This annotated bibliography is reformatted and customized by the Center for Positive Practices. Some of the authors featured on this page include David R. Martin, Janet Tassell, Gerald Tindal, Margaret Yoder, Jeffrey D. Wilhelm, Jennifer D. Turner, Jessica L. Saven, Laurie O. Cavey, Molly H. Fisher, and Michelle M. Herczog.
(2014). Professional Noticing: Developing Responsive Mathematics Teaching, Teaching Children Mathematics. Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult. Although textbooks may provide practitioners with considerable overarching instructional guidance, to complete the picture, mathematics teachers must often focus on individual children. In some instances, they might consider verbal explanations or work samples to gain insight into one's thinking; however, quite often these avenues do not provide a complete or accurate portrayal of a student's understanding. Indeed, a student may unwittingly offer an explanation that differs from her actual strategy (CCSSI 2010). Similarly, work samples may feature deceptive or insufficient details to truly gauge the student's thinking. In these instances, a systematic approach to appraise the mathematical moment is required to fully appreciate the student's true understanding and then respond with effective instructional tactics. This article begins by describing the three interrelated phases of the "Professional Noticing of Children's Mathematical Thinking" (Jacobs, Lamb, and Philipp 2010) framework for teachers to better understand and act on their students' mathematical conceptions and practices. The second half of the article addresses how to put the framework into practice through the progression of the three phases (Attending, Interpreting, and Deciding). [More] Descriptors: Academic Standards, Mathematics Education, Mathematical Concepts, Concept Formation
(2014). Engaging Future Teachers in Problem-Based Learning with the Park City Mathematics Institute Problems, PRIMUS. Problem-based learning (PBL) is a pedagogical technique recommended for K-12 mathematics classrooms. However, the mathematics courses in future teachers' degree programs are often lecture based. Students typically learn about problem-based learning in theory, but rarely get to experience it first-hand in their mathematics courses. The premise for trying an entirely problem-based approach to a capstone course for pre-service secondary mathematics teachers was simple: If the expectations of pre-service mathematics teachers is to engage their own students in the Common Core State Standards Mathematical Practices, then such classroom practice should be modeled in their undergraduate mathematics instruction. The Park City Mathematics Institute has developed several sets of problem-based materials around coherent mathematical themes, for use in 3-week intensive summer in-service workshops, which provide a great resource for pre-service mathematics courses. These materials were implemented with the single overarching goal in mind: To better equip pre-service teachers to use PBL by having them experience PBL for themselves. This article describes the results from both the students' and the instructor's perspectives and assesses how well the goal was achieved. [More] Descriptors: College Mathematics, Problem Based Learning, Teaching Methods, Preservice Teachers
(2014). Engineering Encounters: Elephant Trunks and Dolphin Tails, Science and Children. This article describes how one class at Douglas Jamerson Elementary School in St. Petersburg, Florida, a center for engineering and mathematics, incorporated an Engineering Design Process into its curriculum. At Jamerson Elementary, all students in kindergarten through fifth grade engage in teacher-created, integrated engineering units of study, purposefully aligned to the "Next Generation Science Standards" for engineering design and the "Common Core State Standards" for English language arts and mathematics. The school's vision, "Engineering innovative thinkers for global success," comes to life as students develop the habits of mind–curiosity, creativity, critical thinking, perseverance, and communication–that successful innovators possess. The centerpiece of the curriculum is the Jamerson Engineering Design Process through which students collaborate to identify real-world problems, "plan" multiple solutions and select the most efficient one, "design" models and prototypes to "check" against rigorous design constraints, and "share" their findings. The article describes a series of lessons that spanned across a two-week period, 45 minutes per day, that were the conclusion to an integrated unit of study entitled "Nature of Science and Engineering." Taught at the beginning of the school year, the unit focuses on the comparison of scientific and engineering practices in preparation for a year of similar, real-world design investigations. [More] Descriptors: Elementary School Students, Kindergarten, Grade 1, Grade 2
