Branching of the Falkner-Skan solutions for λ < 0

The Falkner-Skan equation f'" + ff" + λ(1 - f'^2) = 0, f(0) = f'(0) = 0, is discussed for λ < 0. Two types of problems, one with f'(∞) = 1 and another with f'(∞) = -1, are considered. For λ = 0- a close relation between these two types is found. For λ < -1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f' - 1. The numerical results indicate that the solution branches with f'(∞) = 1 and those with f'(∞) = -1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for λ < -1, is presented.

Young children working together:Cooperative learning effects on group work of children in Grade 1 of primary education

It was examined whether cooperative learning within the Success for All (SfA) program led to improved group work behaviour of Grade 1 pupils. 168 pupils of six SfA schools and 144 pupils of four control schools participated. Positive and negative group work behaviour was observed during a group task, taking into account socioemotional ethos, group participation, and type of dialogue. Longitudinal multilevel analysis was used for the sequence of observed 20-s time intervals. SfA groups showed more positive and less negative group work behaviour compared to control groups, whilst controlling for several group characteristics. Results suggest that negative group work behaviour increased gradually during the whole task in control groups, while in SfA groups it increased only towards the end of the task. The findings indicate that cooperative learning may lead to improved group work behaviour of young pupils (6–7 years old)

The proof of the pudding is in the eating? Implementation of cooperative learning:Differences in teachers’ attitudes and beliefs

In the current study differences between primary school teachers classified as high-performing in their implementation of cooperative learning (CL) in their classrooms and teachers who were less successful in implementing cooperative learning were investigated. The levels of implementation of cooperative learning differed significantly between teachers, especially in teaching students the needed cooperative behaviours. Based on semi-structured interviews, it was found that low-performing CL teachers struggle more with student behaviour during cooperative learning, while high-performing CL teachers feel more able to regulate student behaviour. We concluded that teachers who differed in their teacher performance of implementation of cooperative learning also differed in their attitudes and beliefs about this approach. An integrated model on professional development and teacher change is proposed to interpret the results of differences between teachers. This model shows that positive attitudes and beliefs before implementation, but also experiencing positive student outcomes (incl. positive student behaviour) during implementation are important factors in making cooperative learning successful in practice. We suggest that teachers should be prevented from entering a negative spiral in which they experience student behaviour during cooperative learning only as difficult and, therefore, do not succeed in improving students’ cognitive and behavioural outcomes

Enhancing young students' high-level talk by using cooperative learning within Success for All lessons

This study examined whether students achieved high-level talk during group work because of involvement in cooperative learning within the Success for All (SfA) program. SfA is a comprehensive school program in which cooperative learning plays a key role, in addition to several other components such as parental involvement and tutoring. A quasi-experimental design with a treatment and a control group was used. At the end of the school year, grade-1 students (6- and 7-years-old children) executed a group task in small groups of four students. At that moment, SfA students had experienced cooperative learning within SfA lessons for a whole school year. In total, 160 students participated in this study. Using a coding scheme the quality of student's talk during group work was compared between treatment and control group. Compared to the control group, SfA students showed more high-level talk. SfA students expressed more extended elaborations of propositions and asked more open elaboration questions. Hence, the results of this study suggest that cooperative learning activities within SfA-lessons contributed to students' high-level talk.</p