TEACHERS’ KNOWLEDGE OF THE CONCEPT OF A FUNCTION: A THEORETICAL FRAMEWORK

In order to teach mathematics effectively, mathematics teachers need to have a sound mathematical knowledge, but what constitutes sound mathematical knowledge for teaching is subject to debate. This paper is an attempt to unpack what constitutes teacher knowledge of the concept of a function which is a unifying idea in the mathematics curriculum. The central components of the framework, which will be elaborated on in this paper, are: teachers’ subject matter knowledge, teachers’ pedagogical content knowledge, teachers’ technological pedagogical knowledge, technological content knowledge, and technological pedagogical content knowledge in relation to the concept of a function. The framework is informed by Shulman’s (Educational Researcher 15:4–14, 1986) Types of Teachers Knowledge Framework, Ball, Bass &; Hill 29:14–17, 20–22, 43–46 (2005) Mathematical Knowledge for Teaching Framework, and Mishra &; Koehler’s (Teachers College Record 108:1017–1054, 2006) Technological Pedagogical Content Knowledge (TPACK) framework.

     

LEARNERS’ AND TEACHERS’ CONCEPTUAL KNOWLEDGE OF SCIENCE PROCESSES: THE CASE OF BOTSWANA

The conceptual knowledge of science processes possessed by University of Botswana science students and senior secondary school science teachers was sought through a three-part questionnaire. One part requested demographic data of subjects, the second part asked them to select their level of familiarity with the processes, and the third part probed their conceptual definitions of the science processes. The definitions were scored as incorrect, partially correct and correct on an ordinal scale. Statistical analysis was done using Spearman rho correlation and one sample t test. The findings revealed that the science teachers did not have sufficient conceptual knowledge of science processes to help their students to understand in a meaningful way; both students’ and teachers’ views of their familiarity of science processes did not corroborate their demonstrated ability to provide acceptable conceptual definitions of the processes; there was no association between students’ and teachers’ conceptions of the science processes; and if conceptual knowledge of science processes was demanded, the entering students, who were the immediate graduates of the senior secondary schools, might not have enough to pursue tertiary level science courses. It is suggested that both conceptual and operational knowledge of science processes be required at secondary and tertiary levels of science education.     

TECHNOLOGY KNOWLEDGE: HIGH SCHOOL SCIENCE TEACHERS’ CONCEPTIONS OF THE NATURE OF TECHNOLOGY

In-depth interviews guided by video elicitations examined 30 high school science teachers’ conceptions of technology and by extension how these conceptions reflected dimensions of nature of technology. Altogether, 64 % of the teachers characterized their schools and departments as aggressive–moderate adopters with generous access and support for technological tools. In comparison, 30 % noted that their school lagged behind due to funding and lack of infrastructure. Definitions of technology revealed emphasis on technology as artifact, overwhelming optimism on the purpose and function of technology to improve and make life easier and as representation of advancement in civilization. In tandem, teachers were most drawn to two video scenarios—medical and everyday tool videos because it reflected notions of progression and expectations of future changes; heightened awareness of the multitude of available technologies; and perceived relevance with classroom content. Perhaps most telling in these findings was that few teachers were drawn to the classroom video scenario, and only three teachers highlighted the technology–science–school science connection. These findings have implications for holistic understandings of technologies, which may inform how science teachers perceive and enact technologies in their science classrooms.     

PRESERVICE ELEMENTARY TEACHERS’ GROWTH IN KNOWLEDGE OF MODELS IN A SCIENCE CAPSTONE COURSE

We used four different methods to determine the best means of assessing over 200 preservice elementary teachers’ growth in knowledge of models and their use in K-8 classrooms while participating in the Science Capstone course that focused on the unifying themes of models in science. Each assessment method probed a different aspect of models (from growth in scientific use to need for greater emphasis on the role and use of models) and each used a different method of gathering student responses (Likert-type responses to concept maps). We determined that growth in student knowledge was demonstrated by all instruments, but some instruments were more useful than others for determining preservice elementary teachers’ prior knowledge as well as growth in knowledge of models necessary for K-8 teachers.     

