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The culminating effects of using GO Math! This two-year study, conducted by independent research firm Cobblestone Applied Research and Evaluation, examined student math performance across 70 classrooms in seven states. Teachers were randomly...
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Boston, MA: Author. Developed around a coherent, focused progression across grade levels, GO Math! The purpose of this document is to demonstrate clearly and explicitly the research upon which GO Math! This research report is organized by the major...
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A list of sources is provided at the end of this document. Introduction to GO Math! Never before has the workplace demanded such complex levels of mathematical thinking and problem solving National Council of Teachers of Mathematics, The Common Core State Standards for Mathematics were written to provide this exact foundation for young students. In addition, the Standards serve the purpose of helping to ensure equity for all American students. Inconsistent standards, curriculum, and assessments across states have raised equity issues in the past Reed, and wide disparities in performance on the National Assessment of Educational Progress NAEP Schneider, While the standards detail the knowledge and skills—content and processes—students need at each grade level, they do not describe the instructional approaches needed to meet the standards. Thus, an effective instructional program is needed to bridge between the expectations set out by the standards and the desired student learning and achievement.
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This alignment between standards, curriculum, instruction, and assessments is critical. Researchers looking at effective educational practices identified nine characteristics of high-performing schools and reported that several of these relate to standards and standards alignment. Coherent—Content is organized into meaningful progressions that seamlessly connect key topics between the grade levels of K— Lessons include coherently sequenced learning experiences to develop critical understandings. This approach facilitates connections between major topics. Rigorous—Content is presented for students to develop a deeper understanding. Throughout GO Math! Strand 1: Teaching and Learning An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically.
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Extensive research has shown that teacher effectiveness has an enormous impact on student learning and achievement—more than any other in-school factor Goldhaber, ; Partnership for Learning, What is it that effective teachers do to make gains in student learning and achievement? Quality teachers use effective classroom practices Wenglinsky, Research—in cognitive science, on classroom practices of master teachers, and on specific supports that help students learn—points to specific principles and methods of effective instruction Rosenshine, Teaching mathematics is not easy, but employing proven research techniques can help teachers ensure all students learn. In its design, the program incorporates research-based strategies for effective teaching to maximize student learning. Program 1. The 5E Instructional Model offers a predictable, structured, research-based sequence consisting of five phases: engagement, exploration, explanation, elaboration, and evaluation, which are briefly described below Bybee et al.
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Engagement: Students access prior knowledge through teaching and tasks to help them become engaged in the concept. Exploration: Students generate new ideas and explore possibilities. Explanation: Students demonstrate understanding through explaining what they know, giving the teacher an opportunity to guide them toward deeper learning. Elaboration: Students extend and apply their knowledge. Evaluation: Students examine their own understanding, while the teacher continues to monitor and evaluate progress. Activities can be structured so that students are able to explore, explain, extend, and evaluate their progress. In support of the NRC findings, recent research by Coulson found that students whose teachers taught with medium or high levels of fidelity to the 5Es experienced learning gains that were nearly double that of students whose teachers implemented the model with a lower level of fidelity or did not implement it at all.
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As well, a study by Boddy, Watson, and Aubusson noted that students whose teachers used the 5Es showed increases in scientific reasoning. Establishing Mathematical Goals Identifying and clarifying what students are expected to learn and understand in a mathematics classroom is an essential component to success Wiliam, Teachers and students benefit from establishing a shared foundation of what is being learned and why it is important to learn. Learning goals must also be positioned and clearly articulated within the larger mathematical trajectory. Research also shows that setting and sharing learning goals with students has a positive impact on their learning. What types of tasks should students practice? Tasks that allow students to make connections based on what they know, explore real-world problems, and promote higher-level thinking.
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Connections—among mathematical ideas, with other content areas, and in real-world contexts—are an essential part of mathematics learning. Students maximize learning when they can make connections between ideas. Students see the purpose and value of learning when they experience it in real-world contexts. Students learn best when they can understand the purpose and relevance of what they are learning in relation to the larger world around them. Student learning is greatest in classrooms where the tasks consistently encourage high-level student thinking and reasoning and least in classrooms where the tasks are routinely procedural in nature. Using and Connecting Mathematical Models and Representations Representations and models include a wide variety of images or likenesses that can be used to support and extend understanding in the mathematics classroom. Representations and models might include pictures, manipulatives, symbols, diagrams, or organizers that students create or teachers provide to show a mathematical construct or action.
