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\"Strategy sharing\" is a certain type of discussion that centers on students' ideas and occurs when children present different approaches to problems and provide information about how they solved the problem (Wood, Williams, and McNeal 2004). A teacher may orchestrate a strategy-sharing discussion to achieve one or more of the following goals (NCTM 2000): (1) Elicit students' mathematical ideas; (2) Represent students' diverse strategies; (3) Make connections between mathematical ideas; (4) Compare similarities and differences across strategies; and (5) Develop students' repertoire of strategies and flexible thinking. During the author's years of teaching and research in elementary school classrooms, she has focused on understanding and supporting students' experiences during strategy-sharing discussions. Building on the work of other researchers, she wanted to understand how to cultivate a classroom atmosphere that encourages problem solving and inquiry (e.g., Yackel and Cobb 1996) and that fosters mathematical discourse where students' problem-solving strategies, no the answers, are the foundation of the discussion (e.g., Lampert 1990). She also wanted to understand how strategy sharing could be mathematically productive and socially supportive for students. In this article, she draws on a larger study in which she spent a year observing and interviewing first-grade and fourth-grade mathematics students who regularly enacted strategy-sharing discussions (Hintz 2010).

By experiencing stories as mathematicians and/or scientists, young children engage in STEM practices such as reasoning and problem solving through discussion within the context of stories and the accompanying illustrations (O'Neill 2011). Three categories of STEM opportunities in children's books We have found several ways that science and math are embedded in a wide range of children's literature. With each turning page, the number of animals in the pond changes and the reader is repeatedly asked, \"How many are in my pond?\" Young mathematicians may count the animals by ones (or, as we have heard children do, note how the numbers change from illustration to illustration), think relationally about quantities, and practice addition and subtraction. [...]the story context was a source of inspiration for young children to engage with the intersecting practices of literacy, math, and science, such as constructing viable arguments, critiquing the reasoning of others, and citing textual evidence to support conclusions drawn from the text (CCSS 2010).

Discussing and exploring concepts is an important element of literacy and mathematics instruction in elementary classrooms. Read‐alouds provide an opportunity for teachers to engage students in meaningful discussion. This article describes a quick three‐step process for mathematizing books, that is, weaving together read‐alouds, discussion, and mathematics in order to maximize student learning using a variety of literary and informational texts. A planning sheet, list of example books, and samples of student work are included.

At a time when students are expected to participate in inquiry-oriented mathematical lessons, this dissertation presents the findings of a qualitative study of the mathematical and interactional demands students experience during the common mathematical discourse pattern of strategy sharing. Mathematical demands were identified as the subject matter knowledge a student must make use of and work with in order to engage in the discourse. Interactional demands were identified as what a child must be able to do socially because s/he is a student in a classroom with other children engaging in the discourse. This study draws upon a sociocultural perspective of learning to frame the study of the demands students' experience. A sociocultural lens focuses the analysis of students' experiences as they engage in mathematical learning through interaction with other people and participate in mathematical discussions where the structured activities have particular mathematical goals. To examine the mathematical and interactional demands students experience during strategy sharing, and how students' histories as well as the classroom context shape their experiences with the demands, data from two elementary classroom cases (a primary and an intermediate classroom) and seven student cases, including twenty-four videotaped focus lessons and individual interviews with focus students across the 2008-2009 school year, were collected. Analyses of this data revealed that (1) There is a wide range of mathematical and interactional demands present in strategy sharing lessons for all students. (2) The classroom context and who students are as learners and people shape how different students experience the demands. (3) Students' narrations reveal important reasons why children share (or do not share), reasons why students listen and what they chose to do with what they hear, and students' experiences working through mathematical mistakes publicly. This dissertation concludes with implications for teaching practices, and future research, that may help support all students through mathematically productive and socially supportive strategy sharing.

