This annotated bibliography is reformatted and customized by the Center for Positive Practices. Some of the authors featured on this page include Carrie D. Allen, Sidney C. Li, Kim Markworth, Joshua Wilson, Jane S. Hirschi, Mariah Kornbluh, Laura Hill, Kevin Murphy, Kristen D. Kent, and Patrick McGuire.
(2015). Making the Most of Modeling Tasks, Mathematics Teaching in the Middle School. While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts, relationships, diagrams, and symbolic expressions; manipulating and reasoning about those representations to derive new information; making predictions based on the results; and verifying predictions in the original problem situation (Lesh and Doerr 2003; Lesh and Zawojewski 2007). During the process of modeling, students apply what they already know as well as build and deepen their mathematical understanding of new mathematical content. For these reasons, modeling is important, which may be why the Common Core State Standards for Mathematics (CCSSI 2010) emphasizes the topic as not only a conceptual category in the high school curriculum but also a Standard for Mathematical Practice. As such, mathematical modeling should be part of mathematics learning, starting in the early grades. This implies that modeling is not an area of mathematics to be taught in isolation, but one that should permeate across content in the curriculum for all grades. In this article the authors consider the opportunities that students have to engage in tasks that strongly support modeling practices as well as those in which modeling is less visible. They describe examples of two types of tasks from existing curricula and online resources to illustrate their potential for supporting students in their modeling endeavors. [More] Descriptors: Middle School Students, Secondary School Mathematics, Mathematics Instruction, Mathematical Models
(2015). Problem Solving in All Seasons: Prekindergarten-Grade 2, National Council of Teachers of Mathematics. Holidays and seasonal activities provide excitement and a change of pace for teachers and students alike. They also offer perfect backdrops for mathematical tasks that can be related to other topics and themes in the classroom. "Problem Solving in All Seasons, Prekindergarten-Grade 2" delivers thirty-two appealing, real-world situations, arranged in grade-level order, to engage young learners in mathematical tasks that are tied to the Common Core State Standards or other content standards; and designed to allow children to participate in the Common Core Standards for Mathematical Practice. An implementation guide furnishes specifics on each task and includes the following: (1) Problem Discussion, supplying details about the mathematics; (2) Strategies, identifying possible student solution methods; (3) Student Misconceptions/Difficulties, describing the confusion and challenges that students may encounter; (4) Launch/Explore/Summarize, detailing the three-phase lesson format through which students might engage in each task; and (5) Differentiation, highlighting approaches to expanding or simplifying problems for students while maintaining the mathematical integrity of the task. Handouts and ancillary materials for each task can be downloaded for printing at NCTM's online More4U website (nctm.org/more4u). "Problem Solving in All Seasons, Prekindergarten-Grade 2" is an all-in-one practical handbook for problem solving in the primary years. [More] Descriptors: Primary Education, Early Childhood Education, Problem Solving, Kindergarten
(2014). Mathematics Formative Assessment System–Common Core State Standards: A Randomized Field Trial in Kindergarten and First Grade, Society for Research on Educational Effectiveness. The Florida Center for Research in Science, Technology, Engineering and Mathematics (FCR-STEM) was awarded a grant by the Florida Department of Education to develop a Mathematics Formative Assessment System (MFAS) aligned with the Common Core State Standards (CCSS). Intended for both teachers and students, formative assessment is a process that provides feedback to adjust ongoing teaching and learning to improve students' achievement of instructional goals. The evidence collected enables teachers to differentiate instruction based on students' mathematical thinking and reasoning rather than solely on incorrect answers. The MFAS-CCSS was designed to provide teachers with tasks and rubrics to employ the following five key strategies: (1) assess the student's level of understanding during instruction; (2) identify the student's specific misconceptions and errors; (3) examine samples of student work for further evidence of student understanding; (4) pose additional questions to elicit student thinking; and (5) obtain guidance on next steps for instruction. The current study–the MFAS-CCSS 2012-13 Study–is the third randomized field trial conducted on MFAS. The purpose was to evaluate the effect the MFAS-CCSS has on teachers' knowledge of elementary mathematics and students' mathematics learning in Grades K-1. The MFAS-CCSS 2012-13 Study made use of intervention protocols and measures developed, field tested, and validated in the prior two pilot studies. Two tables are appended. [More] Descriptors: Formative Evaluation, Common Core State Standards, Kindergarten, Grade 1
