Early childhood teachers' feedback in natural mathematical learning situations: Development and validation of a detailed category system.

In many countries, early mathematical learning takes place in informal and play-based situations. To support children's mathematical learning, the interactions that occur in the daily contact between the early childhood (EC) teacher and the child in kindergarten play an important role. In these interactions, the feedback provided by the EC teacher is considered to have effects on learning. However, how EC teachers actually give specific or non-specific feedback in everyday activities and play situations with a potential for mathematical learning (natural mathematical learning situations) has been little studied so far. To comprehensively characterize the EC teacher's feedback in natural mathematical learning situations, the current study developed a detailed category system based on categories from previous feedback studies, conducted under various conditions and with different objectives. To verify our category system, we coded mathematical teacher-child interactions (N = 162). The coding provided us with evidence that the category system allows to capture the given feedback in natural mathematical learning situations reliably and in detail. The category system can be useful for further research examining the effects of naturally given feedback on children's mathematical learning and, in the long run, for training teachers in the use of potentially supportive feedback in natural learning situations.

Effects of affiliation-, achievement-, and power-related topics in mathematical word problems on students' performance, task-related values, and expectancies.

A motivational downturn in mathematics during secondary school has been well documented for many students. As a way to address this, creating personally relevant tasks is supposed to increase students' motivation for mathematical tasks. According to recent research, topics relating to affiliation, achievement, and power are personally relevant for young people. Prior research showed that motive imagery in school tasks increases students' task-related intrinsic value and success expectancies. The present study examined the effect of motive topics in word problems on students' task performance. We contextualized mathematical tasks either with affiliation, achievement, and power topics or with neutral topics not related to motive topics. The tasks were comparable regarding their mean word count, text, and mathematical complexity. In three experimental studies (N1 = 56, N2 = 63, N3 = 62), the students solved four tasks for each motive topic and neutral tasks, respectively. The dependent variables were task performance, intrinsic values, and expectancies of success. Repeated measures analyses of variance with the four-level, within-subjects factor motive imagery revealed positive effects of motive imagery in word problems on students' task performance. This was particularly true for achievement-related tasks compared with neutral tasks. The results also indicated slightly positive effects for affiliation-related word problems on students' performance. In addition, the intrinsic value for affiliation-related (Experiment 1) and achievement-related tasks (Experiment 3) was higher than for neutral tasks. Power imagery did not affect students' task performance; it negatively affected students' intrinsic value compared with neutral tasks. Task-related success expectancies were not influenced by motive imagery. The present study replicates and extends previous findings that indicate that tasks referring to affiliation and achievement imagery are more appealing to students and can benefit their performance.

Fostering early numerical competencies by playing conventional board games.

Recent evidence indicates that playing numerical board games is beneficial for the numerical development of preschoolers. However, board games used in these studies were often specifically developed for training numerical skills. Therefore, we examined whether similar beneficial effects could be observed for playing conventional board games such as Parcheesi. In an intervention study with seven 30-min training sessions over a period of 4 weeks, we observed that 4- to 6-year-old children (Mage = 4 years 11 months) who played conventional board games with traditional number dice (with dot faces numbered from one to six) benefitted more from the board games than children who played board games with color or non-numerical symbol dice. Pretest-posttest comparisons indicated differential effects on counting skills and the ability to recognize and use structures. Beyond these immediate training effects observed in posttest, the differential beneficial effects of playing board games using traditional dot dice on recognizing and using structures was still present in a follow-up test 1 year after the intervention. Thus, playing conventional board games using traditional number dice seems to be an effective low-threshold intervention to foster early numerical competencies.