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Background: National ranking from the triennial Programme of International Student Assessment (PISA) often serves as a barometer of national performance and human capital. Though excessive student- and school-level covariates (n > 700) may prove intractable for traditional least-squares estimate procedures, shrinkage methods may be more suitable for subset selection., Aims: With a focus on the United States, this paper proposes sparse regression for PISA 2012 to discover salient student- and school-level predictor variables for mathematical literacy achievement., Sample: The sparse regression analysis was conducted on 10 top-tiered OECD countries/economies, Canada, and the United States in mathematical literacy on the 2012 PISA. Two- and three-level hierarchical regression analyses were performed on Canadian and US students (N = 26,522) along with five of the ten top-tiered countries/economies (N = 58,385)., Methods: Using the 'least absolute shrinkage and selection operator' (LASSO) technique, the study (1) identified salient predictor variables of mathematical literacy performance for the top-tiered countries/economies, Canada, and the United States and (2) used these salient variables to perform two- and three-level hierarchical regression on data from Canada and the United States along with five top-tiered countries/economies. Weights and replicates were used to account for complex sample design. A weighted, two-level confirmatory factor analysis was performed to identify latent constructs. Missing data were handled through multiple imputation., Results: Separate two-level hierarchical models accounted for 32-35% student-level and 58-70% school-level variance in Canada and the United States, respectively; three-level models accounted for 33% of level-one variance, 62-65% level-two variance, and 13-44% of level-three variance for the US/Canada and US/Canada/top-tiered students, respectively. Following top-tiered countries/economies, Canadian students had high levels of self-efficacy, were more likely to encounter advanced concepts in class, were less activity/small group-centred, and were more likely to consider truancy a learning hindrance. Factor analyses revealed a positive relation with rigour and class organization (teacher-centred) for top-tiered countries and Canada, though not for the United States. For all countries, there was a strong relation between rigour and self-beliefs., Conclusion: Compared to top performers, a less rigorous curriculum, coupled with class and school factors, may explain lag in US performance., (© 2018 The British Psychological Society.)

This paper presents some ongoing findings from a larger project exploring the growth of mathematical understanding in a variety of construction trades training programs. In this paper we specifically focus on the notion of collective mathematical understanding in an ironworking apprenticeship classroom. We identify the particular ways in which a group of three apprentices work collaboratively together to solve a workplace problem with a substantial mathematical element. Through drawing on the notion of "improvisational coactions" (Martin & Towers, 2009) we detail the ways that individual ideas, understandings and contributions mesh together and are collectively built on by the group to allow a shared understanding to emerge. From this analysis we suggest that improvisational coactions can be a powerful means through which apprentices in the workplace-training classroom might effectively learn to tackle workplace problems that involve thinking and working mathematically. Although our conclusions are specific to this case, we would suggest that there are implications that may be relevant to other areas of workplace training.

The secondary-school mathematics curriculum is narrow in scope and technical in character; this is quite different from the nature of the discipline itself. As a result, it offers little inspiration to both students and teachers, and provides students with poor preparation for university mathematics courses and indeed for life. Over the past century, recently more than ever, there have been calls for change, for a curriculum that is true to the subject of mathematics as the creation and study of patterns and structures. While there are hopeful responses to this at the elementary level, there is almost nothing at the secondary level. Ironically, it is felt that in order to prepare students for university calculus, the secondary curriculum simply has to be what it is. This is a special case of a myth that needs to be destroyed.

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills, such as debate, argument and disagreement. The students were told in advance to use the online material to prepare, which had a short handout on matrix determinants posted, as the lesson would be interactive and would rely on them having studied this. At the beginning of the lesson, the two mathematicians worked together to model the skill of professional disagreement, one arguing for the cofactor expansion method and the other for the row reduction method. After voting for their preferred method, the students worked in small groups on examples to defend their choice. Each group elected a spokesperson and a political style debate followed as the students argued the pros and cons of each technique. Although one lecture does not establish whether the flipped lecture model is preferable for student instruction, the paper presents a case study for pursuing this approach and for further research on incorporating this style of teaching in Science, Technology, Engineering and Mathematics subjects.

