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The frequentist and classical models of probability provide students with different lenses through which they can view probability. Prior research showed that students may bridge these two lenses through instructional designs that begin with a clear connection between the two, such as coin tossing. Considering that this connection is not always clear in our life experiences, we aimed to examine how an instructional design that begins with a scientific scenario that does not naturally connect to theoretical probability, such as the weather, may support students' bridging of these two models. In this paper, we present data from a design experiment in a sixth-grade classroom to discuss how students' shifts of reasoning as they engaged with such a design supported their construction of bridges between the two probability models. [ABSTRACT FROM AUTHOR]

Through a constructivist teaching experiment, we studied how a 6th-grade student (Adam, pseudonym) struggling in mathematics may reorganize his available additive scheme (count-upto) into a more advanced scheme involving the decomposition of composite units (break-apart-make-ten, or BAMT). First, we posed a task that led us to infer Adam was yet to construct the BAMT scheme at the anticipatory stage (solving a task without prompting). We thus turned to promote reorganization of his anticipatory, count-up-to scheme used to solve missing-addend tasks. Through reflection on the relationships between his goal, count-up-to actions, and effect of those actions, Adam independently brought forth what he called "easy number-pairs" (i.e., 10+X = X-teen). This seemed to afford his reorganization of count-up-to into the BAMT scheme. We discuss implications of this reorganization for theory building and practice. [ABSTRACT FROM AUTHOR]

In this contribution, we present a follow-up work-in-progress on an innovative system for facilitating small-group online discussions using an avatar during a video conference. A previous study has shown that the system had an effective, understandable, and more participatory interaction. Here, we examine long-term usage and its effects on subjective perceptions as well as objective engagement measures. Five groups of fifth and sixth grade students had six interactions with the avatar's facilitation. The results of the study show that all measures remained stable throughout the entire interaction, suggesting that the previous results were not due to the novelty effect and that the system is capable of maintaining long-term engagement and learning. [ABSTRACT FROM AUTHOR]

The phenomenon of the sea level rise is a pressing environmental and social issue of the present age. Starting with the assumption that mathematics can be utilized to help students explore this phenomenon, we designed a simulation in NetLogo, in which students investigated the relationships between the quantities of temperature rise, height of future sea level, and total land area. In this paper, we present the analysis of a whole-class design experiment in a sixth-grade classroom and discuss how our design helped students to examine sea level rise as both an environmental and a social issue. [ABSTRACT FROM AUTHOR]

In this report, we discuss five forms of reasoning about multiple quantities that sixth-grade students exhibited as they examined mathematical relationships within the context of science. Specifically, students exhibited forms of sequential, transitive, dependent, and independent multivariational reasoning as well as relational reasoning. We use data from whole-class design experiments with students to illustrate examples of each of these forms of reasoning. [ABSTRACT FROM AUTHOR]

This paper describes how a cohort of sixth-grade mathematics students shifted their collective understanding of being "good at math" from passive recipiency to active agency. [ABSTRACT FROM AUTHOR]

The paper reports the results from an ongoing project that aims to develop an engaging and effective digital game for training conceptual rational number knowledge. The overall research approach is design science. In the paper we report the results of an iteration in which we studied how students used a Semideus School game prototype and how they experienced the core mechanics of the game. 20 fourth graders and 32 sixth graders played Semideus School game for approximately 2.5 hours. Students were allowed to freely play the game with their iPads. Playing experience was studied with a digital questionnaire that included items about flow experience (Flow Short Scale), perceived playability, and acceptance of game-based math training. Additionally, a researcher observed the playing sessions and discussed with the students about the implementation of the game. Students experienced reasonable high flow experience while playing the game. The results revealed that 4th graders would be more willing to study rational numbers with a game and they also appreciated the playability of the game more than sixth graders. Moreover, sixth graders demanded more complex game mechanics, but 4th graders were happy with the core mechanics. We redesigned the game mechanics based on the findings. The paper describes the new mechanics and the theoretical basis of the new design. [ABSTRACT FROM AUTHOR]

A study of computational strategies developed by sixth-grade students and prospective and practicing teachers revealed two-step approaches for measurement and partitive division of fractions problems which extend one-step strategies developed for division of whole numbers by adding a step which converts units by multiplying (unitizing). Also observed were use of co-measure units, and some common errors. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

The article presents the result of studies which examined the development of algebraic reasoning in first- and sixth-grade students in the U.S. The study also examined the direct correlation between teachers' content knowledge and students' achievement in learning and understanding of mathematics. The recommendations of pre-service mathematics teachers for students in elementary schools are discussed.

This research traces two years of one sixth-grade teacher's developing pedagogical content knowledge defined as coupled student thinking and teacher assistance Discourses. Systemic Functional Linguistics coding is applied to a chronological string of student-teacher interactions about ratio. This provides detailed linguistic evidence that teachers develop PCK from their teaching, an often spoken claim that is not well documented or understood. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

The article discusses a study on written assessments of units coordination (UC) in elementary mathematics learning. The study examined UC that occurs in a variety of contexts, including fractional and whole number continuous contexts. It indicated the participation of 96 sixth-grade students in the first iteration of the assessment.

This paper concerns a project to explore factors affecting improvement in mathematics achievement at Grades 3 and 6. We believe that understanding the relationship between school practices and patterns of improvement is fundamental to understanding strategies that provide opportunities for all students to successfully learn mathematics.The concept of "learning environment" as set out by Bransford et al. (2000) informs our analysis of the data. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

In this poster presentation, I present investigations related to interactions of teaching and learning: specifically, how students understand and use classroom instruction in similar contexts. For this purpose, a sixth grade classroom was videotaped when studying fractions and some of those videotapes were used in the student interviews when investigating sixth graders understanding of equivalent fractions on the number line. ..PAT.-Conference Proceeding [ABSTRACT FROM AUTHOR]

Purpose: In this presentation we describe initial analysis of data from a long-term, on-going constructivist teaching experiment whose purpose is to understand how sixth grade students can build algebraic reasoning out of their evolving quantitative operations and quantitative reasoning. We focus on two of the quantitative operations we identified as important to students’ generation and solution of basic linear equations and the ways in which we worked to help students build these operations. [ABSTRACT FROM AUTHOR]

An abstract of the article "Sixth Grade Iranian Students Engage in Mathematical Modelling Activities" by Samira Mehraein and Abolfazl Rafiepour Gatabi, is presented.

An abstract of an article about the ways of thinking of sixth grade students regarding solving algebraic verbal problems is presented.

In recent years, public schools have moved away from traditional grade configurations with junior high schools and have shifted towards integrating sixth grade students into middle schools. It has been argued that the effect this will have on students is to allow for additional freedom and earlier social growth. However, the counterargument to this debate is that these sixth grade students would then be exposed to an older cohort sooner and therefore would be exposed to negative peer influences. This study investigates the behavioral and emotional differences between sixth grade students in elementary schools and their counterparts in middle schools, including suicidal thoughts and a range of substance abuse behaviors. The data used come from the 2007 Delaware Youth Risk Behavior Survey, which surveyed 4,005 Delaware public school students in sixth through eighth grades. Preliminary analysis indicates significant differences between sixth grade students based on the type of school they attend. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

The article investigates variations in strategies used by sixth grade students to solve linear equations. The researchers videotaped interviews of more than 20 students about their choice of problem-solving strategies. They found that students' utterances about their problem-solving strategies increased in detail and rationale as they got more problem solving experience. The students also became more successful in problem solving as their strategies became more sophisticated.