We investigate thirty-three second and fifth-grade students' solution strategies on integer addition problems before and after analyzing contrasting cases with integer addition and participating in a lesson on integers. The students took a pretest, participated in two small group sessions and a short lesson, and took a posttest. Even though the…

Numeracy is a key competency for living in our modern knowledge society. Therefore, it is essential to support numerical learning from basic to more advanced competency levels. From educational psychology it is known that learning is most effective when the respective content is neither too easy nor too demanding in relation to learners'…

The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

Proportional reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop proportional reasoning naturally. Research suggests that many students do not apply proportional methods appropriately and that they often erroneously…