(2014). Teacher Practices and Student Growth in Mathematics: Grades 6-8. Technical Report #1401, Behavioral Research and Teaching. Schools and districts across the United States have adopted response to intervention (RTI) as a means for both identifying and intervening with students at risk for low achievement. The validity of RTI rests largely upon teachers making appropriate instructional decisions based on students' responses to a given practice. This study was designed to explore how teachers' instructional practices relate to progress monitoring data in math in Grades 6 and 7. A total of eight teachers participated (five in Grade 6, three in Grade 7). They administered an easyCBM Common Core State Standards (CCSS) Math measure to their students monthly and provided information on their instructional practices for each student at least three times (fall, winter, and spring). Analyses included: (a) textual analyses of teachers' self-reported instructional practices, (b) multilevel growth analyses of students' math data, and (c) ordinal regression analyses of students' intercept and slope predicting the number of interventions the student received. Results indicate that self-report methods may not be sufficient to adequately address the relation between teacher practices and students' growth. Nonetheless, in Grade 6, a relation was found between students' average growth in math performance and the likelihood that they would be administered multiple interventions. [More] Descriptors: Mathematics Achievement, Educational Practices, Teaching Methods, Teaching Styles
(2014). A Sociocognitive Perspective on Assessing EL Students in the Age of Common Core and Next Generation Science Standards, TESOL Quarterly: A Journal for Teachers of English to Speakers of Other Languages and of Standard English as a Second Dialect. Subject-area standards such as Common Core State Standards for Language Arts and Mathematics and Next Generation Science Standards offer deeper, richer views of subject-area proficiency. In science, they underscore doing things with facts and concepts, such as explaining, planning, and investigating–activities that are intertwined with language, with specialized structures and functions of academic English. This article explores the implications of a sociocognitive view of learning for assessment based on these standards, focusing on English learners (ELs). The authors describe how ELs and native English speakers alike develop subject-area and language resources jointly through activities, and how teachers use local knowledge to scaffold this development for students from diverse cultures and varying English experience. They then describe concomitant assessment strategies. The grounding of the standards in learning progressions enables the design of tasks which, while complex, challenge particular aspects of capability at targeted levels. A strategy can be used to craft tasks that are at once consistent with the standards but targeted to students with differing profiles of capabilities. This design strategy is well suited to contextualized formative assessment in local contexts such as classrooms. It supports design for large-scale assessment as well, although rich and complex tasks that are not matched to students' language and subject-area profiles face the low generalizability that plagued performance assessments in the 1980s. We consider ways that assessment design and tailored adaption can ameliorate some of the difficulties. [More] Descriptors: Science Education, Standards, English Language Learners, Student Evaluation
(2014). Authenticity of Mathematical Modeling, Mathematics Teacher. Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in students' lives while developing a positive attitude toward mathematics? Incorporating tasks that are situated in real-life contexts and involve modeling can address these demands. These types of tasks may help students see the purpose of mathematics. In this article, the authors examine criteria that teachers can use to choose tasks that embody modeling. Their choices may offer some ways to create better student performance. They provide examples to illustrate modeling activities linked to the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) and present two frameworks–authenticity and modeling hierarchy–to analyze problems. They then use these frameworks in selecting and designing tasks to promote student engagement and learning. A bibliography is included. [More] Descriptors: Mathematics Instruction, Relevance (Education), Mathematics Achievement, Learner Engagement
(2014). Learning to Love the Questions: How Essential Questions Promote Creativity and Deep Learning, Knowledge Quest. Educators know that creativity and innovation involve questioning and the capacity to frame topics as problems to be solved. They know that we are living in a time of a new generation of standards, including the Common Core State Standards (CCSS). In the U.S., compliance with these standards requires that educators encourage students to ask questions of texts, of disciplinary issues, and of the world. The new generation of standards also requires deep understanding and application of higher-order strategies that are best cultivated through inquiry. To work toward the next generation standards, to foster student engagement, and to teach toward transfer and creativity, teachers can pose essential questions that frame learning as a problem to be solved. This article begins by defining essential questions as those questions which probe for deeper meaning and set the stage for further questioning and creative activity. Essential questions foster the development of critical-thinking skills and higher order capabilities such as problem solving and understanding complex systems. This article offers guidance in composing essential questions, typical characteristics of essential questions, the requirements and rewards involved in using essential questions, and helpful tips for generating them. Common problems with the questions are also discussed. [More] Descriptors: Creativity, Questioning Techniques, State Standards, Problem Solving
