Use of comics to enhance students’ learning for the development of the twenty-first century competencies in the mathematics classroom

Abstract

This paper discusses the use of comics in teaching mathematics in the secondary mathematics classroom. We explicate how the use of comics in teaching mathematics can prepare students for the twenty-first century competencies. We developed an alternative teaching package using comics for two lower secondary mathematics topics. This alternative teaching package consists of (1) several sets of comic strips expounding all related mathematical concepts in a lively way; (2) tiered practice questions for learning reinforcement; and (3) a set of proposed lesson outlines with suggestions on how to use the comics for mathematics teaching. We also report how one of the teachers in our study used this teaching package in her mathematics lessons. Her lessons were video-recorded and 11 students were interviewed to help us understand how the mathematics comics lessons were enacted and the students’ perception of comics as instruction. We identified instances in which the teacher tweaked the provided resource to further enhance student learning and incorporated elements of the twenty-first century competencies during her lessons. Through selected student interviews, we also identified instances in which students commented on their gain from the new approach from the perspective of the twenty-first century competencies.     

视频资料在英语教学中的应用

视频以其丰富的语言信息承载优势,成为英语教学中普遍使用的教学资料和手段。教师如何在课堂上系统、合理、有效地运用视频资料,激发学生的学习兴趣,组织教学活动,成为值得思考的问题。视频资料在英语教学中的成败,从视频资料的选择,设计观影任务和活动以促进有效的语言学习,组织学生进行观看前、观看中、观看后各阶段的教学活动,激发学生语言意识,到将视频资料与英语教学有机结合起来,教师的作用至关重要。     

A research‐based teaching sequence for teaching the concept of modelling to seventh‐grade students

The purpose of this study was to construct and study the impact of a research‐based sequence for teaching the concept of modelling to seventh‐grade science students. We identified students' notions of models and the aspects of school science to be addressed regarding the model concept, which were then taken into account when we planned the learning sequence. The idea of modelling in science was taught while the students were learning about the change of states of matter in seventh‐grade physics. A pre‐interview revealed that the students' notions of models were very limited, while a post‐interview showed that this improved in the course of the series of lessons. There was also a statistically significant difference in the students' understanding of modelling between our target group and a control group consisting of ninth‐grade students who had received only the normal teaching. However, a delayed post‐questionnaire completed a few months after the teaching sequence showed that the stability of learning results were dependent on whether models and modelling were used in the normal teaching conducted after the teaching sequence. Implications for teaching, teacher education and research are also addressed in this paper.     

Bridging the implementation gap: a teacher‐as‐learner approach to teaching and learning policy

A major dilemma facing higher educational institutions around the world is how to achieve quality outcomes for students in an increasingly internationalised and competitive environment. To effect change in teaching and learning, we advocate a teacher‐as‐learner approach to the implementation of teaching and learning policy. Our approach has been influenced by approaches to change management as well as contemporary educational theories, such as constructive alignment and deep and surface approaches to learning. In this paper we use these approaches to evaluate the success of a policy initiative designed to encourage subject coordinators to use a faculty‐endorsed template to embed graduate attributes into their subject outlines. The difficulties experienced by teachers at the disciplinary level in using the subject outline template illustrate how a seemingly positive and well‐intentioned initiative can have a potentially minimal effect on teaching and learning practice and, as a consequence, student learning. We suggest that the Course Experience Questionnaire provides a useful model for evaluating not only teaching but also the management of teaching. As teachers responsible for the implementation of teaching and learning policies, we hope our views will provide a more integrated approach to teaching and learning changes in the higher educational context.     

Self-Study of a Teacher's Journey toward Standards-Based Mathematics Teaching

The authors describe a journey of self-study during which one author shifted from traditional, teacher-driven approaches to a more problem-based inquiry approach to teaching mathematics. He videotaped a series of lessons taught to sixth-grade students over a semester and analyzed his teaching during discussions with his mentor at the university. The shared analysis helped him learn to involve his students more directly in their own learning. A major lesson learned was that understanding the potential value of a problem-solving approach to teaching mathematics does not guarantee corresponding changes in the classroom. Two vital elements of lesson development emerged as focal points for self-study. After first learning how to prepare worthwhile mathematical tasks, the teacher also learned the importance of implementing effective questioning strategies to help students think more deeply about the mathematics they were learning.     

