The document discusses best practices for teaching mathematics to close the achievement gap. It summarizes that effective math instruction focuses on problem solving, reasoning and real-world applications over rote memorization. It also emphasizes starting math early, using standards-based lessons, and ensuring all students have access to challenging math curricula.
This document discusses principles and rationale for developing mathematics curriculum. It provides definitions of curriculum and aims such as stimulating pupil interest and developing mathematical concepts. Principles for curriculum development like disciplinary value and utility are outlined. The existing mathematics curriculum is then critically analyzed, noting shortcomings like lack of conformity with aims, emphasis on examinations, and lack of practical work. Suggestions for improvement include considering cognitive/affective domains, practical work, and organizing content logically from simple to complex.
The document discusses the topical approach to teaching social science. It explains that the topical approach revolves content around a series of interconnected topics that are suitable for students' ages, abilities, and interests. Examples provided include focusing on discrete historical events, eras, or other topics. Key merits are that an integrated knowledge is imparted, learning is related to life, and student interest and motivation remain high. However, difficulties include that the approach is challenging to adopt and requires good resources like libraries and competent teachers.
Mathematics has many educational values including developing knowledge, skills, intellectual habits, and desirable attitudes. It has practical, cultural, and disciplinary value. Mathematically, it trains the mind through reasoning that is simple, accurate, certain, original, and similar to real-life reasoning. Culturally, mathematics reflects and advances civilization. It also has social, moral, aesthetic, intellectual, and international values by organizing society, developing good character, providing beauty and entertainment, training thought processes, and promoting international cooperation. In conclusion, mathematics education cultivates numerous skills and capacities that are personally and socially beneficial.
Approaches for curriculum organizationjeniferdivya
There are different approaches to organizing curriculum, including logical, psychological, concentric, spiral, and modular approaches. Curriculum is broader than syllabus and includes all academic and non-academic activities implemented in schools. It is a framework for all planned learning experiences, both inside and outside the classroom. Curriculum provides opportunities for development and is a tool for teachers to mold students according to objectives.
ICT Resources For teaching and learning MathematicsSharme1
This document discusses using internet and multimedia resources for teaching mathematics. It explains that technology can make abstract math concepts more tangible by providing visualizations. Some benefits of technology include engaging students, motivating interest, and illustrating real-world applications. The document then describes several online resources for teaching math, including interactive games, videos, simulations and virtual manipulatives. These resources range from early learners to high school and cover websites, apps and online libraries. Teachers can use these technologies to enhance instruction, facilitate learning, and develop students' higher-order thinking skills.
This document discusses teaching mathematics using the model method. It begins by explaining the origins of the model method in Singapore, where it was developed in the 1980s to help students with word problems. The model method uses bars or boxes to represent quantities in word problems visually. It then provides examples of how the model method can be used to solve problems involving part-whole, comparison, and change concepts. Several lessons are outlined that teach students how to apply the model method by drawing diagrams and solving sample problems step-by-step.
Here are some possible mathematical problems that could be posed from the given situation:
1) The master worker can paint 1 square meter of the billboard per hour. The apprentice can paint 0.5 square meters per hour. If they work for 8 hours, how many square meters of the billboard can they paint?
2) The billboard measures 20 square meters. If the master worker and apprentice work together for x hours, write an equation to represent the relationship between the number of hours worked (x) and the area painted (y).
3) The billboard measures 20 square meters. The master worker and apprentice work together for 8 hours. How much of the billboard do they paint?
This document discusses principles and rationale for developing mathematics curriculum. It provides definitions of curriculum and aims such as stimulating pupil interest and developing mathematical concepts. Principles for curriculum development like disciplinary value and utility are outlined. The existing mathematics curriculum is then critically analyzed, noting shortcomings like lack of conformity with aims, emphasis on examinations, and lack of practical work. Suggestions for improvement include considering cognitive/affective domains, practical work, and organizing content logically from simple to complex.
The document discusses the topical approach to teaching social science. It explains that the topical approach revolves content around a series of interconnected topics that are suitable for students' ages, abilities, and interests. Examples provided include focusing on discrete historical events, eras, or other topics. Key merits are that an integrated knowledge is imparted, learning is related to life, and student interest and motivation remain high. However, difficulties include that the approach is challenging to adopt and requires good resources like libraries and competent teachers.
Mathematics has many educational values including developing knowledge, skills, intellectual habits, and desirable attitudes. It has practical, cultural, and disciplinary value. Mathematically, it trains the mind through reasoning that is simple, accurate, certain, original, and similar to real-life reasoning. Culturally, mathematics reflects and advances civilization. It also has social, moral, aesthetic, intellectual, and international values by organizing society, developing good character, providing beauty and entertainment, training thought processes, and promoting international cooperation. In conclusion, mathematics education cultivates numerous skills and capacities that are personally and socially beneficial.
Approaches for curriculum organizationjeniferdivya
There are different approaches to organizing curriculum, including logical, psychological, concentric, spiral, and modular approaches. Curriculum is broader than syllabus and includes all academic and non-academic activities implemented in schools. It is a framework for all planned learning experiences, both inside and outside the classroom. Curriculum provides opportunities for development and is a tool for teachers to mold students according to objectives.
ICT Resources For teaching and learning MathematicsSharme1
This document discusses using internet and multimedia resources for teaching mathematics. It explains that technology can make abstract math concepts more tangible by providing visualizations. Some benefits of technology include engaging students, motivating interest, and illustrating real-world applications. The document then describes several online resources for teaching math, including interactive games, videos, simulations and virtual manipulatives. These resources range from early learners to high school and cover websites, apps and online libraries. Teachers can use these technologies to enhance instruction, facilitate learning, and develop students' higher-order thinking skills.
This document discusses teaching mathematics using the model method. It begins by explaining the origins of the model method in Singapore, where it was developed in the 1980s to help students with word problems. The model method uses bars or boxes to represent quantities in word problems visually. It then provides examples of how the model method can be used to solve problems involving part-whole, comparison, and change concepts. Several lessons are outlined that teach students how to apply the model method by drawing diagrams and solving sample problems step-by-step.
Here are some possible mathematical problems that could be posed from the given situation:
1) The master worker can paint 1 square meter of the billboard per hour. The apprentice can paint 0.5 square meters per hour. If they work for 8 hours, how many square meters of the billboard can they paint?
2) The billboard measures 20 square meters. If the master worker and apprentice work together for x hours, write an equation to represent the relationship between the number of hours worked (x) and the area painted (y).
3) The billboard measures 20 square meters. The master worker and apprentice work together for 8 hours. How much of the billboard do they paint?
