Changes in microbial community structure and function within particle size fractions of a paddy soil under different long-term fertilization treatments from the Tai Lake region, China

Greenhouse gas (GHG) production and emission from paddy soils impacts global climate change. Soil particle size fractions (PSFs) of different sizes act as soil microhabitats for different kinds of microbial biota with varying conditions of redox reactions and soil organic matter (SOC) substrates. It is crucial to understand the distribution of soil microbial community structure within PSFs and linkage to the GHG production from paddy soils of China. The change of bacterial and methangenic archaeal community and activity relating to CH₄ and CO₂ production with PSFs under different fertilizer applications was studied in this paper. The fertilization trial was initiated in a paddy soil from the Tai Lake region, Jiangsu, China with four treatments of non-fertilized (NF), fertilized with inorganic fertilizers only (CF), inorganic with pig manure (CFM) and inorganic with straw return (CFS), respectively since 1987, and the PSFs (<2 μm, 2–20 μm, 20–200 μm, and 200–2000 μm) were separated by a low energy sonication dispersion procedure from undisturbed samples. Analysis of bacterial community within different size particles was conducted by PCR-DGGE. The results indicated significant variation of bacterial community structure within different PSFs. The methane was predominantly produced in the coarser fractions, while more species and higher diversity of bacteria survived in the size of <2 μm fractions, in which the bacterial community structure was more significantly affected by fertilizer application practices than in the other coarser fractions. Higher bacterial species richness and more diversities in the smallest size fractions was due to the vicinity between microbes, access to carbon resource outside the microaggregates, and smaller pore size as protective agent suitable habitats for microbes rather than high SOC. Whereas, higher CO₂, CH₄ production and methanogenic archaeal community in coarser fractions may be contributed to storage of labile organic carbon in these fractions. It indicated that availability of SOC in PSFs is mainly factor affected survival of methanogenic archaeal community structure, whereas, bacterium community habitation more affected by physical protection of their location in PSFs. Their activity greatly depended on liability of SOC access to PSFs. Fertilizer application caused more change of bacteria community in clay fraction and greatly increased bacterium and methanogen activity in coarser fractions but only a slight effect on methanogenic archaeal community in the particle size fractions.     

Using half-baked microworlds to challenge teacher educators’ knowing

This article illustrates how four teacher educators in training were challenged with respect to their epistemology and perceptions of teaching and learning mathematics through their interactions with expressive digital media during a professional development course. The research focused on their experience of communally constructing artifacts and their reflections on the nature of mathematics and mathematics teaching and learning with digital media. I discussed three different ways in which this media was used by the teachers; first, as a means to engage in technical-applied mathematics to engineer mathematical models; second, as a means to construct models for students to engage in experimental-constructivist activity; thirdly, as a means to engage in a discussion of a challenging mathematical problem.

美国新AP化学考试特点分析

通过对改革后AP化学考试的形式、时间以及2014-2016年的AP化学试题进行分析,总结出新版AP化学考试的特点：增加简答题中实验题的数量,考查学生“科学实践”的能力;加强对图表的认知和理解能力的考查等。并得出对我国高中化学教学和高考的几点思考与启示。     

Relationships between emotional dispositions and mathematics achievement moderated by instructional practices: analysis of TIMSS 2015

ABSTRACT

This research is a secondary analysis with Korean students’ data collected in the TIMSS 2015 to describe the moderation effects of instructional practices on the relationships between students’ emotional dispositions toward mathematics and mathematics achievement. From the TIMSS 2015 database, we collected mathematics achievement scores, a student-level contextual scale for students’ emotional disposition, and teacher-level contextual scales representing teachers’ instructional practices. We applied hierarchical linear modelling to construct multilevel models. The findings showed that the achievement gap between emotional dispositions – like and dislike – became smaller when teachers more frequently implemented certain instructional practices like asking students to complete challenging exercises, decide their own problem-solving procedures, and express their ideas in class. Students who disliked mathematics were likely to have higher scores as their teachers implemented each of those practices more frequently. Findings provide important implications to teachers regarding: It is important to encourage students to reason through instructional practices like asking them to decide their own problem-solving procedures and to solve challenging problems.     