Teaching Social Justice Research to Undergraduate Students in Puerto Rico: Using Personal Experiences to Inform Research

This article explores the process of teaching undergraduate students to conduct social justice research. We were interested in understanding how to develop a social justice perspective among students while training them in conventional research methods. The following questions guided our research activities. How can the principles of social justice inform undergraduate research projects? What pedagogical strategies prepare students to conduct social justice-based research? What are the challenges and opportunities in teaching social justice research? We documented the lessons and activities during the field school and collected students’ comments in journals, extensive observations, focus groups, and interviews to understand the influence of social justice on the students’ approach to research. We identify three lessons in teaching social justice. First, teaching social justice requires that students develop meaningful relationships with the community understudy. Second, gender dynamics can prohibit or promote meaningful student engagement and learning. Third, it is important to consider how to integrate, rather than “add on,” social justice activities and discussions into research lessons.     

浅谈高中英语教学中教法与学法的统一

教学方法是教法和学法的辩证统一。教法与学法相互制约与联系,两者重在学法,并可相互转化。要提高教学质量,既要重视教法又要重视学法。然而长期以来,受传统教学观念“教师中心论”的影响,我国教学改革的重点过分集中在教师的教法和教学观念的更新和变革方面,学校和教师将太多的注意力放在教法方面,忽视对学法的研究和指导,从而造戍教法和学法脱节,教学质量达不到预期效果。要扭转这种教法与学法脱节的局面,师生就要在教法与学法问题上形成良性互动。教师要让学生了解教法,引导和指导学生探索相应学法,充分发挥学生的主体性,达成教法与学法的统一,从而促进教学。     

Biology instruction using a generic framework of scientific reasoning and argumentation

We investigated biology instruction—using a generic framework of scientific reasoning and argumentation (SRA) with eight epistemic activities—on how to foster student learning in biological literacy which had not been clarified in previous studies. Our analysis of videotaped biology lessons and student achievement showed varying frequencies in using these activities and their effects on achievement. Those students taught with more epistemic activities had higher achievement. We believe that the SRA framework can be a worthwhile methodical tool for teaching biology to foster student learning. Therefore, we draw practically orientated implications for educational research, practitioners, teacher educators, and curriculum developers.     

用研究性学习的方法培养学生自主学习物理的意识

研究性学习是一种全新的学习方法和课程形式，在高中物理教学中，利用它可以转变学生的学习方法，培养学生自主学习的意识，可以发挥学生自我学习的潜能，培养学生科学探究的精神。     

Inquiry-Based Whole-Class Teaching with Computer Simulations in Physics

In this study we investigated the pedagogical context of whole-class teaching with computer simulations. We examined relations between the attitudes and learning goals of teachers and their students regarding the use of simulations in whole-class teaching, and how teachers implement these simulations in their teaching practices. We observed lessons presented by 24 physics teachers in which they used computer simulations. Students completed questionnaires about the lesson, and each teacher was interviewed afterwards. These three data sources captured implementation by the teacher, and the learning goals and attitudes of students and their teachers regarding teaching with computer simulations. For each teacher, we calculated an Inquiry-Cycle-Score (ICS) based on the occurrence and order of the inquiry activities of predicting, observing and explaining during teaching, and a Student-Response-Rate (SRR) reflecting the level of active student participation. Statistical analyses revealed positive correlations between the inquiry-based character of the teaching approach and students’ attitudes regarding its contribution to their motivation and insight, a negative correlation between the SRR and the ICS, and a positive correlation between teachers’ attitudes about inquiry-based teaching with computer simulations and learning goal congruence between the teacher and his/her students. This means that active student participation is likely to be lower when the instruction more closely resembles the inquiry cycle, and that teachers with a positive attitude about inquiry-based teaching with computer simulations realize the importance of learning goal congruence.     

Problem-Based Learning for Foundation Computer Science Courses

The foundation courses in computer science pose particular challenges for teacher and learner alike. This paper describes some of these challenges and how we have designed problem-based learning (PBL) courses to address them. We discuss the particular problems we were keen to overcome: the purely technical focus of many courses; the problems of individual learning and the need to establish foundations in a range of areas which are important for computer science graduates. We then outline our course design, showing how we have created problem-based learning courses. The paper reports our evaluation of the approach. This has two parts: assessment of a trial, with a three-year longitudinal follow-up of the students; reports of student learning improve-ment after we had become experienced in full implementation of PBL. We conclude with a summary of our experience over three years of PBL teaching and discuss some of the pragmatic issues around introducing the radical change in teaching, maintaining staff support, and continuing refinement of our PBL teaching. We also discuss some of our approaches to the commonly acknowledged challenges of PBL teaching.     

