Investigation of the computer experiences and attitudes of pre-service mathematics teachers: new evidence from Turkey

This study aimed to investigate the experiences of pre-service mathematics (PSM) teachers with computers and their attitudes toward them. The Computer Attitude Scale, Computer Competency Survey, and Computer Use Information Form were administered to 180 Turkish PSM teachers. Results revealed that most PSM teachers used computers at home and at Internet cafes, and that their competency was generally intermediate and upper level. The study concludes that PSM teachers' attitudes about computers differ according to their years of study, computer ownership, level of computer competency, frequency of computer use, computer experience, and whether they had attended a computer-aided instruction course. However, computer attitudes were not affected by gender.     

Linking Teacher Instruction and Student Achievement in Mathematics: The Role of Teacher Language

Although high-quality early educational environments are thought to be related to the growth of children’s skills in mathematics, relatively little is known about specific aspects of classroom instruction that may promote these abilities. Data from a longitudinal investigation were used to investigate associations between teachers’ language while teaching mathematics and their students’ growth in mathematical skill during the 2nd grade. Specifically, the extent to which mathematics lessons included cognitive-processing language (CPL)—instruction that is rich in references to cognitive processes, metacognition, and requests for remembering—was related to changes in students’ math achievement. Demonstrating the role of the language of instruction, the findings indicated that children whose 2nd-grade teachers included greater amounts of CPL during instruction evidenced greater growth in math fluency and calculation than did their peers whose teachers employed lower levels of CPL.     

The suppression role of positive affect on students’ science achievement in East Asia: the example of Taipei

This study focuses on “high achievement but low motivation” phenomenon that is prevalent in East Asian countries and districts, and uses eighth graders in Taipei that participated in TIMSS 2007 as an example to examine the direct and indirect effects of academic motivation, positive affect, and instruction on science achievement. Confirmatory Factor Analysis and Structural Equation Modeling were employed to test measurement and structural models and indicated a good fit of the models to the data. The results showed that expectancy and value in science and inquiry-based instruction are three significant and positive predictors of students’ positive affect toward science. In addition, expectancy, positive affect, and three types of instruction all significantly predicted students’ science achievement after the number of books at home and mother’s education were controlled. However, inquiry-based and practice-based instructions were negative predictors whereas traditional instruction was positive. The suppression role of the positive affect was partially supported between academic motivation and science achievement.     

The effectiveness of direct graphical entry of topological and geometric data

A study is described that was carried out to determine the feasibility of making interactive graphics terminals available for computer-aided instruction (CAI) in engineering and science courses.     

Mainstreams and Perspectives in Research on Learning (Mathematics) From Instruction

Le domaine de l’enseignement et de l’apprentissage des mathématiques est un exemple des plus représentatives de l’orientation des recherches sur l’apprentissage et l’instruction dans les différentes matières. Au cours du dernier quart de siècle écoulé, ce champ de questionnement a produit nombre d’investigations qui résultent d’une conception de l’apprentissage des mathématiques comme construction sociale de la signification et de la comprehension basée sur la modélisation de la réalité. Dans cet article, quelques tendances majeures et perspectives de recherche s.0s principalement aux Etats‐Unis et en Europe. Il y sera montré que d’une part, les investigations empiriques ont déjà produit des blocs de construction pour l’élaboration d’une théorie de l’apprentissage des mathématiques à partir d’instructions mais que, d’autre part, des questions et des problèmes majeurs requièrent d’être démêlés par la poursuite d’investigations. Ceci y sera documenté de façon exemplaire en utilisant comme cadre de référence quatre composants principaux d’une théorie de l’apprentissage des mathématiques à partir d’instructions: une théorie de l’expertise visant à analyser des compétences dans un domaine; une théorie de l’acquisition tendant à comprendre et expliquer les processus d’apprentissage qui conduisent à la réalisation de compétences; une théorie de l’intervention, focalisée sur la conception d’environnements enseignement‐apprentissage puissants pour provoquer ces processus d’acquisition; et une théorie de l’évaluation s’adressant au développement de méthodes et techniques pour la construction et l’application d’outils et instruments d’évaluation. The domain of mathematics learning and teaching is one of the most representative examples of the subject‐matter orientation in research on learning and instruction. During the last quarter of the past century this field of inquiry has produced a vast body of investigations, resulting in an enriched conception of mathematics learning as involving the (social) construction of meaning and understanding based on modeling of reality. In this article some of the main trends and perspectives in the field of research on mathematics learning and instruction are discussed, and illustrated with examples of empirical research, mainly carried out in Europe and the United States. It will be shown that, on the one hand, the available empirical investigations have already yielded substantial building blocks for the elaboration of a theory of mathematics learning from instruction, but that, on the other hand, major issues and problems need to be unravelled by continued inquiry. This will be documented in an exemplary way, using as a frame of reference four main components of a theory of learning mathematics from instruction: a theory of expertise, aiming at analysing competence in a domain; a theory of acquisition, attempting to understand and explain the processes of learning that are conducive to the attainment of competence; a theory of intervention, focusing on the design of powerful teaching–learning environments for eliciting those acquisition processes; and a theory of assessment, addressing the development of methods and techniques for the construction and application of assessment tools and instruments.     

