This annotated bibliography is reformatted and customized by the Center for Positive Practices. Some of the authors featured on this page include Melissa C. Gilbert, Rongjin Huang, James W. Cunningham, Sandra N. Kaplan, Michelle M. Herczog, Robert Linn, Nathaniel J. Brown, Robert G. Croninger, Hortensia Soto-Johnson, and Joan Herman.
(2014). Visualizing the Arithmetic of Complex Numbers, International Journal for Technology in Mathematics Education. The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and algebraic representations. The purpose of this article is to share Geometer's Sketchpad labs, where students can unearth a geometric interpretation of the arithmetic of complex numbers and their relationship to transformations. With dynamic technologies, students can discover that (1) addition and subtraction of complex numbers corresponds to a translation of the complex plane, (2) multiplication corresponds to a rotation and dilation of the complex plane, and (3) division of complex numbers corresponds to the composition of a reflection about the real axis and dilation of the complex plane. Furthermore, I illustrate how such activities may potentially enrich classroom dialogue. [More] Descriptors: Arithmetic, Mathematics Instruction, High School Students, Secondary School Mathematics
(2014). A Rationale for Irrationals: An Unintended Exploration of "e", Mathematics Teacher. Today, the Common Core State Standards for Mathematics (CCSSI 2010) expect students in as early as eighth grade to be knowledgeable about irrational numbers. Yet a common tendency in classrooms and on standardized tests is to avoid rational and irrational solutions to problems in favor of integer solutions, which are easier for students to comprehend and check. Common irrational numbers as well as their applications in the world are frequently approached from their traditional developments. This article provides an exploration of how the irrational number "e" emerges from various solution strategies to an unconventional problem and an example of how problem posing can lead to interesting mathematics. A bibliography is included. [More] Descriptors: Mathematics Instruction, Academic Standards, Number Concepts, Problem Solving
(2014). How Common Is the Common Core?, Mathematics Teacher. Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources, and "crosswalk" documents summarizing key differences between previous and forthcoming standards. In this article, the authors present what might be considered an abbreviated crosswalk between these two standards documents based on comparative analysis of individual standards in the "Principles and Standards for School Mathematics" (PSSM) and CCSSM. To illustrate potentially new and notable content emphases, they include selected mathematics tasks that correspond to CCSSM standards. [More] Descriptors: State Standards, Mathematics Education, Educational Principles, Educational Practices
(2014). Assessment of Critical-Analytic Thinking, Educational Psychology Review. National policy and standards documents, including the National Assessment of Educational Progress frameworks, the "Common Core State Standards" and the "Next Generation Science Standards," assert the need to assess critical-analytic thinking (CAT) across subject areas. However, assessment of CAT poses several challenges for developers of both large-scale and classroom assessments: Current CAT assessments often suffer from questionable item contexts, subjective rubrics, and underdeveloped construct formulations. Attention to these aspects of assessment would improve understanding of the development of students' CAT and provide tools for helping teachers teach and students learn. We discuss these challenges within the context of several content areas and highlight the importance of developing formative assessments that capture the development of CAT in different domains of learning. [More] Descriptors: Critical Thinking, Thinking Skills, National Standards, National Competency Tests
(2014). Quantitative Measurement of Text Difficulty: What's the Use?, Elementary School Journal. Common Core Reading Standard 10 not only prescribes the difficulty of texts students should become able to read, but also the difficulty diet of texts schools should ask their students to read across the school year. The use of quantitative text-assessment tools in the implementation of this standard warrants an examination into the validity of that use. To do so, we concentrate entirely on the criterion variable that ultimately is the goal of reading instruction and learning: reading comprehension performance. We examine whether the comprehension criterion variables for today's quantitative tools validate how their text-difficulty estimates are being used. We conclude that the Common Core State Standards' new text-difficulty grade bands are inadequate to serve as a criterion variable for quantitative text tools because the data on which these bands are based did not compare comprehension growth for various groups of students reading different difficulty diets over a school year. [More] Descriptors: Difficulty Level, Academic Standards, State Standards, Statistical Analysis
