Common Core State Standards (CCSS) Permission to freely use this ppt is granted under the following...
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Common Core State Standards (CCSS) Permission to freely use this ppt is granted under the following conditions: • It is for educational purposes only, and there is no fee associated with viewing it. • It is not altered in any way. The Comprehensive Strategic Intervention logo and www.ELATestPrep.com footer must remain in place. www.ELATestPrep.com
Common Core State Standards (CCSS) Permission to freely use this ppt is granted under the following conditions: It is for educational purposes only, and
Common Core State Standards (CCSS) Permission to freely use
this ppt is granted under the following conditions: It is for
educational purposes only, and there is no fee associated with
viewing it. It is not altered in any way. The Comprehensive
Strategic Intervention logo and www.ELATestPrep.com footer must
remain in place. www.ELATestPrep.com
Slide 3
Think Like a Mathematician "Only two things are infinite, the
universe and human stupidity, and I'm not sure about the former.
Albert Einstein www.ELATestPrep.com
Slide 4
Think Like a Mathematician "No employment can be managed
without arithmetic, no mechanical invention without geometry.
Benjamin Franklin www.ELATestPrep.com
Slide 5
Think Like a Mathematician "Give me a place to stand, and I
will move the earth. Archimedes www.ELATestPrep.com
Slide 6
Think Like a Mathematician Neglect of mathematics works injury
to all knowledge, since he who is ignorant of it cannot know the
other sciences or the things of the world. Roger Bacon
www.ELATestPrep.com
Slide 7
Think Like a Mathematician Every good mathematician is at least
half a philosopher, and every good philosopher is at least half a
mathematician. Friedrich Ludwig Gottlob Frege
www.ELATestPrep.com
Slide 8
Think Like a Mathematician God does arithmetic. Carl Friedrich
Gauss www.ELATestPrep.com
Slide 9
Think Like a Mathematician "Where there is matter, there is
geometry. Johannes Kepler www.ELATestPrep.com
Slide 10
Think Like a Mathematician "Algebraic symbols are used when you
do not know what you are talking about. Philippe Schnoebelen
(Computer Scientist Oxford University) www.ELATestPrep.com
Slide 11
Think Like a Mathematician The infinite! No other question has
ever moved so profoundly the spirit of man. David Hilbert
www.ELATestPrep.com
Slide 12
Think Like a Mathematician When you can measure what you are
talking about and express it in numbers, you know something about
it. Lord William Thomson Kelvin www.ELATestPrep.com
Slide 13
Think Like a Mathematician Geometry is one and eternal shining
in the mind of God. That share in it accorded to men is one of the
reasons that Man is the image of God. Johannes Kepler
www.ELATestPrep.com
Slide 14
Think Like a Mathematician Let no one ignorant of geometry
enter here. Plato www.ELATestPrep.com
Slide 15
Think Like a Mathematician Number rules the universe.
Pythagoras www.ELATestPrep.com
Slide 16
Think Like a Mathematician The understanding of mathematics is
necessary for a sound grasp of ethics. Socrates
www.ELATestPrep.com
Slide 17
Why the Change to CCSS? www.ELATestPrep.com
Slide 18
Why the Change to CCSS? An example of how multiple-choice
assessments have undermined quality math instruction: 39 8,307
(A)39 (B)213 Students can solve this (C)432 without knowing the
(D)621 division algorithm! www.ELATestPrep.com
Slide 19
Why the Change to CCSS? Multiply the last digit of each answer
choice by the last digit of the divisor. The correct answer MUST
have the same last digit as the dividend. 39 8,307 (A)39 (9x9 = 81)
(B)213 (3x9 = 27) (C)432 (2x9 = 18) (D)621 (1x9 = 9)
www.ELATestPrep.com
Slide 20
Why the Change to CCSS? www.ELATestPrep.com
Slide 21
Agenda/Purpose Become educated about CCSS and understand
implications for change to assessment, standards, curriculum, and
instruction in the area of mathematics 6 Instructional Shifts for
Mathematics Standards for Mathematical Practice How SBAC will
change the nature of assessment Review Depth of Knowledge (DOK)
Structure of CCSS for Mathematics How to move forward/next steps
www.ELATestPrep.com
Slide 22
The 3 Gears of Common Core www.ELATestPrep.com
Slide 23
Highest Quality Mathematics Program Components
www.ELATestPrep.com Resources Tiered Interventions Proven Teaching
Strategies SBAC & Common Core Standards Standards for
Mathematical Practice 6 Instructional Shifts Resources Tiered
Interventions Proven Teaching Strategies SBAC & Common Core
Standards Standards for Mathematical Practice 6 Instructional
Shifts
Slide 24
6 Instructional Shifts for ELA & Math 6 ELA Shifts
1.Balancing Informational & Literary Text 2.Knowledge in the
Disciplines 3.Staircase of Complexity 4.Text-Based Answers
5.Writing From Sources 6.Academic Vocabulary 6 Math Shifts 1.Focus
2.Coherence 3.Fluency 4.Deep Understanding 5.Applications 6.Dual
Intensity www.ELATestPrep.com
Slide 25
Shift 1: Focus Significantly narrow and deepen the scope of how
time is spent in the classroom Spend more time thinking and working
on fewer concepts Focus deeply on only concepts prioritized in the
standards Students: reach strong foundational knowledge deep
conceptual understanding transfer math skills and understanding
across concepts & grades www.ELATestPrep.com
Slide 26
Examining CCSS at your Grade What are the new domains? List the
skills/concepts which carry over from CA97 to CCSS. List the
skills/concepts which will be new to your grade. List the CA97
skills/concepts which will be eliminated by CCSS. link to template
www.ELATestPrep.com
Slide 27
Correlation Between CA97 and CCSS GradeELAMath K76%53% 179%82%
283%72% 373%68% 466%74% 569%67% 674%67% www.ELATestPrep.com
Slide 28
Shift 2: Coherence Build on knowledge in year to year, in a
coherent learning progression Connect learning within and across
grades Spiraling of concepts across grades so that students build
onto foundations built in previous years Deep conceptual
understanding of core content Each standard is NOT a new event, but
