Early Numerical Competencies of Students with Different Forms of Mathematics Difficulty

The purpose of the study was to examine differences in early numerical competencies, as well as subtraction skill, as a function of children's mathematics difficulty (MD) status: computational difficulty (CD), word problem-solving difficulty (PD), concurrent difficulty (CDPD), or neither difficulty (i.e., typically developing; TYP). Based on measures of addition and word-problem skill, second grade students (N = 332) were classified in terms of MD status. Then, students were assessed on three early numerical competency measures (Number Line Estimation, Number Sets Test, and Counting Knowledge) as well as a measure of subtraction. On Number Line Estimation and Number Sets Test, students with CD and those with PD scored comparably, but both outperformed students with CDPD. On Counting Knowledge-Double First, students with CDPD scored lower than the three contrasting groups. On subtraction, students with CD outperformed those with PD, and students with PD and those with CDPD performed comparably. Findings are discussed in terms of differential performance as a function of difficulty status and implications for understanding and teaching subtypes of MD.     

Guiding reinvention of conventional tools of mathematical logic: students’ reasoning about mathematical disjunctions

Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how logic emerges within students’ mathematical activity. This activity entails reflecting on and systematizing their own language use across diverse semantic content. We present categories of students’ untrained strategies for assessing the truth-values for mathematical disjunctions. Students’ initial reasoning heavily reflected content-specific and pragmatic factors in ways inconsistent with the norms and conventions of mathematical logic. Despite this, all student groups reinvented the standard truth-functional definition for simple disjunctions. We demonstrate how this learning depended upon particular forms of reasoning about logic. We also contrast various strategies for assessing quantified disjunctions and their different affordances in students’ mathematical activity.     

Students’ perceptions about peer assessment for writing: their origin and impact on revision work

We investigate students’ negative perceptions about an online peer assessment system for undergraduate writing across the disciplines. Specifically, we consider the nature of students’ resistance to peer assessment; what factors influence that resistance; and how students’ perceptions impact their revision work. We do this work by first examining findings from an end-of-course survey administered to 250 students in ten courses across six universities using an online peer assessment system called SWoRD for their writing assignments. Those findings indicate that students have the most positive perceptions of SWoRD in those courses where an instructor graded their work in addition to peers (as opposed to peer-only grading). We then move to an in-depth examination of perceptions and revision work among 84 students using SWoRD and no instructor grading for assessment of writing in one university class. Findings from that study indicate that students sometimes regard peer assessment as unfair and often believe that peers are unqualified to review and assess students’ work. Furthermore, students’ perceptions about the fairness of peer assessment drop significantly following students’ experience in doing peer assessment. Students’ fairness perceptions—and drops in those perceptions—are most significantly associated with their perceptions about the extent to which peers’ feedback is useful and positive. However, students’ perceptions appear to be unrelated to the extent of their revision work. This research fills a considerable gap in the literature regarding the origin of students’ negative perceptions about peer assessment, as well as how perceptions influence performance.     

Positive biases in self-assessment of mathematics competence, achievement goals, and mathematics performance

The study examined how biases in self-evaluations of math competence relate to achievement goals and progress in math achievement. It was expected that performance goals would be related to overestimation and mastery goals to accurate self-assessments. A sample of French high-school students completed a questionnaire measuring their math achievement goals and their perceived competence in math. Students’ math grades for the three trimesters of the school year were collected from school records. Bias in self-evaluations was computed by comparing students’ rating on the ‘perceived competence in math’ scale with their actual math achievement as measured by their second trimester math grades. Students were classified into one of three groups (over-raters, accurate raters, or under-raters) depending on whether their self-perceptions of competence in math were higher than, similar to, or lower than their relative math achievement in their class. As expected, overrating of one's performance was related to performance goals. Furthermore, the over-raters were the only group who progressed in their math achievement from Trimester 2 to 3. No relation was found between mastery goals and accurate self-assessment.     

Factors (not) affecting what students do with computers and internet at home

This paper presents the results of an analysis of secondary students’ computer use, aimed at understanding how different factors influence the profile of activities carried out by students with computers. The analysis is based on the data from a national study aimed at measuring students’ Information and Communication Technology (ICT) skills for learning. A factor analysis was carried out to categorize students’ activities with computers and several indexes were constructed to define the comparison groups. Finally, a multiple linear regression analysis was performed to explain the frequency of the activities. Results show that students with access to computers at home mainly perform activities categorized as Socializing, Academic, Gaming and Production and that although the absolute frequency of these activities differs across groups, the profiles of computer use are surprisingly similar for groups based on students’ socio-economic group, experience with ICT, and self-confidence in the use of ICT. The only variable that discriminates user profiles is gender. Based on these findings, it can be claimed that Chilean secondary students with access to computers at home tend to show a rather homogenous computer-use profile, once access is equated.     

On the relationship between solution strategies in two mental rotation tasks

Individual differences in solution strategies have frequently been reported for different measures of mental rotation (MR) ability. In the present study (N = 346 German students), we investigated the relationship between solution strategies on two tests commonly used to identify different patterns of strategies: the Mental Rotations Test (MRT; Vandenberg & Kuse, 1978; Peters, Laeng, Lathan, Jackson, Zaiouna, & Richardson, 1995) and the Cube Comparison Test (CCT; Amthauer, 1953; Amthauer, Brocke, Liepmann, & Beauducel, 2001). The results revealed high convergent validity of the solution strategy assignment. Individuals using analytic (holistic) strategies on the MRT tended to use analytic (holistic) strategies also on the CCT. More females than males were identified as users of analytic solution strategies on the MRT. In addition, males tended to generally show a faster performance than did females. Our findings suggest that solution strategies in MR generalize across different tasks and are not an artifact of a particular test.     

Elicitation of situated values: need for tools to help stakeholders and designers to reflect and communicate

Explicitly considering human values in the design process of socio-technical systems has become a responsibility of designers. It is, however, challenging to design for values because (1) relevant values must be identified and communicated between all stakeholders and designers and (2) stakeholders?? values differ and trade-offs must be made. We focus on the first aspect, which requires elicitation of stakeholders?? situated values, i.e. values relevant to a specific real life context. Available techniques to elicit knowledge and requirements from stakeholders lack in providing the context and means for reflection needed to elicit situated values as well as an explicit concept of value. In this paper we present our design of a tool to support active elicitation of stakeholders?? values and communication between stakeholders and designers. We conducted an exploratory user study in which we compared the suitability of methods used in social sciences for (1) eliciting situated values, (2) supporting people??s expressions of values and (3) being implemented in value elicitation tool. Based on the outcomes we propose a design for a value elicitation tool that consists of a mobile application used by stakeholders for data collection and in-situ self-reflection, and a website used collaboratively by designers and stakeholders to analyse and communicate values. Discussion focuses on contributions to value sensitive design.     

Training on the project: a quantifying approach to competence development

In the project ‘Competence-Driven Project Portfolio Analysis’ (CDPPA), an integrated system for supporting R&D project selection, staff assignment and activity scheduling with special consideration of the strategic development of competencies has been designed and implemented prototypically. The system has been field-tested at the Electronic Commerce Competence Center (EC3), a public–private partnership R&D enterprise. Experiences from this trial application are summarised and discussed, particularly concerning data collection and competence measurement, the benefits and limits of the chosen multi-criteria decision analysis approach, the evaluation of introduced changes to the decision-making processes, and the transparency of the formal planning model and its components.