(2014). Implementing the C3 Framework: Monitoring the Instructional Shifts, Social Education. The College, Career, and Civic Life (C3) Framework for Social Studies State Standards calls upon social studies teachers to enhance the rigor of civics, economics, geography, history and the other social studies disciplines while building the critical thinking, problem solving, and participatory skills of students to help them become actively engaged citizens in the twenty-first century. Like the Common Core State Standards and Next Generation Science Standards, the C3 Framework emphasizes the acquisition and application of deep content knowledge through an inquiry-based approach to teaching and learning. The Four Dimensions of the C3 Framework center on the use of questions to spark curiosity, guide instruction, deepen investigations, acquire rigorous social studies content, and apply knowledge and ideas in real world settings. This article suggests ways in which teachers can chart a course toward implementation of C3, review the progress that is made, and identify obstacles to accomplishing the objectives. For teachers, the process of implementation can be a journey of examination and reflection on their own teaching practices. The results of success can be dramatic: to enliven the study of civics, economics, geography, and history so that these subjects are exciting, engaging, rigorous, and meaningful to students. Two accompanying reproducible handouts focus on initiatives that schools can take to implement the C3 Framework by identifying instructional shifts that will need to be made, and developing a plan of action. [More] Descriptors: Social Studies, State Standards, Critical Thinking, Problem Solving
(2014). Activities for Students: Filling a Square with a Curve, Mathematics Teacher. Finding patterns and making conjectures are important thinking skills for students at all levels of mathematics education. Both the Common Core State Standards for Mathematics and the National Council of Teachers of Mathematics speak to the importance of these thought processes. NCTM suggests that students should be able to recognize reasoning and proof as fundamental aspects of mathematics, make and investigate mathematical conjectures, develop and evaluate mathematical arguments and proofs, and select and use various types of reasoning and methods of proof. CCSS states that students should "make conjectures and build a logical progression of statements to explore the truth of their conjectures" (CCSSI 2010, p. 6). The activity presented in this article makes such reasoning accessible to high school students with some previous study of trigonometry. In this activity, students use technology to graph parametric equations, make conjectures based on their graphs, modify their conjectures on the basis of evidence, and find counterexamples or investigate methods of proof. Students will be left with some open-ended questions to engage them in investigations beyond the classroom. Students learn to plot parametric curves, including those involving sine and cosine. After exploring several of these curves, students will conjecture about parameters that will make a curve appear to fill in the area of a square. Students deal with the idea of spacefilling curves from a naive perspective; it is important to note that none of the curves encountered in this activity actually fill space. [More] Descriptors: Mathematics Instruction, Academic Standards, Mathematical Logic, Validity
(2014). Oki-Doku: Number Puzzles, Teaching Children Mathematics. The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) emphasize the Standards for Mathematical Practice (SMP) that describe processes and proficiencies included in the NCTM Process Standards (NCTM 2000) and in the Strands for Mathematical Proficiency (NRC 2001). The development of these mathematical practices should happen in conjunction with the development of content and should provide a balance between procedures and understanding. During the elementary school years, most of the mathematical instruction focuses on developing number sense and operation sense. Being efficient and accurate when operating numbers is one of the most important skills that students must develop to support conceptual understanding. This has been recognized as the foundation for developing procedural fluency. Some curriculum materials have mathematical games to help students develop fluency. However, teachers who do not have access to such materials must search for other ways to develop fluency. In this article, the authors describe a specific type of number puzzle, an Oki-Doku, that is appropriate for elementary school students and requires students to make sense of a problem and persevere in solving it. A number of examples are provided for the reader to try on their own and instructions are given on how to construct the puzzles. [More] Descriptors: Mathematics Instruction, Academic Standards, Numbers, Puzzles
(2014). Developing a Vision for the Common Core Classroom: What Does Elementary Social Studies Look Like?, Social Studies. In each edition of their book "Doing History: Investigating with Children in Elementary and Middle Schools", Levstik and Barton (2011) encourage us to take a mental journey to imagine classrooms where students regularly "do history" (xi). The social studies experiences that many educators envision for elementary classrooms include teaching students to frame questions, read for information, and organize primary and secondary sources to share their knowledge with classmates. NCSS provides an infrastructure for social studies goals in which knowledge, skills and attitudes are developed in meaningful social studies lessons. When viewed through the lens of the Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects (CCSS ELA), we recognize the fundamental nature of aligning social studies standards with literacy strategies for elementary teaching and learning. The purpose of this article is to examine the usefulness of CCSS ELA for teaching elementary social studies. The authors share a vision for the "common core classroom" that includes a range of literacy strategies for teaching standards-based social studies. [More] Descriptors: State Standards, Academic Standards, Social Studies, Literacy