The "Canadian Journal of Science, Mathematics and Technology Education" ("CJSMTE") is celebrating its 20 years in 2020. This paper compares the data from the 2009 review (Wallace, 2009) and the 2015 review (Wiseman & Pegg, 2015) to the data from the past 20 years, from 2001 to 2020. The findings suggest that there was an increase in mathematics education articles, balancing the proportion of science articles to mathematics articles, as well as an increased focus on technology education articles and STEM articles. In very recent volumes, the journal has increased the number of articles from five or six per issue to 12 articles per issue in its transition to Springer. The findings support the 2015 review findings that "CJSMTE" has increased the number of contributions from other countries around the world. The journal should continue to encourage manuscripts from Africa and South America to further pursue its international recognition.

Computerized adaptive testing (CAT) is a mode of testing which enables more efficient and accurate recovery of one or more latent traits. Traditionally, CAT is built upon Item Response Theory (IRT) models that assume unidimensionality. However, the problem of how to build CAT upon latent class models (LCM) has not been investigated until recently, when Tatsuoka ("J. R. Stat. Soc., Ser. C, Appl. Stat." 51:337-350, 2002) and Tatsuoka and Ferguson ("J. R. Stat., Ser. B" 65:143-157, 2003) established a general theorem on the asymptotically optimal sequential selection of experiments to classify finite, partially ordered sets. Xu, Chang, and Douglas (Paper presented at the annual meeting of National Council on Measurement in Education, Montreal, Canada, 2003) then tested two heuristics in a simulation study based on Tatsuoka's theoretical work in the context of computerized adaptive testing. One of the heuristics was developed based on Kullback-Leibler information, and the other based on Shannon entropy. In this paper, we showcase the application of the optimal sequential selection methodology in item selection of CAT that is built upon cognitive diagnostic models. Two new heuristics are proposed, and are compared against the randomized item selection method and the two heuristics investigated in Xu et al. (Paper presented at the annual meeting of National Council on Measurement in Education, Montreal, Canada, 2003). Finally, we show the connection between the Kullback-Leibler-information-based approaches and the Shannon-entropy-based approach, as well as the connection between algorithms built upon LCM and those built upon IRT models.

The concept of "practice makes perfect" was examined in this work in the context of effective learning. Specifically, we wanted to know how much practice was needed for students to demonstrate mastery of learning outcomes. Student learning patterns in two different university courses that use a similar education approach involving problem based learning, outcomes based assessment, and problem sequencing based on elaboration theory were examined. Learning outcomes for each course were explicitly defined and students were repeatedly assessed through sequential assignments. The cumulative proportion of criteria successfully demonstrated for each problem-solving attempt was determined using data retrospectively obtained from instructor grading records. Learning followed a typical growth pattern--it increased rapidly at first and more slowly with succeeding attempts. The precise shape of the learning curve differed between the two courses and is thought to be the result of problem difficulty and problem sequencing. Depending on these two factors, at least one more attempt than the number of times criteria need to be demonstrated is required and often more are needed to demonstrate mastery. This paper presents class-level data and future work should investigate individual performance and particularly why some students learn more quickly than others. Two additional issues for future consideration are the effect of the number of attempts on long-term retention and on the transferability of the learning to other problems. (Contains 4 tables and 2 figures.)

There is not just one mathematics taught at university level, nor is there one group of students. Mathematics is taught differently depending on the discipline and the perceived background of the student. There is engineering mathematics for the students heading towards engineering degrees, life science mathematics for those heading towards biology degrees and so on. This paper considers the phases of transitions that students experience as they embark on a course of study and then go on to professional life. We make inferences about the ways the curriculum should be designed to alleviate the difficulties of these phases as well as to take account of the capabilities that graduates will require in the workplace. It is not only where students are coming from that affects their learning but where they are heading to, in combination with their perceptions of that destination. (Contains 1 table and 1 figure.)