(2010). Using the NCSS "National Curriculum Standards for Social Studies: A Framework for Teaching, Learning, and Assessment" to Meet State Social Studies Standards, Social Education. According to "A Report on the State of U.S. History Education, State Policies and National Programs as of September 2008," "Forty-eight states and the District of Columbia have established academic standards to address academic achievement in history, the social sciences, or social studies. The sole exceptions are Iowa and Rhode Island which allow local jurisdictions to set the history/social studies curriculum." The report also reveals tremendous divergence in the breadth, depth, purpose, and use of state standards across the nation. This disparity is one of the many reasons the Common Core State Standards Initiative was established. The release by the National Council for the Social Studies of "National Curriculum Standards for Social Studies: A Framework for Teaching, Learning, and Assessment" comes at a pivotal moment in the current era of educational reform. As other subject areas create national standards to guide the work of the Common Core State Standards Initiative, these NCSS Standards provide a vision for the future of social studies education in the nation. Just as the Common Core State Standards are designed to create a citizenry that has the knowledge and critical thinking and problem solving skills to "succeed in the global economy and society," the NCSS Standards provide a framework for selecting and organizing knowledge and modes of inquiry for purposes of teaching and learning to meet these same goals. [More] Descriptors: Social Studies, Elementary Secondary Education, National Standards, Academic Standards
(2014). Collaboration: Assumed or Taught?, Gifted Child Today. The relationship between collaboration and gifted and talented students often is assumed to be an easy and successful learning experience. However, the transition from working alone to working with others necessitates an understanding of issues related to ability, sociability, and mobility. Collaboration has been identified as both an asset and a liability and as a constructive or destructive quality of personal or group achievements and innovations. The necessity to develop both an appreciation for and the skill sets required to collaborate is noted formally with references to the 21st Century Skills and the Common Core State Standards. Here, author Sandra Kaplan provides examples of curriculum tasks that can be integrated into the core curriculum to explicitly teach the skills of collaboration across the grade levels. These include self-assessment, roles, and goals. [More] Descriptors: Academically Gifted, Cooperation, Interpersonal Competence, Problem Solving
(2014). Mathematical Explorations: Freshwater Scarcity: A Proportional Representation, Mathematics Teaching in the Middle School. Middle school students' mathematical understanding benefits from connecting mathematics to other content areas in the curriculum. This month's activity explores the issue of the scarcity of freshwater, a natural resource (activity sheets are included). This activity concentrates on the critical areas mentioned in the Common Core State Standards for Mathematics (CCSSM) that call for greater focus on fewer topics (ratios and proportional relationship for the middle school grades) and coherence (using those mathematical skills to solve real-life word problems). In this activity, the water contained in a large water dispenser represents all the water on Earth. Given the composition of the water on the planet, the students replicate the same composition with the water in the dispenser. [More] Descriptors: Mathematics Instruction, Secondary School Mathematics, Middle School Students, Teaching Methods
(2014). Mathematics from High School to Community College: Using Existing Tools to Increase College-Readiness Now. Policy Brief 14-1, Policy Analysis for California Education, PACE. The adoption and implementation of the Common Core State Standards and Smarter Balanced assessments in mathematics are intended to provide all students in California with the knowledge and skills required to transition from high school to college-level coursework. This implementation will take time. Concurrent with these efforts, policymakers and educators can begin to increase college-readiness now, especially for community college-bound students, by using two existing tools–the California High School Exit Exam in mathematics and the Academic Performance Index–to identify 10th-graders who need remediation and to reward high schools for encouraging all students to enroll in appropriate Grade 12 mathematics. This policy brief explains the benefits of these straightforward policy changes. The following are appended: (1) Demographic Overview of Sample;(2) Community College's ACT COMPASS Cut Scores for Placement in Mathematics; and (3) Summary Table of Multinomial Logistic Regression Model. [More] Descriptors: Mathematics Instruction, Secondary School Mathematics, College Mathematics, College Readiness
(2014). Exploration of Patterns in a Calendar, Mathematics Teacher. The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are required to reason both abstractly and quantitatively, construct viable arguments, and critique the reasoning of others. However, studies on algebra learning have documented students' difficulties in algebra concepts and justification (Kieran 2007). Specifically, middle and high school students overwhelmingly rely on examples to justify statements (Koedinger 1998; Usiskin 1988). This article aims to demonstrate how a teacher can develop students' reasoning and justification in an algebra lesson through deliberate sequencing and productive discourse surrounding the implementation of tasks. [More] Descriptors: Algebra, Mathematics Education, Mathematics Instruction, Mathematical Applications
