Mathematical Problem-Solving Through Cooperative Learning—The Importance of Peer Acceptance and Friendships

Mathematical problem-solving constitutes an important area of mathematics instruction, and there is a need for research on instructional approaches supporting student learning in this area. This study aims to contribute to previous research by studying the effects of an instructional approach of cooperative learning on students’ mathematical problem-solving in heterogeneous classrooms in grade five, in which students with special needs are educated alongside with their peers. The intervention combined a cooperative learning approach with instruction in problem-solving strategies including mathematical models of multiplication/division, proportionality, and geometry. The teachers in the experimental group received training in cooperative learning and mathematical problem-solving, and implemented the intervention for 15 weeks. The teachers in the control group received training in mathematical problem-solving and provided instruction as they would usually. Students (269 in the intervention and 312 in the control group) participated in tests of mathematical problem-solving in the areas of multiplication/division, proportionality, and geometry before and after the intervention. The results revealed significant effects of the intervention on student performance in overall problem-solving and problem-solving in geometry. The students who received higher scores on social acceptance and friendships for the pre-test also received higher scores on the selected tests of mathematical problem-solving. Thus, the cooperative learning approach may lead to gains in mathematical problem-solving in heterogeneous classrooms, but social acceptance and friendships may also greatly impact students’ results.

The Development of Civic-Mindedness in College Students

В статье рассмотрена актуальная проблема формирования гражданской позиции у обучающихся гетерогенных групп в колледже. Представлены результаты опытно-экспериментальной работы по формированию гражданской позиции обучающихся гетерогенных групп в колледже. Сформулированы цель и гипотеза; описаны критерии и показатели сформированности гражданской позиции обучающихся в возрасте 15–19 лет (когнитивный, мотивационно-ценностный и деятельностный); организация и этапы экспериментальной работы. Методики диагностики гражданской позиции (бланковый тест М. Рокича «Ценностные ориентации», опросник А. Мехрабиена, Н. Эпштейна «Способность к эмпатии», анкета Е. Н. Титовой, Т. А. Мирошиной) позволили выявить доминирующие ценностные ориентации, уровень эмпатии обучающихся колледжа и степень осознания ими сущности гражданской позиции. Описана теоретическая модель формирования гражданской позиции у обучающихся гетерогенных групп колледжа, на основе которой создана авторская программа «Моя страна», стимулирующая развитие этой позиции. Дана краткая характеристика программы, предполагающей взаимодействие педагогов с разновозрастной группой первокурсников 15–19 лет с учетом индивидуально-личностных особенностей обучающихся и социальных условий их воспитания, в частности социального благополучия/неблагополучия семей. Описаны результаты проверки авторской программы, экспериментально подтверждающие ее эффективность. The article treats an urgent issue associated with the development of civic-mindedness in college students in heterogeneous classrooms. The article accounts for the aim and the hypothesis of the research, describes the criteria that can be used to assess the levels of civic-mindedness development in 15-19-year olds (cognitive, motivational, value-based, and activity-based), focuses on the organization and stages of experimental work. The methods of assessing civic-mindedness (the Rokeach Value Survey, the Mehrabian Questionnaire, the Epstein Questionnaire Measure of Emotional Empathy, the Titova and Miroshina Questionnaire) enable the author to single out dominant value orientations, the level of emotional empathy in college students, the level of their civic-mindedness. The author of the article describes a theoretical model of civic-mindedness development in college students in heterogeneous classrooms and presents her own course “My Country” aimed at the development of civic-mindedness in students. The article describes the My Country course, which presupposes teachers’ interaction with 15-19-year old first-year students. It is expected that teachers should take into account their students’ individual characteristics and personality traits, their social backgrounds, the level of their family wellbeing. The article describes the results of the course elaborated by the author, and provides experimental evidence that the course is efficient.

Complex Instruction: A Model for Reaching Up—and Out

Complex Instruction is a multifaceted instructional model designed to provide highly challenging learning opportunities for students in heterogeneous classrooms. The model provides a rationale for and philosophy of creating equity of access to excellent curriculum and instruction for a broad range of learners, guidance for preparing students for successful groupwork, direction for the teacher’s role, and principles and practices for “groupworthy tasks”—assignments worthy of student investment and designed to draw on a broad range of abilities for successful task completion. This article focuses on the nature and importance of “groupworthy tasks.”