The document outlines several values of teaching mathematics, dividing them into 10 categories: practical or utilitarian value, intellectual value, social value, moral value, disciplinary value, and cultural value. It provides examples and explanations for each value. Mathematics provides practical benefits in daily life for tasks like calculating wages. It develops important intellectual skills like reasoning, creativity, and problem-solving. Socially, the study of mathematics helps social progress and the development of qualities like cooperation. It fosters moral development and discipline through teaching honesty, orderliness, and perseverance. Culturally, mathematics has helped advance civilization and transmit cultural heritage.
1 need and significance of teaching mathematicsAngel Rathnabai
This document discusses the need and significance of teaching mathematics. It notes that improving education quality is key to achieving universal education goals. Mathematics is an essential skill for the knowledge society, providing benefits like technology literacy, collaboration, creativity, effective communication, and critical thinking. Teaching mathematics is necessary for the birth of a new digital native generation that is surrounded by technology and multi-tasks. Educational systems need to evolve from a conventional teacher-centered model to a new learner-centered model that facilitates inquiry-based, collaborative, and technology-enhanced learning. Policies recommend teaching mathematics with ICT to fulfill its significance and necessity, as well as to develop a deeper understanding through appropriate technology use.
Proffessional qualities and competencies of mathematics teacherJovin John
The document discusses the qualities of effective teachers. Effective teachers have expertise in their subject matter but also the ability to interact with people and help students understand new perspectives. Good teachers are prepared, set clear expectations, have a positive attitude, are patient, and regularly assess their teaching. They adjust their teaching strategies to fit different students and learning styles, and serve as role models who motivate students through their enthusiasm and commitment.
The workshop will provide middle level mathematics teachers with ideas for engaging students in the understanding of math concepts and the creative aspects of mathematics topics in the 6-8 curriculum. The workshop will be hands-on and based upon a constructivist approach to learning and teaching. Handouts will be provided.
Presenter(s): Shirley Disseler
The document discusses the nature of mathematics and defines conceptual knowledge and procedural knowledge in mathematics. Conceptual knowledge refers to understanding mathematical concepts, while procedural knowledge involves being able to physically solve problems by applying mathematical skills and tools. The document states that conceptual understanding supports applying principles to new situations, while procedural knowledge is built upon conceptual understanding. It emphasizes that both conceptual understanding and procedural knowledge are important for students to master, as it helps them solve problems, draw inferences, and establish relationships between concepts.
A mathematics teacher must have several key qualities to be effective. They must have a strong interest and positive attitude towards mathematics to fully understand the subject matter. They must also understand individual differences in students and how to identify where students are struggling. An effective math teacher presents the material in a clear and skillful manner, inspires students to practice, and motivates them to engage in problem solving and mathematical discourse. Professional development programs help mathematics teachers stay updated on the latest research and teaching models to improve their instructional skills and better address the needs of their students.
The document discusses various methods for teaching mathematics, including teacher-centered methods like lecture, analytical, synthetic, deductive, and inductive methods. It also discusses student-centered methods such as project, peer tutoring, individual activities, and experiential learning. Interactive learning methods covered include student seminars, group discussions, mixed-ability grouping, and games/puzzles. Recent trends mentioned are constructivist learning, problem-based learning, brain-based learning, collaborative learning, flipped learning, blended learning, e-learning, and video conferencing. The lecture method is then described in more detail, noting its merits of being economical and helping develop concentration, but that it provides little student activity and does not consider individual differences
Pre-service teacher training starts with microteaching skills. This presentation is about black board writing skill. Student teachers will get idea about how to use black board and why to use black board. By using effective blackboard writing skill teacher can reinforce her/his ideas easily.
TNTEU - BEd New Syllabus - Semester 1 - BD1MA - Pedagogy of Mathematics - Unit I - Aims and Objectives of Teaching Mathematics - Blooms and Anderson - Affective domain and Psychomotor domain
this presentation consist the four stages of teaching or you can also called the elements of teaching process. which contain Planning, Implementation, Evaluation, Reflection.
Aim & objective of teaching mathematics suresh kumar
The document discusses the aims and objectives of teaching mathematics. It states that mathematics encourages logical thinking and helps students discriminate between essential and non-essential information. The significance of teaching mathematics is that it develops the ability to apply mathematical concepts to daily life situations and inculcates self-reliance. The aims are categorized as practical, social, disciplinary and cultural. Objectives are directed towards achieving these aims and are specific, precise and observable goals. Bloom's taxonomy is discussed as a framework for classifying educational objectives into cognitive, affective and psychomotor domains. The revised Bloom's taxonomy changes some terms to verb forms and reorganizes categories. It also identifies different types and levels of knowledge.
The document provides an overview of mathematics curriculum, including its definition, objectives, principles of construction, approaches to organization, characteristics of modern curriculums, and major reforms. It defines curriculum as the sum of planned learning experiences and activities provided to students. The objectives of mathematics curriculum are to develop fundamental skills, comprehension of concepts, appreciation of meanings, desirable attitudes, and ability to apply mathematics. Principles for developing curriculum include being child-centered, activity-based, integrated, and flexible. Approaches to organizing curriculum include topical, spiral, logical/psychological, unitary, and integrated approaches. Modern curriculums should prepare students for the future, incorporate new concepts, and be culturally relevant. Major reforms discussed
A pupil actively constructs their own mathematical knowledge by interacting new ideas with existing ideas, which can lead to misconceptions. Diagnostic teaching is important as it involves identifying misconceptions, challenging them through discussion to resolve conflicts, and replacing misconceptions with correct understanding. The teacher must understand the source of the misconception to effectively challenge it, and research shows this diagnostic approach promotes better learning compared to simply explaining again.
The document provides information on different methods of teaching mathematics, including the inductive method, deductive method, analytic method, and synthetic method. It compares and contrasts these methods and discusses their merits and demerits. The key points are:
- The inductive method proceeds from particular to general and known to unknown, using examples to derive rules and formulas. The deductive method goes from general to particular and abstract to concrete, applying given rules.
- The analytic method breaks problems down from unknown to known through analysis, while the synthetic method combines known elements to derive the unknown.
- Each method has advantages like developing different skills, but also limitations in terms of time efficiency, complexity of topics covered, and
Mathematics is an abstract subject and most of the people hate mathematics. so Mathematics has a great role in developing interest of the students in Mathematics.
This document discusses various tools and techniques for assessing mathematics learning at the primary level. It outlines different types of test items like objective and open-ended items. It also discusses developing question banks and different forms of assessment like projects, portfolios, exhibitions, quizzes and games. Key aspects of mathematics like concepts, reasoning, problem solving and communication can be assessed using these tools and techniques.