When is student teaching teacher education?

This paper presents a conceptual framework that relates empirical aspects of student teaching (facts about the experience) to considerations of value (what student teachers ought to learn). First, the authors explain what they mean by calling student teaching an “occasion for teacher learning.” Next based on their observational and interview data, the authors present two cases of student teaching to illustrate how the relative influence of program, setting, and participants interact to shape opportunities for teacher learning. One teaching episode that elicited considerable pride in each student teacher is presented to highlight how and what the students teachers learned. The conclusion appraises the lessons learned in student teaching in terms of the framework and suggests how teacher educators can increase the educative power of the student teaching experience.     

Curricular design and implementation as a site of teacher expertise and learning

Previously, research about teacher expertise has adhered to relatively fixed notions of teacher expertise. However, in this study, we share data from teacher study group (TSG) meetings, which demonstrate a dynamic understanding of teacher expertise. In these meetings, teachers discursively positioned themselves, their colleagues, and the research team as both experts and learners as they engaged in a community of enquiry around questions of curriculum design and implementation. We argue that teachers’ dynamic and multiple positionings generated especially striking opportunities for learning. As teachers externalized their expert knowledge, their assumptions were brought forth to be examined, challenged, and reconsidered, thus opening space for further learning. We argue that these TSGs thus existed as a site for teacher learning, in which teacher dialog around curricular design, redesign, and the student learning that occurred in the lessons influenced their own learning about their students’ capabilities. We make a case for further research that explores how teacher expertise is interwoven with episodes of teacher learning. We assert that a complex understanding of teacher expertise, grounded in principles of learning occurring through social interaction, has important implications for how the field should move forward in its approach to fostering teacher learning throughout teachers’ careers.     

When Teaching Makes a Difference: Developing science teachers’ pedagogical content knowledge through learning study

It is a common view that developing teachers’ competence to restructure or reframe their knowledge and beliefs is inevitably a complex challenge. This paper reports on a research project with the aim to develop science teachers’ pedagogical content knowledge (PCK) through their participation in a learning study. A learning study is a collegial process in which teachers work together with a researcher to explore their own teaching activities in order to identify what is critical for their students’ learning. During one semester, three secondary science teachers worked in a learning study together with a researcher in a cyclical process in order to create prerequisites and further identify conditions for students’ learning. During the learning study, data were collected from video-recorded lessons and stimulated recall sessions in which the teachers and the researcher reflected on the lessons to analyze their development of PCK, their students’ learning and the impact of that knowledge on their own teaching. The results provide an insight into how the teachers developed their self-understanding in which they questioned their own epistemological beliefs, aims and objectives of teaching and taken-for-granted assumptions about science teaching and learning. As such, the study provides an understanding of teacher professional learning through a careful investigation of how teachers’ PCK is enhanced through their participation in the learning study, and further, how students’ learning might be developed as a consequence.     

Developing Practical Knowledge of the <Emphasis Type="Italic">Next Generation Science Standards</Emphasis> in Elementary Science Teacher Education

Just as the Next Generation Science Standards (NGSSs) call for change in what students learn and how they are taught, teacher education programs must reconsider courses and curriculum in order to prepare teacher candidates to understand and implement new standards. In this study, we examine the development of prospective elementary teachers’ practical knowledge of the NGSS in the context of a science methods course and innovative field experience. We present three themes related to how prospective teachers viewed and utilized the standards: (a) as a useful guide for planning and designing instruction, (b) as a benchmark for student and self-evaluation, and (c) as an achievable vision for teaching and learning. Our findings emphasize the importance of collaborative opportunities for repeated teaching of the same lessons, but question what is achievable in the context of a semester-long experience.     

