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This qualitative case study explored an elementary foundations mathematics course and the mathematics vocabulary elementary pre-service teachers (PSTs) encounter at various stages in their preparation as mediated by curriculum, standards, and assessment materials. Guided by the theoretical lens of a constructivism-informed conceptual framework, text analyses indicated varying degrees of alignment of mathematics vocabulary when comparing across the materials gathered from different points in PSTs' preparation and future careers as educators. Further investigation indicated that considering alignment as a process provided possible opportunities for continued curricular improvement related to promoting mathematics vocabulary for elementary PSTs.

This study explored associations among children's prior attitudes, prior mathematics knowledge, and frequency of digital game use, with children's perceptions of game affordances, and transfer to out-of-game performance when interacting with digital math games, with respect to gender. Participants were 187 children (ages 8-12). An SEM mediation path analysis using MPLUS software showed significant direct effects for all pathways for all children, and significant indirect effects on all pathways for male children and five of six pathways for female children. More favorable attitudes, prior math knowledge, and perception of the helping affordances were associated with increased posttest performance, while increased frequency of digital game use and stronger perception of the hindering affordances was associated with decreased posttest performance. The model showed stronger connections for male children between frequency of digital game use, prior mathematics knowledge, and hindering affordances to the posttest, while female children showed stronger connections between attitude and perception of helping affordances to the posttest.

This study focused on an examination of how type, quality and children's awareness of design features in digital math games, along with an awareness of the mathematics goals of the game, were related to learning outcomes. We conducted a parallel conversion mixed methods study with 45 students in Grades 3 and 4 (ages 9-10). Students participated in clinical interviews using three digital math games. The results suggest a moderated mediation relationship in which the quality of the design features moderated the mediating impact of children's awareness of the game's design features, specifically when the child was aware of the mathematics content learning goal (MCLG) of the game. These findings show how important it is that design features are of high quality in a digital math game, and how this is intertwined with children's awareness of the features and the MCLG. When these variables intertwined in just the right way, the interactions between the children and the digital math game afforded mathematical learning growth.

In this qualitative, grounded theory, pedagogical action research study, we, as mathematics teacher educators, sought to develop a conceptual framework in which we could help elementary pre-service teachers (PSTs) construct understanding of, and then fluently use, mathematics vocabulary essential to PSTs' future work as elementary teachers. The resulting Guided Mathematics Vocabulary (GMaV) Conceptual Framework represents growth in our PSTs' constructed knowledge of mathematics vocabulary as the intersection of our explicit mathematics vocabulary focus using contextualized problems embedded within guided notes as a scaffolding device. With the GMaV framework, we will then be able to conduct future inquiry into this conceptualization of our PSTs' learning process to test our theoretical understanding of how our PSTs are understanding mathematics vocabulary.

This paper introduces the Affording Understanding Conceptual Framework as a way for mathematics teacher educators to analyze student 's perceptions of a digital math tool 's helpfulness (e.g., GeoGebra) versus the instructor's perceptions when seeking insights into how a lesson design could be improved. An example of this action research process is provided using GeoGebra to help pre-service middle grades mathematics teachers (MGMTs) develop their conceptual understandings of definite integrals. Findings showed that the pre-service MGMTs noticed four categories of what they considered to be primarily helpful features: "Ease of Use," "Pictorial Representation," "Colored," and "Slider/Dynamic Movement" types. While the pre-service MGMTs all described these as helpful, the content of their comments showed that there was a material difference in how they viewed the "Ease of Use" type from the other three suggesting ways in which the lesson could be revised to be more effective.

The region hosts numerous species of fish, mammals, birds, and has even been a home ro humans for over 10,000 years. Unfortunately, the Arctic is also unique in its susceptibility [...]

The purpose of this study was to contribute to the research on mathematics app use by very young children, and specifically mathematics apps for touch-screen mobile devices that contain virtual manipulatives. The study used a convergent parallel mixed methods design, in which quantitative and qualitative data were collected in parallel, analyzed separately, and then merged. During the study, 35 children, ages 3-4, interacted with four touch-screen mathematics apps on iPad devices during one-on one clinical interviews while learning seriation and counting. Researchers administered pre and post assessments of learning during the interviews. Each interview was videotaped using a wall-mounted camera and a GoPro camera to provide different views of the interview. Videos were analyzed to examine children's learning progressions, access of affordances, and patterns of behavior while interacting with the mathematics apps. The results suggest that different affordances of the individual apps were perceived in different ways, depending on the age of the child, and that these perceptions were observable in young children's patterns of behavior. Implications are discussed for iPad app use in young children's educational settings.

The Mighei‐like carbonaceous (CM) chondrites, the most abundant carbonaceous chondrite group by number, further our understanding of processes that occurred in their formation region in the protoplanetary disk and in their parent body/bodies and provide analogs for understanding samples returned from carbonaceous asteroids. Chondrules in the CMs are commonly encircled by fine‐grained rims (FGRs) whose origins are debated. We present the abundances, sizes, and petrographic observations of FGRs in six CMs that experienced varying intensities of parent body processing, including aqueous and thermal alteration. The samples studied here, in approximate order of increasing thermal alteration experienced, are Allan Hills 83100, Murchison, Meteorite Hills 01072, Elephant Moraine 96029, Yamato‐793321, and Pecora Escarpment 91008. Based on observations of these CM chondrites, we recommend a new average apparent (2‐D) chondrule diameter of 170 μm, which is smaller than previous estimates and overlaps with that of the Ornans‐like carbonaceous (CO) chondrites. Thus, we suggest that chondrule diameters are not diagnostic for distinguishing between CM and CO chondrites. We also argue that chondrule foliation noted in ALH 83100, MET 01072, and Murchison resulted from multiple low‐intensity impacts; that FGRs in CMs formed in the protoplanetary disk and were subsequently altered by both aqueous and thermal secondary alteration processes in their parent asteroid; and that the heat experienced by some CM chondrites may have originated from solar radiation of their source body/bodies during close solar passage as evidenced by the presence of evolved desiccation cracks in FGRs that formed by recurrent wetting and desiccation cycles. [ABSTRACT FROM AUTHOR]

