Elementary and Middle School Mathematics: Teaching Developmentally
11th Edition
by John Van de Walle, Karen Karp
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, TABLE OF CONTENT
PART I: Teaching Mathematics Developmentally: Big Ideas and Research-Based
Practices
Teaching to Build Confident and Competent Mathematics Learners
Exploring What It Means to Know and Do Mathematics
Teaching Problem-based Mathematics
Planning in the Problem-Based Classroom
Creating Assessments for Learning
Teaching Mathematics Equitably to All Students
PART II: Teaching Mathematics Developmentally: Concepts and Procedures in PreK-8
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Developing Early Number Concepts and Number Sense
Developing Meanings for the Operations
Developing Basic Fact Fluency
Developing Whole-Number Place-Value Concepts
Developing Strategies for Addition and Subtraction Computation
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Developing Strategies for Multiplication and Division Computation
Algebraic Thinking
Developing Fraction Concepts
Developing Fraction Operations
Developing Decimal and Percent Concepts and Decimal Computation
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Ratios and Proportional Reasoning
Developing Measurement Concepts
Developing Geometric Thinking and Geometric Concepts
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Developing Concepts of Data and Statistics
Exploring Concepts of Probability
Developing Concepts of Exponents, Negative Numbers, and Real Numbers
APPENDICES
Standards for Mathematical Practice
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NCTM Mathematics Teaching Practices from Principles to Actions
Guide to Blackline Masters
Activities at a Glance
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, All Chapters Included
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All Answers Included
Chapter 1 Developing Confident and Competent Mathematics
Learners
Chapter 1 Learning Outcome Quizzes
Learning Outcome 1.1: Summarize the factors that influence the teaching of mathematics
[Q1]
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Many factors influence how mathematics is taught in a school system and which mathematics is
covered. What are some of the most influential factors?
1. Research on how students learn mathematics [correct]
2. The size and wealth of the school system
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3. The students’ geographic location
4. Teacher’s opinions of students
[Feedback for Correct Answer 1]
Research in mathematics education on how students learn informs how mathematics should be
taught. Mathematics instruction is evolving and transforming through expert knowledge about
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how students learn and how to design effective mathematics instruction
[Feedback for Answer Choice 2]
The size and wealth of a school should not influence how mathematics is taught at that school.
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[Feedback for Answer Choice 3]
Geographic locations should not influence how mathematics is taught in that school.
[Feedback for Answer Choice 4]
Teacher’s opinions of students should not inform how mathematics is taught in the classroom.
Teachers should be using data and assessments to inform how their students are taught.
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[Q2]
Which of the following would be a strengths-based approach comment to a student?
1. The problems we are doing today are easy.
2. You picked up that concept really quickly. [correct]
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3. I think you need more practice with adding.
4. You can try harder next time with the task.
[Feedback for Answer Choice 1]
While you may think this statement might set students up for success, if students struggle with
the “easy” problems they may feel worse about themselves.
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[Feedback for Correct Answer 2]
This is an asset-based statement as it focuses on the strengths of the student, they got a
concept, rather than focusing on what they did not get or understand.
[Feedback for Answer Choice 3]
This statement could negatively affect students’ confidence in mathematics, especially if they
have been practicing with addition and are not having success.
[Feedback for Answer Choice 4]
This statement could negatively affect students’ confidence in mathematics, especially if they
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have been working hard on the task and are not having success.
[Q3]
Which statement describes a catalyst for change in mathematics education?
1. Developing a love of math in students.
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2. STEM jobs take twice as long to fill as other jobs.
3. U.S. student performance in national and international studies. [correct]
4. Preparing students for jobs that do not currently exist.
[Feedback for Answer Choice 1]
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While we want student to develop a love of mathematics, and we should work to create spaces
in our classrooms that foster this, it is not a driving force in what changes mathematics
education.
[Feedback for Answer Choice 2]
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While we want students to be successful in mathematics and pursue S TEM careers, especially
as there is a need for STEM majors, it is not a major influence in mathematics education.
[Feedback for Correct Answer 3]
One factor in mathematics education is the public or political pressure for change in
mathematics education due largely to information about student performance in national and
international studies. These large-scale comparisons of student performance continue to make
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headlines, provoke public opinion, and pressure legislatures to call for tougher standards
backed by testing.
[Feedback for Answer Choice 4]
We are preparing students for a global society and the jobs they take may not even exist yet,
but this is not a driving force in changing mathematics education.
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Learning Outcome 1.2: Describe the importance of content standards, process standards, and
standards of mathematical practice.
[Q1]
The six Principles and Standards for School Mathematics articulate high-quality mathematics
education. Which of the following statements represents the equity principle?
1. Mathematics instruction includes tasks that develop students’ ability to think and reason.
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