Videodisc instruction in science and mathematics: Implications for media research and instructional design

This article summarizes research conducted over the last seven years on videodisc instruction in science and mathematics. Research findings, as well as the instructional design principles used to create programs, have direct implications for the general debate over media and its effects on learning. The array of studies conducted with the videodisc programs indicates that the medium is very cost effective. High quality instruction can be presented reliably and with much less human effort than traditional methods of instruction. By using videodiscs, developers are also able to exploit the strong graphic features of the medium, thus allowing carefully-designed visual images to play a key role in the instruction. Empirical support for non-text presentations along with examples of the graphics used in the science and mathematics programs are discussed.     

College-level instruction: derived relations and programmed instruction

Recent research has demonstrated the effectiveness of programmed instruction that integrates derived relations to teach college-level academic material. This method has been demonstrated to be effective and economical in the teaching of complex mathematics and biology concepts. Although this approach may have potential applications with other domains of college learning, more studies are needed to evaluate important technological variables. Studies that employ programmed instruction are discussed in relation to future directions for research.     

初中生数学焦虑的调查及其调控研究

数学焦虑既是心理科学研究的对象,又与教育、教学,特别是学科教学密切相关。本文调查发现:部分初中生存在过度的数学焦虑,并且在年级、性别等维度上具有明显差异;教师的评价方式、课堂气氛、数学考试是形成数学焦虑的主要原因。运用三条教学策略的实验研究表明,数学焦虑是可以调控的,而且数学焦虑的缓解对学生数学成绩的提高有一定的促进作用。     

Teaching for adaptive expertise in biomedical engineering ethics

This paper considers an approach to teaching ethics in bioengineering based on the How People Learn (HPL) framework. Curricula based on this framework have been effective in mathematics and science instruction from the kindergarten to the college levels. This framework is well suited to teaching bioengineering ethics because it helps learners develop “adaptive expertise”. Adaptive expertise refers to the ability to use knowledge and experience in a domain to learn in unanticipated situations. It differs from routine expertise, which requires using knowledge appropriately to solve routine problems. Adaptive expertise is an important educational objective for bioengineers because the regulations and knowledge base in the discipline are likely to change significantly over the course of their careers. This study compares the performance of undergraduate bioengineering students who learned about ethics for stem cell research using the HPL method of instruction to the performance of students who learned following a standard lecture sequence. Both groups learned the factual material equally well, but the HPL group was more prepared to act adaptively when presented with a novel situation.     

From Number Lines to Graphs in the Coordinate Plane: Investigating Problem Solving Across Mathematical Representations

This article reports on students’ problem-solving approaches across three representations—number lines, coordinate planes, and function graphs—the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a hierarchical representational narrative (HRN), a discursive narrative around a set of representations that model conventional mathematics in structurally consistent ways. A paper-and-pencil assessment was administered to students in grades 5 and 8 along with videotaped interviews with a subset of students. Results revealed students’ application of particular meta-rules, which reflect their attempts to find and make use of recurring patterns in mathematics discourse. One such meta-rule, consistent with the HRN, was characterized by students’ coordination of geometric and numeric properties of an axis, whereas alternate meta-rules reflected coordinations inconsistent with conventional mathematics. Detailed analyses of problem-solving strategies are reported, and implications for theory, curriculum, and instruction are discussed.     

