Transcript Mathematics for College Success/Readiness Courses

CONNECTIONS 2012
Mathematics for College
Success/Readiness Courses
Jennifer Winchester
Florida Department of Education
Teaching Channel video explains
key features of the Common Core
Math Standards
The Teaching Channel has developed a 14-minute
video about the key features and differences of the
Common Core math standards:
https://www.teachingchannel.org/videos/commoncore-state-standards-for-math?fd=1
The video discusses the purpose of the standards for
mathematical practice and how these should be
integrated with the content; how teaching fewer topics
in each grade changes planning; and, how the
standards can help in closing the achievement gap. It
is an easy-to-understand introduction that can be used
to explain the new Math Common Core Standards to a
general audience.
Features of the Standards
• Standards for Mathematical Practice
– Outline the expertise and habits of mind that should be
developed in all students
• Standards for Mathematical Content
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–
–
–
K-8 standards presented by grade level
High school standards presented by conceptual theme
Aligned with college and work expectations
Focused and coherent
• Focus: doing fewer things at any given grade so that
students have time to internalize, practice, and learn what is
being done in that grade
3
Standards for Mathematical Practice
“The Standards for Mathematical
Practice describe varieties of
expertise that mathematics
educators at all levels should
seek to develop in their students.
These practices rest on
important ‘processes and
proficiencies’ with longstanding
importance in mathematics
education.”
- Common Core State Standards for Mathematics,
page 6
Mathematical Practices
1.
Make sense of problems and persevere in solving them
2.
Reason abstractly and quantitatively
3.
Construct viable arguments and critique the reasoning of
others
4.
Model with mathematics
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure
8.
Look for and express regularity in repeated reasoning
Pairs of Practices
Reasoning and Explaining
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the
reasoning of others
Modeling and Using Tools
4. Model with mathematics
5. Use appropriate tools strategically
Seeing Structure and Generalizing
7. Look for and make use of structure
8. Look for and express regularity in repeated
reasoning
Overarching Habits of Mind of a Productive
Mathematical Thinker
1. Make sense of problems and persevere in
solving them
6. Attend to precision
Adapted from (McCallum, 2011)
6
The Standards for
Mathematical Practice
• Turn to page 6 of the Common Core State
Standards for Mathematics
• Take a moment to examine the first three
words of the narrative description for each
of the 8 mathematical practices.
• What do you notice?
Mathematically Proficient Students…
• Read Mathematical Practices 1 and 6.
• Identify the verbs that illustrate the
student actions for this practice.
8
Common Core Standards
Interpret the Structure of Expressions
MACC.912.A-SSE.1.1 Interpret expressions
that represent a quantity in terms of its
context.*
MACC.912.A-SSE.1.2 Use the structure of
an expression to identify ways to rewrite it.
For example, see x4 – y4 as (x2)2 – (y2)2, thus
recognizing it as a difference of squares that
can be factored as (x2 – y2)(x2 + y2).
Mathematics Postsecondary
Readiness Competencies
• MPRCC1
– Understand that to solve certain problems and equations,
number systems need to be extended from whole numbers to
the set of all integers (positive, negative and zero), from integers
to rational numbers, and from rational numbers to real numbers
(rational and irrational numbers); define and give examples of
each of these types of numbers
• MPRCC6
– Locate the position of a number on the number line, know that its
distance from the origin is its absolute value, and know that the
distance between two numbers on the number line is the
absolute value of their difference
• MPRCC9
– Use estimation and approximation to solve problems
(Include evaluating answers for their reasonableness, detecting
errors, and giving answers to an appropriate level of precision)
Student Goals
Goal: The student will be able to demonstrate
understanding of an expression in terms of its
context and value.
Learning Scale:
4:
3: Proficient
2:
1:
Number Line Activity
• White cards
• Tan cards
• Blue cards
Middle Grades to High School
Progression
•
•
•
•
MACC.7.NS.1.1 Apply and extend previous understandings of addition and
subtraction to add and subtract rational numbers; represent addition and
subtraction on a horizontal or vertical number line diagram.
MACC.8.NS.1.2 Use rational approximations of irrational numbers to
compare the size of irrational numbers, locate them approximately on a
number line diagram, and estimate the value of expressions (e.g., π2). For
example, by truncating the decimal expansion of √2, show that √2 is
between 1 and 2, then between 1.4 and 1.5, and explain how to continue on
to get better approximations.
MACC.912.N-RN.1.2 Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
MACC.912.A-SSE.1.1 Interpret expressions that represent a quantity in
terms of its context.*
– MACC.912.A-SSE.1.1a Interpret parts of an expression, such as terms, factors, and
coefficients.*
– MACC.912.A-SSE.1.1b Interpret complicated expressions by viewing one or more of
their parts as a single entity. For example, interpret P(1+r) n as the product of P and a
factor not depending on P.*
•
MACC.912.A-SSE.1.2 Use the structure of an expression to identify ways
to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a
difference of squares that can be factored as (x2 – y2)(x2 + y2).
Note on courses and transitions
Some of the highest priority content for
college and career readiness comes from
Grades 6-8.
Because important standards for college
and career readiness are distributed
across grades and courses, systems for
evaluating college and career readiness
should reach as far back in the standards
as Grades 6-8.
Planning Reflection
1. How will you use the Common Core
Standards for Mathematical Practices to
inform instruction and lesson planning?
2. Identify the benefits of integrating the
Common Core Standards for
Mathematical Practices.
Digital Resources
• Common Core App
• http://itunes.apple.com/us/app/commoncore-standards/id439424555?mt=8
• www.masteryconnect.com
Resources
• Common Core homepage
( http://www.corestandards.org/)
• Progressions
(http://ime.math.arizona.edu/progressions/)
• Illustrative Mathematics Project
(http://illustrativemathematics.org)
• William McCallum’s blog, Tools for the Common Core,
(http://commoncoretools.wordpress.com)
• Institute for Mathematics & Education
(http://ime.math.arizona.edu/commoncore/)
• Mathematics Practices and includes video clips of the practices
(http://www.insidemathematics.org/index.php/common-core-standards)
• video clips that align with the common core
(https://www.teachingchannel.org/)