The design principles we have used in developing these activities include: (a) a focus on concrete examples of P-12 student work (Kazemi & Franke, 2004); (b) collaborative participation by pre-service teachers, veteran teachers and university faculty; and (c) potential for learning outcomes of direct relevance to the core institutional mission and responsibilities for each group of participants. In developing a visual representation of these principles, we colloquially defined the \"sweet spot\" of our collaborative work as the intersection of opportunities to learn by pre-service teachers, veteran teachers, and university teacher education faculty in a shared context which focused on analysis of P-12 student learning (see Figure 1).

Understanding how rising seawater pCO2 and temperatures impact coral aragonite accretion is essential for predicting the future of reef ecosystems. Here, we report 2 long-term (10–11 month) studies assessing the effects of temperature (25 and 28 °C) and both high and low seawater pCO2 (180–750 μatm) on the calcification, photosynthesis and respiration of individual massive Porites spp. genotypes. Calcification rates were highly variable between genotypes, but high seawater pCO2 reduced calcification significantly in 4 of 7 genotypes cultured at 25 °C but in only 1 of 4 genotypes cultured at 28 °C. Increasing seawater temperature enhanced calcification in almost all corals, but the magnitude of this effect was seawater pCO2 dependent. The 3 °C temperature increase enhanced calcification rate on average by 3% at 180 μatm, by 35% at 260 μatm and by > 300% at 750 μatm. The rate increase at high seawater pCO2 exceeds that observed in inorganic aragonites. Responses of gross/net photosynthesis and respiration to temperature and seawater pCO2 varied between genotypes, but rates of all these processes were reduced at the higher seawater temperature. Increases in seawater temperature, below the thermal stress threshold, may mitigate against ocean acidification in this coral genus, but this moderation is not mediated by an increase in net photosynthesis. The response of coral calcification to temperature cannot be explained by symbiont productivity or by thermodynamic and kinetic influences on aragonite formation.

Coral skeletal Sr/Ca is a palaeothermometer commonly used to produce high resolution seasonal sea surface temperature (SST) records and to investigate the amplitude and frequency of ENSO and interdecadal climate events. The proxy relationship is typically calibrated by matching seasonal SST and skeletal Sr/Ca maxima and minima in modern corals. Applying these calibrations to fossil corals assumes that the temperature sensitivity of skeletal Sr/Ca is conserved, despite substantial changes in seawater carbonate chemistry between the modern and glacial ocean. We present Sr/Ca analyses of 3 genotypes of massive Porites spp. corals (the genus most commonly used for palaeoclimate reconstruction), cultured under seawater p CO 2 reflecting modern, future (year 2100) and last glacial maximum (LGM) conditions. Skeletal Sr/Ca is indistinguishable between duplicate colonies of the same genotype cultured under the same conditions, but varies significantly in response to seawater p CO 2 in two genotypes of Porites lutea , whilst Porites murrayensis is unaffected. Within P. lutea , the response is not systematic: skeletal Sr/Ca increases significantly (by 2–4%) at high seawater p CO 2 relative to modern in both genotypes and also increases significantly (by 4%) at low seawater p CO 2 in one genotype. This magnitude of variation equates to errors in reconstructed SST of up to −5 °C.

Ocean acidification typically reduces the calcification rates of massive Porites spp. corals, but increasing seawater temperatures (below the stress and bleaching threshold) can offset this effect. Here, we use δ11B to reconstruct the pH of the calcification media (pHECM) used to precipitate the skeleton in poritid corals cultured over a range of seawater pCO2 and at 25 °C and 28 °C. Increasing temperature had no significant effect on pHECM at high pCO2 although corals increased their calcification rates. pHECM was reduced at 28 °C compared to 25 °C at low seawater pCO2, although calcification rates remained constant. Increasing calcification rates could reflect the positive influence of temperature on aragonite precipitation rate, an increase in calcification media saturation state or a change in the concentration/behaviour of the skeletal organic matrix. The two temperatures utilized in this study were within the seasonal range at the coral collection site and do not represent a heat stress scenario. Increasing seawater temperatures may promote calcification in some corals in the future but are unlikely to benefit the majority of corals, which are already living close to their maximum thermal tolerance limits.