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Essentially, representations can show what students know, help students explain what they know, and be the foundation for making connections and achieving a deeper understanding of mathematics. For young students, representations are especially important because they can be physical objects or actions they perform as they are trying to solve problems NRC, As students create representations, they have the opportunity to internalize and process what they are doing, what they are creating, and what they are seeing, which in turn allows them an active role in their learning.
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This is especially beneficial to students who have special needs, struggle with learning, or are English learners. When examining multiple representations, students can decide how to best solve problems and practice looking at problems from different points of view. When students write about and discuss math concepts, they have the chance to think through, defend, and support their ideas. Numerous studies have emphasized the importance of writing in the mathematics classroom. Bosse and Faulconer report that writing in the mathematics classroom results in deeper student learning. As noted by several researchers, conceptual understanding and problem-solving skills improve when students are encouraged to write about their mathematical thinking Burns, ; Putnam, ; Russek, ; Williams, Writing can be incorporated into the mathematics classroom in numerous ways, including free writing, biography, learning logs, blogs, journals, summaries, word problems, and formal writing Urquhart, Students can engage in more structured or more informal journaling or note taking.
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Providing opportunities for students to talk about mathematics and mathematical concepts also enhances their understanding of mathematics. Hatano and Inagaki found that students who discussed and justified their solutions with peers demonstrated greater mathematical understanding than students who did not engage in such discussions. Leinwand and Fleischman reviewed research on effective mathematics instruction and concluded that talking about math and explaining the rationale for solutions can help ensure that students have a conceptual understanding. Talking about math has also been found to benefit students at different levels of learning and in different contexts. In their study, Hufferd-Ackles, Fuson, and Sherin found a math-talk community to be beneficial with students who were English learners in an urban setting.
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Understanding the language of mathematics is essential to understanding and doing mathematics. Research by Freeman and Crawford found that focused and explicit attention to vocabulary and language helps students develop a deeper understanding of content. Why is vocabulary learning so tied to mathematics achievement? This may be because the language of mathematics is so closely tied to the content of mathematics; mathematics vocabulary terms offer the means to communicate mathematical ideas that are by nature abstract and complex Kouba, Certain strategies have been shown to be particularly effective. While types of questions vary from asking students to recall facts to requesting an explanation for an answer, presenting questions throughout the learning process is necessary to understand how students are making sense of the math.
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As noted in research by Weiss and Pasley , questions are critical in helping students make connections and learn important mathematics concepts—especially questioning that effectively gauges student understanding. In contrast, as noted in the study Inside the Classroom, Weiss et al. Building Procedural Fluency from Conceptual Understanding To achieve understanding, students need instruction that recognizes the relationship between procedural fluency and conceptual understanding.
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A wide body of reports recognizes the critical relationship and balance between concepts and procedures in mathematics instruction for student learning National Mathematics Advisory Panel, ; National Research Council, Research by Hiebert suggests that once students have memorized and practiced procedures that they do not understand, they have less motivation to understand their meaning or the reasoning behind them Hiebert, When learning is not meaningful and disconnected, students have a more difficult time absorbing concepts.
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All students need to have a deep and flexible knowledge of a variety of procedures, along with an ability to make critical judgments about which procedures or strategies are appropriate for use in particular situations for best success in the mathematics classroom NRC, , , ; Star,
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Numerous advantages are there when solving the 7th grade Go math solution key. It helps to hold a strong foundation on the subject fundamentals and make you score better marks in the exams. This perfect guide helps you prepare to the fullest and learn the concepts efficiently. Practicing the mathematical concepts from the Middle School Grade 7 Go Math Answer Key makes you familiar with a huge number of questions. So that you can develop your skills and clear your tests effectively with maximum grades. Is there any possibility to solve the toughest Math problems easily? Yes, by preparing all the chapters of mathematical concepts from the Go Math Grade 7 Answer Key and Practice book you can easily solve complex problems too.
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