This document summarizes the key findings and recommendations from the US National Mathematics Advisory Panel's 2008 report on modernizing mathematics curriculum and instruction in the United States. The summary highlights that the Panel recommended streamlining the K-8 mathematics curriculum to focus on mastery of key topics like fractions that are critical foundations for algebra. It also recommended ensuring all students have access to an authentic algebra course by 8th grade and that teachers need to have strong content knowledge in algebra topics. The Panel found limited evidence that calculators improve math skills and called for more high-quality research on effective instructional practices.
The document summarizes two foreign studies related to mathematics education. The first study discusses a math summit held by Mosaica Education to explore strategies for improving math achievement. As a result, Mosaica will implement a new Math Initiative focusing on math coaches, teachers, scheduling, and making math fun. The second section discusses mathematics course requirements and learning objectives at the college level, including applying math concepts to problem solving and other disciplines.
The document outlines several values of teaching mathematics, dividing them into 10 categories: practical or utilitarian value, intellectual value, social value, moral value, disciplinary value, and cultural value. It provides examples and explanations for each value. Mathematics provides practical benefits in daily life for tasks like calculating wages. It develops important intellectual skills like reasoning, creativity, and problem-solving. Socially, the study of mathematics helps social progress and the development of qualities like cooperation. It fosters moral development and discipline through teaching honesty, orderliness, and perseverance. Culturally, mathematics has helped advance civilization and transmit cultural heritage.
1 need and significance of teaching mathematicsAngel Rathnabai
This document discusses the need and significance of teaching mathematics. It notes that improving education quality is key to achieving universal education goals. Mathematics is an essential skill for the knowledge society, providing benefits like technology literacy, collaboration, creativity, effective communication, and critical thinking. Teaching mathematics is necessary for the birth of a new digital native generation that is surrounded by technology and multi-tasks. Educational systems need to evolve from a conventional teacher-centered model to a new learner-centered model that facilitates inquiry-based, collaborative, and technology-enhanced learning. Policies recommend teaching mathematics with ICT to fulfill its significance and necessity, as well as to develop a deeper understanding through appropriate technology use.
Proffessional qualities and competencies of mathematics teacherJovin John
The document discusses the qualities of effective teachers. Effective teachers have expertise in their subject matter but also the ability to interact with people and help students understand new perspectives. Good teachers are prepared, set clear expectations, have a positive attitude, are patient, and regularly assess their teaching. They adjust their teaching strategies to fit different students and learning styles, and serve as role models who motivate students through their enthusiasm and commitment.
The workshop will provide middle level mathematics teachers with ideas for engaging students in the understanding of math concepts and the creative aspects of mathematics topics in the 6-8 curriculum. The workshop will be hands-on and based upon a constructivist approach to learning and teaching. Handouts will be provided.
Presenter(s): Shirley Disseler
The document discusses the nature of mathematics and defines conceptual knowledge and procedural knowledge in mathematics. Conceptual knowledge refers to understanding mathematical concepts, while procedural knowledge involves being able to physically solve problems by applying mathematical skills and tools. The document states that conceptual understanding supports applying principles to new situations, while procedural knowledge is built upon conceptual understanding. It emphasizes that both conceptual understanding and procedural knowledge are important for students to master, as it helps them solve problems, draw inferences, and establish relationships between concepts.
A mathematics teacher must have several key qualities to be effective. They must have a strong interest and positive attitude towards mathematics to fully understand the subject matter. They must also understand individual differences in students and how to identify where students are struggling. An effective math teacher presents the material in a clear and skillful manner, inspires students to practice, and motivates them to engage in problem solving and mathematical discourse. Professional development programs help mathematics teachers stay updated on the latest research and teaching models to improve their instructional skills and better address the needs of their students.
The document discusses various methods for teaching mathematics, including teacher-centered methods like lecture, analytical, synthetic, deductive, and inductive methods. It also discusses student-centered methods such as project, peer tutoring, individual activities, and experiential learning. Interactive learning methods covered include student seminars, group discussions, mixed-ability grouping, and games/puzzles. Recent trends mentioned are constructivist learning, problem-based learning, brain-based learning, collaborative learning, flipped learning, blended learning, e-learning, and video conferencing. The lecture method is then described in more detail, noting its merits of being economical and helping develop concentration, but that it provides little student activity and does not consider individual differences
Pre-service teacher training starts with microteaching skills. This presentation is about black board writing skill. Student teachers will get idea about how to use black board and why to use black board. By using effective blackboard writing skill teacher can reinforce her/his ideas easily.
TNTEU - BEd New Syllabus - Semester 1 - BD1MA - Pedagogy of Mathematics - Unit I - Aims and Objectives of Teaching Mathematics - Blooms and Anderson - Affective domain and Psychomotor domain
this presentation consist the four stages of teaching or you can also called the elements of teaching process. which contain Planning, Implementation, Evaluation, Reflection.
Aim & objective of teaching mathematics suresh kumar
The document discusses the aims and objectives of teaching mathematics. It states that mathematics encourages logical thinking and helps students discriminate between essential and non-essential information. The significance of teaching mathematics is that it develops the ability to apply mathematical concepts to daily life situations and inculcates self-reliance. The aims are categorized as practical, social, disciplinary and cultural. Objectives are directed towards achieving these aims and are specific, precise and observable goals. Bloom's taxonomy is discussed as a framework for classifying educational objectives into cognitive, affective and psychomotor domains. The revised Bloom's taxonomy changes some terms to verb forms and reorganizes categories. It also identifies different types and levels of knowledge.
The document provides an overview of mathematics curriculum, including its definition, objectives, principles of construction, approaches to organization, characteristics of modern curriculums, and major reforms. It defines curriculum as the sum of planned learning experiences and activities provided to students. The objectives of mathematics curriculum are to develop fundamental skills, comprehension of concepts, appreciation of meanings, desirable attitudes, and ability to apply mathematics. Principles for developing curriculum include being child-centered, activity-based, integrated, and flexible. Approaches to organizing curriculum include topical, spiral, logical/psychological, unitary, and integrated approaches. Modern curriculums should prepare students for the future, incorporate new concepts, and be culturally relevant. Major reforms discussed
A pupil actively constructs their own mathematical knowledge by interacting new ideas with existing ideas, which can lead to misconceptions. Diagnostic teaching is important as it involves identifying misconceptions, challenging them through discussion to resolve conflicts, and replacing misconceptions with correct understanding. The teacher must understand the source of the misconception to effectively challenge it, and research shows this diagnostic approach promotes better learning compared to simply explaining again.
The document provides information on different methods of teaching mathematics, including the inductive method, deductive method, analytic method, and synthetic method. It compares and contrasts these methods and discusses their merits and demerits. The key points are:
- The inductive method proceeds from particular to general and known to unknown, using examples to derive rules and formulas. The deductive method goes from general to particular and abstract to concrete, applying given rules.
