How do secondary students approach different types of division with remainder situations? Some evidence from Spain     

Purificación Rodríguez  M. Oliva Lago  M. Lourdes Hernández  Laura Jiménez  Silvia Guerrero  Sonia Caballero 《European Journal of Psychology of Education - EJPE》2009,24(4):529-543

Division-With-Remainder (DWR) problems are particularly complex, as suggested in many studies. The purpose of this work was to establish whether students’ difficulties in DWR problems came from an inadequate initial representation or from an inadequate final interpretation of the numerical answers, and whether remainders could be grouped into two blocks depending on the kind of answer, either directly matching the terms of the division or not. Forty-five Spanish secondary students, aged 12–13, were requested to solve two Types of Division Situations (i.e., Equal Groups and Comparison), each one involving four Types of Remainder (i.e., Remainder-Not-Divisible, Remainder-Divisible, Remainder-as-the-Result, and Readjusted-Quotient-by-Partial-Increments). Our data showed that: (a) the selection of the correct solution procedure depended on the Type of Division Situations, being easier in Equal Groups than in Comparison problems; (b) correct interpretations were higher than the percentages reported in other researches; and (c) success in problems whose answers were the quotient or the remainder was higher than in Readjusted-Quotient-by-Partial-Increments problems. The results obtained suggest that students’ difficulties originate in the initial representation of the DWR problems and that it would be more adequate to refer to the difficulty of Readjusted-Quotient-by-Partial-Increments problems in particular, rather than to the difficulty of DWR problems in general.  相似文献   

Using Least-to-Most Assistive Prompt Hierarchy to Increase Child Compliance with Teacher Directives in Preschool Classrooms     

Cynthia F. DiCarlo  Jennifer I. Baumgartner  Jamie O. Caballero  Courtney Powers 《Early Childhood Education Journal》2017,45(6):745-754

Prompt strategies have been used to increase the compliance of preschool-aged children to teacher directives. This paper describes two experiments conducted to determine if classroom teachers could learn to use the LtM prompt hierarchy and if child compliance would increase in response to teacher behavior. This study builds on the current literature base by using prompting, specifically LtM with the additional requirement of teacher-child proximity and teacher-child eye level prior to beginning the prompt sequence, which is consistent with recommended practice in early childhood (Copple and Bredekamp, Developmentally appropriate practice in early childhood programs (revised edition), National Association for the Education of Young Children, Washington, DC, 2009). The participants consisted of 6 preschool teachers, with varying levels of education and experience, across 2 different early childhood classrooms. Teacher prompts and children's completion of teacher directives were measured during free choice center time. Results were consistent with previous research in that compliance to teacher directives increased in preschool children with the implementation of the LtM.  相似文献