Reconceptualizing Mathematics
Fourth Edition ©2023 Judith Sowder; Larry Sowder; Susan Nickerson; Ian Whitacre Formats: Achieve, E-book, Print
As low as $70.99
As low as $70.99
- Product Overview
- Content Material
- Assessment
- Teaching Resources
- Reports and Insights
- Support and Services
Authors
-
Judith Sowder
Judith Sowder is a Professor Emerita of Mathematics and Statistics at San Diego State University. Her research has focused on the development of number sense and on the instructional effects of teachers mathematical knowledge at the elementary and middle school level. She served from 1996 to 2000 as editor of the Journal for Research in Mathematics Education and served a three-year term on the National Council of Teachers of Mathematics Board of Directors. She has directed numerous projects funded by the National Science Foundation and the Department of Education. In 2000 she received the Lifetime Achievement Award from the National Council of Teachers of Mathematics.
-
Larry Sowder
Larry Sowder is Professor Emeritus of Mathematics and Statistics at San Diego State University. He taught mathematics to preservice elementary school teachers for more than 30 years. His work in a special program in San Diego elementary schools also shaped his convictions about how courses in mathematics for preservice teachers should be pitched, as did his joint research investigating how children in the usual Grades 4-8 curriculum solve "story" problems. He served on teh National Research Council Committee that published Educating Teachers of Science, Mathematics, and Technology(NRC, 2001).
-
Susan Nickerson
Susan Nickerson is an Associate Professor in San Diego State Universitys Department of Mathematics and Statistics. Her research interest is long-term professional development of elementary and middle school teachers. In particular, her focus is describing, analyzing, and understanding effective contexts that promote teachers knowledge of mathematics and mathematics teaching.
-
Ian Whitacre
Ian Whitacre is an Associate Professor in Elementary Mathematics Education in the School of Teacher Education at Florida State University. He studies mathematical thinking and learning at the elementary and middle-school levels. He has also done extensive research specifically focused on preservice elementary teachers’ development of number sense. He regularly teaches courses for preservice elementary teachers and is always looking for ways to better support their learning.
Table of Contents
Chapter 1
Reasoning About Quantities
Goals for Reconceptualizing Mathematics
1.1 Ways of Thinking About Solving Story Problems
1.2 Quantitative Analysis
1.3 Problem Solving
1.4 Issues for Learning: Ways of Illustrating Story Problems
Review
Chapter 2
Numeration Systems
Goals for Reconceptualizing Mathematics
2.1 Ways of Expressing Values of Quantities
2.2 Place Value
2.3 Bases Other Than Ten
2.4 Operations in Different Bases
2.5 Issues for Learning: Understanding Place Value
Review
Chapter 3
Understanding Whole Number Operations
Goals for Reconceptualizing Mathematics
3.1 Ways of Thinking About Addition and Subtraction
3.2 Children’s Ways of Adding and Subtracting
3.3 Ways of Thinking About Multiplication
3.4 Ways of Thinking About Division
3.5 Children Find Products and Quotients
3.6 Issues for Learning: Developing Number Sense
Review
Chapter 4
Some Conventional Ways of Computing
Goals for Reconceptualizing Mathematics
4.1 Addition and Subtraction on Whole Numbers and Decimal Numbers
4.2 Issues for Learning: The Role of Algorithms
Review
Chapter 5
Using Numbers in Sensible Ways
Goals for Reconceptualizing Mathematics
5.1 Mental Computation
5.2 Computational Estimation
5.3 Estimating Values of Quantities
5.4 Using Scientific Notation for Estimating Values of Very Large and Very Small Quantities
5.5 Issues for Learning: Mental Computation
Review
Chapter 6
Meanings for Fractions
Goals for Reconceptualizing Mathematics
6.1 Understanding the Meanings of
6.2 Comparing Fractions
6.3 Equivalent (Equal) Fractions
6.4 Relating Fractions, Decimals, and Percentages
6.5 Issues for Learning: Understanding Fractions and Decimals
Review
Chapter 7
Making Sense of Fraction Operations
Goals for Reconceptualizing Mathematics
7.1 Problem Solving with Fractions
7.2 Making Sense of Addition and Subtraction of Fractions
7.3 Making Sense of Multiplication of Fraction
7.4 Making Sense of Division of Fractions
7.5 Issues for Learning: Teaching Fraction Operations Review
Review
Chapter 8
Multiplicative Comparisons and Multiplicative Reasoning
Goals for Reconceptualizing Mathematics
8.1 Quantitative Analysis of Multiplicative Situations
8.2 Fractions in Multiplicative Comparisons
8.3 Issues for Learning: Standards for Learning
Review
Chapter 9
Ratios, Rates, Proportions, and Percentages
Goals for Reconceptualizing Mathematics
9.1 Ratio as a Measure
9.2 Comparing Ratios
9.3 Percentages in Comparisons and Changes
9.4 Issues for Learning: Developing Proportional Reasoning
Review
Chapter 10
Integers and Other Number Systems
Goals for Reconceptualizing Mathematics
10.1 Big Ideas About Signed Numbers
10.2 Children’s Ways of Reasoning About Signed Numbers
10.3 Other Models for Signed Numbers
10.4 Operations with Signed Numbers
10.5 Multiplying and Dividing Signed Numbers
10.6 Number Systems
10.7 Issues for Learning: Open Number Sentences
Review
Chapter 11
Number Theory
Goals for Reconceptualizing Mathematics
11.1 Factors and Multiples, Primes and Composites
11.2 Prime Factorization
11.3 Divisibility Tests to Determine Whether a Number Is Prime
11.4 Greatest Common Factor, Least Common Multiple
11.5 Issues for Learning: Understanding the Unique Factorization Theorem
Review
Part II Reasoning About Algebra and Change
Chapter 12
What Is Algebra?