Statistics is taught in mathematics courses in all school levels. We suggest that using rich tasks in statistics can develop statistical reasoning and create both intra and interdisciplinary links in students. In this paper, we present three case studies where middle school mathematics teachers used different tasks in lessons on pie charts. We analyzed the actions implemented/performed/attempted by teachers to support the development of statistical reasoning and the creation of intra and interdisciplinary links in their lessons. Results show that their procedural vision of statistics led them to focus more on graphical representation, neglecting aspects of statistical reasoning. Results also reveal an interdisciplinary intersection between mathematics and statistics, which may prevent the development of statistical reasoning.

In an effort to increase our understanding of what mathematics young children are capable of when provided with playful yet purposeful opportunities to learn, Canadian researchers initiated lesson study over 4 years with teams of teachers of young children (ages 4-7). The lesson study process followed a lesson study cycle of goal setting, planning, implementation and reflection, with one major variation: a focus on the design and implementation of exploratory tasks. Exploratory tasks are brief, collaboratively planned activities that focus on precise mathematics content with engaging contexts. The lesson study team featured in this paper presented students with challenging exploratory tasks to investigate length, perimeter and area measurement concepts as they progressed toward the public research lesson. Through the process, lesson study teachers increased their abilities to look and listen for student mathematics thinking that affected their subsequent planning to tasks. Notably, teacher estimations of what young children can do were expanded and raised. Students also made significant gains on pre-post interviews, suggesting that exploratory tasks are a powerful variation of lesson study that increases teacher and student learning due to increases in frequency, emphasis and implementation of quality tasks.

The NCTM Research Committee identifies key influences on mathematics education that are largely outside the domain of the academic world in which most mathematics education researchers live. The groups that are identified--including the media, companies and foundations, and other academic domains--affect the public's perception of mathematics and mathematics education. They argue that mathematics education researchers can intervene to shift these storylines and positionings and have greater impact on policy, practice, and public perception in the future.

This paper is an examination of the way mathematics, and STEM, arises through stories of teaching and learning on, with, and alongside Land. It emerges from research, undertaken in different Nations (Cree, Dene, Métis, Mi'kmaw, Naskapi, Canada), that considers what locally meaningful K-12 STEM teaching and learning might look like in Indigenous contexts. The paper reflects our research process. Each story is followed by a conversation that surfaces elements of how mathematics, language, learning, and different ways of knowing, being, and doing circulate together and emerge in relation to Land and all relations living within it. We frame the work in ethical relationality to open a space where Indigenous and Western knowledges might co-exist, attending to ongoing tensions in the work between ways of knowing, being, and doing of different people and peoples/nations, between perspectives and experiences of indigenous and non-indigenous participants, between languages, while still creating spaces where we might move closer together through iterative processes of collective learning. This exploration provides insight into how and when we might remember that mathematics has spirit, how quantity and pattern live in various contexts, when numbers might be inadequate for a context, and how all these ideas can meaningfully inform mathematics teaching and learning via relationships between language, mathematics and learners. We seek a mathematics that resists abstraction as extraction and instead lives and enspirits teaching and learning through relationships. [ABSTRACT FROM AUTHOR]

Although women's representation in STEM fields and occupations has increased, science and math continue to be stereotyped as male domains. This paper links psychological and sociological explanations for gendered disparities in STEM by examining the relationship between the local "micro-situational" female learning environment and the gender gap in academic self-concept in math and science. We applied hybrid models to TIMSS 2015 data comprised of a pseudo-panel of repeated measures for individual student and peer achievement, academic self-concept, utility value, and interest-enjoyment value in math/science (at age 14). We analyzed data from three countries, including a subsample of students who were taught by the same teacher in both math and science, thus eliminating unobserved teacher heterogeneity. Results indicate that female peer climate in the classroom is important for understanding how girls' self-concept in math/science is formed, even though it was unrelated to the gender gap. [ABSTRACT FROM AUTHOR]