- The analytic method breaks problems down from unknown to known through analysis, while the synthetic method combines known elements to derive the unknown.
- Each method has advantages like developing different skills, but also limitations in terms of time efficiency, complexity of topics covered, and
Mathematics is an abstract subject and most of the people hate mathematics. so Mathematics has a great role in developing interest of the students in Mathematics.
This document discusses various tools and techniques for assessing mathematics learning at the primary level. It outlines different types of test items like objective and open-ended items. It also discusses developing question banks and different forms of assessment like projects, portfolios, exhibitions, quizzes and games. Key aspects of mathematics like concepts, reasoning, problem solving and communication can be assessed using these tools and techniques.
This document summarizes the key findings and recommendations from the US National Mathematics Advisory Panel's 2008 report on modernizing mathematics curriculum and instruction in the United States. The summary highlights that the Panel recommended streamlining the K-8 mathematics curriculum to focus on mastery of key topics like fractions that are critical foundations for algebra. It also recommended ensuring all students have access to an authentic algebra course by 8th grade and that teachers need to have strong content knowledge in algebra topics. The Panel found limited evidence that calculators improve math skills and called for more high-quality research on effective instructional practices.
The document summarizes two foreign studies related to mathematics education. The first study discusses a math summit held by Mosaica Education to explore strategies for improving math achievement. As a result, Mosaica will implement a new Math Initiative focusing on math coaches, teachers, scheduling, and making math fun. The second section discusses mathematics course requirements and learning objectives at the college level, including applying math concepts to problem solving and other disciplines.
The document discusses integrating math concepts into career and technical education (CTE) courses. It outlines a Math-in-CTE model that maps math standards to CTE curriculum, provides teacher professional development to enhance lessons with math, and evaluates the approach through a study on its impact on students' math skills. The goal is to improve academic achievement in math required by federal laws while maintaining high-quality CTE.
The document provides an introduction and overview of the Common Core State Standards for Mathematics. It discusses the need for mathematics standards and curriculum in the US to become more focused and coherent in order to improve student achievement. The introduction emphasizes concentrating early mathematics learning on number, measurement, and geometry and developing conceptual understanding of key ideas. It also outlines how the standards are organized and are intended to define what students should understand and be able to do in their mathematics education.
Math Textbook Review First Meeting November 2009dbrady3702
The document summarizes information from a mathematics textbook review committee in Massachusetts. It discusses the state's high performance on national and international math assessments. It also reviews research on best practices in mathematics education and outlines the committee's process for reviewing and piloting elementary and middle school math textbooks based on this research. Key aspects of the review include using a rubric to evaluate textbooks, visiting schools currently using the programs, and monitoring a pilot of selected textbooks before making an adoption recommendation.
Metacognitive Strategies: Instructional Approaches in Teaching and Learning o...IJAEMSJORNAL
The purpose of the study is to determine the effectiveness of the metacognitive strategies as instructional approaches in teaching and learning of Basic Calculus. A number of 48 students consisting of 24 boys and 24 girls were purposively sampled in this study. Pretest-posttest quasi experimental research design was used which applied t-test and descriptive statistics. Both groups were subject to two instruments that were comprised of problem-solving test (pretest and posttest) and observation guide. Experimental group was taught Basic Calculus using metacognitive strategies while the control group was taught Basic Calculus using traditional teaching strategies. Both groups were subject to a pretest. Class observation was done while the two teaching strategies were applied. In the end, the posttest was administered to both groups to identify the effectiveness of the two teaching strategies. The data gathered were treated using paired sample t-test and independent sample t-test. The results of the study showed that the experimental group had significantly higher posttest scores as compared to control group which proved that metacognitive teaching strategies were more effective in improving the performance and problem-solving skills of the students than the traditional teaching strategies. It was also observed that students who taught using metacognitive strategies helped the students to be extremely engaged in Basic Calculus lessons cognitively, behaviorally, and affectively. The study reveals that the significant increase of the students’ learning engagement in Basic Calculus lessons led the students to a corresponding increase in their posttest scores.
All Students Can Learn And Should Be Presented The Opportunity To Learnnoblex1
The current reform movement in the United States began in the 1990s and has manifested itself as a standards movement. It is a movement to establish state and national frameworks, to which local school districts are encouraged to link their efforts to implement local standards. The linchpin that holds together the standards framework is that they are rigorous; voluntary, in that states and localities decide whether or not to use them; and flexible, in that states and localities can decide which strategies are best for their own schools.
Today, virtually every state in the nation has gone about the business of articulating standards, revising curricular offerings, and developing assessments to measure whether the standards are being met. At the national level, initiatives by the federal government and national organizations have been joined in an effort to produce a comprehensive and coherent standards movement. Currently, many national professional organizations have developed or are in the process of developing national standards for their particular subject areas. States have connected to these efforts on numerous fronts.
The current movement has focused primarily on three types of standards: 1) content or curriculum standards; 2) performance or accountability standards; and 3) capacity or delivery standards (also referred to as opportunity-to-learn standards). The three types of standards are linked - one will not succeed without the other two.
The purpose of this paper is four-fold: First, we define "students of diverse needs and cultures" and the "standards movement." Second, we address specific initiatives of current reform efforts in progress in mathematics and science education. Third, we discuss critical issues related to the successful implementation of mathematics and science standards (i.e., teachers professional development, technological advancements, opportunity-to-learn standards, school organization, and assessments.) Fourth, we suggest references to be used as curriculum materials, how-to articles of use to teachers in the classroom, and seminal research and philosophical literature related to mathematics and science reform initiatives.
Who Are Students of Diverse Needs and Cultures?
American society has haltingly come to understand itself as being culturally diverse and pluralistic. Schools, public schools in particular, mirror what our society will look like in the 21st Century. The culture of schools and the capacity of teachers to implement standards and other initiatives are indispensable elements in the effort to reform mathematics and science education.
Source: https://ebookschoice.com/all-students-can-learn-and-should-be-presented-the-opportunity-to-learn/
AN ANALYSIS OF USING JAPANESE PROBLEM SOLVING ORIENTED LESSON STRUCTURE TO SW...Joe Andelija
This document outlines the aims and themes of Topic Study Group 15 on Problem Solving in Mathematics Education at the 12th International Congress on Mathematical Education. The Study Group will examine the origins, frameworks, research programs, curriculum proposals, assessment, and future directions of mathematical problem solving. It provides the names and contact information of the co-chairs and organizing committee overseeing the group's activities and paper submissions. Submitted papers will be reviewed and authors given feedback to improve their final contributions to be shared at the Congress.
The Primary Exit Profile: What does this mean for STEM in Jamaican Primary Sc...Lorain Senior
This document represents my original contribution as a part of the criteria for completion off the Capstone Experience Project in fulfillment of the M/Ed. in S.T.E.M Leadership at the American College of Education.
