In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on prekindergarten and kindergarten students’ ability to rote count, read two-digit numerals, model two-digit numbers, and identify the place value of individual digits in two-digit numerals. Through individual student interviews, preand post-assessments were administered to evaluate rote counting, reading five two-digit numerals, modeling five two-digit numbers, and identifying place value in two two-digit numerals. Chi-square tests for independence showed two significant relations: (1) the relationship between the control and treatment group membership on the postassessment of modeling two-digit numbers and (2) the relationship between place value identifications and group membership. Analysis of the children’s performance and error patterns revealed interesting differences between children taught with explicit number names and children taught with traditional number names. The improvement of the treatment group overall exceeded the improvement of the control group. This study indicates that teaching children to use explicit number names can, indeed, have a positive influence on their understanding of place value.

In this workshop, participants engaged with and reflected on authentic artifacts from data modeling projects related to the solar system and to deforestation that were completed by elementary students in grade 5 (average age 11). These authentic examples were used to ground a discussion of using a data modeling approach to help elementary students make sense of and meaningful integrated use of mathematics and science concepts and tools. School-based ways of helping teachers understand this approach in order to be able to use it in their classrooms were also discussed.

No description available.

In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on prekindergarten and kindergarten students’ ability to rote count, read two-digit numerals, model two-digit numbers, and identify the place value of individual digits in two-digit numerals. Through individual student interviews, preand post-assessments were administered to evaluate rote counting, reading five two-digit numerals, modeling five two-digit numbers, and identifying place value in two two-digit numerals. Chi-square tests for independence showed two significant relations: (1) the relationship between the control and treatment group membership on the postassessment of modeling two-digit numbers and (2) the relationship between place value identifications and group membership. Analysis of the children’s performance and error patterns revealed interesting differences between children taught with explicit number names and children taught with traditional number names. The improvement of the treatment group overall exceeded the improvement of the control group. This study indicates that teaching children to use explicit number names can, indeed, have a positive influence on their understanding of place value.

In this workshop, participants engaged with and reflected on authentic artifacts from data modeling projects related to the solar system and to deforestation that were completed by elementary students in grade 5 (average age 11). These authentic examples were used to ground a discussion of using a data modeling approach to help elementary students make sense of and meaningful integrated use of mathematics and science concepts and tools. School-based ways of helping teachers understand this approach in order to be able to use it in their classrooms were also discussed.

No description available.

Many countries are reporting of difficulties in exact education at schools: mathematics, informatics, physics etc. Various methods are proposed to awaken and preserve students’ interest in these disciplines. Among them, the simplification, accent on applications, avoiding of argumentation (especially in mathematics) etc. must be mentioned. As one of reasons for these approaches the growing amount of knowledge/skills to be acquired at school is often mentioned. In this paper we consider one of the possibilities to integrate partially teaching of important chapters of discrete mathematics and informatics not reducing the high educational standards. The approach is based on the identification and mastering general combinatorial principles underlying many topics in both disciplines. A special attention in the paper is given to the so-called “pigeonhole principle” and its generalizations. In folklore, this principle is usually formulated in the following way: “if there are n + 1 rabbits in n cages, you can find a cage with at least two rabbits in it“. Examples of appearances of this principle both in mathematics and in computer science are considered.

Many countries are reporting of difficulties in exact education at schools: mathematics, informatics, physics etc. Various methods are proposed to awaken and preserve students’ interest in these disciplines. Among them, the simplification, accent on applications, avoiding of argumentation (especially in mathematics) etc. must be mentioned. As one of reasons for these approaches the growing amount of knowledge/skills to be acquired at school is often mentioned. In this paper we consider one of the possibilities to integrate partially teaching of important chapters of discrete mathematics and informatics not reducing the high educational standards. The approach is based on the identification and mastering general combinatorial principles underlying many topics in both disciplines. A special attention in the paper is given to the so-called “pigeonhole principle” and its generalizations. In folklore, this principle is usually formulated in the following way: “if there are n + 1 rabbits in n cages, you can find a cage with at least two rabbits in it“. Examples of appearances of this principle both in mathematics and in computer science are considered.