Students’ mathematical work on absolute value: focusing on conceptions,errors and obstacles

ZDM – Mathematics Education - This study investigates students’ conceptions of absolute value (AV), their performance in various items on AV, their errors in these items and the...     

Mathematical Working Spaces in schooling: an introduction

ZDM – Mathematics Education - The theoretical and methodological model of Mathematical Working Space (MWS) is introduced in this paper. For over 10 years, the model has been the...     

Behind the scenes of pseudo-proportionality

In this study, we attempt to put in question students’ spontaneous and uncritical application of the simple and neat mathematical formula of linearity. This is impelled with the help of a written test involving geometrical problems, which is based on an original experimental setting. In this setting, grade 9 and 10 students were instructed first to solve all the geometrical problems and then to select only one problem as the appropriate for a given numerical answer. The difficulty of this choice lied in fact that a superficial handling of each problem would resolve to the same numerical answer as the one given. The results show that students’ choices are systematic and based on the solutions given to the tasks. However, the experimental setting has managed to help students question in some degree the applicability of the linear model in situations that appear to be linear but are not.     

Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics

Many researchers have investigated flexibility of strategies in various mathematical domains. This study investigates strategy use and strategy flexibility, as well as their relations with performance in non-routine problem solving. In this context, we propose and investigate two types of strategy flexibility, namely inter-task flexibility (changing strategies across problems) and intra-task flexibility (changing strategies within problems). Data were collected on three non-routine problems from 152 Dutch students in grade 4 (age 9–10) with high mathematics scores. Findings showed that students rarely applied heuristic strategies in solving the problems. Among these strategies, the trial-and-error strategy was found to have a general potential to lead to success. The two types of flexibility were not displayed to a large extent in students’ strategic behavior. However, on the one hand, students who showed inter-task strategy flexibility were more successful than students who persevered with the same strategy. On the other hand, contrary to our expectations, intra-task strategy flexibility did not support the students in reaching the correct answer. This stemmed from the construction of an incomplete mental representation of the problems by the students. Findings are discussed and suggestions for further research are made.     

Word problem solving and pictorial representations: insights from an exploratory study in kindergarten

The aim of this study was to investigate how pictorial representations with different semiotic characteristics affect additive word problem solving by kindergartners. The focus of the study is on three categories of additive problems (change problems, combine problems and equalize problems) and on representational pictures with different semiotic characteristics: (a) pictures in which the problem quantities are represented in pictorial form, that is, as groups of illustrated objects (PP pictures), (b) pictures in which the quantities are represented partly in pictorial form and in symbolic form (PS pictures), and (c) pictures in which the quantities are represented in symbolic form (SS pictures). Data were collected from 63 kindergartners using a paper-and-pencil test. Results showed that the semiotic characteristics of representational pictures had a strong and significant effect on performance. Children’s performance was higher in the problems with PP pictures but declined in the problems with PS and SS pictures. However, the differences in children’s performance across the problems with different representational format varied between the problem categories and their mathematical structures. The semiotic characteristics of representational pictures had an important role in the establishment of close relations between children’s solutions in problems in different categories. Detailed analysis of children’s answers to the problems revealed a number of picture-related difficulties. Findings are discussed and directions for future research are drawn considering the methodological limitations of the study.     

Kindergartners’ performance in length measurement and the effect of picture book reading

This paper addresses: firstly, kindergartners’ performance in length measurement, the components of their performance and its growth over time; secondly, the possibility to develop kindergartners’ performance in length measurement by reading to them from picture books. To answer the research questions, an experiment with a pretest–posttest experimental control group design was carried out involving nine experimental classes and nine control classes. The children in the experimental group participated in a 3-month picture book program that, among other things, spotlighted the measurement of length situated in meaningful contexts. Before and after the intervention, the children’s performance in length measurement was assessed in both groups. The responses of 308 kindergartners (4- to 6-year-olds) from two kindergarten years (K1 and K2) were analyzed. Analysis of the pretest data showed that the measurement tasks included in the test were not easy to solve. However, the children belonging to K2 did better than the younger children belonging to K1. Within children’s performance, three components could be identified: holistic visual recognition, ordering and unitizing. Finally, the effect of the intervention was investigated by comparing the performances of the experimental and control group in the pretest and the posttest. We found a weak but significant effect of reading picture books to children on their general measurement performance. However, this effect was only found for K1 children on the component of holistic visual recognition.