This study examines the effects of Math Teachers' Circles (MTC), a professional development program for middle school math teachers, on teachers' mathematical knowledge. MTCs focus on developing teachers' problem solving and reasoning skills through regular meetings where teachers work on mathematical problems led by mathematicians. The study administered a test of mathematical knowledge for teaching to teachers at three MTC sites before and after participation. Results showed participation in MTCs improved teachers' performance on number concepts and operations questions, indicating MTCs may positively impact aspects of teachers' mathematical knowledge.
The document provides an introduction to the Common Core Georgia Performance Standards for mathematics. It discusses how the standards focus on applying mathematical concepts in authentic problems, problem solving, reasoning and representation. It emphasizes concentrating early learning on numbers, measurement and geometry with less emphasis on data analysis and algebra. The standards aim to present mathematics concepts clearly and specifically to improve focus and coherence.
The document provides an introduction to the Common Core Georgia Performance Standards for Mathematics. It discusses the focus of the Georgia mathematics curriculum on developing conceptual understanding through problem solving, representation, reasoning and communication. It emphasizes applying math concepts in authentic contexts. The standards are designed to increase coherence and focus from grade to grade to improve math achievement. They define what students should understand and be able to do at each grade level.
Naslund-Hadley, E., and Bando, R. (2016) All Children Count -- Early Mathemat...Johan Luiz Rocha
This document provides an overview of a forthcoming book titled "All Children Count" which examines mathematics and science education in Latin America and the Caribbean. It finds that students in the region perform poorly on international standardized tests in mathematics and science. The book explores why education systems are failing to develop problem-solving, critical thinking, and other skills demanded by the 21st century. It highlights research on effective early mathematics and science education programs and practices. The overview reports on experiments showing what approaches are likely to improve mathematics and science learning in the region. The goal is to provide ideas and suggestions to help educators ensure all children receive quality early education in these subjects.
This document provides a critical appraisal of the secondary level mathematics curriculum in Kerala, India. It discusses the importance of mathematics based on national education policies and frameworks. The National Curriculum Framework (NCF) 2005 and Kerala Curriculum Framework (KCF) 2007 emphasize developing students' ability to think mathematically and solving problems. However, many students struggle with mathematics and consider it difficult. The document analyzes whether deficiencies in the current secondary curriculum contribute to these difficulties, and how well the curriculum aligns with NCF and KCF guidelines, with a focus on high school mathematics textbooks. Suggestions are provided to address limitations and improve the curriculum.
Curriculum jeremy kilpatrick and john dosseyGlaiden Rufino
This document discusses key aspects of developing a coherent mathematics curriculum. It emphasizes that a curriculum must clearly define its purpose and intended outcomes. It recommends focusing content domains and cognitive processes concisely while ensuring connections. A philosophy of pedagogy should value reasoning, problem-solving, multiple perspectives and mathematical autonomy. Finally, developing coherence across all elements and attending to challenges of implementation are vital.
A meta analysis-of_the_effects_of_computer_technology_on_school_students’_mathCathy Cavanaugh
This study analyzed 85 independent research studies involving over 36,000 K-12 students to determine the impact of computer technology on mathematics learning. The meta-analysis found statistically significant positive effects, with computer technology promoting greater mathematics achievement for elementary students compared to secondary students. Special needs students also benefited more than general education students. Studies employing constructivist teaching approaches in conjunction with computer technology reported larger effects than those using traditional teaching. The analysis identified several technology, implementation, and learner characteristics that influence mathematics achievement outcomes.
Influence of Policy and Curriculum Formulation Procedures on The Implementati...inventionjournals
ABSTRACT: Several factors have been highlighted as impediments to effective implementation of Alternative ‘B’ Mathematics curriculum in secondary schools that include; level of involvement of stakeholders and policy issues. This study however specifically dealt with the Influence of policy and curriculum formulation procedures on the implementation of Alternative ‘B’ Mathematics curriculum in secondary schools with reference to Kericho County. Leithwood's model of evaluation of curriculum implementation was adopted in this study. Descriptive survey design was chosen as the study design. A population of 157 principals, 401 teachers of Mathematics and 20 heads of secondary Mathematics curriculum at KIDC, MoE and KNEC were targeted. Simple random sampling was employed to select respondents.. Data were collected by use questionnaires and interview guides. The findings indicate that there is a strong correlation between Policy and Curriculum Formulation Procedures and acceptability of new curriculum as indicated in the Chi Square test.
The document discusses effective mathematics teaching practices and analyzes a classroom video from West Virginia. It begins by establishing clear learning goals for students, which in the video involve designing a statistical question based on catching a ruler, collecting two data sets, creating graphs, calculating measures of center and variability, and answering the statistical question with data analysis. The video task allows for multiple entry points and engages students in reasoning and problem solving. Students use and connect mathematical representations like data tables and graphs to explore and model the problem.
Effectiveness of Division Wheel in Basic Mathematics Operation Case Study: Pr...iosrjce
Mathematics is important in everyday life. Mathematics involve with the concept of addition,
subtraction, multiplication, and division. Advance topic in mathematics may cause students to experience
difficulty catching up with the syllabus, especially as a majority primary students are not able to understand
basic concept of division. Therefore, this research study has been conducted to determine the effectiveness of
‘division wheel’ in mathematics division operations. The target for sample size is 400 respondents involving
only standard five in between excellent, moderate and poor classes. This research study involves a
questionnaire using the Likert scale, while the analysis used is descriptive analysis. A test will be carry out
before (pre-test) and after (post-test) teaching method using ‘division wheel’. Pre-test analysis shows majority
male respondents have poor achievement, while female respondents have moderate achievement. After applied
the ‘division wheel’, there are increasing numbers for excellent and moderate achievement for male respondents
and excellent for female respondents after taking post-test. Questionnaire results shows that the majority of
students prefer to use ‘division wheel’ as concrete material in learning process. ‘Division wheel’ had helps
students understand the concept of basic division operation and confident to answer question properly without
teacher’s help. Students start to love doing mathematics especially divide questions. In conclusion, the ‘division
wheel’has become a new method in mastering the concept of division.
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
4. CLOSING THE ACHIEVEMENT GAP:
BEST PRACTICES IN TEACHING MATHEMATICS
Introduction
Mathematics is a form of reasoning. Thinking mathematically consists of thinking
in a logical manner, formulating and testing conjectures, making sense of things, and
forming and justifying judgments, inferences, and conclusions. We demonstrate
mathematical behavior when we recognize and describe patterns, construct physical and
conceptual models of phenomena, create symbol systems to help us represent,
manipulate, and reflect on ideas, and invent procedures to solve problems (Battista,
1999).
