Let $\pi$ be a ${\rm SL}(3,\Bbb{Z})$ Hecke-Maass cusp form. Let $\chi=\chi_1\chi_2$ be a Dirichlet character with $\chi_i$
primitive modulo $M_i$. Suppose $M_1$, $M_2$ are primes such that ...$\sqrt{M_2}M^{4\delta}<M_1<M_2M^{-3\delta}$, where
$M=M_1M_2$ and $0<\delta<1/28$. In this paper we will prove the following subconvex bound
$$
L\left({1\over 2},\pi\otimes\chi\right)\ll_{\pi,\varepsilon} M^{{3\over 4}-\delta+\varepsilon}.
$$
Abstract
Polya propose the didactic problem-solving strategy to strengthen the teaching and learning processes in the mathematic field. Thus, this strategy can be applied in other fields such as ...physics teaching the article proposes an evaluation strategy based on the design of a rubric to assess the processes associated with solving mathematical problems, as a classroom research work based on Research, Pedagogical Action. As one of the results, an analytical rubric composed of criteria and indicators associated with the steps of Polya problem solving is proposed, as well as a reflection associated with the teaching of problem solving in the engineering area.
Problems and Solutions Edgar, Gerald A.; Ullman, Daniel H.; West, Douglas B.
The American mathematical monthly,
10/21/2018, Letnik:
125, Številka:
9
Journal Article
Recenzirano
Several proposed mathematical problems are presented.
Assessing problem-solving remains a challenge for both teachers and researchers. With the aim of contributing to the understanding of this complex process, this paper presents an exploratory study of ...peer assessment in mathematical problem-solving activities. The research was conducted with a group of future Secondary mathematics teachers who first were asked to individually solve an open-ended problem and then, to assess a classmate’s answer in pairs. We present a study of two cases involving two pairs of students, each of whom assessed the solution of a third classmate. The analysis was carried out in two interrelated phases: (a) individual solutions to the mathematical problem and (b) the peer assessment process. The results show that, in both cases, the assessors were strongly attached to their own solutions, which directly influenced the assessment process, focused on aspects that involve the general problem-solving process and the results. The main difference between the evaluation processes followed by the two pairs lies in the concept of assessment. While the first pair focuses on assessing the resolution process and errors, the other focuses its discussion on giving a numerical grade.
Latent variable analyses of cognitive abilities are among the major means by which cognitive psychologists test theories regarding the structure of human cognition. Models are fit to observed ...variance-covariance structures, and the fit of those models are compared to assess the merits of competing theories. However, an often unconsidered and potentially important methodological issue is the precise sequence in which tasks are delivered to participants. Here we empirically tested whether differences in task sequences systematically affect the observed factor structure. A large sample (N = 587) completed a battery of 12 cognitive tasks measuring four constructs: working memory, long-term memory, attention control, and fluid intelligence. Participants were assigned to complete the assessment in one of three sequences: fixed and grouped by construct vs. fixed and interleaved across constructs vs. random by participant. We generated and tested two hypotheses: grouping task sequences by construct (i.e., administering clusters of tasks measuring a cognitive construct consecutively) would (1) systematically increase factor loadings and (2) systematically decrease interfactor correlations. Neither hypothesis was supported. The measurement models were largely invariant across the three conditions, suggesting that latent variable analyses are robust to such subtle methodological differences as task sequencing.
For a given graph F, graph G is called F-saturated if G does not contain a copy of F, but G+e has a copy of F, where e∉EG. The saturation number, denoted by satn,F, is the minimum size of a graph ...with order n in all F-saturated graphs. For n≥6t+22, this paper considers the saturation number of linear forests 2P4∪tP2 and describes the extremal graph.
PDF
