The document discusses several factors that have driven changes in mathematics education, including international assessments showing needs for improvement and shared standards developed by organizations like NCTM. It describes six principles for high-quality math education put forth by the NCTM, including equity, curriculum, teaching, learning, assessment, and technology. It also discusses the five content standards and five process standards from the NCTM, as well as the Common Core State Standards for Mathematics.

1. CHAPTER 1
Teaching Mathematics in the 21st
Century
Elementary and Middle School Mathematics
Teaching Developmentally
Ninth Edition
Van de Walle, Karp and Bay-Williams
Developed by E. Todd Brown /Professor Emeritus
University of Louisville

2. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-2
Changing World: Factors to Consider
International and national assessments
provide strong evidence that
mathematics teaching must change:
NAEP & TIMSS
•for our students to be competitive in
the global market
•for our students to be able to
understand the complex issues they
must confront as responsible citizens.

3. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-3
Movement Toward Shared
Standards
1980s response to “back to basics”
1989 NCTM published Curriculum and
Evaluation Standards for School Mathematics
1991 NCTM published Professional Standards
for Teaching Mathematics
2000 NCTM published Principles and
Standards for School Mathematics
2010 Common Core State Standards
initiative

4. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-4
PSSM guidance and direction
for teachers and leaders
Six principles fundamental to high-quality
mathematics education
Equity
Curriculum
Teaching
Learning
Assessment
Technology

5. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-5
The Equity Principle
Excellence in mathematics education
requires equity—high expectations and
strong support for all students.
(NCTM 2000, p. 12)

6. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-6
The Curriculum Principle
A curriculum is more than a collection of
activities: It must be coherent, focused on
important mathematics, and well
articulated across the grades. (NCTM
2000, p. 14)

7. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-7
The Teaching Principle
Effective mathematics teaching requires
understanding what students know and
need to learn and then challenging and
supporting them to learn it well. (NCTM
2000, p. 16)
Pause and reflect:
What teacher actions will best facilitate
students doing mathematics?

8. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-8
The Learning Principle
Students must learn mathematics with
understanding, actively building new
knowledge from experience and prior
knowledge. (NCTM 2000, p. 20)
Pause and reflect:
How were you given opportunities to
develop understanding of math?

9. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-9
The Assessment Principle
Assessment should support the learning
of important mathematics and furnish
useful information to both teachers and
students. (NCTM 2000, p. 22)

10. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-10
The Technology Principle
Technology is essential in teaching and
learning mathematics; it influences the
mathematics that is taught and enhances
students’ learning. (NCTM 2000, p. 24)
Pause and reflect:
How does technology enhance the
learning of mathematics?

11. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-11
The Five Content Standards
Numbers and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability

12. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-12
The Five Process Standards
Process standards direct the methods of
doing all mathematics (Table 1.1)
Problem Solving
Reasoning and Proof
Communication
Connection
Representation

13. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-13
Common Core State Standards
Common Core State Standards for Mathematics
(CSSM-M)
Standards for Mathematical Practice (Table 1.2)
•Longstanding important processes and proficiencies
•Teachers must develop these practices in all
students

14. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-14
Guiding Principles from NCTM
Principles to Action
Pause and reflect on these statements
•Use meaningful instructional tasks
•Provide instructional opportunities for
students to demonstrate their competence in
different ways
•Avoid thinking of a curriculum as a checklist
or disconnected set of daily lessons
•Consider the use of multiple assessments to
capture a variety of student abilities

15. Van de Walle, Karp, Bay-Williams, Elementary and Middle School
Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007,
2004 by Pearson Education, Inc. All Rights Reserved.
1-15
An Invitation to Learn and Grow
•Knowledge of Mathematics-profound,
flexible and adaptive knowledge
•Persistence-stave off frustration and
demonstrate persistence
•Positive attitude-changing attitudes toward
mathematics is easy
•Readiness for change-unlearn and relearn
mathematical concepts
•Life-Long learning-highly effective teachers
never “finish” learning