Recent national test results provide continuing documentation of the need to
increase the focus on improving student achievement in mathematics. The National
Assessment of Educational Progress (NAEP) recently released the 2005 math scores
which reflected student achievement in the areas of measurement, geometry, data
analysis, probability and algebra. Nationally, only 30% of eighth graders were deemed
proficient. Although reflecting an increase from previous assessments, only 69% of the
eighth graders nationally demonstrated a basic skills level on the NAEP assessment
(Olson, 2005).
The need for effective instruction in mathematics was further documented in a
February 2006 study by the U.S. Department of Education. The study findings are based
on data from a nationally representative sample of students from the high school class of
1992 who attended a four-year college. The study found that taking a full schedule of
academically demanding courses in high school, including mathematics beyond
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5. Algebra II, was the single most significant pre-collegiate variable in determining if
students graduated from college. The study also found significant disconnects between
the high school curriculum and the expectations of the first year of college, suggesting
the need to increase the level of challenging academic content in high school. This need
to offer a more challenging high school curriculum is even more critical for poor and
minority students as they are less likely than higher socioeconomic and white students to
attend high schools that offer a challenging curriculum. States moving to increase unit
requirements for graduation must also attend to content requirements if they expect to
make a difference in student performance (Adelman, 2006).
Masini and Taylor (2000) report research documenting that the number of
mathematics topics covered prior to eighth grade is positively correlated to mathematics
achievement while the number of new topics presented at the eighth grade level is
negatively correlated to mathematics achievement. Regardless of math skills before high
school, taking algebra in the middle school is strongly related to achievement gains in
high school. The math curriculum must provide students with opportunities to learn math
at an early age.
The poor performance of U.S. students in math can be traced to the method used
to teach math at the elementary level. The focus is on specific problems and not on
building the foundations necessary for understanding higher level math. These
foundations can only be built with a mathematics program that teaches concepts and
skills, and problem-solving (Daro, 2006).
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6. The Mathematics Reform Movement
The reform movement in mathematics education can be traced to the mid-1980’s
and was a response to the failure of traditional teaching methods, the impact of
technology on curriculum and the emergence of new approaches to the scientific study of
how mathematics is learned. Basic to the reform movement was a standards-based
approach to the “what and how” of mathematics teaching (Battista, 1999).
In the new mathematics, the focus is on problem solving, mathematical reasoning,
justifying ideas, making sense of complex situations and independently learning new
ideas. Students must be provided with opportunities to solve complex problems,
formulate and test mathematical ideas and draw conclusions. Students must be able read,
write and discuss mathematics, use demonstrations, drawings and real-world objects, and
participate in formal mathematical and logical arguments (Battista, 1999).
The driving force behind the standards-based approach to mathematics instruction
has been the standards developed by the National Council of Teachers of Mathematics
(NCTM). The Principles and Standards for School Mathematics, published by NCTM in
2000, outlines the principles and standards for developing a comprehensive school
mathematics program. The document delineates six guiding principles related to equity,
curriculum, teaching, learning, assessment and technology, and identifies five content and
process standards outlining what content and processes students should know and be able
to use. The content standards are organized around content strands related to numbers
and operations, algebra, geometry, measurement and data analysis and probability. The
process standards are organized around the areas of problem solving, reasoning and
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7. proof, communication, connections and representations (National Council of Teachers of
Mathematics, 2000).
A set of basic assumptions about teaching and schooling practices is implicit in
this reform movement. First, all students must have an opportunity to learn new
mathematics. Second, all students have the capacity to learn more mathematics than we
have traditionally assumed. Third, new applications and changes in technology have
changed the instructional importance of some mathematics concepts. Fourth, new
instructional environments can be created through the use of technological tools. Fifth,
meaningful mathematics learning is a product of purposeful engagement and interaction
which builds on prior experience (Romberg, 2000).
A recent concept paper published by the American Mathematical Society has
been influential in identifying some common areas of agreement about mathematics
education. The identified areas of agreement are based on three fundamental premises;
basic skills with numbers continue to be important and students need proficiency with
computational procedures, mathematics requires careful reasoning about precisely
defined objects and concepts, and students must be able to formulate and solve problems.
The areas of agreement emerging from these premises include:
•
Mathematical fluency requires automatic recall of certain procedures and
algorithms.
•
Use of calculators in instruction can be useful but must not impede the
development of fluency with computational procedures and basic facts.
•
Using and understanding the basic algorithms of whole number arithmetic is
essential.
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8. •
Developing an understanding of the number meaning of fractions is essential.
•
Teachers must ensure that the use of “real-world” contexts for teaching
mathematics maintains a focus on mathematical ideas.
•
Mathematics should be taught using multiple strategies, however, the teacher is
responsible for selecting the strategies appropriate for a specific concept.
•
Mathematics teachers must understand the underlying meaning and justifications
for ideas and be able to make connections among topics.
(Ball, Ferrini-Mundy, Kilpatrick, Milgram, Schmid, & Scharr, 2005).
Standards-Based Mathematics
Standards-based instruction in mathematics is designed to clearly identify what
students should learn at each level. Standards provide more than a curriculum framework
as they delineate the skills, concepts and knowledge that are to be mastered. For
successful standards-based implementation, teachers must understand the rationale for
using standards, know applicable national and state standards and use them as a basis for
planning instruction, and implement best practices instructional strategies. Essential
characteristics of an effective standards-based mathematics classroom include:
•
Lessons designed to address specific standards-based concepts or skills.
•
Student centered learning activities.
•
Inquiry and problem solving focused lessons.
•
Critical thinking and knowledge application skills
•
Adequate time, space, and materials to complete tasks.
•
Varied, continuous assessment, designed to evaluate both student progress and
teacher effectiveness.
(Teaching Today, 2005a)
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9. The implementation of a standards-based math curriculum brings with it some
special challenges. In addition to ensuring students are actively engaged, teachers should
adhere to the following guidelines:
•
Create a safe environment where students feel comfortable.
•
Establish clear procedures and routines.
•
Provide both challenge and support.
•
Use carefully assigned and well-managed cooperative groups.
•
Make frequent real life connections.
•
Use an integrated curriculum.
•
Provide engaging educational experiences that are relevant to students.
•
Present activities where students produce and share products.
(Teaching Today, 2005b, ¶ 3)
The Thomas B. Fordham Foundation has conducted three analyses of state
mathematics standards. The most recent study was released in 2005. Although the
weighting of the specific criteria has shifted, the same criteria: clarity of the standards,
content, sound mathematical reasoning, and the absence of negative features, have been
used to evaluate standards in each of the studies. Overall, only six states received grades
of A of B. Twenty-nine states received grades of D or F, and 15 received Cs. The report
identified nine major areas of concern including excessive emphasis on calculator use,
memorization of basic number facts, lack of focus on the standard algorithms, insufficient
focus on fractions, inadequate attention to mathematical patterns, counterproductive use
of manipulatives, overemphasis on estimation skills, improper sequencing of statistics
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10. and probability standards, and a lack of standards that appropriately guide the
development of problem-solving (Klein, 2005).