Goals for Reconceptualizing Mathematics
12.1 Algebraic Reasoning in Elementary School
12.2 Numerical Patterns and Algebra
12.3 Functions and Algebra
12.4 Algebra as Generalized Arithmetic
12.5 Algebraic Reasoning About Quantities
12.6 Issues for Learning: The National Assessment of Educational Progress and Achievement in Algebra
Review
Chapter 13
A Quantitative Approach to Algebra and Graphing
Goals for Reconceptualizing Mathematics
13.1 Using Graphs and Algebra to Show Quantitative Relationships
13.2 Understanding Slope: Making Connections Across Quantitative Situations, Graphs, and Algebraic Equations
13.3 Linear Functions and Proportional Relationships
13.4 Nonlinear Functions
13.5 Issues for Learning: Algebra in the Elementary Grades
Review
Chapter 14
Understanding Change: Relationships Among Time, Distance, and Rate
Goals for Reconceptualizing Mathematics
14.1 Distance–Time and Position–Time Graphs
14.2 Using Motion Detectors
14.3 Graphs of Speed Against Time
14.4 Interpreting Graphs
14.5 Issues for Learning: Common Graphing Errors
Review
Chapter 15
Further Topics in Algebra and Change
Goals for Reconceptualizing Mathematics
15.1 Finding Linear Equations
15.2 Solving Two Linear Equations in Two Variables
15.3 Different Approaches to Problems
15.4 Average Speed and Weighted Averages
15.5 More About Functions
15.6 Issues for Learning: Topics in Algebra
Review
PART III Reasoning About Shapes and Measurement
Chapter 16
Polygons
Goals for Reconceptualizing Mathematics
16.1 Review of Polygon Vocabulary
16.2 Organizing Shapes
16.3 Triangles and Quadrilaterals
16.4 A Focus on Problem-Solving Strategies
16.5 Issues for Learning: Some Research on Two-Dimensional Shapes
Review
Chapter 17
Polyhedra
Goals for Reconceptualizing Mathematics
17.1 Shoeboxes Have Faces and Nets!
17.2 Introduction to Polyhedra
17.3 Representing and Visualizing Polyhedra
17.4 Congruent Polyhedra
17.5 Some Special Polyhedra
17.6 Issues for Learning: Dealing with 3D Shapes
Review
Chapter 18
Symmetry
Goals for Reconceptualizing Mathematics
18.1 Symmetry of Shapes in a Plane
18.2 Symmetry of Polyhedra
18.3 Issues for Learning: What Is Geometry in the Pre-K–8 Curriculum?
Review
Chapter 19
Tessellations
Goals for Reconceptualizing Mathematics
19.1 Tessellating the Plane
19.2 Tessellating Space
Review
Chapter 20
Similarity
Goals for Reconceptualizing Mathematics
20.1 Similarity and Dilations in Planar Figures
20.2 More About Similar Figures
20.3 Similarity in 3D Figures
20.4 Issues for Learning: Similarity and Proportional Reasoning
Review
Chapter 21
Curves, Constructions, and Curved Surfaces
Goals for Reconceptualizing Mathematics
21.1 Planar Curves and Constructions
21.2 Curved Surfaces
21.3 Issues for Learning: Standards for Mathematical Practice
Review
Chapter 22
Transformation Geometry
Goals for Reconceptualizing Mathematics
22.1 Some Types of Rigid Motions
22.2 Finding Images for Rigid Motions
22.3 A Closer Look at Some Rigid Motions
22.4 Composition of Rigid Motions
22.5 Transformations and Earlier Topics
22.6 Issues for Learning: Promoting Visualization in the Curriculum
Review
Chapter 23
Measurement Basics
Goals for Reconceptualizing Mathematics
23.1 Conceptualizing and Measuring Length
23.2 Key Ideas of Measurement
23.3 Conceptualizing and Measuring Angle
23.4 Further Exploration of Angles
23.5 Issues for Learning: Measurement of Length and Angle Size
