Prospective High School Research Articles

Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers

In this paper, we describe a study conducted with 68 prospective mathematics teachers (PMTs) who took part in a Euclidian geometry didactical course. During the course, PMTs were required to solve Multiple Solution Tasks (MSTs) and perform mathematical investigations in DGE (Dynamic Geometry Environment) on a systematic basis. This paper describes and exemplifies Problem Posing through Investigations (PPI) as an integral part of investigation tasks. We introduce a model for the evaluation of proof-related skills and creativity skills using PPI. We employ this model to demonstrate significant changes in PMTs’ proficiency related to proving and creativity skills. Using the model we describe the connections between different creativity-related and proof-related skills and the PMTs’ knowledge base.

Practical Learning Model Assisted by Mobile Workshop for Enhancing Practical Skills and Entrepreneurial Spirit for Prospective Vocational High School Graduates

The problem revealed in this practical learning model developing assisted by mobile workshops research is to find out the validity, practicality and effectiveness of the learning model assisted by mobile workshop for students' practical skills and entrepreneurial spirit. Research conducted using research and development (R & D) methods with a 4D development model (define, design, develop, disseminate) limited scale trials with the technique before-after without control group design. The practical learning model applies 6 (six) aspects of practical skills and 4 (four) aspects of students' entrepreneurial spirit. The results showed that the learning model assisted by mobile workshop was declared valid based on the average score of Expert 1 cycle II of 3.57 and Expert 2 of cycle II with a mean score of 3.74 with a very valid category and very feasible to use. Based on the practicality questionnaire given to 42 students and 3 teachers the results were "very practical". Based on the assessment of effectiveness using the t test for a 95% significance level obtained the probability value / p value of the test t paired is 0,000 < 0,05. The gain test result with a mean score 0.5359 means that there is increasing level of practical skills and an entrepreneurial spirit of the students after implementing the practical learning model assisted mobile workshop in medium scale, so that the practical learning model assisted mobile workshop is proven to enhance the practical skills and entrepreneurial spirit of the students.

High school prospective teachers’ problem-solving reasoning that involves the coordinated use of digital technologies

ABSTRACTThe aim of this study was to characterize and discuss ways of reasoning that prospective high school mathematics teachers develop and exhibit in a problem-solving scenario that involves the coordinated use of digital technologies. A conceptual framework that includes Virtual Learning Spaces (VLS) and Resources, Activities, Support and Evaluation (RASE) essentials is used to introduce and support a problem-solving approach to structure learners’ problem-solving activities that encouraged them to share ideas, discuss and extend mathematical discussions beyond formal settings. Main results indicated that prospective high school teachers relied on a set of tool affordances (dragging objects, looking and exploring object’s loci, using sliders, quantifying and visualizing mathematical relations, etc.) to formulate, explore and identify properties or relations to share, discuss and support mathematical conjectures. In this context, the participants recognized and valued the importance of using several tools to both dynamically represent and explore mathematical tasks and to share and constantly refine their mathematical ideas and problem-solving approaches.

Analysis of Praxis physics subject assessment examinees and performance: Who are our prospective physics teachers?

A generally agreed upon tenant of the physics teaching community is the centrality of subject-specific expertise in effective teaching. However, studies which assess the content knowledge of incoming K–12 physics teachers in the U.S. have not yet been reported. Similarly lacking are studies on if or how the demographic makeup of aspiring physics educators is different from previously reported analyses of the actual high school physics teaching workforce. Here we present findings about the demographics and subject knowledge of prospective high school physics teachers using data from Praxis physics subject assessments administered between 2006 and 2016. Our analysis reveals significant variations in exam participation and performance between men and women, as well as those with different undergraduate majors and academic performance over the past decade. Findings from this work inform understandings and decisions about the quality, recruitment, and preparation of the high school physics teaching workforce.Received 9 November 2017DOI:https://doi.org/10.1103/PhysRevPhysEducRes.14.010126Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEducational policyProfessional TopicsK-12 teachersGeneral Physics

Virtual forms, actual effects: how amplifying student voice through digital media promotes reflective practice and positions students as pedagogical partners to prospective high school and practicing college teachers

AbstractDigital media have unique potential to amplify student voice in both high school teacher preparation and academic development for college faculty. This paper applies narrative analysis to participant descriptions of how three uses of digital media amplify student voice in the context of a single higher education consortium: (1) high school students and prospective high school teachers use email to engage in dialogue as part of a larger project within the consortium's secondary teacher preparation program, (2) undergraduate student consultants use visual mapping technology as a classroom observation tool through one of the consortium's academic development programs for college faculty and (3) graduate and undergraduate students, faculty and staff engaged in pedagogical partnerships within and beyond this consortium use on an online platform to publish reflective essays on their collaborative work. Amplifying student voice through these uses of digital media has the following actual effects: it creates the possibility for exchanges between students and teachers across space and time; it supports the development of reflective practice; and it encourages the embrace of a partnership approach to teaching and learning.