The study also offers suggestions for state policy makers seeking to strengthen
their K-12 math standards. These recommendations include the use of standards
developers who thoroughly understand mathematics, the development of coherent
arithmetic standards that emphasize both conceptual understanding and computational
fluency, avoid and rectify the nine major concerns related to math standards, and consider
borrowing a complete set of math standards from one of the states with high-quality
standards (Klein, 2005).
Best Practices
Sabean and Bavaria (2005) have synthesized a list of the most significant
principles related to mathematics teaching and learning. This list includes the
expectations that teachers know what students need to learn based on what they know,
teachers ask questions focused on developing conceptual understanding, experiences and
prior knowledge provide the basis for learning mathematics with understanding, students
provide written justification for problem solving strategies, problem based activities
focus on concepts and skills, and that the mathematics curriculum emphasizes conceptual
understanding.
Concurrently, the following best practices for implementing effective standardsbased math lessons should be followed:
•
Students’ engagement is at a high level.
•
Tasks are built on students’ prior knowledge.
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11. •
Scaffolding takes place, making connections to concepts, procedures, and
understanding.
•
High-level performance is modeled.
•
Students are expected to explain thinking and meaning.
•
Students self-monitor their progress.
•
Appropriate amount of time is devoted to tasks.
(Teaching Today, 2005b, ¶ 7)
The role of discovery and practice and the use of concrete materials are two
additional topics that must be considered when developing a program directed at
improving mathematics achievement. Sabean and Bavaria (2005) examined research
which suggested that such a program must be balanced between the practice of skills and
methods previously learned and new concept discovery. This discovery of new concepts,
they suggest, facilitates a deeper understanding of mathematical connections.
Johnson (2000) reported findings that suggest that when applied appropriately, the
long-term use of manipulatives appears to increase mathematics achievement and
improve student attitudes toward mathematics. The utilization of manipulative materials
helps students understand mathematical concepts and processes, increases thinking
flexibility, provides tools for problem-solving, and can reduce math anxiety for some
students. Teachers using manipulatives must intervene frequently to ensure a focus on
the underlying mathematical ideas, must account for the “contextual distance” between
the manipulative being used and the concept being taught, and take care not to
overestimate the instructional impact of their use.
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12. Sabean and Bavaria (2005) have summarized research suggesting that the
development of practical meaning for mathematical concepts is enhanced through the use
of manipulatives. They further suggest that the use of manipulatives must be long term
and meaningfully focused on mathematical concepts.
The National Council of Teachers of Mathematics has developed a position
statement which provides a framework for the use of technology in mathematics teaching
and learning. The NCTM statement endorses technology as an essential tool for effective
mathematics learning. Using technology appropriately can extend both the scope of
content and range of problem situations available to students. NCTM recommends that
students and teachers have access to a variety of instructional technology tools, teachers
be provided with appropriate professional development, the use of instructional
technology be integrated across all curricula and courses, and that teachers make
informed decisions about the use of technology in mathematics instruction (National
Council of Teachers of Mathematics, 2003).
Acknowledging and responding to the varied learning styles of students is a
critical component of effective inquiry oriented standards-based math instruction.
Effective strategies for differentiating mathematics instruction include rotating strategies
to appeal to students’ dominant learning styles, flexible grouping, individualizing
instruction for struggling learners, compacting (giving credit for prior knowledge), tiered
assignments, independent projects, and adjusting question level (Computing Technology
for Math Excellence, 2006).
A 1998 meta-analysis of 100 research studies on teaching mathematics provided
support for a three-phase instructional model. In the first phase of the model, teachers
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13. demonstrated, explained, questioned, conducted discussions and checked for
understanding. Students are actively involved in discussions and responding to
questions. In phase two, teachers and student peers provide student assistance that is
gradually reduced while students receive feedback on their performance, corrections,
additional explanations, and other assistance as needed. In phase three, teachers assess
students’ ability to apply the knowledge gained while students demonstrate their ability to
recall, generalize or transfer what they have learned. Effective lessons do not require
students to apply new knowledge independently until they have demonstrated an ability
to successfully do so (Dixon, Carnine, Lee, Wallin, & Chard, 1998).
The recent results from the Third International Mathematics and Science Study
(TIMSS) have caused many teachers in the United States and Canada to take a closer
look at strategies and techniques used by Japanese teachers in teaching mathematics.
TIMSS results documented the advanced performance and more in depth mathematical
thinking of Japanese students. A central strategy in the success of the Japanese
mathematics teachers has been the use of Lesson Study, an instructional approach that
includes a group of teachers developing, observing, analyzing and revising lesson plans
that are focused on a common goal. This process is focused on improving student
thinking and includes selecting a research theme, focusing the research, creating the
lesson, teaching and observing the lesson, discussing the lesson, revising the lesson and
documenting the findings. A key element of the Lesson Study process is that it helps to
facilitate teachers working together using interconnecting skills across grade levels and
lessons (Teaching Today, 2006).
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14. Professional Development, High Quality Teaching and Student
Achievement in Mathematics
A September, 2005 report, A Study of Professional Development for Public
School Educators in West Virginia, provides a framework for viewing the relationship
between professional development, teacher quality, and student achievement in
mathematics. The report, prepared by the National Staff Development Council for the
Legislative Oversight Commission on Education Accountability, notes that there is
conclusive evidence from current research that the single most critical factor in
improving student learning is teaching quality. Concurrently, the accountability
provisions of NCLB have substantially increased the pressure on states and school
districts to provide highly qualified teachers. A number of legislative and policy
initiatives have been implemented to ensure that teachers entering the classroom are high
quality. Experienced teachers, however, must look to professional development to expand
their content knowledge and assist in learning new standards-based instructional
strategies (National Staff Development Council, 2005).
The training and preparation received by many current teachers did not prepare
them to address the new student performance standards which stress higher-order
thinking and analytical skills and require teachers to teach the use of critical thinking,
problem solving and inquiry. Teachers are not able to teach what they do not know.
Consequently, the role of professional development in assuring quality teaching for
experienced teachers is critical (National Staff Development Council, 2005).
Using the concept of professional development and professional learning
interchangeably, the No Child Left Behind Act provides the following definition of highquality professional development:
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15. Professional learning needs to give teachers and school leaders the skills
to support students’ mastery of states’ academic standards; enhance the
content knowledge of teachers in their teaching subjects; be integrated into
overall school and district improvement plans; be research based; align
with state student standards; and be sustained, intensive, and focused on
classroom practice. In fact, the legislation explicitly specifies that one-day
or short-term workshops do not qualify as effective professional
development. (U.S. Department of Education, 2002, p.13)
This definition is closely aligned with the professional development standards developed
by the National Staff Development Council (2001).