Review
Chapter 24
Area, Surface Area, and Volume
Goals for Reconceptualizing Mathematics
24.1 Area and Surface Area
24.2 Volume
24.3 Issues for Learning: Measurement of Area and Volume
Review
Chapter 25
Counting Units Fast: Measurement Formulas
Goals for Reconceptualizing Mathematics
25.1 Circumference, Area, and Surface Area Formulas
25.2 Volume Formulas
25.3 Issues for Learning: What Measurement Topics Are in the Curriculum?
Review
Chapter 26
Special Topics in Measurement
Goals for Reconceptualizing Mathematics
26.1 The Pythagorean Theorem
26.2 Some Other Kinds of Measurements
Review
PART IV Reasoning About Chance and Data
Chapter 27
Quantifying Uncertainty
Goals for Reconceptualizing Mathematics
27.1 Understanding Chance Events
27.2 Methods of Assigning Probabilities
27.3 Simulating Probabilistic Situations
27.4 Issues for Learning: Research on the Understanding of Probability
Review
Chapter 28
Determining More Complicated Probabilities
Goals for Reconceptualizing Mathematics
28.1 Tree Diagrams and Lists for Multistep Experiments
28.2 Probability of One Event or Another Event
28.3 Probability of One Event and Another Event
28.4 Conditional Probability
28.5 Issues for Learning: What Does it Mean to Understand Probability?
Review
Chapter 29
Introduction to Statistics and Sampling
Goals for Reconceptualizing Mathematics
29.1 What Are Statistics?
29.2 Sampling: The Why and the How
29.3 Simulating Random Sampling
29.4 Types of Data
29.5 Conducting a Survey
29.6 Issues for Learning: Sampling
Review
Chapter 30
Representing and Interpreting Data with One Variable
Goals for Reconceptualizing Mathematics
30.1 Representing Categorical Data
30.2 Representing and Interpreting Measurement Data
30.3 Examining the Spread of Data
30.4 Measures of Center
30.5 Deviations from the Mean as Measures of Spread
30.6 Examining Distributions
30.7 Issues for Learning: Understanding the Mean
Review
Chapter 31
Dealing with Multiple Data Sets or with Multiple Variables
Goals for Reconceptualizing Mathematics
31.1 Comparing Data Sets
31.2 Lines of Best Fit and Correlation
31.3 Issues for Learning: More Than One Variable
Review
Chapter 32
Variability in Samples
Goals for Reconceptualizing Mathematics
32.1 Having Confidence in a Sample Statistic
32.2 Confidence Intervals
32.3 Issues for Learning: What Probability and Statistics Should Be in the Curriculum?
Review
Chapter 33
Special Topics in Probability
Goals for Reconceptualizing Mathematics
33.1 Expected Value
33.2 Permutations and Combinations
33.3 Issues for Learning: Children Finding Permutations
Review
Product Updates
- NEW! All online resources, assessment and e-book housed in Achieve.
- Increased use of technology throughout. This includes links to external sites or to newly developed digital manipulatives with Desmos or Geogebra.
- Increased focus on in-class activities, adding more depth to current activities. Select Discussions and Activities from the text have been adapted to Instructor Activity Guides, housed online in Achieve.
- Within Chapter 4 Some Conventional Ways of Computing, sections have been created to separate addition and subtraction (Section 4.1) and multiplication and division (Section 4.2). Chapter 4’s Issues for Learning feature deepens the discussion of the Role of Algorithms, emphasizing the importance of understanding the standard algorithms conceptually.
