8. Common Core Introduction
The State has provided each grade level
with its own introduction to the Common
Core Learning Standards
What do you notice about the focus of the
introduction in your grade-level?
9. Math Practices
• On posters around the room, you will find the eight
math practices.
– These represent the 8 ’habits of mind’ that connect the entire
pre-K through 12 continuum.
• Please take a few minutes to reflect on each math
practice statement and consider
– What does it mean?
– What does it look like?
10. 1. Make Sense of Problems and
Persevere in Solving Them
• Read and understand the problem
• Organize information to make a plan
(more than one approach is acceptable)
• Solve and adjust the process as necessary
• Evaluate the solution and decide how you will use
the solution to answer the question
11. 2. Reason Abstractly and Quantitatively
• Take a given situation and represent it
symbolically (de-contextualization)
• Assign meaning to the symbols by putting
them back in context (contextualize)
12. 3. Construct Viable Arguments and
Critique the Reasoning of Others
• Listen to or read the arguments of others
• Decide whether the arguments make sense
• Ask useful questions to clarify or improve the
arguments
13. 4. Model With Mathematics
• Apply math concepts to solve problems that arise in
every day life
• Simplify a complicated situation and make revisions
as needed
• Use tools such as diagrams, graphs charts to analyze
math relationships and draw conclusions
• Interpret results and reflect, “Does this make sense?”
• Make adjustments, if necessary
14. 5. Use Appropriate Tools Strategically
• Consider available tools such as
paper/pencil, concrete models, rulers,
software
• Develop a familiarity with tools
• Make sound decisions about which tools to
use for the situation
• Use technological tools to deepen the
understanding of concepts
15. 6. Attend to Precision
• Calculations are accurate and efficient
• Explanations include clear definitions, correct
use of symbols (especially the equal sign),
units of measure, axes labels, etc.
16. 7. Look For and Use Structure
• Look for patterns and use what is known
to apply or extend the pattern
• Look for structure by identifying the
conceptual way that we think about math
• Find and follow the “rules” that
mathematicians use to solve problems
17. 8. Look For and Express Regularity
in Repeated Reasoning
• Notice repetitive actions in counting and
computation
• Look for shortcuts such as rounding
• Continuously check work to see if answers
are reasonable
• Ask, “Does the answer match the question?”
18. The Six Shifts in Mathematics
• SHIFT 1: FOCUS
• SHIFT 2: COHERENCE
• SHIFT 3: FLUENCY
• SHIFT 4: DEEP UNDERSTANDING
• SHIFT 5: APPLICATION
• SHIFT 6: DUAL INTENSITY
Group Discussion:
• What does this shift mean?
• What does it look like in the classroom?
From the teacher’s perspective?
From the students’ perspectives?
19. Mathematics Shift 1: Focus
What the Student Does… What the Teacher Does… What the Principal Does…
•Spend more time thinking and •Make conscious decisions about •Work with groups of math
working on fewer concepts. what to excise from the curriculum teachers to determine what
•Being able to understand and what to focus content to prioritize most deeply
concepts as well as processes •Pay more attention to high and what content can be removed
(algorithms). leverage content and invest the (or decrease attention).
appropriate time for all students to •Determine the areas of intensive
learn before moving onto the next focus (fluency), determine where
topic. to re-think and link (apply to core
•Think about how the concepts understandings), sampling (expose
connects to one another students, but not at the same
•Build knowledge, fluency and depth).
understanding of why and how we •Determine not only the what, but
do certain math concepts. at what intensity.
•Give teachers enough time, with a
focused body of material, to build
their own depth of knowledge.
19
20. An Examination of Focus
• The standards were Intense focus Rethink and link Sampling
written to reflect a 70% 20% 10%
deepening of key K-2 Addition and Geometry and Patterns
Subtraction Measurement Statistics and Data
understandings at Concepts Probability
certain grade levels. Skills Estimating Arithmetic
Problem Solving
3-5 Multiplication and Area Patterns
• There are 2-4 focal areas Division of Whole Volume Statistics and Data
Numbers and Fractions Probability
per grade-level. A good balance of
o Concepts
o Skills
• To ensure the degree of o Problem
Solving
understanding and
6-8 Proportional Reasoning Quantitative Statistics
application required, & Linearity Relationships &
more time and practice Algebra Functions
Geometric
will need to be devoted Measurement
to these particular
concepts.
21. Priorities in Math
Priorities in Support of Rich Instruction and Expectations of
Grade Fluency and Conceptual Understanding
Addition and subtraction, measurement using
K–2
whole number quantities
Multiplication and division of whole numbers and
3–5
fractions
Ratios and proportional reasoning; early
6
expressions and equations
Ratios and proportional reasoning; arithmetic of
7
rational numbers
8 Linear algebra
21
22. Mathematics Shift 2: Coherence
What the Student Does… What the Teacher Does… What the Principal Does…
•Build on knowledge from •Connect the threads of •Ensure that teachers of
year to year, in a coherent math focus areas across the same content across
learning progression grade levels grade levels allow for
•Think deeply about what discussion and planning to
you’re focusing on and the ensure for
ways in which those focus coherence/threads of main
areas connect to the way it ideas
was taught the year before
and the years after
22
23. Mathematics Shift 3: Fluency
What the Student Does… What the Teacher Does… What the Principal Does…
•Spend time practicing, •Push students to know •Take on fluencies as a
with intensity, skills (in high basic skills at a greater stand alone CC aligned
volume) level of fluency activity and build school
•Focus on the listed culture around them.
