Amplification of cox2 (∼620 bp) from 2 mg of Up to 129 Years Old Herbarium Specimens, Comparing 19 Extraction Methods and 15 Polymerases

During the past years an increasing number of studies have focussed on the use of herbarium specimens for molecular phylogenetic investigations and several comparative studies have been published. However, in the studies reported so far usually rather large amounts of material (typically around 100 mg) were sampled for DNA extraction. This equals an amount roughly equivalent to 8 cm2 of a medium thick leaf. For investigating the phylogeny of plant pathogens, such large amounts of tissue are usually not available or would irretrievably damage the specimens. Through systematic comparison of 19 DNA extraction protocols applied to only 2 mg of infected leaf tissue and testing 15 different DNA polymerases, we could successfully amplify a mitochondrial DNA region (cox2; ∼620 bp) from herbarium specimens well over a hundred years old. We conclude that DNA extraction and the choice of DNA polymerase are crucial factors for successful PCR amplification from small samples of historic herbarium specimens. Through a combination of suitable DNA extraction protocols and DNA polymerases, only a fraction of the preserved plant material commonly used is necessary for successful PCR amplification. This facilitates the potential use of a far larger number of preserved specimens for molecular phylogenetic investigation and provides access to a wealth of genetic information in preserved in specimens deposited in herbaria around the world without reducing their scientific or historical value

Opportunities to Learn Mathematics Pedagogy and Connect Classroom Learning to Practice: A Study of Future Teachers in the United States and Singapore

In this study, we conducted secondary analyses using the TEDS-M database to explore future mathematics specialists teachers’ opportunities to learn (OTL) how to teach mathematics. We applied latent class analysis techniques to differentiate among groups of prospective mathematics specialists with potentially different OTL mathematics pedagogy within the United States and Singapore. Within the United States, three subgroups were identified: (a) Comprehensive OTL, (b) Limited OTL, and (c) OTL Mathematics Pedagogy. Within Singapore, four subgroups were identified: (a) Comprehensive OTL, (b) Limited Opportunities to Connect Classroom Learning with Practice, (c) OTL Mathematics Pedagogy, and (d) Basic OTL. Understanding the opportunities different prospective teachers had to learn from and their experiences with different components of instructional practice in university and practicum settings has implications for teacher preparation programs

The Relations Among School Climate, Instructional Quality, and Achievement Motivation in Mathematics

Instructional quality is considered to be an important classroom variable, as it is significantly related to student achievement and motivation in mathematics. Existing studies in educational effectiveness furthermore identified a positive relation between instructional quality and school climate, suggesting that the school environment plays a significant role in teachers’ instructional practices. In order to bring together these two core findings, the relations among different aspects of school climate, instructional quality, and students’ achievement motivation for the TIMSS 2011 grade eight mathematics data sets comprising 50 countries are investigated. In particular, the role of instructional quality as a potential mediator between school climate and student motivation is examined, thereby focusing on three aspects of school climate (emphasis on academic success, safety, and order in schools) and three aspects of achievement motivation (self-concept, intrinsic value, and extrinsic value). In general, there was a significant positive relation between instructional quality and achievement motivation at the classroom level in mathematics; in some countries, a partial mediation of instructional quality between school climate and achievement motivation was apparent. Four main patterns of relations occurred. These findings are discussed with respect to implications for educational effectiveness research

Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai

This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students’ understanding towards a structural view of linear function