(2015). Making Early Math Education Work for All Children, Phi Delta Kappan. Preparing children to be successful in mathematics begins with what they learn before they reach 1st grade. Math knowledge in prekindergarten and kindergarten predicts school achievement in math and in other topics, such as reading. Indeed, early math knowledge is one of the strongest predictors of math grades in high school, high school graduation, and college entry. But children enter kindergarten with a huge range of numerical knowledge and skills. So early educators must be attentive to practices that will aid in closing the gaps in learning. They can attend to this by following the guidance outlined in the National Research Council's report, "Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity," which identified math concepts that young children can and should learn. Especially important are children's competence with quantity and number, as well as geometry and spatial reasoning. The NRC's research summary and recommendations helped guide the Common Core State Standards in mathematics for kindergarten through 2nd grade. [More] Descriptors: Mathematics Education, Mathematics Achievement, Early Experience, Young Children
(2015). Integrating Modeling Steps into the High School Curriculum, Mathematics Teacher. According to a 2012 study from the Program for International Student Assessment, twenty-nine out of sixty-five participating nations and other jurisdictions outperformed the United States in mathematics by a statistically significant margin (up from twenty-three in 2009) (Heitin 2013). To improve students' mathematical understanding, the authors argue that educators need to focus on fewer topics in greater detail. To accomplish this, the Common Core State Standards (CCSSI 2010) highlights specific mathematical skills and concepts with a three-step approach: focus, coherence, and rigor. The inclusion of modeling, as a Standard for Mathematical Practice and also as a content category, demands a more rigorous understanding of mathematical tools and how they can be used in everyday situations. This refocusing requires an overhaul with new books and other materials geared toward this new approach. To ease the transition for in-service teachers, this article provides suggestions on how to incorporate modeling into the classroom with the resources already available. A bibliography is included. [More] Descriptors: Mathematics Instruction, Mathematics Achievement, Common Core State Standards, Mathematics Skills
(2015). Ripe for Change: Garden-Based Learning in Schools. Harvard Education Letter Impact Series, Harvard Education Press. "Ripe for Change: Garden-Based Learning in Schools" takes a big-picture view of the school garden movement and the state of garden-based learning in public K–8 education. The book frames the garden movement for educators and shows how school gardens have the potential to be a significant resource for teaching and learning. In this inviting and accessible book, the author: summarizes the current school gardening movement and the emerging field of garden-based learning; provides an overview of the origins, benefits, and barriers to school gardening; explores sustainable models for garden-based learning; includes five case studies of successful partnerships between urban districts and nonprofit school gardening organizations around the country; illustrates how gardens can be used for integrating academic lessons aligned with the Common Core State Standards and Next Generation Science Standards; includes examples of important tools available for assessing the impact of school gardens. "Ripe for Change" reveals a wealth of resources to show how garden-based learning is being implemented in a systematic way in public education, and offers next steps to widen and deepen the practice to reach children in all schools. Three appendices are included: Appendix A: Sample Teacher Usage Surveys; Appendix B: Cambridge Public Schools Curriculum Connections; and Appendix C: Sample Garden Assessment. Resources, notes, and an index are also included. [Forward by David Sobel.] [More] Descriptors: Integrated Activities, Learning Activities, Gardening, Case Studies
(2015). Changing the Equation: Ensuring the Common Core Math Standards Enable All Students to Excel in California Schools. K-12 Practice, Education Trust-West. Schools around California are implementing the new Common Core State Standards. In math specifically, where significant disparities in proficiency exist for African American, Latino, and low-income students as compared to their white, Asian and higher-income peers, these new standards provide an opportunity to close achievement and opportunity gaps. Our new report, "Changing the Equation Ensuring the Common Core Math Standards Enable All Students to Excel in California Schools", describes both the challenges districts face in implementing the new math standards and best practices for addressing these challenges. Specific examples include ways to create a culture of high expectations for all students, models for supporting teachers as they design and implement rigorous curriculum, and strategies for meaningfully engaging students and parents with the standards. In highlighting practices from the field, the report illuminates how districts can ensure the standards not only raise the bar for all students but also help close achievement gaps for students of color and low-income students. [This report was written with the assistance of Brentt Brown.] [More] Descriptors: Common Core State Standards, Mathematics Education, Best Practices, Barriers