- New activities and interactives added for the following chapters:
- Chapter 7 Making Sense of Fraction Operations
- Chapter 15 Further Topics in Algebra and Change
- Chapter 22 Transformation Geometry
- Chapter 23 Measurement Basics
- Chapter 28 Determining More Complicated Probabilities
Authors
-
Judith Sowder
Judith Sowder is a Professor Emerita of Mathematics and Statistics at San Diego State University. Her research has focused on the development of number sense and on the instructional effects of teachers mathematical knowledge at the elementary and middle school level. She served from 1996 to 2000 as editor of the Journal for Research in Mathematics Education and served a three-year term on the National Council of Teachers of Mathematics Board of Directors. She has directed numerous projects funded by the National Science Foundation and the Department of Education. In 2000 she received the Lifetime Achievement Award from the National Council of Teachers of Mathematics.
-
Larry Sowder
Larry Sowder is Professor Emeritus of Mathematics and Statistics at San Diego State University. He taught mathematics to preservice elementary school teachers for more than 30 years. His work in a special program in San Diego elementary schools also shaped his convictions about how courses in mathematics for preservice teachers should be pitched, as did his joint research investigating how children in the usual Grades 4-8 curriculum solve "story" problems. He served on teh National Research Council Committee that published Educating Teachers of Science, Mathematics, and Technology(NRC, 2001).
-
Susan Nickerson
Susan Nickerson is an Associate Professor in San Diego State Universitys Department of Mathematics and Statistics. Her research interest is long-term professional development of elementary and middle school teachers. In particular, her focus is describing, analyzing, and understanding effective contexts that promote teachers knowledge of mathematics and mathematics teaching.
-
Ian Whitacre
Ian Whitacre is an Associate Professor in Elementary Mathematics Education in the School of Teacher Education at Florida State University. He studies mathematical thinking and learning at the elementary and middle-school levels. He has also done extensive research specifically focused on preservice elementary teachers’ development of number sense. He regularly teaches courses for preservice elementary teachers and is always looking for ways to better support their learning.
Table of Contents
Chapter 1
Reasoning About Quantities
Goals for Reconceptualizing Mathematics
1.1 Ways of Thinking About Solving Story Problems
1.2 Quantitative Analysis
1.3 Problem Solving
1.4 Issues for Learning: Ways of Illustrating Story Problems
Review
Chapter 2
Numeration Systems
Goals for Reconceptualizing Mathematics
2.1 Ways of Expressing Values of Quantities
2.2 Place Value
2.3 Bases Other Than Ten
2.4 Operations in Different Bases
2.5 Issues for Learning: Understanding Place Value
Review
Chapter 3
Understanding Whole Number Operations
Goals for Reconceptualizing Mathematics
3.1 Ways of Thinking About Addition and Subtraction
3.2 Children’s Ways of Adding and Subtracting
3.3 Ways of Thinking About Multiplication
3.4 Ways of Thinking About Division
3.5 Children Find Products and Quotients
3.6 Issues for Learning: Developing Number Sense
Review
Chapter 4
Some Conventional Ways of Computing
Goals for Reconceptualizing Mathematics
4.1 Addition and Subtraction on Whole Numbers and Decimal Numbers
4.2 Issues for Learning: The Role of Algorithms
Review
Chapter 5
Using Numbers in Sensible Ways
Goals for Reconceptualizing Mathematics
5.1 Mental Computation
5.2 Computational Estimation
5.3 Estimating Values of Quantities
5.4 Using Scientific Notation for Estimating Values of Very Large and Very Small Quantities
5.5 Issues for Learning: Mental Computation
Review
Chapter 6
Meanings for Fractions
Goals for Reconceptualizing Mathematics
6.1 Understanding the Meanings of
6.2 Comparing Fractions
6.3 Equivalent (Equal) Fractions
6.4 Relating Fractions, Decimals, and Percentages
6.5 Issues for Learning: Understanding Fractions and Decimals
Review
Chapter 7
Making Sense of Fraction Operations
Goals for Reconceptualizing Mathematics
7.1 Problem Solving with Fractions
7.2 Making Sense of Addition and Subtraction of Fractions
7.3 Making Sense of Multiplication of Fraction
7.4 Making Sense of Division of Fractions
7.5 Issues for Learning: Teaching Fraction Operations Review
Review
Chapter 8
Multiplicative Comparisons and Multiplicative Reasoning
Goals for Reconceptualizing Mathematics
8.1 Quantitative Analysis of Multiplicative Situations
8.2 Fractions in Multiplicative Comparisons
8.3 Issues for Learning: Standards for Learning
Review
Chapter 9
Ratios, Rates, Proportions, and Percentages
Goals for Reconceptualizing Mathematics
9.1 Ratio as a Measure
9.2 Comparing Ratios
9.3 Percentages in Comparisons and Changes
9.4 Issues for Learning: Developing Proportional Reasoning
Review
Chapter 10
Integers and Other Number Systems
Goals for Reconceptualizing Mathematics
10.1 Big Ideas About Signed Numbers
10.2 Children’s Ways of Reasoning About Signed Numbers
10.3 Other Models for Signed Numbers
10.4 Operations with Signed Numbers
10.5 Multiplying and Dividing Signed Numbers
10.6 Number Systems
10.7 Issues for Learning: Open Number Sentences
Review
Chapter 11
Number Theory
Goals for Reconceptualizing Mathematics
11.1 Factors and Multiples, Primes and Composites
11.2 Prime Factorization
11.3 Divisibility Tests to Determine Whether a Number Is Prime
11.4 Greatest Common Factor, Least Common Multiple
11.5 Issues for Learning: Understanding the Unique Factorization Theorem
Review
Part II Reasoning About Algebra and Change
Chapter 12
What Is Algebra?