What Does it Mean to Notice my Students’ Ideas in Science Today?: An Investigation of Elementary Teachers’ Practice of Noticing their Students’ Thinking in Science

Abstract

Efforts toward improving K-12 science education emphasize teachers noticing students’ thinking as they engage in disciplinary practices and reasoning. This noticing requires specialized teacher knowledge and skills as it involves attending to students’ ideas, as well as making sense of and responding to those ideas so that the disciplinary substance in them is recognized, made explicit, and supported. This study investigates three elementary teachers’ in-the-moment noticing of students’ ideas while teaching science and their thinking about what it means to engage in this teaching practice. Results indicate that teachers notice many different kinds of student science ideas, and also that teachers have different ways of thinking about which student ideas are substantive during a science lesson. This research contributes to our theoretical understanding of the nature of teacher noticing in science. Noticing students’ science ideas involves not only the presence of ideas and the ability to notice them, but also a teacher’s understanding of this teaching practice in the moment.     

学校教育资源对学生数学素养预测效应的跨文化比较

采用国际学生评价项目PISA2006的数据,使用多水平线性模型方法,比较中国香港、日本、芬兰和美国四个国家（地区）的学校教育资源与学生数学素养成绩的关系。结果发现,在控制学生背景变量的情况下,学校教育资源对学生数学素养成绩的影响在四个国家（地区）之间存在一定的文化差异：学校大小、生师比对中国香港学生数学素养成绩有显著的正向预测作用;学校大小、班级大小、学校类型、有硕士研究生学历的教师比例对日本学生数学素养成绩有显著的正向预测作用,用于教学的计算机比例对日本学生数学素养成绩有显著的反向预测作用;学校教育资源对芬兰学生数学素养成绩没有显著的预测作用;学校类型对美国学生数学素养成绩具有显著的反向预测作用。     

Investigating Links from Teacher Knowledge,to Classroom Practice,to Student Learning in the Instructional System of the Middle-School Mathematics Classroom

Using data collected in 125 seventh-grade and 56 eighth-grade Texas classrooms in the context of the “Scaling Up SimCalc” research project in 2005–07, we examined relationships between teachers’ mathematics knowledge, teachers’ classroom decision making, and student achievement outcomes on topics of rate, proportionality, and linear function—three important and cognitively demanding prealgebra topics. We found that teachers’ mathematical knowledge was correlated with student achievement in only one study out of three. We also found a lack of correlations between teachers’ mathematical knowledge and critical aspects of instructional decision making. Curriculum and other learning resources (e.g., technology, student–student interactions) are clearly important factors for student learning in addition to, and in interaction with, teachers’ mathematical knowledge. Our results suggest that mathematics knowledge for teaching may have a nonlinear relationship with student learning, that those effects may be heavily mediated by other instructional factors, and that short-term content knowledge gains in teacher workshops may not persist in classroom instruction. We discuss a need in the field for richer models of how “mathematical knowledge for teaching” works in the context of complete instructional systems.     

The Influence of Relational Knowledge and Executive Function on Preschoolers’ Repeating Pattern Knowledge

Children’s knowledge of repeating patterns (e.g., ABBABB) is a central component of early mathematics, but the developmental mechanisms underlying this knowledge are currently unknown. We sought clarity on the importance of relational knowledge and executive function (EF) to preschoolers’ understanding of repeating patterns. One hundred twenty-four children aged 4 to 5 years old were administered a relational knowledge task, 3 EF tasks (working memory, inhibition, set shifting), and a repeating pattern assessment before and after a brief pattern intervention. Relational knowledge, working memory, and set shifting predicted preschoolers’ initial pattern knowledge. Working memory also predicted improvements in pattern knowledge after instruction. The findings indicated that greater EF ability was beneficial to preschoolers’ repeating pattern knowledge and that working-memory capacity played a particularly important role in learning about patterns. Implications are discussed in terms of the benefits of relational knowledge and EF for preschoolers’ development of patterning and mathematics skills.     

