Group Of Solvers Research Articles

Investigating the Variety and Usualness of Correct Solution Procedures of Mathematical Word Problems

The contribution focuses on issues related to the implementation of formative assessment methods into inquiry based teaching, by means of issues related to solving twelve multiple-step arithmetic word problems based on operations with natural and rational numbers. These word problems have multiple correct solution procedures and the presented qualitative exploratory empirical study investigates how varied and how usual might be correct solution procedures provided by diverse groups of solvers – future primary school teachers attending diverse university mathematics courses of diverse forms and/or time extent. According to written data collected from 149 solvers, six notions are introduced in the paper: majority, minority and even solution procedures, and majority, minority and mixed solvers. Issues regarding minority solvers are recognized as an important element for implementing formative assessment methods. All the six notions are illustrated in the paper by samples of solution procedures and diagrams of relative frequency. Implications are given for formative assessment within any kind of education involving multiple-step word problems, regardless of the extent of implemented inquiry.

A simulation environment to simulate lower-hybrid-wave-driven plasmas efficiently

In this study a hybrid simulation environment to investigate the lower-hybrid-wave-driven tokamak plasmas is presented, and its application to the spherical tokamak TST-2 is described. These plasma are formed and driven by radio-frequency waves without the use of the central solenoid, and are characterized by low density and low magnetic field. A hybrid simulation environment which is divided into two groups, one using magneto-hydrodynamic (MHD) as well as particle-in-cell (PIC) approaches, and the second group using ray-tracing and Fokker–Planck solvers, is applied to describe the behavior of energetic electrons, bulk plasma, wave propagation, and the wave-particle interaction. Both groups of solvers can be coupled via the energetic-particle velocity distribution function and the equilibrium conditions of magnetic field, pressure, and density profiles to obtain a self-consistent solution. First results show the impact of a self-consistent equilibrium on ray trajectories and current density profiles. Therefore, new insights in lower-hybrid-wave-driven plasmas of TST-2 can be obtained using the proposed hybrid simulation environment.

Women and mental rotation: Incremental theory and spatial strategy use enhance performance

Mental rotation is a spatial skill in which men outperform women. The present research tested a motivational explanation of this gender difference with the hypothesis that positive beliefs will in women favor use of spatial strategies, which in turn will lead to improved MRT performance. Spatial strategy use and two beliefs, namely incremental theory and self-perception of ability in stereotypically masculine (i.e., requiring spatial ability) tasks, were assessed in a sample of 120 women. Two groups of solvers – one spatial, one non-spatial – were selected on the basis of self-rated strategy use. Results demonstrated that use of spatial strategies mediates the effect of incremental theory of masculine tasks on MRT performance, whereas self-perception of ability directly influences MRT performance. Findings are discussed on the basis of a socio-cognitive explanation of gender differences in mental rotation.

Evolving artificial neural network ensembles

Using a coordinated group of simple solvers to tackle a complex problem is not an entirely new idea. Its root could be traced back hundreds of years ago when ancient Chinese suggested a team approach to problem solving. For a long time, engineers have used the divide-and-conquer strategy to decompose a complex problem into simpler sub-problems and then solve them by a group of solvers. However, knowing the best way to divide a complex problem into simpler ones relies heavily on the available domain knowledge. It is often a manual process by an experienced engineer. There have been few automatic divide-and-conquer methods reported in the literature. Fortunately, evolutionary computation provides some of the interesting avenues to automatic divide-and-conquer methods. An in-depth study of such methods reveals that there is a deep underlying connection between evolutionary computation and ANN ensembles. Ideas in one area can be usefully transferred into another in producing effective algorithms. For example, using speciation to create and maintain diversity had inspired the development of negative correlation learning for ANN ensembles, and an in-depth study of diversity in ensembles. This paper will review some of the recent work in evolutionary approaches to designing ANN ensembles.

A Parsimony Tree for the SAT2002 Competition

Twenty of the programs (solvers) submitted to the SAT 2002 Contest had no disqualifying errors. These solvers were run on 2023 satisfiability problems of varying hardnesses. Each solver was judged by which problems it could solve within the allowed time limit. Twelve solvers were best on some problem – they could solve it and the others could not. Only two solvers could not beat each remaining solver on some problems (where the problems could vary depending on which solver it was trying to beat). Thus, there is evidence that 18 solvers were extremely good. It is interesting to analyze the contest results in a way that groups together solvers with similar strengths and weaknesses. This paper uses the parsimony algorithm to produce a classification of the twenty solvers. The paper also has a second classification, almost the same as the first, for the twenty solvers, updated versions of two solvers, and a fictitious state of the art solver. The contest problems came in three groups, Industrial, Hand Made, and Random. The Random group of problems was about three times as large as the other two together. The classification identifies four groups of solvers (plus a miscellaneous group): weak solvers, incomplete solvers which are very good at some satisfiable Random problems, complete solvers which are very good at most Random problems, and complete solvers which are very good at Industrial and Hand Made problems.

Use of absorbing Markov chains as a measurement model for the process of analogical transfer

An absorbing Markov chain is introduced to the major states of the process of analogical transfer. Through this approach some useful conclusions are drawn concerning the analogical problem‐solving abilities of a group of solvers.

Measuring problem‐solving skills

We apply Markov chain process and through this we obtain several possibilities about the ‘behaviour’ of a group of solvers during the process of the problem‐solving strategy, which may be useful to the teacher of mathematics in organizing and planning lectures. As an example, we study the progress in mathematics of the second term students of our institution. Finally, we describe.