THE TAYLOR EXPANSION OF A FUNCTION OF FUNCTIONS

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ELEMENTARY SCHOOL TEACHERS’ KNOWLEDGE OF MODEL FUNCTIONS AND MODELING PROCESSES: A COMPARISON OF SCIENCE AND NON-SCIENCE MAJORS

This study aimed to: (a) understand practicing teachers’ knowledge of model functions and modeling processes, (b) compare the similarities and differences between the knowledge of science and non-science major teachers, and (c) explore the possible reasons for the similarities and differences between the knowledge of these 2 groups. A 4-point Likert scale questionnaire was developed and used to measure the knowledge of 187 practicing elementary school teachers (94 science majors and 93 non-science majors) on model functions and modeling processes. The author selected 10 target teachers to conduct think-aloud interview and to explore their ranking. One month after completing the questionnaire, 28 volunteer teachers were selected for a follow-up interview to better understand the reasons for their responses. The results show that these teachers tend to agree or strongly agree with the items about model functions and modeling processes. The only significant difference between science and non-science majors was for the item “generating new ideas.” Qualitative analyses of the follow-up interviews and think-aloud results showed that teacher education and professional development did not focus on understanding and using models. Science-major teachers tended to formulate their responses with reference to specific models, while the non-science major teachers’ responses contained acquiescence bias. Finally, implications for science education are discussed.     

PRESERVICE TEACHERS’ VIEWS ABOUT NATURE OF SCIENTIFIC KNOWLEDGE DEVELOPMENT: AN INTERNATIONAL COLLABORATIVE STUDY

This article presents the findings of an international collaborative investigation into preservice teachers’ views on the nature of scientific knowledge development with respect to six elements: observations and inferences, tentativeness, scientific theories and laws, social and cultural embeddedness, creativity and imagination, and scientific methods. A total of 640 preservice teachers, 209 from the United States, 212 from China, and 219 from Turkey, participated in the study. The survey “Student Understanding of Science and Scientific Inquiry (SUSSI)”, having a blend of Likert-type items and related open-ended questions, was used to gain a fuller understanding of the preservice teachers’ views of the nature of scientific knowledge development. Across the three countries, the participants demonstrated better understanding of the tentative NOS aspect but less understanding of the nature of and relationship between scientific theories and scientific laws. The Chinese sample scored highest on five of the six Likert sub-scales, the USA sample demonstrated more informed views on observation and inference, and the Turkish preservice teachers possessed relatively more traditional views in all six NOS aspects. Conclusions and limitations of the present study as well as implications and recommendations for future studies, are also discussed.     

THE EFFECT OF KNOWLEDGE LINKING LEVELS IN BIOLOGY LESSONS UPON STUDENTS’ KNOWLEDGE STRUCTURE

Knowledge structure is an important aspect for defining students’ competency in biology learning, but how knowledge structure is influenced by the teaching process in naturalistic biology classroom settings has scarcely been empirically investigated. In this study, 49 biology lessons in the teaching unit blood and circulatory system in 9th grade German classrooms were videotaped and analyzed. Before the lesson, a questionnaire was administered to the students to solicit their responses about learning motivation. After the lesson, students’ learning outcomes on knowledge structure were examined with the concept mapping method. The video coding used in this study focused on the knowledge linking levels during the biology lesson. Out of the 49 classes, those with the highest and those with the lowest linking levels were selected based on the coding results. In high-linking classes, interrelated facts were introduced more often in the lessons, whereas in the lessons of the low-linking classes, isolated pieces of knowledge were predominant. The results from the concept mapping task showed that the students in the high-linking classes constructed more correct relations among the concepts compared to the students in the low-linking classes. The results remained stable even after controlling for learning motivation. These findings confirm the importance of teaching interrelated facts and concepts instead of isolated facts for fostering students’ knowledge structure. As a result, based on the Bavarian biology curriculum, we develop materials and programs to enable students, student teachers, and teachers to focus on interrelated facts and basic concepts instead of isolated facts in biology lessons.     

ELEMENTARY SCHOOL TEACHERS’ UNDERSTANDING OF THE MEAN AND MEDIAN

This study provides a snapshot of elementary school teachers’ understanding of the mean and median. The research is presented in light of recent work regarding preservice teachers’ understanding of the mean. Common misconceptions are identified which lead to potential implications for teacher preparation programs. One of the primary concerns regarding increasing the standards expected of students to learn statistics is teachers’ preparation to address those standards. Exploring issues with teachers’ understanding of two of the most prominent concepts in the enacted curriculum provides a glimpse into the need to adequately prepare teachers to teach statistics.     

ENHANCING MATHEMATICS TEACHERS’ KNOWLEDGE OF STUDENTS’ THINKING FROM ASSESSING AND ANALYZING MISCONCEPTIONS IN HOMEWORK

This study focuses on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions. The data were collected from 10 teachers at fifth?Ceighth grade levels in the USA. The results show that assessing and analyzing misconceptions from grading homework is an important approach to acquiring knowledge of students?? thinking. By engaging in the inquiry process of the 4 steps of identifying errors, analyzing reasons for the errors, designing approaches for correction, and taking action for correction, the teachers made obvious progress in their knowledge of students?? thinking, understood the difficulties and challenges their students had in learning mathematics, and enhanced their pedagogical content knowledge.     