(2014). Problem Solvers: Problem–Jesse's Train, Teaching Children Mathematics. Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by engaging students in structured group activities or collaborative problem solving activities. Encouraging students to work together on a problem solving task can be difficult. One way of helping students work together on a problem solving task is to present them with "group-worthy" problems. Such problems meet the following criteria: (1) Illustrate important mathematical concepts; (2) Include multiple tasks that draw effectively on the collective resources of a group, (3) Allow for multiple representations; and (4) have several possible solution paths. The problem presented in this article is modeled after those in "United We Solve 116 Math Problems for Groups" (Erickson 1996). This task allows students the opportunity to explore the magnitude of fractions compared with different-size wholes. [More] Descriptors: Mathematics Instruction, Problem Solving, Academic Standards, Mathematical Concepts
(2014). Accelerating the College and Career Readiness of Diverse K-5 Literacy Learners, Theory Into Practice. Given the increasing demand for a well-educated American workforce, college and career readiness has become a significant educational priority. New educational initiatives, including the Common Core State Standards for English Language Arts, are being developed and implemented to prepare students for success in postsecondary education and the workplace. In this article, we discuss how college and career readiness standards have transformed expectations for literacy instruction in K-5 classrooms, especially for students from diverse cultural and linguistic backgrounds. Given that students of color have been historically underserved in schools, we contend that these children need more equitable and enriched opportunities to learn academic literacies, content knowledge, and communication skills to achieve their future college aspirations and career goals. To that end, we offer key principles (i.e., community-oriented classrooms, close reading of complex texts, content-rich inquiry, and cultural connectedness) that elementary educators can use to design engaging learning environments and robust literacy lessons that advance the college and career readiness of all students. [More] Descriptors: Career Readiness, College Readiness, Acceleration (Education), Elementary School Students
(2014). Language Intervention at the Middle School: Complex Talk Reflects Complex Thought, Language, Speech, and Hearing Services in Schools. Purpose: In this article, the author discusses 2 points raised by Kamhi (2014) in his lead article to this clinical forum: (a) the need for speech-language pathologists to consider typical language development as they plan intervention and (b) the importance of addressing complex syntax. Method: A hypothetical scenario of a 7th grade English class assignment is presented, and aspects of the assignment that would be quite challenging to middle school adolescents with language impairments are highlighted. The author then describes strategies that a speech-language pathologist could use to enhance students' success with the assignment. This approach emphasizes the importance of collaborating with the classroom teacher and reading specialist, having knowledge of the Common Core State Standards and the language demands of the classroom, and understanding later language development and the reasons why speakers and writers use complex syntax. Conclusion: When language intervention incorporates these points, adolescents with language impairments can acquire skills that will help them make meaningful progress in the classroom. [More] Descriptors: Speech Language Pathology, Intervention, Middle School Students, Syntax
(2014). From Whole Numbers to Invert and Multiply, Teaching Children Mathematics. Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to support prospective student teachers as they learned to make sense of the invert-and-multiply algorithm for division of fractions. An examination of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) was consulted to identify standards that closely align with this instructional sequence and how it would relate to the practice of elementary school teachers. Cavey and Kinzel describe four parts of an instructional sequence that represents a progression of ideas that is initiated early in the course and then extended at different points throughout the study, concluding with proportionality at the end of the course. Cavey and Kinzel illustrate how working with whole-number division, especially the measurement, can lead to understanding the invert-and-multiply algorithm and how the range of mathematical ideas associated with the list of Standards might define the learning progression from grade 3 to grade 6 children. Such a progression has the potential to reinforce early concepts while emphasizing meaning for new ideas. [More] Descriptors: Mathematics Instruction, Elementary School Mathematics, Secondary School Mathematics, Preservice Teacher Education