Background: A strong knowledge of mathematics, beginning at the elementary level, is critical for participation in today's complex world. The home may be one way to facilitate individualized mathematics instruction, given that children spend more time at home than in an academic institution. Therefore, researchers are interested to see whether the home numeracy environment (HNE) can provide a solid foundation for children's mathematics understanding. Further, children's digital mathematics exploration at home is increasingly common (e.g., using math apps). Objectives: The present study evaluates the digital home numeracy practice (DHNP) model and explores its effect on children's mathematics knowledge across five domains (numeration, number operation, pattern recognition, spatial sense, and applied problem‐solving). Methods: To conduct this study, 117 Canadian parents and their children from Grade 1 through 5 completed a DHNP survey and a range of in‐person mathematics measures. Results and Conclusions: The results identified significant relations between parents and children's implicit mathematics factors (e.g., math anxiety, motivation). Children's mathematics anxiety and parents' academic estimations and expectations for their children positively predicted children's mathematics knowledge. In terms of DHNP components, parental involvement in DHNP predicted children's numeration and applied problem‐solving knowledge. Implications: Taken together, the results detail the contribution of parental and child factors to children's mathematics knowledge and suggest that parents adjust their role in DHNP according to their children's mathematics ability. Lay Description: What is (not) known about the subject matter?: Research is less developed on the impact of home technology in the mathematics learning processExisting research did not use a multi‐measure approach to assess the relationships between a variety of home numeracy factors and fundamental mathematics concepts and processes What is the contribution of this paper?: The paper highlights the importance of considering different home related factors to understand the role of home numeracy practices in children's mathematics developmentIt provides a holistic view of digital home numeracy practice (DHNP) by examining several implicit and explicit components of home numeracy environmentChildren's mathematics anxiety predicts their mathematics knowledgeParental estimation and expectation about their children's mathematics performance predicts their mathematics knowledge across several domains whereas parental role on DHNP impacts children's numeration only What are the implications of the findings?: The findings provide an understanding of the significant value of including digital mathematics practices in the study of the home mathematics environmentThe outcome of the study provides guidance for educators and researchers to better understand and leverage DHNP, and its impact on children's mathematics educationFuture research should investigate to what extent digital features should be included in the DHNP model. This will provide insights into the impact of using well‐designed apps on children's mathematics learning [ABSTRACT FROM AUTHOR]

As part of a larger project focused on transforming mathematics education for Aboriginal students in Atlantic Canada, this paper reports on the role of the Mi'kmaw language in mathematics teaching. Examining how mathematical concepts are described in Mi'kmaq gives insight into ways of thinking. Shifting classroom discussions to reflect Mi'kmaw verb-based grammar structures, referred to as "verbification", is described through the example of a grade 3 lesson on prisms and pyramids. "Verbification" shows tremendous promise as a way to support Mi'kmaw learners as they negotiate their space between school-based mathematics and their own cultural ways of knowing and doing mathematics.

Background: Play is an important part of the childhood. The learning potential of playing and creating non-digital games, like tabletop games, however, has not been fully explored. Aim: The study discussed in this paper identified a range of activities through which learners redesigned a mathematics-oriented tabletop game to develop their ideas and competencies in an integrated STEM (science, technology, engineering, and mathematics) class. Method: Third and fourth graders worked as teams to make changes on Triominos over a period of six weeks. Considering what could be changed from the original game, each group provided a different design for Triominos to accommodate the changes introduced. We gathered data through weekly observations of two classes (about 45 learners, ranging from age eight to ten) in a west-Canada school. In this paper, we present the works of three groups of three teammates. Results: We found that any change made by learners not only influenced mechanics, dynamics, and aesthetics of the game but also helped engage learners, encourage unconventional ideas, promote learning, and solve problems. Based on our findings, we suggest redesigning games facilitated learners deepen their understanding of mathematical concepts as part of a designed game system in STEM classes. [ABSTRACT FROM AUTHOR]