Benefits of a teacher and coach collaboration: A case study

This paper describes a case study of a math teacher working with a math coach and the effects of their interaction. A guiding question was whether the coaching intervention had affected the teacher's classroom practices and, if so, in what way. The study utilized data from teacher/coach planning sessions, classroom lessons, follow-up debriefing sessions, and interviews with the teacher, coach and school principal. These data enabled the author to study the impact, if any, of the coaching on teacher beliefs and practices.     

Teacher flexibility in mathematical discussion

The significance of discussion in mathematics classes has been prominently debated in the research literature. Different studies have stressed the importance of teacher flexibility in orchestrating the discussion. We introduce an operational definition of teacher flexibility. In a case study with one secondary-school mathematics teacher, we microanalyzed discussion situations in which the teacher had to change her plan according to unforeseen student replies. The analysis was aimed at characterizing situations in which the teacher was either flexible or inflexible in her interactions with students and describing the factors that affected her flexibility. We suggest four basic patterns of teacher flexibility and discuss the complexity of the factors that shape them.     

What “counts” as algebra in the eyes of preservice elementary teachers?

This study examined conceptions of algebra held by 30 preservice elementary teachers. In addition to exploring participants’ general “definitions” of algebra, this study examined, in particular, their analyses of tasks designed to engage students in relational thinking or a deep understanding of the equal sign as well as student work on these tasks. Findings from this study suggest that preservice elementary teachers’ conceptions of algebra as subject matter are rather narrow. Most preservice teachers equated algebra with the manipulation of symbols. Very few identified other forms of reasoning - in particular, relational thinking - with the algebra label. Several participants made comments implying that student strategies that demonstrate traditional symbol manipulation might be valued more than those that demonstrate relational thinking, suggesting that what is viewed as algebra is what will be valued in the classroom. This possibility, along with implications for mathematics teacher education, will be discussed.     

Empirical reconstruction of learning progressions based on teachers’ tagging of didactic metadata

In their enactment of the curriculum, teachers have a substantial role as instructional designers. Accordingly, any evaluation of the progression of students’ learning should first be concerned with the pedagogical intentions of the teacher. In this article we present a method for reconstructing teachers’ implicit and tacit considerations in their selection, sequencing and enactment of tasks. Two 11^th grade teachers tagged all of the tasks that comprised a 5-week learning progression. Tagging consisted of assigning values to prescribed categories of metadata. Visual representations of the metadata revealed patterns in the tagged progressions, and allowed the teachers to reflect upon these patterns. Both teachers, though guided by very different didactical considerations, validated that many of their explicit and implicit intentions were revealed in the representations of the progressions. Furthermore, both teachers had the opportunity to reflect on tacit aspects of their instructional design that they were not previously aware of.     

Mathematics teachers’ views about the limited utility of real analysis: A transport model hypothesis

In the United States and elsewhere, prospective teachers of secondary mathematics are usually required to complete numerous advanced mathematics courses before obtaining certification. However, several research studies suggest that teachers’ experiences in these advanced mathematics courses have little influence on their pedagogical practice and efficacy. To understand this phenomenon, we presented 14 secondary mathematics teachers with four statements and proofs in real analysis that related to secondary content and asked the participants to discuss whether these proofs could inform their teaching of secondary mathematics. In analyzing participants’ remarks, we propose that many teachers view the utility of real analysis in secondary school mathematics teaching using a transport model, where the perceived importance of a real analysis explanation is dependent upon the teacher’s ability to transport that explanation directly into their instruction in a secondary mathematics classroom. Consequently, their perceived value of a real analysis course in their teacher preparation is inherently limited. We discuss implications of the transport model on secondary mathematics teacher education.     

The catwalk task: Reflections and synthesis: Part 1

In this article I recount my experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, I reflect on my own mathematical work on the catwalk task, including my efforts to fit various algebraic models to the data. Second, I reflect on my experiences working with a group of high school students on the catwalk task and my interpretations of their mathematical thinking. Finally, I reflect on the entire experience with the catwalk problem, as a mathematics learner, as a teacher, and as a professional.