Prospective High School Physics Teachers’ Beliefs about Teaching Practices: From Traditionalist to Constructivist

The main aim of this study was to determine the teaching practices of prospective high school physics teachers with respect to their preference for teaching as a traditionalist or as a constructivist. To study the beliefs of prospective high school physics teachers on this subject, firstly, the Teacher Belief Survey was administered to 135 prospective high school physics teachers; and then semi-structured interviews were conducted with eleven prospective high school physics teachers. Analyzing of the survey and interviews showed that most prospective high school teachers had intermediate (traditionalist to constructivist) beliefs about teaching physics.

Una Propuesta para el Análisis de las Prácticas Matemáticas de Futuros Profesores sobre Derivadas

En el presente trabajo se informa de los resultados obtenidos al analizar las prácticas matemáticas de una muestra de futuros profesores de secundaria/bachillerato a propósito de dos tareas sobre derivadas. Este análisis ejemplifica el uso y alcances de las nociones prácticasmatemáticas y configuración de objetos y procesos, proporcionadas por el Enfoque Onto-Semiótico (EOS) del conocimiento matemático, para la caracterización de los conocimientos del profesorado de matemáticas. Los resultados del análisis evidencian tanto una desconexión entre los distintos significados parciales de la derivada como la necesidad de potenciar el conocimiento del contenido. Este aprendizaje puede hacerse mediante actividades que favorezcan el uso e identificación de objetos matemáticos, sus significados y los procesos involucrados en la solución de tareas matemáticas.

Without the Light of Evolution: A Case Study of Resistance and Avoidance in Learning to Teach High School Biology

We present the case of Michael, a prospective high school biology teacher, to explore the implications of teacher resistance and avoidance to the topic of evolution. This case is drawn from a year-long qualitative research study that examined Michael's process of learning to teach high school biology and describes how his avoidance of evolution in his own education led to further disengagement with evolution in his methods coursework and in his student teaching practice. Paradoxically, his high academic abilities obscured substantive knowledge gaps about evolution, and his content knowledge regarding evolution did not appear to improve as a result of his student teaching experience. Kohl's concept of “not-learning” is useful in understanding Michael's avoidance of learning evolution. His use of the discourse of evolution in coursework and in student teaching activities also helped to obscure his opposition to learning evolution. We present an argument that proficiency for teaching biology means not only tolerating evolution as a topic to be covered in class but also advocating for evolution as a foundational theme in the discipline. This research has implications for both the admissions process and curriculum of biology teacher preparation programs.

PHÁT TRIỂN NĂNG LỰC DẠY HỌC CHO SINH VIÊN SƯ PHẠM TOÁN TẠI TRƯỜNG ĐẠI HỌC QUỐC GIA LÀO TRONG DẠY HỌC LÔGARIT LỚP 11

PHÁT TRIỂN NĂNG LỰC DẠY HỌC CHO SINH VIÊN SƯ PHẠM TOÁN TẠI TRƯỜNG ĐẠI HỌC QUỐC GIA LÀO TRONG DẠY HỌC LÔGARIT LỚP 11

Evaluación de sesgos en el razonamiento sobre probabilidad condicional en futuros profesores de educación secundaria

En este trabajo presentamos un estudio dirigido a evaluar los sesgos presentes en el razonamiento probabilístico condicional en futuros profesores de educación secundaria y bachillerato. Se analizan las respuestas a 7 ítems tomados del cuestionario RPC (razonamiento sobre probabilidad condicional) de 196 alumnos de matemáticas de último curso y alumnos del Máster de Secundaria en España, encontrando una alta incidencia en ambos grupos de la falacia del eje temporal, la condicional transpuesta, confusión entre probabilidad condicional y conjunta, falacia de las tasas base y concepciones incorrectas sobre la independencia. Se concluye la necesidad de una mejor formación de los futuros profesores, que evite que estos sesgos puedan transmitirse a sus estudiantes.