DEVELOPMENT, EVALUATION, AND VALIDATION OF A PAPER-AND-PENCIL TEST FOR MEASURING TWO COMPONENTS OF BIOLOGY TEACHERS’ PEDAGOGICAL CONTENT KNOWLEDGE CONCERNING THE “CARDIOVASCULAR SYSTEM”

One main focus of teacher education research concentrates on teachers’ pedagogical content knowledge (PCK). It has been shown that teachers’ PCK correlates with teaching effectiveness as well as with students’ achievement gains. Teachers’ PCK should be analyzed as one of the main important components to evaluate professional development programs. On this account, it is necessary to develop standardized measures of biology teachers’ topic-specific PCK that are labor-efficient. This paper presents a study on the development, evaluation, and validation of a paper-and-pencil test to measure biology teachers’ declarative PCK on the topic of blood and the human cardiovascular system. The development of the test was based, among other considerations, on a review of research literature on PCK and an analysis of 50 videotaped biology lessons. The final test instrument was comprised of 15 items distributed across 2 scales. The findings of the main study—with 93 preservice and in-service biology teachers and 12 biologists—confirmed that this measure of biology teachers’ declarative PCK was reliable, objective, and valid. In-service biology teachers scored higher on the test than preservice teachers (effect size Cohen’s d, 0.65) on one hand and, also, than biologists (Cohen’s d, 1.00) on the other hand. Future versions of this test should explore enlarging the scales and measuring procedural aspects of PCK.     

PREDICTORS OF COLLEGE STUDENTS’ KNOWLEDGE OF AND ATTITUDES TOWARD ELDERLY SEXUALITY: THE RELEVANCE OF GRANDPARENTAL CONTACT

In this study, 241 young and middle‐aged adult college students completed the Aging Sexuality Knowledge and Attitude Scale, and provided information about their demographic and grandparental relationship qualities. Findings showed that greater age was associated with increased knowledge of elderly sexuality. Both the presence of contact and greater than average perceptions of closeness with at least one grandparent were predictive of more permissive attitudes toward elderly sexuality. Among the total sample, greater knowledge was related to more permissive attitudes toward elderly sexuality. However, the presence of contact with at least one grandparent moderated this relationship; young adults without grandparental contact presented a nonsignificant knowledge /attitude relationship. These findings suggest that future studies of younger age cohorts’ attitudes toward elderly sexuality should assess grandparental contact and relationship characteristics, as well as general demographic information such as chronological age. Health‐care educators also may need to reconsider the commonly held assumption that greater knowledge of elderly sexuality is associated exclusively with more permissive attitudes.     

THE PERCEIVED USEFULNESS OF TEACHERS�� GUIDES FOR SCIENCE TEACHERS

The processes of curricula, textbooks and student resources development have been broadly surveyed and studied while teachers’ guides have received comparatively little consideration throughout recent reforms in science education. Ideal curriculum materials align instruction with the goals of reform. Well-designed teachers’ guides contribute to communicating and supporting reform-based teaching. The purpose of this study was to investigate the functions and assistance that guides provide science teachers. A questionnaire was developed and administered to science teachers from a stratified sample of elementary and junior high schools in Taiwan. The findings indicated that the guides were of greater benefit to elementary school science teachers than they were to junior high teachers. These groups of teachers perceived the guides’ usefulness differently, but they believed that a clear, concise presentation of the purpose, reminders, answer keys, concept maps of the main topics and learning progression provided the most helpful and preferred layout. Teachers felt that the function of a teachers’ guide is to provide teaching resources rather than to guide teacher thinking. This study discusses design suggestions that can engage teacher thinking.     

EFFECTS OF FUTURE MATHEMATICS TEACHERS’ AFFECTIVE, COGNITIVE AND SOCIO-DEMOGRAPHIC CHARACTERISTICS ON THEIR KNOWLEDGE AT THE END OF THE TEACHER EDUCATION IN GERMANY AND TAIWAN

How individual characteristics affect the acquisition of knowledge in teacher education has been widely unexplored thus far. The “Teacher Education and Development Study—Learning to Teach Mathematics (TEDS-M)” provides a database for examining this research question across countries. Based on the Taiwanese and German sample of TEDS-M, the relationship between future lower secondary mathematics teachers’ knowledge and their affective, cognitive and socio-demographic characteristics was examined using multilevel modelling whilst controlling for the teachers’ opportunities to learn. The results reveal that in Germany, teacher knowledge is more strongly affected by future teachers’ individual characteristics than teacher knowledge in Taiwan. These results are interpreted against the background of cultural differences between “the West” and “the East” or “individualism” and “collectivism”, respectively.