fluencies by grade level
•Create high quality
worksheets, problem sets,
in high volume
23
24. The Special Case of Fluency
• Fluency is more than just “knowing facts by memory”
• It is the fast and
accurate completion
of a continuum of
mathematical
operations and
procedures
• Each grade level has
1-2 key fluency goals
25. Mathematics Shift 4: Deep
Understanding
What the Student Does… What the Teacher Does… What the Principal Does…
•Show, through numerous •Ask yourself what •Allow teachers to spend
ways, mastery of material mastery/proficiency really time developing their own
at a deep level looks like and means content knowledge
•Use mathematical •Plan for progressions of •Provide meaningful
practices to demonstrate levels of understanding professional development
understanding of different •Spend the time to gain the on what student mastery
material and concepts depth of the understanding and proficiency really
•Become flexible and should look like at every
comfortable in own depth grade level by analyzing
of content knowledge exemplar student work
25
26. Mathematics Shift 5: Application
What the Student Does… What the Teacher Does… What the Principal Does…
•Apply math in other •Apply math including •Support science teachers
content areas and areas where its not directly about their role of math
situations, as relevant required (i.e. in science) and literacy in the science
•Choose the right math •Provide students with real classroom
concept to solve a problem world experiences and •Create a culture of math
when not necessarily opportunities to apply application across the
prompted to do so what they have learned school
26
27. Mathematics Shift 6: Dual Intensity
What the Student Does… What the Teacher Does… What the Principal Does…
•Practice math skills with •Find the dual intensity •Provide enough math
an intensity that results in between understanding class time for teachers to
fluency and practice within focus and spend time on
•Practice math concepts different periods or both fluency and
with an intensity that different units application of
forces application in novel •Be ambitious in demands concepts/ideas
situations for fluency and practice, as
well as the range of
application
27
29. Highlight
• In one color, highlight the content that we
currently teach
• In another color, highlight the content that
is NEW to our grade level
30. An example from 4th grade
Skill (verb) Content (noun) Method (using…)
Recognize Relationship between digits
(any place is 10 times the digit to its right)
Read Multi-digit whole numbers Base-ten numerals, number
names, expanded form
Compare Multi-digit whole numbers Place value
31. Let’s Continue
• We will break into groups
• Each group will complete a portion of the
Skills-Content-Method activity
• Be ready to share out with the entire
grade-level group
32. How to Access Go-Math Online
1. Go to www-k6.thinkcentral.com
2. Click on the blue “Evaluators Click Here”
button
3. Access word: gocommoncore
4. Check the boxes for the Privacy Policy and
Terms of Use
5. Fill out your name and email address
33. Resources
http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm
CCLS aligned Performance tasks and instructional supports (units)
http://illustrativemathematics.org/standards/k8
A small but growing list of sample activities for the CCLS
http://commoncoretools.wordpress.com/category/progressions/
Some still in draft form but its getting there!
http://ime.math.arizona.edu/commoncore/
Bring together some of the best math minds…
http://insidemathematics.org/index.php/classroom-video-visits
A collection of videos, open-ended problem solving task
http://nymathstandards.pbworks.com/w/page/45609650/Unpacking%20t
he%20Content%20Standards%20for%20Math
NYS math teacher-created break down of each standard
Editor's Notes
In reference to the TIMMS study, there is power of the eraser and a gift of time. The Core is asking us to prioritize student and teacher time, to excise out much of what is currently being taught so that we can put an end to the mile wide, inch deep phenomenon that is American Math education and create opportunities for students to dive deeply into the central and critical math concepts. We are asking teachers to focus their time and energy so that the students are able to do the same.
Focus on the math that matters mostFocusing on far fewer topics and treat them with much better care and detail.As shown by the TIMMS study, in the high performing countries there is a relentless focus on specific areas of mathematics ie. addition and subtraction and the quantities they measure at the K-2 level.For the first time, we will model these countries by having fewer topics learned more deeply. These core masteries will lead much fuller level of understanding. In middle and high school, students with this mastery can move on to do work in data and statistics and applying their knowledge to fields such as Algebra, Trigonometry and Calculus. It will also enable them to engage in rich work in modeling multiple representation to other fields such as economics.
We need to ask ourselves – How does the work I’m doing affect work at the next grade level? Coherence is about the scope and sequence of those priority standards across grade bands. How does multiplication get addressed across grades 3-5? How do linear equations get handled between 8 and 9? What must students know when they arrive, what will they know when they leave a certain grade level?
Fluency is the quick mathematical content; what you should quickly know. It should be recalled very quickly. It allows students to get to application much faster and get to deeper understanding. We need to create contests in our schools around these fluencies. This can be a fun project. Deeper understanding is a result of fluency. Students are able to articulate their mathematical reasoning, they are able to access their answers through a couple of different vantage points; it’s not just getting to yes; it’s not just getting the answer but knowing why. Students and teachers need to have a very deep understanding of the priority math concepts in order to manipulate them, articulate them, and come at them from different directions.
The Common Core is built on the assumption that only through deep conceptual understanding can students build their math skills over time and arrive at college and career readiness by the time they leave high school. The assumption here is that students who have deep conceptual understanding can: Find “answers” through a number of different routesArticulate their mathematical reasoningBe fluent in the necessary baseline functions in math, so that they are able to spend their thinking and processing time unpacking mathematical facts and make meaning out of them. Rely on their teachers’ deep conceptual understanding and intimacy with the math concepts
The Common Core demands that all students engage in real world application of math concepts. Through applications, teachers teach and measure students’ ability to determine which math is appropriate and how their reasoning should be used to solve complex problems. In college and career, students will need to solve math problems on a regular basis without being prompted to do so.
This is an end to the false dichotomy of the “math wars.” It is really about dual intensity; the need to be able to practice and do the application. Both things are critical.