Goals for Reconceptualizing Mathematics
12.1 Algebraic Reasoning in Elementary School
12.2 Numerical Patterns and Algebra
12.3 Functions and Algebra
12.4 Algebra as Generalized Arithmetic
12.5 Algebraic Reasoning About Quantities
12.6 Issues for Learning: The National Assessment of Educational Progress and Achievement in Algebra
Review
Chapter 13
A Quantitative Approach to Algebra and Graphing
Goals for Reconceptualizing Mathematics
13.1 Using Graphs and Algebra to Show Quantitative Relationships
13.2 Understanding Slope: Making Connections Across Quantitative Situations, Graphs, and Algebraic Equations
13.3 Linear Functions and Proportional Relationships
13.4 Nonlinear Functions
13.5 Issues for Learning: Algebra in the Elementary Grades
Review
Chapter 14
Understanding Change: Relationships Among Time, Distance, and Rate
Goals for Reconceptualizing Mathematics
14.1 Distance–Time and Position–Time Graphs
14.2 Using Motion Detectors
14.3 Graphs of Speed Against Time
14.4 Interpreting Graphs
14.5 Issues for Learning: Common Graphing Errors
Review
Chapter 15
Further Topics in Algebra and Change
Goals for Reconceptualizing Mathematics
15.1 Finding Linear Equations
15.2 Solving Two Linear Equations in Two Variables
15.3 Different Approaches to Problems
15.4 Average Speed and Weighted Averages
15.5 More About Functions
15.6 Issues for Learning: Topics in Algebra
Review
PART III Reasoning About Shapes and Measurement
Chapter 16
Polygons
Goals for Reconceptualizing Mathematics
16.1 Review of Polygon Vocabulary
16.2 Organizing Shapes
16.3 Triangles and Quadrilaterals
16.4 A Focus on Problem-Solving Strategies
16.5 Issues for Learning: Some Research on Two-Dimensional Shapes
Review
Chapter 17
Polyhedra
Goals for Reconceptualizing Mathematics
17.1 Shoeboxes Have Faces and Nets!
17.2 Introduction to Polyhedra
17.3 Representing and Visualizing Polyhedra
17.4 Congruent Polyhedra
17.5 Some Special Polyhedra
17.6 Issues for Learning: Dealing with 3D Shapes
Review
Chapter 18
Symmetry
Goals for Reconceptualizing Mathematics
18.1 Symmetry of Shapes in a Plane
18.2 Symmetry of Polyhedra
18.3 Issues for Learning: What Is Geometry in the Pre-K–8 Curriculum?
Review
Chapter 19
Tessellations
Goals for Reconceptualizing Mathematics
19.1 Tessellating the Plane
19.2 Tessellating Space
Review
Chapter 20
Similarity
Goals for Reconceptualizing Mathematics
20.1 Similarity and Dilations in Planar Figures
20.2 More About Similar Figures
20.3 Similarity in 3D Figures
20.4 Issues for Learning: Similarity and Proportional Reasoning
Review
Chapter 21
Curves, Constructions, and Curved Surfaces
Goals for Reconceptualizing Mathematics
21.1 Planar Curves and Constructions
21.2 Curved Surfaces
21.3 Issues for Learning: Standards for Mathematical Practice
Review
Chapter 22
Transformation Geometry
Goals for Reconceptualizing Mathematics
22.1 Some Types of Rigid Motions
22.2 Finding Images for Rigid Motions
22.3 A Closer Look at Some Rigid Motions
22.4 Composition of Rigid Motions
22.5 Transformations and Earlier Topics
22.6 Issues for Learning: Promoting Visualization in the Curriculum
Review
Chapter 23
Measurement Basics
Goals for Reconceptualizing Mathematics
23.1 Conceptualizing and Measuring Length
23.2 Key Ideas of Measurement
23.3 Conceptualizing and Measuring Angle
23.4 Further Exploration of Angles
23.5 Issues for Learning: Measurement of Length and Angle Size
Review
Chapter 24
Area, Surface Area, and Volume
Goals for Reconceptualizing Mathematics
24.1 Area and Surface Area
24.2 Volume
24.3 Issues for Learning: Measurement of Area and Volume
Review
Chapter 25
Counting Units Fast: Measurement Formulas
Goals for Reconceptualizing Mathematics
25.1 Circumference, Area, and Surface Area Formulas
25.2 Volume Formulas
25.3 Issues for Learning: What Measurement Topics Are in the Curriculum?
Review