Background: Computer‐based assessment allows for the monitoring of reader behaviour. The identification of patterns in this behaviour can provide insights that may be useful in informing educational interventions. Objectives: Our study aims to explore what different patterns of reading activity exist, and investigates their interpretation and consistency across different task sets (units), countries, and languages. Three patterns were expected: on‐task, exploring and disengaged. Methods: Using log data from the PISA 2012 digital reading assessment (9226 students from seven countries), we conducted hierarchical cluster analyses with typical process indicators of digital reading assessments. We identified different patterns and explored whether they remained consistent across different units. To validate the interpretation of the identified patterns, we examined their relationship to performance and student characteristics (gender, socio‐economic status, print reading skills). Results and Conclusions: The results indicate a small number of transnational clusters, with unit‐specific differences. Cluster interpretation is supported by associations with student characteristics—for example, students with low print reading skills were more likely to show a disengaged pattern than proficient readers. Exploring behaviour tended to be exhibited only once across the three units: It occurred in the first unit for proficient readers and in later units for less skilled readers. Major Takeaways: Behavioural patterns can be identified in digital reading tasks that may prove useful for educational monitoring and intervention. Although task situations are designed to evoke certain behaviours, the interpretation of observed behavioural patterns requires validation based on task requirements, assessment context and relationships to other available information. Lay Description: What is already known about the subject matter?: Students differ in how they read, comprehend and use digital information.Indicators from process data provide insight about how students engage with digital reading tasks. What does this paper add to the subject matter?: Based on multiple process indicators, a small number of clusters indicating different behavioural activity can be distinguished.These clusters can be described as on‐task, passive, hasty, exploring, disengaged, persistent and lost interest.A meaningful interpretation of the clusters must consider the requirements of the underlying tasks. Implications for practice and/or policy: Knowledge of how students engage with digital resources may provide useful feedback for teachers to guide students' learning or intervene when they struggle.Educational monitoring: The high comparability of country‐specific results suggests an invariant set of solution strategies in the digital reading assessment. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal for the Scholarship of Teaching & Learning is the property of Society for Teaching & Learning in Higher Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Robitaille and O'Shea used the Rasch model in developing a set of 40-item mathematics achievement tests. The Rasch model is inappropriate for such a purpose; their article presents the model in a too favorable light and continued application of the model encourages less desirable educational practice and misdirects scarce resources. (BRR)

Floating Catchment Area (FCA) methods are a popular tool to investigate accessibility to public facilities, in particular health care services. FCA approaches are attractive because, unlike other accessibility measures, they take into account the potential for congestion of facilities. This is done by 1) considering the population within the catchment area of a facility to calculate a variable that measures level of service, and then 2) aggregating the level of service by population centers subject to catchment area constraints. In this paper we discuss an effect of FCA approaches, an artifact that we term demand and level of service inflation. These artifacts are present in previous implementations of FCA methods. We argue that inflation makes interpretation of estimates of accessibility difficult, which has possible deleterious consequences for decision making. Next, we propose a simple and intuitive approach to proportionally allocate demandand and level of service in FCA calculations. The approach is based on a standardization of the impedance matrix, similar to approaches popular in the spatial statistics and econometrics literature. The result is a more intiuitive measure of accessibility that 1) provides a local version of the provider-to-population ratio; and 2) preserves the level of demand and the level of supply in a system. We illustrate the relevant issues with some examples, and then empirically by means of a case study of accessibility to family physicians in the Hamilton Census Metropolitan Area (CMA), in Ontario, Canada. Results indicate that demand and supply inflation/deflation affect the interpretation of accessibility analysis using existing FCA methods, and that the proposed adjustment can lead to more intuitive results. [ABSTRACT FROM AUTHOR]

