This study used fraction number line estimation tasks to evaluate students' developmental patterns, and the relationship of such tasks with whole number bias was explored. In total, 189 fourth-grade students in a northern Taiwan elementary school were followed over 2 years. The results demonstrated that the students' fraction learning development…

To assess the strength of conceptual understanding of number sense, a three-tier number sense test (TTNST) for fifth-grade students was developed and validated in this study. The three-tier test includes a content tier that assesses content knowledge of number sense, a reason tier that assesses a reason given for selecting a first-tier response,…

The purpose of this study is to compare the differences of four essential aspects (i.e., representational forms, contextual features, cognitive demand levels, and response types) embedded in mathematical problems within the topics of numbers and operations in mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This…

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to…

This study investigated the performance of 790 fourth graders from Taiwan for judging the reasonableness of a computational result by using corresponding methods pertaining to whole numbers. A number-sense web-based two-tier diagnostic test was used to assess the number-sense performance of the fourth graders who participated in this study. The…

This paper presents some results of an investigation on the number sense of a group of pre-service secondary teachers from Spain. The objective of this research was to analyze students' use of strategies associated to number sense and compare them with those obtained in a previous study with pre-service primary teachers in Taiwan, (Yang, Reys…

Numerical and symbolic representations are used extensively in physics problems. However, relatively little is understood about how students respond to these two representational formats when they are solving problems. This study examined the effect of the representational format (numeric vs symbolic) on the problem-solving performance,…

To examine the relative performance in number sense among low-SES students, new immigrant students, and typical learners in grades 4 through 6, data were collected through a number sense web-based, two-tier test. A total of 628 fourth graders, 535 fifth graders, and 524 sixth graders in Taiwan participated in this study. Results showed that there…

The goal of this study was to investigate understanding of in-service elementary school teachers in Taiwan about number sense, teaching strategies of number sense and the development of number sense of students. Data were gathered through interviews of nine elementary mathematics teachers, regarding their understanding about number sense. The data…

Background: Number sense is a key topic in mathematics education, and the identification of children's misconceptions about number is, therefore, important. Information about students' serious misconceptions can be quite significant for teachers, allowing them to change their teaching plans to help children overcome these misconceptions. In…

A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In…

The goal of this study was to investigate understanding of inservice elementary school teachers in Taiwan about number sense, teaching strategies of number sense and the development of number sense of students; and the profile of integrating number sense into mathematical instruction , and teaching practice. Data was gathered through interviews of…

To investigate the structure of number sense and then to assess its uses in fifth-grade children's number sense development, a computerized number sense scale was developed and evaluated. The findings of the study indicate that the newly developed scale, with four dominant factors identified and reconfirmed, is internally consistent and…

Two 12-question estimation instruments were designed to compare the differences of estimating strategies used by the 8th-graders when solving contextual and numerical problems. Both instruments are parallel, meaning that the numbers used in both instruments are the same; however, they were presented differently. One hundred and ninety-eight…

Textbooks, like many other resources teachers have at hand, are meant to be an aid for instruction; however there is little research with textbooks or on their potential to develop metacognitive knowledge. Metacognitive knowledge has received substantial attention in the literature, in particular for its relationship with problem-solving in…