Chapter 26
Special Topics in Measurement
Goals for Reconceptualizing Mathematics
26.1 The Pythagorean Theorem
26.2 Some Other Kinds of Measurements
Review
PART IV Reasoning About Chance and Data
Chapter 27
Quantifying Uncertainty
Goals for Reconceptualizing Mathematics
27.1 Understanding Chance Events
27.2 Methods of Assigning Probabilities
27.3 Simulating Probabilistic Situations
27.4 Issues for Learning: Research on the Understanding of Probability
Review
Chapter 28
Determining More Complicated Probabilities
Goals for Reconceptualizing Mathematics
28.1 Tree Diagrams and Lists for Multistep Experiments
28.2 Probability of One Event or Another Event
28.3 Probability of One Event and Another Event
28.4 Conditional Probability
28.5 Issues for Learning: What Does it Mean to Understand Probability?
Review
Chapter 29
Introduction to Statistics and Sampling
Goals for Reconceptualizing Mathematics
29.1 What Are Statistics?
29.2 Sampling: The Why and the How
29.3 Simulating Random Sampling
29.4 Types of Data
29.5 Conducting a Survey
29.6 Issues for Learning: Sampling
Review
Chapter 30
Representing and Interpreting Data with One Variable
Goals for Reconceptualizing Mathematics
30.1 Representing Categorical Data
30.2 Representing and Interpreting Measurement Data
30.3 Examining the Spread of Data
30.4 Measures of Center
30.5 Deviations from the Mean as Measures of Spread
30.6 Examining Distributions
30.7 Issues for Learning: Understanding the Mean
Review
Chapter 31
Dealing with Multiple Data Sets or with Multiple Variables
Goals for Reconceptualizing Mathematics
31.1 Comparing Data Sets
31.2 Lines of Best Fit and Correlation
31.3 Issues for Learning: More Than One Variable
Review
Chapter 32
Variability in Samples
Goals for Reconceptualizing Mathematics
32.1 Having Confidence in a Sample Statistic
32.2 Confidence Intervals
32.3 Issues for Learning: What Probability and Statistics Should Be in the Curriculum?
Review
Chapter 33
Special Topics in Probability
Goals for Reconceptualizing Mathematics
33.1 Expected Value
33.2 Permutations and Combinations
33.3 Issues for Learning: Children Finding Permutations
Review
Product Updates
- NEW! All online resources, assessment and e-book housed in Achieve.
- Increased use of technology throughout. This includes links to external sites or to newly developed digital manipulatives with Desmos or Geogebra.
- Increased focus on in-class activities, adding more depth to current activities. Select Discussions and Activities from the text have been adapted to Instructor Activity Guides, housed online in Achieve.
- Within Chapter 4 Some Conventional Ways of Computing, sections have been created to separate addition and subtraction (Section 4.1) and multiplication and division (Section 4.2). Chapter 4’s Issues for Learning feature deepens the discussion of the Role of Algorithms, emphasizing the importance of understanding the standard algorithms conceptually.
- New activities and interactives added for the following chapters:
- Chapter 7 Making Sense of Fraction Operations
- Chapter 15 Further Topics in Algebra and Change
- Chapter 22 Transformation Geometry
- Chapter 23 Measurement Basics
- Chapter 28 Determining More Complicated Probabilities
Reconceptualizing Mathematics, founded on research and studies of mathematics teaching and learning, promotes an active experience in learning by doing in math. The esteemed author team has written the only textbook of its kind to both incorporate aspects of student-centered learning into lessons and model the teaching that will be expected of their students. This active approach is brought to life online in Achieve with flexible tools like hands-on activity guides, Desmos-powered interactives, and a variety of assessment types designed to coach students toward a deeper conceptual understanding.
