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1.
When faced with a false generalization and a counterexample, what types of claims do prospective K-8 teachers make, and what factors influence the type and prudence of their claims relative to the data, observations, and arguments reported? This article addresses that question. Responses to refutation tasks and cognitive interviews were used to explore claiming. It was found that prospective K-8 teachers’ claiming can be influenced by knowledge of argumentation; knowledge and use of the mathematical practice of exception barring; perceptions of the task; use of natural language; knowledge of, use of, and skill with the mathematics register; and abilities to technically handle data or conceptual insights. A distinction between technical handlings for developing claims and technical handlings for supporting claims was made. It was found that prudent claims can arise from arguer-developed representations that afford conceptual insights, even when searching for support for a different claim.  相似文献   
2.
Dong Ye 《Discrete Mathematics》2018,341(5):1195-1198
It was conjectured by Mkrtchyan, Petrosyan and Vardanyan that every graph G with Δ(G)?δ(G)1 has a maximum matching M such that any two M-unsaturated vertices do not share a neighbor. The results obtained in Mkrtchyan et al. (2010), Petrosyan (2014) and Picouleau (2010) leave the conjecture unknown only for k-regular graphs with 4k6. All counterexamples for k-regular graphs (k7) given in Petrosyan (2014) have multiple edges. In this paper, we confirm the conjecture for all k-regular simple graphs and also k-regular multigraphs with k4.  相似文献   
3.
We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.  相似文献   
4.
In this article, we study the construction of piecewise linear prewavelets over type-2 triangulations. Different from a so-called semi-prewavelet approach, we investigate the orthogonal conditions directly and obtain parameterized prewavelets with a smaller support. The conditions for parameterized prewavelet basis on the parameters are also given.  相似文献   
5.
This paper shares results from a secondary analysis of data from the participation of Japanese, Singaporean, and U.S. students in the International Project on Mathematical Attainment (IPMA). IPMA was a longitudinal study to assess the mathematics achievement of primary students from their first year of schooling through the end of fifth grade. Tests were constructed to enable achievement on the same items to be assessed over multiple years, thus permitting the assessment of growth in achievement throughout primary school. Achievement is compared to the grade at which the content is introduced so that achievement can be related to students’ opportunity to learn.  相似文献   
6.
Deep eutectic solvents (such as the combination of either urea or glycerol with choline chloride) are effective solvents/organocatalysts for Pictet–Spengler condensations to form carbolines. The reaction conditions are quite mild and do not require additional Bronsted or Lewis acid catalyst. Given the inexpensive, non-toxic, and recyclable nature of the DES, these reaction conditions are simple and highly environmentally friendly.  相似文献   
7.
This paper sets the scene for a special issue of ZDMThe International Journal on Mathematics Education—by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers’ and didacticians’ engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice.  相似文献   
8.
Well‐defined ultrathin nanotubes (30 nm in diameter and of micrometer‐scale length) were generated through the self‐assembly of a novel alternative copolymer synthesized using an epoxy–thiol click‐chemistry reaction. The self‐assembly mechanism was investigated both by experiments and using dissipative particle dynamics (DPD) simulations. The obtained nanotubes can be readily functionalized with carboxy groups, amino groups, peptides, or other groups by simple modular click copolymerization.  相似文献   
9.
Zinc oxide nanoparticles were tethered to carbon nanotubes to form an electrochemical sensing composite, which was characterized using transmission electron microscopy, and X‐ray photoelectron and attenuated total reflectance infrared spectroscopies. The sensor′s electrocatalytic response for measuring hydrogen peroxide was investigated using cyclic voltammetry and chronoamperometry in a dynamic, well defined swimming pool environment. A wide, linear response in the concentration range of 0.025–7.0 mM at a potential of ?0.360 V was shown, with rapid response time (<5 s). The sensor had excellent reproducibility, exhibited stability and selectivity, and was able to measure concentrations in a dynamic environment as they varied.  相似文献   
10.
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