예비 고등학생들과 고등학교 과학 교사들의 '신소재'에 대한 인식 탐색

본 연구의 목적은 2009 개정 교육과정에 맞추어 개편된 고등학교 '과학' 교과서에 새롭게 도입된 '신소재'에 대한 예비 고등학생들과 고등학교 과학 교사들의 인식을 조사하여 신소재 수업을 효과적으로 진행하기 위해 필요한 기초자료를 제시하는 것이다. 서울, 인천, 경기 지역의 예비 고등학생 1,499명과 과학 교사 123명을 대상으로 설문을 진행하였으며 그 결과는 다음과 같다. 첫째, 학생들과 교사들의 신소재에 대한 태도는 긍정적이었지만 신소재에 대한 관심은 매우 낮았다. 학생들은 개정 과학 교과서의 신소재 단원에 대해 높은 관심을 보이지 않았고, 교사들도 신소재 단원 수업을 어렵게 생각하는 것으로 나타났다. 둘째, 학생들과 교사들의 신소재에 대한 인지도와 신소재 관련 지식에 대한 이해도는 낮은 편이었다. 학생과 교사 모두 다양한 경로를 통하여 신소재에 대해 접했던 것으로 나타났으나 신소재에 대해 잘 알고 있다고 응답한 학생과 교사는 많지 않았으며, 신소재에 대한 구체적인 정보를 올바르게 이해하고 있지 못한 교사들도 다수 있었다. 셋째, 학생과 교사 모두 신소재 수업이 필요하다는 점에 대해서는 공감하고 있었다. 신소재의 용도에 대해 알 필요가 있으며 매체 활용 수업을 가장 선호한다는 공통점을 나타냈지만 학생들은 교사들보다 체험학습을 선호하는 등 교사와 학생 입장에서 원하는 수업 진행 방식에는 차이점도 있었다. 이러한 연구 결과를 바탕으로 신소재 수업을 진행하는 교사들이 필요로 하는 것과 이들이 수업을 계획하고 진행할 때 고려할 점들을 제안하였다. Prospective high school students and science teachers' perceptions of 'advanced material', which was first introduced in the science textbooks of the 2009 revised curriculum, were surveyed. One thousand four hundred and ninety nine students and 123 teachers from Seoul, Incheon, and the Kyeonggi areas participated in this survey. The results are as follows. First, the attitude of students and teachers towards 'advanced material' was positive, but their interests in 'advanced material' was low. Also, some teachers mentioned that 'advanced material' was one of the difficult subjects to teach. Second, the perception of 'advanced material' was relatively low for both students and teachers. Both of them had heard of 'advanced material' through various routes, however not many of them thought that they knew what 'advanced material' was exactly. Also there were some teachers who didn't understand the detailed information of 'advanced material'. Third, both students and teachers agreed that 'advanced material' was worthwhile to learn and teach. However, each party had their own desire of 'what to learn', 'what to teach', 'how to learn' and 'how to teach'. Based on the results, some suggestions were made for effective teaching of this new subject.

From personal to conventional probabilities: from sample set to sample space

This article is a systematic reflection on a sequence of episodes related to teaching probability. Our central claim is that reducing problems to a consideration of the sample space, which consists of equiprobable outcomes, may not be in accord with learners’ initial ways of reasoning. We suggest a “desirable pedagogical approach” in which the solution builds on the set of outcomes as identified by learners and serves as a bridge towards mathematical convention. To explore prospective high school mathematics teachers’ ideas related to addressing a potential learner’s mistake and their reactions towards the suggested approach, we presented them with two tasks. In Task I, participants (n = 30) were asked to suggest a pedagogical remedy to a frequent mistake found in dealing with a standard probability problem, whereas in Task II, they were asked to solve a probabilistic problem, which they had not encountered previously. We discuss participants’ mathematical solutions to Task II in reference to their pedagogical approaches to Task I. The presented disparity serves in extending the convincing power of the suggested pedagogical approach.

Literacy pedagogical content knowledge in the secondary curriculum

In this paper, I address the challenge of raising the consciousness of prospective secondary teachers about their roles in supporting their students in the advanced literacy demands of their subject specializations. I argue that to better equip them in supporting the conceptual development of diverse groups of students, prospective high school teachers need, as part of their pedagogical content knowledge, an understanding of the pervasive role of language and literacy in learning. I illustrate how, after even a short but intense input, one group of prospective teachers with no prior knowledge of language developed a capacity to plan content area learning with an informed consciousness of the role of language and literacy in the learning of diverse groups of their students. The continued development of literacy pedagogical content knowledge, I argue, will be crucial to the strength of those pillars of government reform related to lifting the academic achievement of adolescents in disadvantaged schools.

Higher Education and Class Mobility in the State of California: “What Is to Be Done?”

