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Empirical research highlights the benefits for the development of children's mathematical competencies when they play linear number board games with dice and receive feedback. We, therefore, investigated mathematical competencies in two training studies with six sessions and a 3 × 2 design. The sample in the first experiment consisted of N = 79 German 5- to 7-year-old preschoolers and in the second of N = 64 German 6- to 8-year-old primary school students. Participants either belonged to a passive control group or played the board game House of Numbers up to number 20 (HoN-20). Some members of the HoN-20 group received specific feedback (e.g. 'well calculated'), while the remaining children received unspecific feedback (e.g. 'good'). Pre-posttest comparisons pointed to diverse effects: Playing the HoN-20 game and receiving feedback led to significantly greater gains in different levels of acquisition of basic arithmetic skills.

In this quasi-experimental study, we investigated whether basic arithmetic skills and mathematical self-concept of young children can be influenced by feedback during an interactive session in which a game was played. German 5- to 7-year-old children (n = 79) played an adaption of the game House of Numbers six times, either in a specific or an unspecific feedback group, or they belonged to a passive control group. In a pre- and post-test design, children's mathematical performance and self-concept were assessed twice. The results show that playing the game and receiving any feedback led to significantly greater gains in the acquisition of basic arithmetic skills than being in the passive control group. Children in the specific feedback group showed greater benefits. Children in all groups displayed very high mathematical self-concepts at pre-test, which they maintained in the specific and control groups but not in the unspecific feedback group.

The study evaluates the linear number board game "100 House." Taking into account Krajewski's (2003, 2013) development model of mathematical competencies, this game supports the development of mathematical competencies in 6-year-old children. The board game design is based on the American cognitive alignment framework approach and aims to enhance the number board game "Race to Space" (Laski & Siegler, 2014). German 6-year-old children (N = 48) received four game-playing sessions, either counting on from their current position on the board game (count-on condition) or counting their steps from one (count-from-1 condition). In a pretest, posttest, and follow-up session, children's mathematical performance was assessed. The results show that playing the game led to stable improvements, especially in mathematical competencies of the first and second level of the underlying development model. Children in the count-on condition displayed a greater benefit. Supporting mathematical competencies by playing number board games is discussed.

Accurate teacher judgments of student characteristics are considered to be important prerequisites for adaptive instruction. A theoretically important condition for putting these judgments into operation is judgment confidence. Using a German sample of 96 teachers and 1,388 students, the authors examined how confident teachers are in their judgments of students' mathematic and verbal self-concepts, and whether judgment confidence is related to judgment accuracy. Judgment confidence was largely student specific, and the majority of teachers were overconfident of their judgments. Moreover, teacher confidence was higher for extreme judgments. In the subject of mathematics, judgment confidence was moderately associated with judgment accuracy. The findings challenge the efficacy of adapting instruction to student characteristics, as it is obvious that many teachers are not aware of their judgment inaccuracy. (Contains 4 tables, 1 figure, and 4 notes.)