Success Stories
Here are a few examples of how Achieve has helped instructors like you improve student preparedness, enhance their sense of belonging, and achieve course goals they set for themselves.
Prof. Kiandra Johnson, Spelman College
See how the resources in Achieve help you engage students before, during, and after class.
Prof. Jennifer Duncan
Use diagnostics in Achieve for a snapshot into cognitive and non-cognitive factors that may impact your students’ preparedness.
Prof. Ryan Elsenpeter
Here’s why educators who use Achieve would recommend it to their peers.
Looking for instructor resources like Test Banks, Lecture Slides, and Clicker Questions? Request access to Achieve to explore the full suite of instructor resources.
Instructor Resources
Instructor Resources
Access Test Bank
You need to sign in as a verified instructor to access the Test Bank.
Test Bank for Reconceptualizing Mathematics 4e
Judith Sowder; Larry Sowder; Susan Nickerson; Ian Whitacre | Fourth Edition | ©2023 | ISBN:9781319508913
You've selected:
Click the E-mail Download Link button and we'll send you an e-mail at with links to download your instructor resources. Please note there may be a delay in delivering your e-mail depending on the size of the files.
Warning! These materials are owned by Macmillan Learning or its licensors and are protected by copyright laws in the United States and other jurisdictions. Such materials may include a digital watermark that is linked to your name and email address in your Macmillan Learning account to identify the source of any materials used in an unauthorised way and prevent online piracy. These materials are being provided solely for instructional use by instructors who have adopted Macmillan Learning’s accompanying textbooks or online products for use by students in their courses. These materials may not be copied, distributed, sold, shared, posted online, or used, in print or electronic format, except in the limited circumstances set forth in the Macmillan Learning Terms of Use and any other reproduction or distribution is illegal. These materials may not be made publicly available under any circumstances. All other rights reserved. For more information about the use of your personal data including for the purposes of anti-piracy enforcement, please refer to Macmillan Learning's.Privacy Notice
Thank you!
Your download request has been received and your download link will be sent to .
Please note you could wait up to 30 to 60 minutes to receive your download e-mail depending on the number and size of the files. We appreciate your patience while we process your request.
Check your inbox, trash, and spam folders for an e-mail from InstructorResources@macmillan.com.
If you do not receive your e-mail, please visit macmillanlearning.com/support.
FAQs
-
-
Are you a campus bookstore looking for ordering information?
MPS Order Search Tool (MOST) is a web-based purchase order tracking program that allows customers to view and track their purchases. No registration or special codes needed! Just enter your BILL-TO ACCT # and your ZIP CODE to track orders.
Canadian Stores: Please use only the first five digits/letters in your zip code on MOST.
Visit MOST, our online ordering system for booksellers: https://tracking.mpsvirginia.com/Login.aspx
Learn more about our Bookstore programs here: https://www.macmillanlearning.com/college/us/contact-us/booksellers
-
-
-
Our courses currently integrate with Canvas, Blackboard (Learn and Ultra), Brightspace, D2L, and Moodle. Click on the support documentation below to find out more details about the integration with each LMS.
Integrate Macmillan courses with Blackboard
Integrate Macmillan courses with Canvas
-
-
-
If you’re a verified instructor, you can request a free sample of our courseware, e-book, or print textbook to consider for use in your courses. Only registered and verified instructors can receive free print and digital samples, and they should not be sold to bookstores or book resellers. If you don't yet have an existing account with Macmillan Learning, it can take up to two business days to verify your status as an instructor. You can request a free sample from the right side of this product page by clicking on the "Request Instructor Sample" button or by contacting your rep. Learn more.
-
-
-
Sometimes also referred to as a spiral-bound or binder-ready textbook, loose-leaf textbooks are available to purchase. This three-hole punched, unbound version of the book costs less than a hardcover or paperback book.
-
-
-
Achieve (full course) includes our complete e-book, as well as online quizzing tools, multimedia assets, and iClicker active classroom manager.
Most Achieve Essentials courses do not include our e-books and adaptive quizzing.
Visit our comparison table for details: https://www.macmillanlearning.com/college/us/digital/achieve/compare
-
-
-
Achieve (full course) includes our complete e-book, as well as online quizzing tools, multimedia assets, and iClicker active classroom manager.