I met Gabriela Macias a few months ago in an undergraduate class in history that I teach to prospective high school teachers. A diminutive middle-aged woman, Gabriela was watchful in class and seemed indifferent to my attempts to reach through her stony silences. But a couple of weeks into the class, I made a breakthrough. We had been discussing the role of passion in education. I had started the discussion by insisting that unless teachers feel a real sense of commitment to the student body and feel passionate about empowering students with knowledge and ideas, they have no business being in the classroom. In retrospect, my statements seemed a little extreme, but it is hard to entice students to enter the teaching profession by the prospect of tests, more state-administered tests, and even more standardized examinations! When Gabriela started speaking, the class fell silent. But it was not her eloquence that silenced us; it was her accent. Her accent was impenetrable! I am troubled by this public admission and even considered omitting this sentence from this essay. As an immigrant from India, I find people often have trouble understanding the stubborn Indian cadences that litter my superficially Americanized speech. But that day we all strained to understand Gabriela.

Using dynamic geometry software Cabri 3D for teaching analytic geometry

In this study, we investigated that whether Cabri 3D can be a useful tool for teaching analytic geometry of space or not. For this purpose, we focused on solving some traditional spatial analytic problems by using Cabri 3D. Experiments were conducted with 24 prospective high school teachers who had a mathematics degree and were attending the postgraduate teacher training course. Results of the study show that Cabri 3D is potentially very useful software for learning and teaching spatial analytic geometry. Another important result of the study is that Cabri 3D facilitates understanding by visualizing.

Understanding the influence of two mathematics textbooks on prospective secondary teachers’ knowledge

This study examines the influence of reading and planning from two differently organized mathematics textbooks on prospective high school mathematics teachers’ pedagogical content knowledge and content knowledge of exponential functions. The teachers completed a pretest and two posttests. On the pretest, the teachers possessed an incomplete understanding of content and pedagogical content knowledge related to exponential functions. The teachers’ understanding of how to translate from table to closed-form and recursive equations grew as a result of their use of the Mathematics: Modeling Our World textbook, while the Discovering Algebra textbook appeared to be more beneficial in terms of pedagogical content knowledge. Teachers read from the student lessons in both textbooks, but read differently from the sections of both textbooks intended for the teacher. They focused more on the purpose of the Mathematics: Modeling Our World lesson and more on the places where students might experience difficulties in the margins of the Discovering Algebra lesson. The teachers’ learning was influenced by their own personal characteristics (e.g., previous textbook experiences) as well as textbook qualities (e.g., organization).

Extended analyses: Promoting mathematical inquiry with preservice mathematics teachers

This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying mathematical structure of the problem. The results of this study revealed that with careful implementation, these tasks were effective for generating powerful mathematical thinking in preservice mathematics teachers, improving their problem solving, and generally enhancing the habits-of-mind exhibited by successful mathematicians (Carlson & Bloom, 2005).

Prospective High School Mathematics Teachers’ Attitudes toward Integrating Computers in Their Future Teaching

This article presents the findings of a study on the attitudes of prospective high school mathematics teachers toward integrating computers into their future classroom teaching. Ninety-four prospective teachers in four classes that focused on didactic and cognitive aspects of learning mathematics with computers were asked to present pro and con arguments that would influence their use of computers in their future mathematics teaching. A two-dimensional framework is used to present an analysis of the prospective teachers’ arguments, which were collected through written questionnaires and class discussions. One dimension relates to the class components of a lesson: learner, teacher, mathematical content, learning environment, and class atmosphere. The second dimension is made up of the psychological aspects: cognitive, affective, and social.

The Initial Teacher Training National Curriculum forsecondary science: on learning to be a high school physicsteacher

A National Curriculum for postgraduate science teachertraining courses in England and Wales was first introduced inSeptember 1999. In this article the new curriculum andassociated assessment procedures are reviewed and points fordiscussion raised. Particular attention is paid to theimplications for prospective high school physics teachers.

Meta-Problems in Mathematics

Let's call the problem of making up a nice problem a meta-problem. Meta-problems in mathematics are not meta-mathematics problems. The idea is to apply mathematics to the design of pleasing mathematics problems. So, we are dealing with applied mathematics rather than with philosophy. Talking with teachers over the years, Fve found an amazing number of these meta-problems. Every now and then, someone publishes a method to solve some class of them (see [1,2,3,4], for example). One purpose of this paper is to show how classical algebra and number theoiy can be applied to meta-problems; another is to lobby for the inclusion of such applications in courses for prospective high school teachers.