Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Fractions

This article presents a research summary of prospective elementary teachers’ (PTs’) mathematical content knowledge in the area of fractions. The authors conducted an extensive review of the research literature and present the findings across three time frames: a historical look (pre-­‐1998), a current perspective (1998–2011), and a look at the horizon (2011–2013). We discuss 43 articles written across these time frames that focus on PTs’ fraction knowledge. Consistent across these papers is that PTs’ fraction knowledge is relatively strong when it comes to performing procedures, but that they generally lack flexibility in moving away from procedures and using “fraction number sense” and have trouble understanding the meanings behind the procedures or why procedures work. Across the time frames, the trend in the research has moved from looking almost entirely at PTs’ understanding of fraction operations, particularly multiplication and division, to a more balanced study of both their knowledge of operations and fraction concepts. What is lacking in the majority of these studies are ways to help improve upon PTs’ fraction content knowledge. Findings from this summary suggest the need for a broader study of fractions in both content and methods courses for PTs, as well as research into how PTs’ fraction content knowledge develops

Empowering Young People through Conflict and Conciliation: Attending to the Political and Agonism in Democratic Education

Deliberative models of democratic education encourage the discussion of controversial issues in the classroom (e.g., Hess, 2009); however, they tend to curtail conflicts for the sake of consensus. Agonism, on the other hand, can help support the deliberative model by attending to antagonism in productive ways (Ruitenberg, 2009). In this paper, I present how agonistic deliberation (the infusion of agonism into deliberation) can work as an account of the political that may help empower young people. The paper presents two classic democratic classroom practices—structured academic controversy (SAC) and debate—together as examples of how agonistic deliberation can help students engage politically. This paper suggests that while deliberation can help students learn about political participation, agonistic deliberation (with its focus on conflict) has the potential to help students harness social frustrations into political action

Reinventing the High School Government Course: Rigor, Simulations, and Learning from Text

The high school government course is arguably the main site of formal civic education in the country today. This article presents the curriculum that resulted from a multiyear study aimed at improving the course. The pedagogic model, called Knowledge in Action, centers on a rigorous form of project-based learning where the projects are weeks-long simulations. The first section introduces the course and the study, the second describes the methodology and design principles, the third describes the political simulations that are the spine of the course, and the fourth examines implementation and design issues that emerged across the years. The latter are concerned with the centrality of simulations, the selection of core content and skills for deeper learning, and the ongoing struggle to help students learn from texts. Readers are invited to adopt or adapt any of the design elements to suit their needs

Blended Spaces: Reimagining Civic Education in a Digital Era

While traditional civic education in the United States is inextricably linked to notions of a public sphere, this paper argues that the digital era requires a reimagining of this premise. The opaque nature of digital spaces makes it difficult for young people to understand how large of an audience they are interacting with and to what extent a conversation that may feel private is rebounding across public contexts. In this conceptual paper, we (1) use semiotic squares to present publicly private and privately public as two ways to reinterpret traditional presumptions about the role of “the public” in civic education and (2) present the implications of these blended spaces for civic education and civic learning. The paper asks, what does it mean to prepare young people for interaction in the “public” sphere within our classrooms today? By drawing on a vignette of teacher practice, we articulate what civic education could be for students around the world in the 21st century

Prospective Elementary Mathematics Teacher Content Knowledge: What Do We Know, What Do We Not Know, and Where Do We Go?

In this Special Issue, the authors reviewed 112 research studies from 1978 to 2012 on prospective elementary teachers’ content knowledge in five content areas: whole numbers and operations, fractions, decimals, geometry and measurement, and algebra. Looking across these studies, this final paper identifies the trends and common themes in terms of the counts and types of studies and commonalities among findings. Analyses of the counts show that the number of articles published each year focusing on prospective teacher (PT) content knowledge is increasing. Most articles across the content areas show that PTs tend to rely on procedures rather than concepts. However, the focus of most articles is identifying PTs’ misconceptions rather than understanding PTs’ conceptions and the development thereof. Both the limitations of the reviews and the directions for future research studies are elaborated