(2015). Academic Standards for Writing: To What Degree Do Standards Signpost Evidence-Based Instructional Practices and Interventions?, Grantee Submission. Though writing plays an important role in academic, social, and economic success, typical writing instruction generally does not reflect evidence-based practices (EBPs). One potential reason for this is limited signposting of EBPs in standards. We analyzed the content of writing standards from a representative sample of states and the Common Core State Standards (CCSS) for writing and language to determine to what degree EBPs were signposted, variability of this signposting, and the overlap of practices signposted in states' standards and the CCSS. We found a few practices signposted fairly consistently (e.g., isolated components of writing process instruction) and others rarely so (e.g., use of text models), as well as great variability across standards, with some covering almost half of the EBPs and others far fewer. Only a few states' writing standards overlapped considerably with the CCSS. We discuss the implications of these findings for teacher professional development and for evaluating standards. [This article was published in "Elementary School Journal," v116 n2 p291-321 Dec 2015 (EJ1084264).] [More] Descriptors: Academic Standards, Writing Instruction, Evidence Based Practice, Common Core State Standards
(2015). Journey to Centers in the Core, Mathematics Teaching in the Middle School. Considerable discrepancies between the mean and median often occur in data sets that are skewed left, skewed right, or have other unusual features. In such cases, it is important to analyze the data and context carefully to decide how best to describe centers of distributions. The importance of this type of statistical thinking is acknowledged in the grade 6 Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010): Students are to engage in "relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered" (CCSSI 2010, p. 45). Given the steep challenge set in the grade 6 CCSSM, the authors set out to investigate how students' reasoning about choosing appropriate measures of center might be developed. They conducted a classroom research study during a summer mathematics program funded by the National Science Foundation. The study focused on a small group of students: two females and two males. It involved intensive data gathering and analysis using videorecorded clinical interviews over a period of nine weeks. In this article, the authors share the lessons they learned about developing students' abilities to choose appropriate measures of center. [More] Descriptors: Common Core State Standards, Mathematics Instruction, Statistical Analysis, Statistics
(2015). California's Future: K-12 Education, Public Policy Institute of California. California educates more than six million children in its K-12 public schools. More than half of these children are economically disadvantaged, and almost a quarter are not native English speakers (compared to less than one in ten nationwide). California is working to address these challenges, in part by adopting a new, simplified school finance system, known as the Local Control Funding Formula (LCFF). This system will provide long-term funding increases for districts with more low-income, English Learner, and foster youth students. In the 2014-15 school year, the Common Core State Standards–adopted across 43 states and the District of Columbia–replaced California's old standards in mathematics and English. This same school year is also seeing the first statewide administration of new standardized tests. As these reforms take hold, school districts around the state face fundamental changes in the ways that K-12 education is delivered, assessed, and funded. This brief document reports on how these reforms are creating new challenges, student achievement has been improving but the switch to Common Core may affect test scores and achievement gaps are still significant, and an improved fiscal picture with more work to be done. It also recommends several steps policymakers can take to improve the state's economic well-being, ensure that California's children are equipped to succeed in the 21st century, and help the state's school systems maintain and build on recent improvements. [More] Descriptors: Elementary Secondary Education, Educational Trends, Futures (of Society), Public Schools
(2015). Royalty, Racing, and Rolling Pigs, Teaching Children Mathematics. Some statisticians have pointed out that the field of statistics essentially exists to study the variability seen in everyday life. Because variability is so foundational, the "Guidelines for Assessment and Instruction in Statistics Education" (GAISE 2007), published by the American Statistical Association (ASA), recommend that teachers help students understand the nature of variability and its origins during their earliest experiences learning statistics. Given the importance of early work with statistical variability, elementary school teachers who are implementing the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) may face a dilemma: The word "variability" is not mentioned at all in K-grade 5 CCSSM. Randall Groth faced the CCSSM variability dilemma in a summer math camp for students in grades 2-5. He wanted to provide experiences to help them succeed with the measurement and data standards in CCSSM, but he also wanted the students to understand the nature and importance of statistical variability. He found that by selecting problem contexts carefully, he could provide experiences with all types of variability recommended for young learners in the GAISE report while addressing the graphing-focused standards of CCSSM. Herein he describes how within the span of three lessons, students worked with three types of variability from GAISE–natural, measurement, and induced–while also working with the types of statistical graphs required in CCSSM. [More] Descriptors: Statistics, Mathematics Instruction, Elementary School Mathematics, Common Core State Standards