This paper focuses on understanding the role that affordances played in children's learning performance and efficiency during clinical interviews of their interactions with mathematics apps on touch-screen devices. One hundred children, ages 3 to 8, each used six different virtual manipulative mathematics apps during 30-40-min interviews. The study used a convergent mixed methods design, in which quantitative and qualitative data were collected concurrently to answer the research questions (Creswell and Plano Clark 2011). Videos were used to capture each child's interactions with the virtual manipulative mathematics apps, document learning performance and efficiency, and record children's interactions with the affordances within the apps. Quantitized video data answered the research question on differences in children's learning performance and efficiency between pre- and post-assessments. A Wilcoxon matched pairs signed-rank test was used to explore these data. Qualitative video data was used to identify affordance access by children when using each app, identifying 95 potential helping and hindering affordances among the 18 apps. The results showed that there were changes in children's learning performance and efficiency when children accessed a helping or a hindering affordance. Helping affordances were more likely to be accessed by children who progressed between the pre- and post-assessments, and the same affordances had helping and hindering effects for different children. These results have important implications for the design of virtual manipulative mathematics learning apps.

Author(s): Evan M. Smith [sup.1] , Steven B. Shirey [sup.2] , Stephen H. Richardson [sup.3] , Fabrizio Nestola [sup.4] , Emma S. Bullock [sup.5] , Jianhua Wang [sup.2] , Wuyi [...], Geological pathways for the recycling of Earth's surface materials into the mantle are both driven and obscured by plate tectonics.sup.1-3. Gauging the extent of this recycling is difficult because subducted crustal components are often released at relatively shallow depths, below arc volcanoes.sup.4-7. The conspicuous existence of blue boron-bearing diamonds (type IIb).sup.8,9 reveals that boron, an element abundant in the continental and oceanic crust, is present in certain diamond-forming fluids at mantle depths. However, both the provenance of the boron and the geological setting of diamond crystallization were unknown. Here we show that boron-bearing diamonds carry previously unrecognized mineral assemblages whose high-pressure precursors were stable in metamorphosed oceanic lithospheric slabs at depths reaching the lower mantle. We propose that some of the boron in seawater-serpentinized oceanic lithosphere is subducted into the deep mantle, where it is released with hydrous fluids that enable diamond growth.sup.10. Type IIb diamonds are thus among the deepest diamonds ever found and indicate a viable pathway for the deep-mantle recycling of crustal elements.Mineral inclusions in blue boron-bearing diamonds reveal that such diamonds are among the deepest diamonds ever found and indicate a viable pathway for the deep-mantle recycling of crustal elements.

The detection and quantification of metal sulfides in host rocks by electrical measurements have been priorities for field and laboratory studies, motivated by mineral prospecting and fundamental interest in the mantle structure or core/mantle differentiation, among other reasons. Here, we reanalyze electrical data for a dunite host with added FeS or Fe-S-Ni (Saxena et al. 2021), and report additional experimental runs along with electron microprobe analyses. The applied pressure was 2 GPa; impedance spectra were acquired while annealing at 1023 K (below the metal-sulfide solidus), and while varying temperature from 570 to 1650 K. Addition of 6.5 or 18 vol% FeS strongly enhances conductivity of the bulk sample compared with that of the dunite host, though values are 100–100 000 times less than those of pure FeS. These results indicate that most metal sulfide content is not part of a viable conductive path, even for the 18 vol% quantity. Nevertheless, the relatively high conductivity and weak temperature dependence of the 18 vol% sample reveal that contiguous paths of solid or molten FeS span the electrodes. The sample with 6.5 vol% sulfide also exceeds the percolation threshold for temperatures as low as ~100 K below the eutectic melting point, likely because FeS softens. Conductivity is nearly unchanged upon crossing the eutectic temperature, however a decline over 1400–1500 K reveals that the 6.5 vol% molten FeS forms a fragile electrical network in dunite. Samples with Fe50S40Ni10 or Fe40S40Ni20 (at%) are less conductive than pure dunite at temperatures below ~1450 K. This surprising result, likely caused by a reducing influence of Fe or Ni metal, does not support the use of FeS as an analog for compositions with nickel or excess metal. Our findings suggest that probing the electrical network of metal sulfides as solids complements other studies focused on connectivity of molten metal sulfides. [ABSTRACT FROM AUTHOR]

Part of a larger initiation mixed methods study (Greene, Caracelli, & Graham, 1989), this paper discusses the changes in young children's learning performance and efficiency (one element of the quantitative portion of the larger study) during clinical interviews in which each child interacted with a variety of virtual manipulative mathematics iPad apps. Researchers interviewed 100 children ages 3 to 8 using a protocol format with two pre-assessment apps, four learning apps, and two post-assessment apps. Following 30-40 minute interviews where children interacted individually with the mathematics apps, results showed that children in the Preschool group increased efficiency while maintaining performance, children in the Kindergarten group increased performance while maintaining efficiency, and children in the Grade 2 group increased their performance and efficiency in skip counting, but not in place value. Overall, children in different age groups responded in different ways to the apps and some apps had a greater influence on children's learning performance and efficiency than others. To conduct this study, researchers created a variety of research tools that were not readily available because research on children's interactions with iPad-based virtual manipulative mathematics apps is still in its infancy. The paper describes the processes our research team used to develop new tools for novel and unique research situations.