstructing elementary teacher candidates' understanding of mathematics and science content

This paper examines the mathematics and science content knowledge of elementary teacher candidates. Data are presented which demonstrate that many elementary teacher candidates enter teacher education seriously deficient in their understanding of the subject matter they will teach to elementary students. The authors argue that these candidates are weakly prepared in content because of deficiencies in the pedagogy practiced in traditional didactic mathematics and science courses. They describe a conceptual approach to teaching mathematics and science content and contrast this with a didactic approach. Data are presented which demonstrate that these conceptual approaches significantly improved novice teachers understanding of content.     

Some methods for examining content structure and cognitive structure in instruction 1

Reform in science and mathematics curricula has moved from rote learning of facts and computation skills toward learning a structure of a subject matter. While the reasons for this shift, such as greater understanding, transfer and intellectual excitement are admirable, there is little empirical evidence to support them. A first step in examining such claims is to develop methodology for representing structure in the to‐be‐learned instructional material and in students' memories. The purposes of this paper, then, are to present (a) a method for examining a subject‐matter structure in prose materials, (b) methods for examining a subject‐matter structure in students’ memories, and (c) data bearing on the validity of structural interpretations of these measures. If these structures can be represented objectively and independently — even if not in a complete form or error free — a beginning has been made in validating the reasons for teaching structure.     

Double Visions: Educational Technology in Standards and Assessments for Science and Mathematics

For educational technology integration in content disciplines to succeed, teachers and teacher educators need clear standards delineating why, how, where, and how much educational technology they should include in their teaching. This paper examines the visions offered by current science, mathematics, and educational technology standards for educational technology integration in K-12 schools. Since national assessments exert a profound influence on what teachers and students choose to teach and learn, the vision of educational technology use supported by national assessments is also examined. The National Council of Teachers of Mathematics Standards (NCTM, 2000. Principles and Standards for School Mathematics. Retrieved April 6, 2002 from http://standards.nctm.org), the National Science Education Standards (National Research Council (NRC) 1996. National Science Education Standards. Available at http://books.nap.edu/catalog/4962.html), and the National Educational Technology Standards (International Society for Technology in Education (ISTE) 2000. National Educational Technology Standards for Students: Connecting Curriculum and Technology, ISTE, Eugene, Oregon) provide different visions of educational technology use in the classroom. In addition, the current technology use policies for national assessments in science and mathematics, in particular the college admission tests (ACT, SAT I and SAT II subject area tests), Advanced Placement (AP) course assessments, and the Praxis Series assessments indicate that while mathematics assessments often recommend or require the use of educational technology, few science assessments permit the use of educational technology by students. Recommendations are offered for science educators regarding teacher preparation for the technology-rich classrooms of the future.     

Examining the relationships among academic self-concept,instrumental motivation,and TIMSS 2007 science scores: a cross-cultural comparison of five East Asian countries/regions and the United States

Many American authors expressed their concern that US competitiveness in science, technology, engineering, and mathematics (STEM) is losing ground. Using the Trends in International Mathematics and Science Study (TIMSS) 2007 data, this study investigated how academic self-concept and instrumental motivation influence science test performance among East Asian and American students. Jackknife regression modelling indicated that in East Asia science competency is not tied to enjoying science or estimated ability while in the US both variables are negatively correlated with performance. Additionally, the test performance of the East Asian students does not seem to be boosted by the perception of the role of science in career advancement, but this perception could significantly predict the test performance of their American counterparts. It is the conviction of the author that these findings related to student-level factors could lead to practical implications for educational policies and pedagogical strategies, such as placing emphasis on daily applications of science.     

Reflections on the Dilemmas and Tensions in Mathematics Education Courses for Student Teachers

The paper outlines the dilemmas and paradoxes faced by lecturers and student teachers as they interact in a mathematics education subject that deals with both mathematics as a discipline and as a language, and with appropriate pedagogies for the teaching and learning of mathematics in primary schools. For the lecturer there is a tension between comforting and challenging the students. Are they to be wooed into a more positive attitude to mathematics, at the cost of avoiding the complexity of the discipline; or are they to be challenged by the unique character of mathematics, at the risk of alienation and exclusion? The latter often returns students to their original perception of maths as a harsh and unforgiving subject which is beyond their capabilities as they struggle with unfamiliar concepts and the discomfort of ‘not knowing’. For student teachers there is, paradoxically, a desire to ‘instil understanding’ when they themselves may not fully understand. They often idealise what is good practice but deny it in their own learning.     

Education reform and subject matter knowledge

This article raises the question of what K–12 teachers need to know to teach mathematics and science well. It begins by examining reform proposals for K–12 science and mathematics teaching with an eye toward defining what good teaching practice consists of. It then examines a wide range of literature to delineate the varieties of knowledge that have been associated with this kind of teaching. While the focus is on subject matter knowledge, the article addressed the character of that knowledge rather than the content of that knowledge. Types of knowledge identified in the literature include conceptual understanding of the subject, pedagogical content knowledge, beliefs about the nature of work in science and mathematics, attitudes toward these subjects, and actual teaching practices with students. The literature is incomplete with respect to which of these is relatively more or relatively less important. © 1998 John Wiley & Sons, Inc. J Res Sci Teach 35: 249–263, 1998.