Freely-available satellite data streams and the ability to process these data on cloud-computing platforms such as Google Earth Engine have made frequent, large-scale landcover mapping at high resolution a real possibility. In this paper we apply these technologies, along with machine learning, to the mapping of peatlands–a landcover class that is critical for preserving biodiversity, helping to address climate change impacts, and providing ecosystem services, e.g., carbon storage–in the Boreal Forest Natural Region of Alberta, Canada. We outline a data-driven, scientific framework that: compiles large amounts of Earth observation data sets (radar, optical, and LiDAR); examines the extracted variables for suitability in peatland modelling; optimizes model parameterization; and finally, predicts peatland occurrence across a large boreal area (397, 958 km2) of Alberta at 10 m spatial resolution (equalling 3.9 billion pixels across Alberta). The resulting peatland occurrence model shows an accuracy of 87% and a kappa statistic of 0.57 when compared to our validation data set. Differentiating peatlands from mineral wetlands achieved an accuracy of 69% and kappa statistic of 0.37. This data-driven approach is applicable at large geopolitical scales (e.g., provincial, national) for wetland and landcover inventories that support long-term, responsible resource management. [ABSTRACT FROM AUTHOR]

The Government of Canada identifies numeracy as a foundational skill for work, learning, and life. Libraries have historically been champions of literacy; however, the role of libraries in developing numeracy skills is understudied. Specifically, there is a critical gap in studying numeracy programs offered by public libraries. This exploratory study examines the state of numeracy programming at five major urban public libraries in Canada (Calgary Public Library, Edmonton Public Library, Bibliothèques de Montréal, Ottawa Public Library, and Toronto Public Library) to understand the types and varieties of numeracy programs that they offer. The frequency of programs, the intended age range, and the program content are the main foci of this paper. The researchers examined 1166 program listings by scraping programming information from the five libraries' websites. The data was collected for the second week of December 2015 and relied on programming descriptions from libraries' websites. Results showed that a total of 65 programs (5.6% of total programs) covered numeracy related skills. Overall, the options to learn about numeracy concepts were very limited at all of the libraries in the sample. Calgary offered the highest number of children-focused numeracy programs, while Toronto offered the greatest number of adult-focused numeracy programs. "Math/mathematics" was the most common term used to describe numeracy-related programs. This exploratory study underscores the need for greater investigation of numeracy programming in public libraries. [ABSTRACT FROM AUTHOR]

The act of making provides students with an opportunity to create and design by using materials and technologies. Scholars who examine learning through making maintain that maker approaches to solving problems, creating designs, and thinking about real-world ideas promote the development of abstract thinking skills, such as modeling, and computational thinking (CT) skills. Our goal is to research the use of specific methods of maker education—such as experimenting with tools and hands-on designs—in learning mathematics. We ask: what are the benefits and potential outcomes for designing and teaching learning activities which integrate technology maker practices and pedagogies in mathematics and other school concepts in STEM contexts? We analyzed qualitative data on the benefits and potential outcomes of maker practices and pedagogies from three cases in Canada and Brazil. The researchers designed and facilitated the tasks to study the experiences of participants. Participants were observed, interviewed (or asked interview questions via a questionnaire), and completed reflection prompts. Their activities were recorded. The results show that learning from maker practices and pedagogies augments the learning of individual STEM disciplines, with specific settings and activity designs offering varied foci on mathematics and technology, on science, engineering and mathematics, or on science, technology and mathematics. Students, preservice teachers and teachers benefit in cognitive, interdisciplinary and social (situated) ways. Further research is needed to explore how deeper and other benefits, including critical benefits, may be achieved for learning and teaching mathematics and to explore which practices and pedagogies are associated with more potential outcomes. [ABSTRACT FROM AUTHOR]

TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS) is a multi-year, multi-institution collaborative project funded by the US National Science Foundation aimed at developing and testing student projects based on primary historical sources related to the original or subsequent development of core topics in today's tertiary mathematics curriculum. In addition to developing a broad range of projects and supporting their site testing by instructors across the US and Canada, TRIUMPHS includes a major Evaluation-with-Research component that is studying the effects of their classroom use on students and instructors. Our goal in this article is to share an overview of our research efforts related to the student learning experience—and as importantly, the tale of how we arrived at them—with others engaged in the effort to transform instruction in the field of undergraduate mathematics education. We provide a summary of three research initiatives undertaken by TRIUMPHS: a metadiscursive rules investigation based on Sfard's theory of commognition, an exploratory study of the concepts of transgressive actions and boundary crossings (first put forth by Polish psychologist Jozef Kozielecki) within the context of student learning of mathematics, and an examination of the different views students hold regarding the nature of mathematics. Additionally, we offer methodological reflections on how we revised our research questions and analytic tools based on theoretical constructs from mathematics education and beyond as the project unfolded over the first 6 years. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal of Higher Education is the property of Canadian Society for the Study of Higher Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A new body of sociological research is finding that northern and rural youth, and in particular, low‐SES youth, face difficulties accessing higher levels of postsecondary education and lucrative fields of study such as the STEMs. However, existing research has yet to systematically measure the skills proficiencies of youth in these regions nor have we understood the factors which might account for regional differences. We draw on multiple cycles of Statistics Canada's Youth in Transition Survey, Cohort A linked to the Programme for International Student Assessment scores to investigate how location of residence impacts skills proficiencies at age 15 in math, science, and reading outcomes. Overall, our results point to three key findings. First, southern youth outperform northern youth in mathematics skills. Second, we uncover a southern (both urban and rural) and northern urban advantage in reading proficiencies. Third, in science literacy, southern and northern urban youth experience significant advantages over youth from northern rural locations. While some of the skills differences are attributable to parenting styles, parental socioeconomic status, student academics, and province of residence, they are not completely attenuated by these factors. We conclude with a discussion of the implications for future research and public policy. [ABSTRACT FROM AUTHOR]

The article features the conference "Renaissance Banff: Mathematics, Music, Art, Culture" that was held on July 30 to August 3, 2005. The conference was the first interdisciplinary conference on mathematics and the arts to be held at the famed Banff Centre and brought a diverse group of about 200 participants from the United States, Canada, and abroad. Several activities are detailed.

BACKGROUND: Despite 20 y of biomonitoring studies of per- and polyfluoroalkyl substances (PFAS) in both serum and urine, we have an extremely limited understanding of PFAS concentrations in breast milk of women from the United States and Canada. The lack of robust information on PFAS concentrations in breast milk and implications for breastfed infants and their families were brought to the forefront by communities impacted by PFAS contamination. OBJECTIVES: The objectives of this work are to: a) document published PFAS breast milk concentrations in the United States and Canada; b) estimate breast milk PFAS levels from maternal serum concentrations in national surveys and communities impacted by PFAS; and c) compare measured/estimated milk PFAS concentrations to screening values. METHODS: We used three studies reporting breast milk concentrations in the United States and Canada We also estimated breast milk PFAS concentrations by multiplying publicly available serum concentrations by milk:serum partitioning ratios for perfluorooctanoic acid (PFOA), perfluorooctane sulfonate (PFOS), perfluorohexane sulfonate (PFHxS), and perfluorononanoic acid (PFNA). Measured and estimated breast milk concentrations were compared to children’s drinking water screening values. DISCUSSION: Geometric means of estimated breast milk concentrations ranged over approximately two orders of magnitude for the different surveys/ communities. All geometric mean and mean estimated and measured breast milk PFOA and PFOS concentrations exceeded drinking water screening values for children, sometimes by more than two orders of magnitude. For PFHxS and PFNA, all measured breast milk levels were below the drinking water screening values for children; the geometric mean estimated breast milk concentrations were close to—or exceeded—the children’s drinking water screening values for certain communities. Exceeding a children’s drinking water screening value does not indicate that adverse health effects will occur and should not be interpreted as a reason to not breastfeed; it indicates that the situation should be further evaluated. It is past time to have a better understanding of environmental chemical transfer to—and concentrations in—an exceptional source of infant nutrition. [ABSTRACT FROM AUTHOR]

Responds to comments made to the author's paper the local uses of international tests in Canada. Version of modern mathematics; Transparency in educational data that describes teaching and learning; Curriculum change.