A Microgenetic Study of the Conceptual Development of Inversion on Multiplication/Division Inversion Problems
نویسنده
چکیده
The purpose of this study was to conduct a microgenetic study of the development of the concept of inversion as it applies to multiplication and division inversion problems. The study was modelled on Siegler and Stern’s (1998) study in which Grade 2 participants solved addition and subtraction inversion problems (a + b b) for 6 weekly sessions. In session 7, modified inversion problems (b + a b) as well as lure problems (b a + b) were also included. In the current study, Grade 6 participants solved multiplication and division inversion problems (d x e ÷ e) during 6 weekly sessions. Previous research has shown that this latter type of inversion problems is more difficult than the former type. The present results indicate that there are differences in how frequently participants discover and apply the inversion concept compared to Siegler and Stern’s (1998) work. The findings add to the recent body of knowledge indicating that the concept of inversion as it applies to multiplication and division is significantly more difficult than it is for addition and subtraction.
منابع مشابه
Individual and Collaborative Output Tasks: Effects on the Acquisition of English Inversion Structures
This study investigated the effectiveness of individual and collaborative outputbasedfocus-on-form instructional tasks on the acquisition of English inversionstructures by EFL learners. Moreover, it explored the developmental trend oflearners’ inversion acquisition. To this end, 60 homogeneous EFL learners wereassigned to individual and collaborative output groups. They were exposed to textsenc...
متن کاملJoint inversion of ReMi dispersion curves and refraction travel times using particle swarm optimization algorithm
Shear-wave velocity ( ) is an important parameter used for site characterization in geotechnical engineering. However, dispersion curve inversion is challenging for most inversion methods due to its high non-linearity and mix-determined trait. In order to overcome these problems, in this study, a joint inversion strategy is proposed based on the particle swarm optimization (PSO) algorithm. The ...
متن کاملComparing Geostatistical Seismic Inversion Based on Spectral Simulation with Deterministic Inversion: A Case Study
Seismic inversion is a method that extracts acoustic impedance data from the seismic traces. Source wavelets are band-limited, and thus seismic traces do not contain low and high frequency information. Therefore, there is a serious problem when the deterministic seismic inversion is applied to real data and the result of deterministic inversion is smooth. Low frequency component is obtained fro...
متن کاملDiscretized Adjoint State Time and Frequency Domain Full Waveform Inversion: A Comparative Study
This study derives the discretized adjoint states full waveform inversion (FWI) in both time and frequency domains based on the Lagrange multiplier method. To achieve this, we applied adjoint state inversion on the discretized wave equation in both time domain and frequency domain. Besides, in this article, we introduce reliability tests to show that the inversion is performing as it should be ...
متن کاملInverse Problems in Imaging Systems and the General Bayesian Inversion Frawework
In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Baye...
متن کامل