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Meeting the Learning Challenges of NCLB in Mathematics So many of our dreams at first seem impossible, then they seem improbable, and then, when we summon the will, they soon become inevitable. Christopher Reeve SUPERMAN SUPER Dan Mulligan Blue Ridge Council of Teachers of Mathematics MAN

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Mathematics Percentage of Students Passed Percentage of Students Not Tested All Students822 Black703 White871 Hispanic752 Disabled574 Economically Disadvantaged722 Limited English Proficient752 2003-2004 Annual Measurable Objectives (AMO): for reading 61% for mathematics 59%

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“A positive attitude may not solve all of your problems, but it will annoy enough people to make it worth it.” “A positive attitude may not solve all of your problems, but it will annoy enough people to make it worth it.” - Maya Angelou

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My Personal Learning Goals I will understand the latest data on student achievement by subgroup as measured by SOL tests. (achievement gaps?) I will understand the latest data on student achievement by subgroup as measured by SOL tests. (achievement gaps?) I will explore the latest research on improving the performance of underachieving students. I will explore the latest research on improving the performance of underachieving students. I will imagine effective learning strategies that boost the achievement of ALL students in my classroom. I will imagine effective learning strategies that boost the achievement of ALL students in my classroom. I will not write notes on the paper napkins. I will not write notes on the paper napkins. I will not fall asleep and drop my head in the desert plate. I will not fall asleep and drop my head in the desert plate.

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Benefits of Focus Activities Help students focus and pay attention Help students focus and pay attention Eliminate distractors Eliminate distractors Open “mental files” Open “mental files” Provide choices Provide choices Encourage self-directed learning Encourage self-directed learning

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You have 24 quarters, one of which is defective and weighs more than the others. You also have a balance scale that will tell you which of the two stacks of coins is heavier. It will not provide you information about the actual weight. How can you identify the heavy coin using the balance scale only three times? As you solve the problem, reflect on what you do before, during, and after. What kinds of core reasoning skills do you use?

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Good Instruction (Keep it Simple…Keep it Real) “Good instruction is good instruction, regardless of students’ racial, ethnic, or socioeconomic backgrounds. To a large extent, good teaching – teaching that is engaging, relevant, multicultural, and that appeals to a variety of modalities and learning styles – works well with ALL children.” Educating Everybody’s Children, ASCD, 1995.

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Teaching for Meaning Practices Positively Associated with Student Achievement Scores on the NAEP MathematicsScienceReadingCivics Problems that involve multiple solutions Hands-on activities Real-world problems Hands-on activities Hands-on activities Project- based learning Project- based learning Learning metacognitive skills Learning metacognitive skills Reading real books Reading real books Writing about literature Writing about literature Service learning Service learning Using the Internet Using the Internet

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Mathematics Strategies for Higher Student Achievement on NAEP Although basic skills have their place in pedagogy, critical thinking skills are essential. In math at both the 4th grade and 8th grade levels, practices that emphasize critical thinking skills are associated with higher student achievement. Although basic skills have their place in pedagogy, critical thinking skills are essential. In math at both the 4th grade and 8th grade levels, practices that emphasize critical thinking skills are associated with higher student achievement. Learning math is an interactive process, rather than a linear process in which students’ progress from simple fact to more complicated facts (McLaughlin & Talbert, 1993). Learning math is an interactive process, rather than a linear process in which students’ progress from simple fact to more complicated facts (McLaughlin & Talbert, 1993). Effective strategies in math included applications of higher order thinking skills, project-based learning, opportunities to solve problems that have multiple solutions, and such hands-on techniques as using manipulatives. Effective strategies in math included applications of higher order thinking skills, project-based learning, opportunities to solve problems that have multiple solutions, and such hands-on techniques as using manipulatives.

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Stool – 42 cm LaToya – 159 cm Shoulder – 135 cm Counter – 73 cm Silk – 108 cm 42 + 135 177 - 108 69 - 73 4 cm below

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Opportunity to Learn Three types of math curricula were identified by SIMS: Three types of math curricula were identified by SIMS: The Intended Curriculum: content specified by the state, division, or school at a particular grade level. The Intended Curriculum: content specified by the state, division, or school at a particular grade level. The Implemented Curriculum: content actually delivered by the teacher. The Implemented Curriculum: content actually delivered by the teacher. The Attained Curriculum: content actually learned by the students. The Attained Curriculum: content actually learned by the students. Intended Curriculum Implemented Curriculum Attained Curriculum Has the strongest relationship with student achievement of all school-level factors.

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7.6 The student will use proportions to solve practical problems, which may include scale drawings, that contain rational numbers (whole numbers, fractions, and decimals) and percents. UNDERSTANDING THE STANDARD (Teacher Notes) ESSENTIAL UNDERSTANDINGSESSENTIAL KNOWLEDGE AND SKILLS A proportion is a statement of equality between two ratios. A common property relates the numerators of the two ratios, and another common property relates the denominators of the two ratios. For example, both numerators relate to one property, such as length, while both denominators relate to another property, such as width. Alternatively, both numerators could relate to scale lengths, while both denominators relate to actual lengths. The dimensions of a scale model are proportional to the corresponding dimensions of the object (e.g., a blueprint of a house floor plan is proportional to the actual dimensions of the floor). All students should Understand that a proportion is an equation showing that two ratios are equal. Understand how to set up a proportion, given the relationship between two items. Understand that when two quantities are proportional, a change in one quantity corresponds to a predictable change in the other. Understand that proportions are useful in solving many types of problems. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Write proportions that represent equivalent relationships between two sets. Solve a proportion to find a missing term. Apply proportions to solve problems that involve percents. Apply proportions to solve practical problems, including scale drawings. Scale factors shall have denominators no greater than 12 and/or decimals no less than tenths.