Evaluate to improve: useful approaches to student evaluation

Many teachers in higher education use feedback from students to evaluate their teaching, but only some use these evaluations to improve their teaching. One important factor that makes the difference is the teacher’s approach to their evaluations. In this article, we identify some useful approaches for improving teaching. We conducted focus groups with award-winning university teachers who use student evaluations to improve their teaching, and we identified how they approach their evaluation data. We found that these teachers take a reflective approach, aiming for constant improvement, and see their evaluation data as formative feedback, useful for improving learning outcomes for their students. We summarise this as the improvement approach, and we offer it for other teachers to emulate. We argue that if teachers take this reflective, formative, student-centred approach, they can also use student evaluations to improve their teaching, and this approach should be fostered by institutions to encourage more teachers to use student evaluations to improve their teaching.     

Shifting epistemologies during instructional conversations about “good” argumentative writing in a high school English language arts classroom

A widespread instructional practice in the teaching of argumentative writing is the use of writing samples or models during instructional conversations about what counts as “good argumentative writing.” In this article, we focus on a set of lessons in a high school English language arts classroom in order to gain insight into how a teacher’s use of writing samples contributed not only to what counts as “good argumentative writing” in that classroom, but how her instructional conversations with a group of 11th grade students revealed a shift in her “argumentative epistemologies” for teaching literature-related argumentative writing. We examine simultaneously the impact of instructional conversations on the evolution of the socially constructed definitions of good argumentative writing and the teacher’s shifting argumentative epistemologies by tracing the teacher’s socially constructed definitions of good argumentative writing in the instructional conversations around argumentative writing samples as they evolve and change over time. The findings suggest that the interactional construction of “good argumentative writing” in instructional conversations was influenced by the broader instructional context (e.g., a testing regimen), by the teacher’s argumentative epistemologies for what counts as good writing, and by the conversational interaction of teachers and students in classroom lessons.

     

Knowing Inquiry as Practice and Theory: Developing a Pedagogical Framework with Elementary School Teachers

In this paper, we characterize the inquiry practices of four elementary school teachers by means of a pedagogical framework. Our study revealed core components of inquiry found in theoretically-driven models as well as practices that were regarded as integral to the success of day-to-day science teaching in Singapore. This approach towards describing actual science inquiry practices—a surprisingly neglected area—uncovered nuances in teacher instructions that can impact inquiry-based lessons as well as contribute to a practice-oriented perspective of science teaching. In particular, we found that these teachers attached importance to (a) preparing students for investigations, both cognitively and procedurally; (b) iterating pedagogical components where helping students understand and construct concepts did not follow a planned linear path but involved continuous monitoring of learning; and (c) synthesizing concepts in a consolidation phase. Our findings underscore the dialectical relationship between practice-oriented knowledge and theoretical conceptions of teaching/learning thereby helping educators better appreciate how teachers adapt inquiry science for different contexts.     

Relationships between emotional climate and the fluency of classroom interactions

This study examined emotional climate in relation to the teaching and learning of grade 7 science. A multi-method and multi-theoretic approach used sociocultural frameworks as a foundation for interpretive research, conversation analysis, prosody analysis, and studies of nonverbal conduct. Emotional climate varied continuously throughout a lesson. Dialogues occurred and afforded learning when interactions between the teacher and students were fluent and included humour and collective effervescence. Emotional climate was negatively valenced when the teacher and/or students endeavoured to establish and maintain power by restricting others’ participation to spectator roles. The teacher’s endeavours to maintain and establish control over students were potentially detrimental to teaching and learning, teachers and learners. This type of teaching gradually evolved into a form we referred to as cranky teaching, whereby the teacher and her students showed signs of frustration and the enacted teaching and learning roles lacked fluency. The methods we pioneered in the present study might be helpful for other teachers who wish to participate in research on their classes to ascertain what works and should be strengthened, and identify practices and rituals that are deleterious and in need of change.     

Mathematics, computers, and young children as a research-oriented learning environment for a teacher candidate

The advent of computer technology in the classroom raised the issue of its appropriate use by teachers and their students alike. It has been recommended that teacher education programs provide more opportunities for teacher candidates’ use of technology including teaching their own technology-enhanced lessons. With a goal of integrating scholarship into student teaching, a teacher candidate enrolled in a graduate program in childhood education carried out a technology-enhanced research project within a professional development school. Examining the impact of the project on the teacher candidate, this article describes how one’s pedagogical content knowledge and technological competence can be developed through a research-oriented teaching experience. The article also demonstrates the emergence of a community of practice that shares the goal of providing learning spaces for the teacher candidate and young children in the context of mathematics enrichment with computers.