将矿物学理论与实验知识引入基础无机化学教学的探讨

矿物学是与无机化学密不可分的兄弟学科之一。无机化学知识的一个重要来源就是人类对矿物的观察与研究,同时元素化学的基础研究也被广泛应用于矿物学。对于矿物的认识可以加深学生对于无机化学理论联系实际的感性和理性认识,并进一步熟悉相关元素的性质。本文从基础无机化学教学的角度整理了矿物学的理论与实验教学要点,并以多种典型矿物为实验对象描述其实验性质,并阐述如何结合矿物实例进行矿物学理论与实验的教学。将矿物学相关内容引入基础无机化学教学,不失为一种交叉学科与基础化学教育相结合的新模式。     

基于Leslie模型的北京市基础教育学龄人口分城乡预测

以2010年第六次人口普查数据为基点,考虑到已经开放的单独二胎政策以及全面放开的二胎政策等因素,对北京市2020—2030年基础教育学龄人口变动情况分城乡进行预测.研究发现:北京学龄人口总体上呈现先上升后下降趋势;城市学龄人口远远高于农村学龄人口;城市各个阶段学龄人口均出现了先升后降趋势;农村幼儿园学龄人口呈现快速下降趋势,小学、初中学龄人口均呈现了先升后降趋势,农村高中学龄人口呈现了"下降-上升-下降-上升"的反复波动.学龄人口的变化反映了未来教育需求的变动,在未来10-15年,北京市还需要加大教师队伍建设、加强基础设施建设,努力实现城乡教育资源均衡化,最大限度地实现教育公平.     

A different perspective of the teaching philosophy of RL Moore

Dr RL Moore was undoubtedly one of the finest mathematics teachers ever. He developed a unique teaching method designed to teach his students to think like mathematicians. His method was not designed to convey any particular mathematical knowledge. Instead, it was designed to teach his students to think. Today, his method has been modified to focus on using student participation toward the goal of the conveyance of mathematical knowledge rather than on Dr Moore's goal of teaching students to think. This article proposes that undergraduates would be better served if they took at least one course using Dr Moore's original method and his original goal.     

Symmetry and the golden ratio in the analysis of a regular pentagon

The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to the golden ratio. Here, we will study some relations existing between a regular pentagon and this ratio. First, we will focus on the group of fivefold rotational symmetry, to find the position in the complex plane of the vertices of this geometric figure. Then, we will propose an analytic method to solve the same problem based on the Cartesian coordinates, a method where we find the golden ratio without any specific geometric consideration. This study shows a comparison of the use of complex numbers, symmetries and analytic methods, applied to a subject which can be interesting for general education in mathematics. In fact, the proposed approach can convey and link several concepts, requiring only a general pre-college education, showing at the same time the richness that mathematics can offer in solving geometric problems.     

Finding Alignment: The Perceptions and Integration of the Next Generation Science Standards Practices by Elementary Teachers

Preparing elementary‐level teachers to teach in alignment with the eight Next Generation Science Standards (NGSS) practices could prove to be a daunting endeavor. However, the process may be catalyzed by leveraging elements of teacher science instruction that inherently attend to the practice standards. In this study, we investigated the science instruction of three grade 3–5 elementary‐level teachers. We used observation, interviews, and surveys to determine the level to which the teachers perceived they taught and engaged in teaching science aligned with the eight NGSS practices. We found that the teachers were partially, and intrinsically implementing several of these practices in their instruction, and at the same time could not articulate the eight NGSS practices. Our results suggest there may be ample opportunity to build on the current science instruction of elementary‐level teachers to bring their instruction into alignment with the NGSS. We found that teachers’ perceive professional development, school culture, and access to additional instructional resources to be essential to their adoption of the NGSS practices.     

What Is a Fraction? Developing Fraction Understanding in Prospective Elementary Teachers

Classroom teachers need a well‐developed deep understanding of fractions and pedagogic practices so they can provide meaningful experiences for students to explore and construct ideas about fractions. This study sought to examine prospective elementary teachers' understandings of fraction by focusing specifically on their use of fractions meanings and interpretations. Results indicated that prospective elementary teachers bring with them to their final methods course a limited understanding of fractions and that experiences in methods courses resulted only in minor improvement of those limited understandings. The limited part‐whole understanding of fractions that prospective elementary teachers entered the course with was resilient. The implications of this study suggest a need for prospective elementary teachers to continue to develop their conceptual understanding of fractions and for changes to the content and instructional strategies of mathematics content courses designed for prospective elementary teachers.     

