Yukari Okamoto

Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are implemented. The present study compared two ways in which number lines were used to teach fourth graders fraction magnitudes. One was an iPad digital game and the other was a paper-and-pencil workbook. The students in the digital-game condition played the game on their own whereas those in the workbook condition received one-on-one tutoring. Taking part in just four lessons, both groups improved their fraction knowledge compared to the control group. The current findings confirm that number lines are an effective representational tool. The results further suggest that number lines – when implemented as a digital game or in a workbook – are on the average equally effective in improving students' fraction knowledge. Implications for classroom instruction are discussed.

Spatial reasoning plays a vital role in choice of and success in science, technology, engineering, and mathematics (STEM) careers, yet the topic is scarce in grade school curricula. We conjecture that this absence may be due to limited knowledge of how spatial reasoning is discussed and engaged across STEM professions. This study aimed to address that gap by asking 19 professionals to comment on a video that documented children's progression through 5 days of building and programming robots. Their written opinions on the skills relevant to their careers demonstrated by the children revealed that spatial thinking and design thinking are central to what they see.

Understanding numerical magnitudes is a foundational skill that significantly impacts later learning of mathematics concepts. The current study tested the idea that encoding of “10ness” is crucial to improving children’s estimation of two-digit number magnitudes. We used commercially available base-10 blocks for this purpose. The children in the experimental condition were asked to construct two-digit numbers by laying down the precise combinations of 10- and 1-blocks horizontally (e.g., three 10-blocks and seven 1-blocks for 37). Two control conditions were also included. In one control condition, children used 1-blocks only. In another control condition, children used one 10-block and as many 1-blocks as necessary. After working with the experimenter for only 15 minutes twice, the children in the experimental condition were significantly more accurate on the estimation task than those in the control conditions. The findings confirmed the importance of encoding 10ness as a unit in making accurate estimates of two-digit number magnitudes. The importance of encoding other units in the base-10 system is discussed.

Much research has been conducted comparing education in the United States with education in Asian nations, such as Japan, but just how much of this research has been of real use to teachers in the United States? We believe that despite the significant amount of impressive research that has been done analyzing Japanese teaching practices, the manner in which these important findings have been reported to teachers has been largely ineffective. This is unfortunate, because one of the unique strengths of crossnational research is that it provides intact working models of successful practices. Japan is particularly important in this respect because, in many ways, it represents one of the most successful models of constructivist mathematics teaching in the world. We believe that this information is not pursued by U.S. teachers for two general reasons. First, research studies frequently couch results in terms of U.S. deficits. Although we believe these results to be accurate and important, it is difficult for teachers in the United States to compare themselves to teachers in Japan when much of the research that is available makes the persistent lament that U.S. teachers and their students are underachievers. Second, we believe that although important differences exist between Japanese and U.S. school systems (e.g., length of the school year, total time spent on mathematics), the truth is that teachers in both nations have a great deal to learn from each other in terms of the successful practices they use. An unfortunate consequence of the focus on test scores is that school system differences have been mistakenly conflated with teaching practices. This has led to the propagation of several myths about Japanese practices that U.S. teachers tend to cite as evidence of the unsuitability of Japanese practices for U.S. classrooms. We believe that U.S. teachers should separate differences in school systems from differences in teaching practices that could be beneficial to teachers in both nations.

Two studies were conducted to explore mathematical precocity in young children. Study 1 examined mathematically gifted first and third graders' working memory development. The results showed that mathematically gifted children's working memory growth was similar to that expected of their age peers. Study 2 examined changes in mathematically gifted children's conceptual structures. Mathematically gifted children were roughly a year ahead of their age peers in the rate of development of conceptual structure in the numerical domain. A neo‐Piagetian theory of intellectual development was used to explain these seemingly conflicting findings. The relation between working memory growth and conceptual development was discussed throughout the paper.