A recent research report, The Role of Professional Development for Teachers
(2005), published by the Education Alliance, provides additional support for the use of
the NCLB definition and NSDC standards. Synthesizing the current research on effective
professional development, the report concludes that effective professional development
for teachers is teacher driven, ongoing and sustained, school-based and job-embedded,
content-focused, focused on student needs and uses appropriate adult learning strategies.
Administrators in Boston and San Diego believe that a concentrated focus on
building students’ conceptual math skills and investing in professional development for
their elementary and middle school teachers were major factors behind their gains on the
most recent National Assessment of Educational Progress. Both school systems worked
to lessen the focus on memorizing facts, formulas and procedures, and increase the
emphasis on developing problem solving skills. The districts also provided additional
support for teachers by providing additional instructional materials such as curriculum
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16. maps and pacing guides. Other support strategies include the establishment of math
leadership teams and providing math coaches (Cavanagh, 2006).
Mathematics Instruction and Assessment
Johnson (2000) reported research suggesting that the impact of standards in
establishing external assessment expectations is profound. Understanding these standards
and their related assessments allows teachers to plan and adjust instruction accordingly.
Effective assessment of mathematics learning must be performance-based, use multiple
strategies and employ more open-ended assessment tasks than have been used in the past.
Effective assessment practices are essential to support mathematics instruction
that produces improved student performance. Teachers and students have been placed
under tremendous pressure to prepare students for the accountability measures and
standardized tests required by the No Child Left Behind legislation. Despite these
pressures, mathematics teachers must resist the tendency to rely on the results of
standardized tests only to measure student performance in mathematics (Computing
Technology for Math Excellence, 2006).
Assessment in a standards-based environment requires that students be judged in
terms of mathematical literacy, understanding of concepts and procedures, and the
application of mathematical knowledge in problem-solving situations. Since most
traditional assessment strategies were not designed for these purposes, new assessment
models must be developed. One such model, developed by the Organization for
Economic Cooperation and Development, focuses on assessing large ideas such as
change and growth, space and shape, and chance. The model also organizes the
assessment of thinking skills into three categories focused on tasks requiring simple
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17. computations and definitions, tasks requiring that connections be made to solve problems
and tasks requiring higher level mathematical thinking and analysis (Romberg, 2000).
Assessment strategies can be classified as diagnostic, formative or summative.
The manner in which teachers use assessment in their instruction is a major variable in
determining student achievement. Diagnostic assessment strategies are focused on
assessing students’ prior knowledge, strengths, weaknesses and skill levels. Formative
assessments are directed at providing immediate feedback and evidence of student
performance. Summative assessments are more comprehensive and are typically
administered at the end of a specific unit or timeframe (Computing Technology for Math
Excellence, 2006).
Assessment strategies can also be characterized as traditional or alternative in
nature. Multiple choice, true/false or matching tests represent traditional approaches to
assessment, whereas, strategies such as portfolios, journal writing, student selfassessment, and performance tools may be considered alternative assessment strategies.
Traditional and alternative assessments may be used for diagnostic, formative or
summative purposes (Computing Technology for Math Excellence, 2006).
Best Practices Summary
Viewed from the classroom, mathematics instruction that is standards-based is
different from traditional mathematics instruction. Students approach mathematics
differently as they explore functions, develop formulas, and actively engage in
nonroutine problem-solving and interaction about mathematics. Students use calculators
for computational assistance and as tools for solving problems. This open and focused
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18. approach on problem-solving, reasoning and communication processes allows teachers
and students to learn from each other (Smith, Smith, & Romberg, 1993).
Research from the past 15 years provides a clear picture of the impact of a
standards-based math curriculum. Students who take rigorous mathematics courses are
much more likely to go to college than those who do not. The gateway to advanced
mathematics in high school is Algebra. We also know that achievement in mathematics is
based on the type of courses a student takes, not the type of school attended (U.S.
Department of Education, 1997).
As evidenced in this brief review of the literature related to teaching mathematics,
there is a literature basis for a set of best practices for use in teaching mathematics.
These recommended practices are summarized in the following chart.
Instructional Element
Curriculum Design
•
•
•
•
Professional Development for Teachers
•
•
•
Recommended Practices
Ensure mathematics curriculum is
based on challenging content
Ensure curriculum is standardsbased
Clearly identify skills, concepts and
knowledge to be mastered
Ensure that the mathematics
curriculum is vertically and
horizontally articulated
Provide professional development
which focuses on:
§ Knowing/understanding
standards
§ Using standards as a basis
for instructional planning
§ Teaching using best
practices
§ Multiple approaches to
assessment
Develop/provide instructional
support materials such as
curriculum maps and pacing guides
Establish math leadership teams
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19. Technology
•
•
•
and provide math coaches
Provide professional development
on the use of instructional
technology tools
Provide student access to a variety
of technology tools
Integrate the use of technology
across all mathematics curricula and
courses
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20. Manipulatives
•
•
•
Instructional Strategies
•
•
•
•
•
•
•
•
Assessment
•
•
•
•
•
Use manipulatives to develop
understanding of mathematical
concepts
Use manipulatives to demonstrate
word problems
Ensure use of manipulatives is
aligned with underlying math
concepts
Focus lessons on specific
concept/skills that are standardsbased
Differentiate instruction through
flexible grouping, individualizing
lessons, compacting, using tiered
assignments, and varying question
levels.
Ensure that instructional activities
are learner-centered and emphasize
inquiry/problem-solving
Use experience and prior
knowledge as a basis for building
new knowledge
Use cooperative learning strategies
and make real life connections
Use scaffolding to make
connections to concepts, procedures
and understanding
Ask probing questions which
require students to justify their
responses
Emphasize the development of
basic computational skills
Ensure assessment strategies are
aligned with standards/concepts
being taught
Evaluate both student
progress/performance and teacher
effectiveness
Utilize student self-monitoring
techniques
Provide guided practice with
feedback
Conduct error analyses of student
work
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21. •
•
•
Utilize both traditional and
alternative assessment strategies
Ensure the inclusion of diagnostic,
formative and summative strategies
Increase use of open-ended
assessment techniques
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22. References
Adelman, C. (2006). The Toolbox Revisited: Paths to Degree Completion from High
School through College. Washington, DC: U.S. Department of Education, Office
of Vocational and Adult Education.
Ball, D., Ferrini-Mundy, J., Kilpatrick, J., Milgram, J., Schmid, W. & Scharr, R. (2005).
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