(2015). Youth Participatory Action Research as an Approach to Sociopolitical Development and the New Academic Standards: Considerations for Educators, Urban Review: Issues and Ideas in Public Education. Administrators and teachers face changes prompted by the shift to Common Core State Standards (CCSS) and Next Generation Science Standards (NGSS). Youth Participatory Action Research (YPAR) offers a promising approach to supporting students in mastering new content standards, while also offering experiences that promote their sociopolitical development and civic agency. In YPAR, students work with a teacher or other adult ally to critically reflect upon the social and political forces influencing their lives, identify a pressing problem or school need, study it through systematic research, and then develop an action plan to raise awareness or change a policy. Because of its emphasis on educational relevance, critical consciousness, and social justice, YPAR is an especially promising strategy with young people who experience racism or other forms of marginalization in school. In this article we describe the YPAR cycle, make an argument for how it creates opportunities for academic learning, sociopolitical development, and youth leadership, and provide examples of what this might look like in practice. YPAR offers a curricular approach that addresses academic objectives while also supporting democratic education and the sociopolitical development of students. [More] Descriptors: Youth, Participatory Research, Action Research, Reflection
(2015). 21st Century Standards and Curriculum: Current Research and Practice, Journal of Education and Practice. The integration of Common Core State Standards (CCSS) and 21st century skills in the curriculum is not only beneficial to students and teachers, but also necessary to prepare our youth for their future careers. In an age of education where standardized tests determine the success of our schools, it is important to allow students the creativity and use the power of technology to support necessary skills and learn in unique ways. By allowing creative thinking and gauging understanding of content standards through a portfolio based system, students can display their concept retention while producing tangible and valuable outcomes. The future of our students depends on flexibility and resourcefulness not teaching to the test. Education needs to make an instructional shift in order to ensure our students succeed as the innovators of the future. This article explores 21st century skills, as they are defined and describes methods that allow students to enhance these skills. It also highlights how educators can link students' current knowledge with authentic experiences that motivate, as well as allow them to create and collaborate using the latest technologies. The article concludes with a discussion around benefits of integrating multimedia in the classroom, including giving students the opportunity to enhance academic and social skills as they communicate and share information, organize their ideas, and express opinions while preparing a project or conducting research through online experience. [More] Descriptors: Educational Research, Educational Practices, Educational Trends, Academic Standards
(2015). Advancing Multicultural Education: New Historicism in the High School English Classroom, High School Journal. High schools across the country are restructuring their curricular frameworks to meet the new Common Core State Standards (CCSS), which emphasize an understanding of cultural diversity in addition to critical thinking and literacy. Despite curricular variance among high schools, the significant roles non-white races have played in constructing a pluralistic America, and the increasing importance of U.S. minorities in global economic sectors, many history/social studies courses fall short of presenting culturally diverse material to students. This paper presents a theoretical argument for using New Historicism, a method of literary criticism, in high school literature/English education courses to meet the goals of the CCSS while generating greater discussion about and appreciation for the contributions of diverse cultural narratives. Using three case studies, one on a U.S. history textbook analysis, another in an English classroom, and a third on a letter written in 1852 by two Asians to the then Governor of California, this paper reveals a striking lack of discussion about cultural diversity in the secondary curricula and demonstrates the historical and cultural richness that can be illuminated in the classroom via New Historicism. [More] Descriptors: Multicultural Education, High Schools, English, Language Arts
(2015). A Smart Way of Coping with Common Core Challenges–Introduction to CAFA SmartWorkbook, Journal of Educational Issues. The Common Core State Standards (CCSS) in mathematics are currently adopted in most U.S. states. Nonetheless, most math teachers across the country are still experiencing difficulties in putting these standards into practice. Teachers and local school administrators are faced with a challenge of adapting methodologies in instruction and assessment to ensure that students master the knowledge and skills required in the new standards. This leads to an urgent need for well-designed teaching and assessment tools for math education that are aligned to the CCSS. The purpose of this paper is to illustrate the Computer Adaptive Formative Assessment (CAFA) SmartWorkbook which is an Information and Communication Technology (ICT) based teaching and assessment tool specially designed for coping with challenges in implementing the CCSS in mathematics. The CAFA SmartWorkbook represents a new stage in exploring opportunities in educational innovation, capitalizing on advances in assessment and technology. This system can be an effective solution to cope with CCSS challenges in both theoretical and practical points of view for students, teachers, parents, and educational administrators. [More] Descriptors: Common Core State Standards, Workbooks, Mathematics Instruction, Formative Evaluation