(2014). New Assessments, New Rigor, Educational Leadership. Researching. Synthesizing. Reasoning with evidence. The PARCC and Smarter Balanced assessments are clearly setting their sights on complex thinking skills. Researchers Joan Herman and Robert Linn look at the new assessments to see how they stack up against Norman Webb's depth of knowledge framework as well as against current state tests. The authors find that approximately one-third of the items on the new assessments fall in the cognitively demanding levels 3 and 4 in the depth of knowledge framework. Current state tests lack such rigor. The increased rigor embodies the intent of the Common Core State Standards and the desire for students in the United States to be internationally competitive and prepared for college and career. The authors note, however, that the demands of these tests are likely to come as a shock for teachers and students alike. "Being forewarned," they note, "is being forearmed." [More] Descriptors: Student Evaluation, Evaluation Methods, Test Items, Knowledge Level
(2014). Reflecting on Data, Science Teacher. This article describes a two-day optics laboratory activity that investigates the scientific phenomenon of reflection, which students are generally familiar with but usually have not studied in depth. This investigation can be used on its own or as part of a larger unit on optics. This lesson encourages students to think critically and mathematically about the data they collect and allows them to develop a model on their own. It addresses scientific and engineering practices identified in the "Next Generation Science Standards" (NGSS Lead States 2013), especially the practice of Analyzing and Interpreting Data. It also addresses the "Common Core State Standards," Mathematics (NGAC and CCSSO 2010), which emphasize mathematical modeling and the application of mathematics to the real world. [More] Descriptors: Science Instruction, Science Laboratories, Optics, Scientific Concepts
(2014). Reasoning and Sense Making with Pythagoras, Mathematics Teacher. In 1996, a new proof of the Pythagorean theorem appeared in the "College Mathematics Journal" (Burk 1996). The occurrence is, perhaps, not especially notable given the fact that proofs of the Pythagorean theorem are numerous in the study of mathematics. Elisha S. Loomis in his treatise on the subject, "The Pythagorean Proposition" (1968), presents more than 350 unique proofs. What is notable about Burk's discovery is that his proof provides mathematics students who have not been exposed to the theorem opportunities to make connections among a rich set of mathematical topics that all precede the presentation of the Pythagorean theorem in the Common Core State Standards (2010). The intent of this article is to demonstrate the connections that Burk's approach to the Pythagorean theorem offers and to make a case for its consideration as a new vehicle for students to arrive at a deep understanding of this venerable theorem. [More] Descriptors: Geometric Concepts, Mathematical Logic, Validity, Mathematics Instruction
(2014). Teacher Education under Audit: Value-Added Measures,TVAAS, EdTPA and Evidence-Based Theory, Citizenship, Social and Economics Education. This article describes how evidence-based theory fuels an audit culture for teacher education in the USA, placing faculty under monitoring and surveillance, and severely constraining judgment, discretion, and professional decision-making. The national education reform efforts, Race to the Top and Common Core State Standards, demand fealty to evidence-based standards, while the Teacher Performance Assessment (EdTPA) requires teacher candidates to videotape their classroom lessons and submit the 'evidence' for review by external reviewers. The history of this theory, findings on the Tennessee Value-Added Assessment System (TVAAS), a discussion between EdTPA and teacher education colleges, and examples of how faculty are expected to provide evidence of effectiveness, are all included in the article. [More] Descriptors: Teacher Education, Value Added Models, Audits (Verification), Evidence Based Practice
(2014). Using Productive Disposition to Differentiate between Students' Level of Precision When Critiquing a Peer's Work, School Science and Mathematics. This study examined the productive disposition of pre-algebra students who demonstrated similar knowledge of the focal content but varied in other academic behaviors expected in the Common Core State Standards for Mathematics (CCSSM). Specifically, the study considered students' attention to precision when critiquing a peer's work. The comprehensive definition of productive disposition used included task values (interest, utility), an ability belief (efficacy), three personal achievement goals, and negative emotions. As hypothesized, the 61 students who provided a more precise critique reported higher productive disposition (in particular, significantly higher mastery-approach personal achievement goals and less frequent negative emotions) than the 79 students who provided a basic critique. These findings illustrate how productive disposition can inform assessments of mathematical competence within the CCSSM recently implemented across the United States. [More] Descriptors: Secondary School Students, Algebra, Mathematics Instruction, State Standards