Teaching a computer to teach

The long-range goal of computer-assisted instruction (CAI) should be to construct computer programs that interact with a student as a human tutor does. In order to make computers act as intelligent tutors, we must consider three aspects of teaching; (1) A tutor makes use of many different knowledge sources. (2) A tutorial session is a kind of problem-solving situation in which the tutor is trying to solve the problem of imparting understanding to the student. (3) There is an analogy between the process of communication and those of teaching in that both require the participants to make a number of inferences about each other’s states and responses. A tutor designs an “instructional act,” anticipating how the student will interpret and learn from it, and the student interprets and learns from the instruction in a manner that depends on his hypotheses about the intent of the tutor. The paper reviews the relevant literature and discusses how we will incorporate such ideas into CAI systems.     

Helping parents to motivate adolescents in mathematics and science: an experimental test of a utility-value intervention

The pipeline toward careers in science, technology, engineering, and mathematics (STEM) begins to leak in high school, when some students choose not to take advanced mathematics and science courses. We conducted a field experiment testing whether a theory-based intervention that was designed to help parents convey the importance of mathematics and science courses to their high school-aged children would lead them to take more mathematics and science courses in high school. The three-part intervention consisted of two brochures mailed to parents and a Web site, all highlighting the usefulness of STEM courses. This relatively simple intervention led students whose parents were in the experimental group to take, on average, nearly one semester more of science and mathematics in the last 2 years of high school, compared with the control group. Parents are an untapped resource for increasing STEM motivation in adolescents, and the results demonstrate that motivational theory can be applied to this important pipeline problem.     

Looking at My (Real) World through Mathematics: Memories and Imaginaries of Math and Science Learning

Abstract

Critical math and science educators have argued for pedagogies that focus on equity, social justice, and the identities of learners. To inform debates about the purposes and values of math and science pedagogy, we need to better understand how different kinds of curriculum and instruction are taken up by learners over time. This study examines the ways one Latinx immigrant learner, Calvin (a pseudonym), constructed the values and purposes of his earlier math and science learning experiences, as an adult hoping to pursue a career in science. Narrative analysis is used to explore the ways Calvin made sense of his learning of math and science in high school, in community colleges, and on his own. Drawing on the construct of appropriation, we examine the conceptual tools Calvin took up from different math and science pedagogies (reform, critical, and traditional) in narrating his desire to explore and understand scientific phenomena. Narrative frames position Calvin with greater or lesser agency as he navigates different learning environments, imagines possible futures, and constructs the purposes of science and mathematics. The narratives of Calvin’s learning illustrate the conceptual tools he appropriates from reform and social justice pedagogies: real-to-my-life mathematics, learning as connecting and imagining, harder-but-easier math for a purpose, and the ways reading and writing the world can be applied to imagining planets and the universe. The analysis suggests the usefulness of restorying as a way to explore how our pedagogies interact with learners’ subjectivities, desires, values, and purposes for learning.     

Issues in the effective use of computers in introductory and advanced courses in psychology

The recent proliferation of time-shared terminals, computers, and instructional software is producing a dramatic change in undergraduate education in psychology. Although computers have been used for many years in research in psychology, their use as instructional alternatives only recently has been thrust upon the academic community, a development for which many faculty-even experienced computer users—are ill prepared. The use of computers and microcomputers in instruction can provide the instructor, and more importantly, the student, with an effective pedagogical tool. However, computers cannot be introduced into the curriculum in a piecemeal or haphazard fashion. In this paper, issues involved in the effective introduction and use of computers in teaching are outlined.     

Overcoming Instructor‐Originated Math Anxiety in Philosophy Students: A Consideration of Proven Techniques for Students Taking Formal Logic

Every university student has his or her nemesis. Biology and social science students anticipate with great apprehension their required statistics course, while many philosophy students live in fear of formal logic. Math anxiety is the common thread uniting all of them. This article argues that since formal logic is an algebra requiring similar kinds of symbol‐manipulation skills needed to succeed in a basic mathematics course, then if logic students have math anxiety, this can impede their progress. Further, it argues that math anxiety is primarily caused by and exacerbated by poor instruction. Formal logic instructors who employ effective instructional techniques for reducing it can help their students overcome math anxiety to foster learning. Methods of instruction leading to anxiety reduction and evidence supporting their efficacy are discussed, including co‐operative learning, the mastery goal approach, and self‐paced learning. None of these methods holds back more advanced students.