GV Middle School Mathematics
2014-15
Mrs. Susan Iocco
December 10, 2014
Characteristics of the “New” Standards
The Standards are:
● fewer and more rigorous than in the past.
● have increased clarity.
● aligned with college and career expectations.
● internationally benchmarked.
● designed to include rigorous content and application of
higher-order skills.
● researched based.
Some Key Terms
● Clarity and Specificity
○ Skills and concepts are clearly defined.
○ An ability to apply concepts and skills to new situations
is expected.
Some Key Terms
● Coherence
○ Instruction, assessment and curriculum are aligned.
○ Conceptual understanding and procedural skills are
equally stressed.
○ Progressions of topics and performances are
developmentally sound.
Some Key Terms
● Focus
○ Key ideas, understandings, and skills are identified.
○ Deep learning of concepts is emphasized.
○ Adequate time is devoted to a topic to counter the
“mile wide, inch deep” criticism leveled at most
current U.S. standards
Practice and Content Standards
Standards for Mathematical Practice
o 8 Practices
o Describe ways in which students ought to engage in
mathematics
Mathematical Content Standards
o 21- 26 Content Standards per grade
o Describe what students should understand and be able to do
Together they provide the “how” and “what” of mathematics
The Changes in the PA Standards
PDE has changed the focus of math from “mile wide, inch deep”
philosophy to a more focused, in-depth set of skills and concepts
at each grade level.
There is:
○ A shift in skills- greatest impact at grades 4, 5, and 6.
○ An expectation of mastery of skills (depth vs. breadth).
○ A drive for students to “explore and express” math
thoughts
Examples of Shifts in Mathematical Teaching
for All Grades
More emphasis at each grade on reasoning, problem solving,
modeling, decision making, and engagement.
More emphasis on connecting practice standards with content
standards at each grade
Examples of Shifts in ContentIntermediate Grades
More emphasis on:
● applying strategies and using properties
● relationships between and among shapes
● developing an understanding of geometric figures based
on their properties
● identifying patterns
● measuring with precision and purpose
● analyzing and solving problems based on data.
Examples of Shifts in ContentIntermediate Grades
Less emphasis on:
❏ Measuring in isolation
❏ Making measurement conversions outside of the context of a
problem solving situation
❏ Locating random points on the coordinate system
❏ Computing in isolation
Shifts in Emphasis
Shifts in Emphasis in Grade 6
Shifts in Emphasis for Grade 7
Shifts in Emphasis for Grade 8
Standards for Mathematical Practice: A Key Component
These eight Practice Standards are designed to help students internalize
concepts for a greater understanding of mathematics. They are the “habits of
mind” of a productive mathematical thinker.
1.
2.
3.
4.
5.
6.
7.
8.
Make sense out of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make sense of structure.
Look for and express regularity in repeated reasoning.
Big Ideas and The Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
❖ Multiple representations are presented to help the students move from
concrete to representative and into abstract thinking.
❖ Essential Questions help students focus and analyze.
❖ In Your Own Words provide opportunities for students to look meaning and
entry points to a problem.
Reason abstractly and quantitatively.
❖ Visual problem solving models help students create a coherent
representation of the problem.
❖ Opportunities for students to decontextualize and contextualize problems
are present in every lesson.
Big Ideas and The Standards for Mathematical Practice
Construct viable arguments and critique the reasoning of others.
❖ Error Analysis; Different Words, Same Question; and Which One Doesn’t
Belong features provide students the opportunity to construct arguments
and critique the reasoning of others.
❖ Inductive Reasoning activities help students make conjectures and build a
logical progression of statements to explore their conjecture.
Model with mathematics.
❖ Real-life situations are translated into diagrams, tables, equations, and
graphs to help students analyze relations and to draw conclusions.
❖ Real-life problems are provided to help students learn to apply the
mathematics they are learning to everyday life.
Big Ideas and The Standards for Mathematical Practice
Use appropriate tools strategically.
❖ Graphic Organizers support the thought process of what, when, and how
to solve problems.
❖ A variety of tools, such as graph paper, number lines, and manipulatives
are available as students consider how to approach a problem.
❖ Opportunities to use the web, graphing calculators, and spreadsheets
support student learning.
Attend to precision.
❖ On Your Own questions encourage students to formulate consistent and
appropriate reasoning.
❖ Cooperative learning opportunities support precise communication.
Big Ideas and The Standards for Mathematical Practice
Look for and make use of structure.
❖ Inductive Reasoning activities provide students the opportunity to see
patterns and structure in mathematics.
❖ Real-world problems help students use the structure of mathematics to
break down and solve more difficult problems.
Look for and express regularity in repeated reasoning.
❖ Opportunities are provided to help students make generalizations.
❖ Students are continually encouraged to check for reasonableness in their
solutions.
Our New Texts
Big Ideas Math
The Authors: Math Educators
Ron Larson
● Professor of Mathematics at Penn State Erie
● Ph.D in mathematics
● Lead author of a comprehensive program for mathematics that spans
middle school, high school, and college courses
● Is in constant touch with the needs of students and teachers through
numerous professional activities
The Authors: Math Educators
Laurie Boswell
●
●
●
●
Lead teacher of mathematics in Lyndonville, Vermont
Teacher of mathematics from elementary through college levels
Ed.D in Mathematics
Recipient of the Presidential Award for Excellence in Mathematics
Teaching
● Co-author of numerous math programs
About the Program
● Big Ideas is activity-based.
● There are less topics presented at a deeper level.
● There are opportunities for students to process
concepts in their own words.
● There are real world connections in every lesson.
● Essential Questions are presented to help students
focus and make connections.
● There are online resources for students, parents and
teachers
Parent/Student Components
Easy access to all components
through the Big Ideas Math website
https://www.bigideasmath.com/
● 24/7 online access to student text
● Parent online resources include:
o Parent letters for each chapter which include “At Home Activities”
o Basic Skills and Skills Review Handbooks
o History of the Standards initiatives
o A Game Closet