Achieve Read & Practice only includes our e-book and adaptive quizzing, and does not include instructor resources and assignable assessments. Read & Practice does integrate with LMS.
Visit our comparison table for details: https://www.macmillanlearning.com/college/us/digital/achieve/compare
-
-
-
We can help! Contact your representative to discuss your specific needs for your course. If our off-the-shelf course materials don’t quite hit the mark, we also offer custom solutions made to fit your needs.
-
ISBN:9781319483050
Access all your course tools in one place!
ISBN:9781319483135
Take notes, add highlights, and download our mobile-friendly e-books.
ISBN:9781319303730
Save money with our hole-punched, loose-leaf textbook.
ISBN:9781319499280
This package includes Achieve and Loose-Leaf.
FAQs
-
-
Are you a campus bookstore looking for ordering information?
MPS Order Search Tool (MOST) is a web-based purchase order tracking program that allows customers to view and track their purchases. No registration or special codes needed! Just enter your BILL-TO ACCT # and your ZIP CODE to track orders.
Canadian Stores: Please use only the first five digits/letters in your zip code on MOST.
Visit MOST, our online ordering system for booksellers: https://tracking.mpsvirginia.com/Login.aspx
Learn more about our Bookstore programs here: https://www.macmillanlearning.com/college/us/contact-us/booksellers
-
-
-
Our courses currently integrate with Canvas, Blackboard (Learn and Ultra), Brightspace, D2L, and Moodle. Click on the support documentation below to find out more details about the integration with each LMS.
Integrate Macmillan courses with Blackboard
Integrate Macmillan courses with Canvas
-
-
-
If you’re a verified instructor, you can request a free sample of our courseware, e-book, or print textbook to consider for use in your courses. Only registered and verified instructors can receive free print and digital samples, and they should not be sold to bookstores or book resellers. If you don't yet have an existing account with Macmillan Learning, it can take up to two business days to verify your status as an instructor. You can request a free sample from the right side of this product page by clicking on the "Request Instructor Sample" button or by contacting your rep. Learn more.
-
-
-
Sometimes also referred to as a spiral-bound or binder-ready textbook, loose-leaf textbooks are available to purchase. This three-hole punched, unbound version of the book costs less than a hardcover or paperback book.
-
-
-
Achieve (full course) includes our complete e-book, as well as online quizzing tools, multimedia assets, and iClicker active classroom manager.
Most Achieve Essentials courses do not include our e-books and adaptive quizzing.
Visit our comparison table for details: https://www.macmillanlearning.com/college/us/digital/achieve/compare
-
-
-
Achieve (full course) includes our complete e-book, as well as online quizzing tools, multimedia assets, and iClicker active classroom manager.
Achieve Read & Practice only includes our e-book and adaptive quizzing, and does not include instructor resources and assignable assessments. Read & Practice does integrate with LMS.
Visit our comparison table for details: https://www.macmillanlearning.com/college/us/digital/achieve/compare
-
-
-
We can help! Contact your representative to discuss your specific needs for your course. If our off-the-shelf course materials don’t quite hit the mark, we also offer custom solutions made to fit your needs.
-
Reconceptualizing Mathematics
Reconceptualizing Mathematics, founded on research and studies of mathematics teaching and learning, promotes an active experience in learning by doing in math. The esteemed author team has written the only textbook of its kind to both incorporate aspects of student-centered learning into lessons and model the teaching that will be expected of their students. This active approach is brought to life online in Achieve with flexible tools like hands-on activity guides, Desmos-powered interactives, and a variety of assessment types designed to coach students toward a deeper conceptual understanding.
These materials are owned by Macmillan Learning or its licensors and are protected by United States copyright law. They are being provided solely for evaluation purposes only by instructors who are considering adopting Macmillan Learning's textbooks or online products for use by students in their courses. These materials may not be copied, distributed, sold, shared, posted online, or used, in print or electronic format, except in the limited circumstances set forth in the Macmillan Learning Terms of Use and any other reproduction or distribution is illegal. These materials may not be made publicly available under any circumstances. All other rights reserved. © 2020 Macmillan Learning.
BY CLICKING ON THE SAMPLE CHAPTER LINK BELOW, YOU ARE AGREEING TO USE THESE MATERIALS ONLY IN ACCORDANCE WITH MACMILLAN LEARNING'S TERMS OF USE.
Select a file to view:
Sample Achieve