The Relationship Between High-School Mathematics Teachers\u27 Beliefs and Their Practices in Regards to Intellectual Quality

This study examines the relationship between mathematics teachers’ beliefs and instructional practices related to learning, pedagogy, and mathematics in regards to components of intellectual quality for eight high-school mathematics teachers. Research has demonstrated that the higher the degree of intellectual quality for instruction is rated the higher student achievement is on standardized assessments. The findings in this study demonstrate a consistent pattern between teachers espoused beliefs and their instructional practices. Even though teachers’ practices changed as they wrote curricular units to be more in line with intellectual quality characteristics, their beliefs stayed consistent over an 18 month period and were correlated to their instructional practices at the beginning and end of the project

PICK1 links Argonaute 2 to endosomes in neuronal dendrites and regulates miRNA activity.

MicroRNAs fine-tune gene expression by inhibiting the translation of mRNA targets. Argonaute (Ago) proteins are critical mediators of microRNA-induced post-transcriptional silencing and have been shown to associate with endosomal compartments, but the molecular mechanisms that underlie this process are unclear, especially in neurons. Here, we report a novel interaction between Ago2 and the BAR-domain protein, PICK1. We show that PICK1 promotes Ago2 localization at endosomal compartments in neuronal dendrites and inhibits Ago2 function in translational repression following neuronal stimulation. We propose that PICK1 provides a link between activity-dependent endosomal trafficking and local regulation of translation in neurons

Exploring and Examining Quantitative Measures

The purpose of this working group is to bring together scholars with an interest in examining the research on quantitative tools and measures for gathering meaningful data, and to spark conversations and collaboration across individuals and groups with an interest in synthesizing the literature on large-scale tools used to measure student- and teacher-related outcomes. While syntheses of measures for use in mathematics education can be found in the literature, few can be described as a comprehensive analysis. The working group session will focus on (1) defining terms identified as critical (e.g., large-scale, quantitative, and validity evidence) for bounding the focus of the group, (2) initial development of a document of available tools and their associated validity evidence, and (3) identification of potential follow-up activities to continue the work to identify tools and developed related synthesis documents (e.g., the formation of sub-groups around potential topics of interest). The efforts of the group will be summarized and extended through both social media tools (e.g., creating a Facebook group) and online collaboration tools (e.g., Google hangouts and documents) to further promote this work

Manganese-catalysed hydrofunctionalisation of alkenes

The development of new first-row transition metal catalysts as both replacements for precious metals catalysts and in the search for novel reactivity is a crucial evolution for catalysis. Manganese is a non-toxic, inexpensive and Earth-abundant metal, making it a perfect candidate for catalysis. Despite this, manganese catalysis has not undergone the same development as for other Earth-abundant metals. The manganese-catalysed hydrosilylation and hydroboration of alkenes has been developed to give hydrofunctionalisation products in typically good yields (up to >95%) with control of regio- and chemo-selectivity. This work uses a bench-stable precatalyst/ activator manifold allowing for a simple methodology, ideal for the nonspecialist. This represents the first example of a developed methodology for the manganesecatalysed hydrosilylation of alkenes. This methodology uses a bis(imino)pyridine manganese(II) pre-catalyst which has previously been unreactive in related reactions. The critical discovery has been in the use of an alkoxide activation system which enables the generation of a catalytically-active manganese species

Practical Mechanically Interlocked Molecules: A Model of Gas Adsorption in Metal OrganicFrameworks Harboring Rotaxane Molecular Shuttles

Metal organic frameworks(MOFs) are a class of crystalline materials utilized in gas storage, chemicalsensing, and other engineering applications. Recently chemists have begun synthesizing MOFs withmoving parts in order to further these applications. A wide array of dynamic MOFs have been created andtheorized. Among them is the interlocking of a ring shaped molecule on the dumbbell like strut of a metalorganic framework called a rotaxane molecular shuttle. Recently a rotaxane molecular shuttle(RMS) MOFwas synthesized for the first time. This RMS-MOF is called UWDM-4 and is a proof of concept materialfor a mechanically interlocked molecule MOF with a moving shuttle harbored in its pores. In order tomotivate further synthesization and experimentation with RMS-MOFs we pose a statistical mechanicalmodel based on the langmuir model of gas adsorption that models the potential for both the shuttle-gascompetition for binding sites and the entropic effects of the moving shuttle to affect gas adsorption.Our model is advantageous in that it can be solved analytically while allowing the two aforementionedeffects to be explored. We defined a usable space of parameters for our model we termed material space,consisting of the bonding energies of the gas at two discrete stations on the strut of the MOF, and anenergetic penalty for the rotaxane to occupy one of the binding sites(this allows us to model the shuttlefavoring one side). We then compared adsorption properties to a single site MOF with the same expectedgas occupancy at a given temperature. We found that an RMS-MOF located properly in material spaceto be less temperature sensitive to adsorption and to have a smaller heating effect from gas adsorption.Both allow for more efficacious gas storage

Shadow process tomography of quantum channels

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scale exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.Comment: 12 pages, 5 figures; Added citation to similar work; Errors corrected. Previous statements of main result first missed and then miscalculated an exponential cost in system size; Version accepted for publicatio

Statewide Mathematics Professional Development: Teacher Knowledge, Self-Efficacy, and Beliefs

We examined the impact of a state mandated K-12 mathematics professional development course on knowledge, self-efficacy and beliefs of nearly 4,000 teachers and administrators. Participants completed the Mathematical Thinking for Instruction course, emphasizing student thinking, problem-solving, and content knowledge specific to mathematics instruction. Inventories utilizing items fromthe Learning Mathematics for Teaching project (2005) measured changes in participants’ Mathematical Knowledge for Teaching (MKT) and an end-of-course self-evaluation enabled analysis of changes in MKT, self-efficacy and beliefs. Statistically significant changes were found in all three variables. This study adds to our understanding of the potential usefulness of mandating professional development as a policy vehicle for influencing educators’ mathematics knowledge and beliefs

Analysis of Students’ Proportional Reasoning Strategies

Proportional reasoning is key to students’ acquisition and application of complex mathematics and science topics. Research is needed regarding how students’ progress towards and come to demonstrate key developmental understandings within proportional reasoning. To this end we created and administered assessment items to 297 middle grades students. We categorized student solution processes qualitatively, followed by Rasch analysis to examine item difficulty and strategy use in relation to an anticipated trajectory. Our findings indicate that different strategies manifest themselves in a hierarchical manner, providing initial confirmation of categories based on strategy efficiency and emphasizing the importance of teacher (and researcher) analysis of classroom assessments from a student cognition perspective

Influence of Proportional Number Relationships on Item Accessibility and Students’ Strategies

Extensive evidence points to the need for mathematics instruction to tap into students’ informal understandings in order to conceptually develop formal mathematical ideas (Ahl, Moore, & Dixon, 1992; Freudenthal, 1973, 1991; Treffers, 1987). Contextual problems are a common means of helping students access their informal mathematical ideas (Lamon, 1993; Moore & Carlson, 2012). However, to successfully use context in this manner, we must ensure these problems are accessible to students and have the potential to promote connections to deeper or more formal mathematics (Jackson, Garrison, Wilson, Gibbons, & Shahan, 2013; Stein, Smith, Henningsen, & Silver, 2000). There is thus a need for research to identify what characteristics make contextual tasks accessible to students as a point of entry and useful for educators in analyzing and pressing students’ thinking