Maintaining Interest in Politics: ‘Engagement First’ in a U.S. High School Government Course

Purpose: Increasing students’ political interest has been a longstanding goal of civic education. One way to trigger students’ interests in political issues is by engaging them first in an attention grabbing activity (i.e., assigning them to roles). Because it is important to examine not only how roles may trigger political interest, but also students’ political interest afterwards, we asked: What happens to students’ interest in political issues after engagement first? Methodology: Drawing from Schwartz and Bransford’s (1998) ‘A Time for Telling’, we conducted a case study of three students, who experienced ‘engagement first’ activities in a class, and report on their interests about political issues in one particular activity. Findings: While role-play can help trigger students’ political interest. Our findings show that for students to maintain political interest, they need follow-up opportunities to engage in meaningful activities around politics. Research implications: Role assignment is a good way to trigger political interest, but productive disciplinary engagement can be coupled with engagement first to extent students’ political interest. Practical implications: Classroom activities that hope to support students’ political interest may need to include both ‘engagement first’ and further scaffolds for students to engage productively with politics

Risk Model Development and Validation for Prediction of Coronary Artery Aneurysms in Kawasaki Disease in a North American Population.

Background Accurate prediction of coronary artery aneurysms ( CAAs ) in patients with Kawasaki disease remains challenging in North American cohorts. We sought to develop and validate a risk model for CAA prediction. Methods and Results A binary outcome of CAA was defined as left anterior descending or right coronary artery Z score ≥2.5 at 2 to 8 weeks after fever onset in a development cohort (n=903) and a validation cohort (n=185) of patients with Kawasaki disease. Associations of baseline clinical, laboratory, and echocardiographic variables with later CAA were assessed in the development cohort using logistic regression. Discrimination (c statistic) and calibration (Hosmer-Lemeshow) of the final model were evaluated. A practical risk score assigning points to each variable in the final model was created based on model coefficients from the development cohort. Predictors of CAAs at 2 to 8 weeks were baseline Z score of left anterior descending or right coronary artery ≥2.0, age <6 months, Asian race, and C-reactive protein ≥13 mg/ dL (c=0.82 in the development cohort, c=0.93 in the validation cohort). The CAA risk score assigned 2 points for baseline Z score of left anterior descending or right coronary artery ≥2.0 and 1 point for each of the other variables, with creation of low- (0-1), moderate- (2), and high- (3-5) risk groups. The odds of CAA s were 16-fold greater in the high- versus the low-risk groups in the development cohort (odds ratio, 16.4; 95% CI , 9.71-27.7 [ P<0.001]), and >40-fold greater in the validation cohort (odds ratio, 44.0; 95% CI, 10.8-180 [ P<0.001]). Conclusions Our risk model for CAA in Kawasaki disease consisting of baseline demographic, laboratory, and echocardiographic variables had excellent predictive utility and should undergo prospective testing

Assessing deeper learning of high school civics

• Deeper learning in civics is conceptually rich and facilitates learning in the future. • We developed and conducted research on an assessment model and a test of deeper learning in high school civics. • We used construct-driven assessment design to develop the assessment. • We conducted research on the assessment using Design-Based Implementation Research across 13 schools. • Core concepts and reasoning strategies for the course provided the framework for assessment alignment. Purpose: Civic education is a central mission of public schools, and deeper learning of civics—learning that is complex and adaptive—is the goal. However, assessment of deeper civic learning is limited. Therefore, we aimed to develop an assessment model and test of deeper learning in the common high school civics course taught across the U.S. Design/methodology/approach: Using Design-Based Implementation Research (DBIR), the assessment model and test were iteratively researched and revised by a  team of researchers and teachers across seven years and multiple settings. Findings: Results of validity and reliability studies show that the model and test are promising tools for assessing deeper civic learning. Research limitations/implications: Additional research is warranted to refine the test-development process, design alternative test forms, and adapt the model to other social studies courses. Practical implications:  We suggest ways to use this assessment model to assess learning in civics and other social studies subjects