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UNDERSTANDING THE STANDARD (Teacher Notes) A proportion can be written as =, a:b = c:d, or a is to b as c is to d. A proportion can be solved by finding the product of the means and the product of the extremes. For example, in the proportion a:b = c:d, a and d are the extremes and b and c are the means. If values are substituted for a, b, c, and d such as 5:12 = 10:24, then the product of extremes (5 24) is equal to the product of the means (12 10). In a proportional situation, both quantities increase or decrease together. In a proportional situation, two quantities increase multiplicatively. Both are multiplied by the same factor. A proportion can be solved by finding equivalent fractions. There is a distinction between a proportion and the idea of equivalent fractions. Equivalent fractions are symbols for the same quantity or amount and they represent the same rational number in different forms. A rate is a special ratio that always has a denominator of 1. Examples of rates include miles/hour and revolutions/minute. A rate compares measures of different types. A percent is a special ratio in which the denominator is 100. Proportions are used in every-day contexts, such as speed, recipe conversions, scale drawings, map reading, reducing and enlarging, comparison shopping, and monetary conversions.

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The Essential Virginia Toy Investigation The Essential Questions: If Barbie came to life, would Ken want to date her? If Ken came to life, would Barbie want to date him?

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Students with Disabilities in the General Education Classroom “…the percentage of students with disabilities placed in regular education classrooms for at least 80 percent of the day increased between 1988-89 and 1998-99…The largest increase occurred among students with specific learning disabilities (from 20 to 40 percent).” “…the percentage of students with disabilities placed in regular education classrooms for at least 80 percent of the day increased between 1988-89 and 1998-99…The largest increase occurred among students with specific learning disabilities (from 20 to 40 percent).” National Center for Education Statistics (NCES), The Condition of Education, 2002

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Instructional Strategies that Facilitate Successful Inclusion Must … Supply students with STRUCTURE and ORGANIZATION Supply students with STRUCTURE and ORGANIZATION Encourage student COMMUNICATION and COLLABORATION Encourage student COMMUNICATION and COLLABORATION Provide students with VISUAL and HANDS-ON learning experiences Provide students with VISUAL and HANDS-ON learning experiences

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“If an educator keeps using the same strategies over and over and the student keeps failing, “If an educator keeps using the same strategies over and over and the student keeps failing, who really is the slow learner?”

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MIND M ultiple I ntelligences N otetaking D esign Mathematics MathematicsSampleNotes The Sample Notes are provided by the talented teachers of mathematics from Prince Edward County Public Schools

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SOL 5.8 The student will describe and determine the perimeter of a polygon and the area of a square, rectangle, and right triangle, given the appropriate measures. Right MIND Notebook Page Right MIND Notebook Page The teacher provides the specific formulas that the students must know to meet the objective of the standard. The teacher provides the specific formulas that the students must know to meet the objective of the standard. Left MIND Notebook Page Left MIND Notebook Page Students process what he/she knows about the formulas using the activities provided by the teacher. Students process what he/she knows about the formulas using the activities provided by the teacher.

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SOL 6.13 The student will a)estimate angle measures, using 45 0, 90 0, and 180 0 as referents, and use the appropriate tools to measure the given angle. Right MIND Notebook Page Right MIND Notebook Page Teacher-provided notes (from the VA Curriculum Framework) Teacher-provided notes (from the VA Curriculum Framework) Student marking and note-taking. Student marking and note-taking. Left MIND Notebook Page Left MIND Notebook Page Students’ visual representations of notes. Students’ visual representations of notes.

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SOL 7.10 The student will identify and draw the following polygons: pentagon, hexagon, heptagon, octagon, nonagon, and decagon. Right MIND Notebook Page Right MIND Notebook Page Teacher-provided narrative of essential knowledge (from the VA Curriculum Framework) Teacher-provided narrative of essential knowledge (from the VA Curriculum Framework) Student underlining and highlighting key concepts Student underlining and highlighting key concepts Teacher-generated activities with hands-on materials (manipulating information) Teacher-generated activities with hands-on materials (manipulating information) Left MIND Notebook Page Left MIND Notebook Page Students drawings of presented essential knowledge Students drawings of presented essential knowledge Student application of presented skills Student application of presented skills

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Creating a Climate for Learning For students to succeed, they need to believe that they: can learn; are learning information and skills that is useful, relevant, and meaningful for them; are valued in the classroom; responsible for their learning; and responsible for their own behavior. “Teachers’ beliefs in and about human potential and in the ability of all children to learn and achieve are critical.” Caine & Caine, 1997

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A definition To differentiate instruction is to recognize students varying background knowledge, readiness, language, preferences in learning, interests and to react responsively. To differentiate instruction is to recognize students varying background knowledge, readiness, language, preferences in learning, interests and to react responsively.

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Reading Comprehension in Mathematics The Kroger Theorem

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Choice Board or Tic-Tac-Toe This assessment strategy allows students to select their own preferences but still achieve the targeted essential knowledge and skills. Algebra Choice Board Summarize the most important information about linear functions and put it to a beat. Draw the sequence of events to graph a linear equation on a timeline. Create a way to remember how to graph linear equations given in standard form. Reflect on the application of linear functions to something in your life in your journal. WILD CARD !!! Your choice after getting approval. Create a series of at least six cartoon frames to capture the most important information about linear fuctions. Condense the information about linear functions and create an advertisement, banner, or slogan. Act a short skit that conveys the life of a linear function. Write a poem that conveys the main ideas about linear functions.

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Thank you for your commitment to children! "It's your attitude, not just your aptitude that determines your ultimate altitude." -- Zig Ziglar Dan Simplyachieve@juno.com 757-754-5920

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