Characteristics of Second Graders' Mathematical Writing

This study compared the characteristics of second graders' mathematical writing between an intervention and comparison group. Two six‐week Project M2 units were implemented with students in the intervention group. The units position students to communicate in ways similar to mathematicians, including engaging in verbal discourse where they themselves make sense of the mathematics through discussion and debate, writing about their reasoning on an ongoing basis, and utilizing mathematical vocabulary while communicating in any medium. Students in the comparison group learned from the regular school curriculum. Students in both the intervention and comparison groups conveyed high and low levels of content knowledge as indicated in archived data from an open‐response end‐of‐the‐year assessment. A multivariate analysis of variance indicated several differences favoring the intervention group. Both the high‐ and low‐level intervention subgroups outperformed the comparison group in their ability to (a) provide reasoning, (b) attempt to use formal mathematical vocabulary, and (c) correctly use formal mathematical vocabulary in their writing. The low‐level intervention subgroup also outperformed the respective comparison subgroup in their use of (a) complete sentences and (b) linking words. There were no differences between groups in their attempt at writing and attempts at and usage of informal mathematical vocabulary.     

Next Generation Science Standards: A National Mixed‐Methods Study on Teacher Readiness

Next Generation Science Standards (NGSS) science and engineering practices are ways of eliciting the reasoning and applying foundational ideas in science. As research has revealed barriers to states and schools adopting the NGSS, this mixed‐methods study attempts to identify characteristics of professional development (PD) that will support NGSS adoption and to improve teacher readiness. In‐service science teachers from across the nation were targeted for the survey and responses represented 38 states. Research questions included: How motivated and prepared are in‐service 7–12 teachers to use NGSS science and engineering practices? What is the profile of 7–12 in‐service teachers who are motivated and feel prepared to use NGSS science and engineering practices? The study revealed that teachers identified engineering most frequently as a PD need to improve their NGSS readiness. High school teachers rated themselves as more prepared than middle school and all teachers who use Modeling Instruction expressed higher NGSS readiness. These findings and their specificity contribute to current knowledge, and can be utilized by districts in selecting PD to support teachers in preparing to implement the NGSS successfully.     

Beliefs,Practical Knowledge,and Context: A Longitudinal Study of a Beginning Biology Teacher's 5E Unit

The purpose of this three‐year case study was to understand how a beginning biology teacher (Alice) designed and taught a 5E unit on natural selection, how the unit changed when she took a position in a different school district, and why the changes occurred. We examined Alice's developing beliefs about science teaching and learning, practical knowledge, and perceptions of school context in relation to the 5E unit. Data sources consisted of interviews, classroom observations, and lesson materials. We found that Alice placed more emphasis on the explore phase, less emphasis on the engage and explain phases, and removed the elaborate phase over time. Alice's beliefs about science teaching and learning acted as a filter for making sense of practical knowledge and perceptions of context. Although her beliefs were student centered, they aligned with discovery learning in which little intervention from the teacher is required. We discuss how her beliefs, practical knowledge, and perceptions of context explained the changes in her practice. This study sheds insight into the nature of beliefs and how they relate to the 5E lesson phases, as well as the different lenses for viewing the 5E instructional model. Implications for science teacher preparation and induction programs are discussed.     

Teachers Describe Epistemologies of Science Instruction Through Q Methodology

Creating scientifically literate students is a common goal among educational stakeholders. An understanding of nature of science is an important component of scientific literacy in K‐12 science education. Q methodology was used to investigate the opinions of preservice and in‐service teachers on how they intend to teach or currently teach science. Q methodology is a measurement tool designed to capture personal beliefs. Participants included 40 preservice and in‐service elementary and secondary science teachers who sorted 40 self‐referential statements regarding science instruction. The results identified three epistemologies toward teaching science: A Changing World, My Beliefs, and Tried and True. Participants with the A Changing World epistemology believe evidence is reliable, scientific knowledge is generated in multiple ways, and science changes in light of new evidence. The My Beliefs epistemology reflects that scientific knowledge is subject to change due to embedded bias, science is affected by culture and religion, and evolution should not be taught in the classroom. The Tried and True epistemology views a scientific method as an exact method to prove science, believes experiments are crucial for scientific discoveries, absolute truth exists in scientific knowledge, and society and cultural factors can be eliminated from investigations. Implications for preservice teacher education programs and in‐service teacher professional development are addressed.