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In this article, we report the findings of a study conducted with 6 Grade 8 students in the United States. The students posed stories for open number sentences involving addition and subtraction of integers. We analysed the stories posed by the students to build models that describe the conceptual structures behind these posed stories – the conceptual models for integer addition and subtraction. These four conceptual models for thinking about and using integer addition and subtraction include Bookkeeping, Counterbalance, Relativity, and Translation, and are generated from the students' posed stories. We also provide profiles of conceptual model use for two of the 6 students that describe how the students posed stories to accommodate conceptual model use, such as posing unconventional or unrealistic stories or changing the structure of the number sentences. The conceptual models and descriptions of how the students used them provide perspective into student thinking about integers and contexts, highlighting the mathematics of the students, and calling for a re-examination of contexts used in school mathematics. [ABSTRACT FROM AUTHOR]

Math proficiency is related to math calculation fluency. Explicit timing provides repeated practice for math fluency. It is enhanced through goal setting, graphic feedback, and rewards. Self-selected goals have potential to increase performance for math fluency. This study compared the effect of goal lines, and researcher goals versus self-selected goals. The authors compared three groups: (a) researcher-selected goals only, (b) researcher-selected goals with goal lines, and (c) self-selected goals with goal lines. First-grade students completed subtraction probes and colored in a bar graph with their performance. When participants met or exceeded their goals, participants received rewards twice per week. Results indicated that the researcher-selected goals with goal lines procedures with explicit timing had the greatest effect on subtraction fluency for first-grade students. The researcher-selected goals with goal lines and self-selected goals with goal lines groups outperformed the researcher-selected goals-only group. [ABSTRACT FROM PUBLISHER]

Achieving fluency with basic subtraction and add-with-8 or -9 combinations is difficult for primary grade children. A 9-month training experiment entailed evaluating the efficacy of software designed to promote such fluency via guided learning of reasoning strategies. Seventy-five eligible first graders were randomly assigned to one of three conditions: guided subtraction (e.g., If 5 + 3 = 8, then 8 – 3 is 5), guided use-a-10 (e.g., If 10 + 7 = 17, then 9 + 7 is 16), or an unguided-practice condition for 30-minute sessions twice a week for 12 weeks. An ANCOVA revealed that at the delayed posttest, the guided-subtraction group outperformed both comparison groups on unpracticed subtraction combinations. Analyses of gains in slow but appropriate use of reasoning and decreases in inefficient strategy use indicated that both types of guided training promoted the learning of a targeted reasoning strategy. [ABSTRACT FROM AUTHOR]

Coordinates social constructivism and socioculturalism orientations to explain second-grade children's reasoning with two-digit quantities. Development of the theoretical orientation used in the study; Background on the second-grade classroom teaching experiment; Processes by which the regular classroom teacher and the students established different explanations to solve subtraction tasks for two-digit quantities.