an extension of previous learning www.ELATestPrep.com
Slide 29
Shift 3: Fluency Spend time practicing skills with intensity
Push students to know basic skills at a greater level of fluency
Students have speed & accuracy Memorize through repetition core
functions Focus on the listed fluencies by grade level Create high
quality worksheets, problem sets, in high volume
www.ELATestPrep.com
Slide 30
Shift 4: Deep Understanding Dont simply teach how to get the
answer Help students access concepts from a number of perspectives
Help students see math as more than a set of mnemonics or discrete
procedures Apply math to new situations; even writing &
speaking Spend the time necessary to gain depth
www.ELATestPrep.com
Slide 31
Shift 5: Applications Apply math across the disciplines and
real world Choose the right concept to solve a problem even when
not prompted to do so Students use math in science particularly
www.ELATestPrep.com
Slide 32
Shift 6: Dual Intensity Practicing & Understanding are
occurring with dual intensity Opportunities for students to
participate in drills Equal opportunities for students to make use
of those skills through extended application Provide enough class
time for mathematics www.ELATestPrep.com
Slide 33
Standards for Mathematical Practice Purpose Describe varieties
of expertise that educators at all levels should seek to develop in
their students They define the essence of what math is and what
mathematicians and proficient students can do. Think like a
disciplinarian Mathematicians... The following link on the Core
Standards site gives the full details of the SMP:
http://www.corestandards.org/Math/Practice www.ELATestPrep.com
Slide 34
1. Make sense of problems & persevere in solving them.
Mathematically proficient students: start by analyzing the meaning
of a problem. plan a solution pathway rather than jump to a
solution. consider analogous problems & try simpler forms. use
concrete objects to help conceptualize problems. check their
answers. www.ELATestPrep.com
Slide 35
2. Reason abstractly & quantitatively Mathematically
proficient students: make sense of quantities and their
relationships in problems. decontextualize (represent a real
problem symbolically) and manipulate the symbols. contextualize
(pause to make sense of symbols). attend to the meaning of
quantities, NOT just how to compute them. www.ELATestPrep.com
Slide 36
3. Construct viable arguments and critique the reasoning of
others. Mathematically proficient students: analyze situations by
breaking them into cases. use counterexamples. justify conclusions
and communicate with others. explain flaws in others arguments.
listen or read others arguments and decide if they make sense.
www.ELATestPrep.com
Slide 37
4. Model with mathematics. Mathematically proficient students:
apply math to solve real life problems. www.ELATestPrep.com
Slide 38
5. Use appropriate tools strategically. Mathematically
proficient students: consider available tools when solving
problems. pencil & paper concrete models ruler or protractor
calculator or computer are able to use technological tools to
explore & deepen understanding of concepts.
www.ELATestPrep.com
Slide 39
6. Attend to precision. Mathematically proficient students:
communicate precisely to others. use clear definitions. state the
meaning of symbols they choose. are careful about specifying units
of measure and labeling. calculate accurately & efficiently.
www.ELATestPrep.com
Slide 40
7. Look for and make use of structure. Mathematically
proficient students: look closely to discern a pattern or
structure. www.ELATestPrep.com
Slide 41
8. Look for and express regularity in repeated reasoning.
Mathematically proficient students: notice if calculations are
repeated. look for both general methods & shortcuts. maintain
oversight of the process, while attending to the details. Evaluate
reasonableness of their intermediate results.
www.ELATestPrep.com
Slide 42
Implications for Curriculum, Instruction, and Assessment CCSS
focus on: Depth of understanding Application of knowledge and
skills Interdisciplinary activities Any assessment that verifies
these factors will necessarily bring fundamental changes to
curriculum and teaching strategies. www.ELATestPrep.com
Slide 43
A revolution in student assessments will soon be upon us. STAR
CST SBAC www.ELATestPrep.com
Slide 44
www.smarterbalanced.org Smarter Balanced is a state-led
consortium developing assessments aligned to the Common Core State
Standards in ELA and Math that are designed to help prepare all
students to graduate high school college- and career-ready. The
assessments are so revolutionary, that even if we kept the exact
same 97 standards, our instructional practices would still need to
transform so that students are prepared. www.ELATestPrep.com
Slide 45
SBAC assessments will go beyond multiple-choice questions to
include extended response and technology enhanced items, as well as
performance tasks that allow students to demonstrate critical-
thinking and problem-solving skills. www.ELATestPrep.com
Slide 46
In 2014-15, students will be assessed through the SBAC
consortium on their mastery of the CCSS standards. Pilots will
begin now. SBAC will assess grades 3-8 and 11 in ELA and Math. The
assessments will be administered online using adaptive technology.
source: SBCOE www.ELATestPrep.com
Slide 47
Selected Response Assessment items where students select from a
given set of response options Constructed & Extended Response
Assessment items where students produce the response instead of
selecting from a list Technology-Enhanced/Technology Enabled
Assessment items that employ technology to elicit a response from a
student Performance Tasks Assessment items where students perform a
skill or create a product. source: SBCOE www.ELATestPrep.com
Slide 48
Selected Response (SR) www.ELATestPrep.com Student
EvidenceMaximum Time Requirement ELA Most Selected Response (SR)
items will relate to a stimulus (e.g., a reading passage or
audio/visual stimulus). Grade 3: 1-3 minutes per item Grades 4-11:
1-2 minutes per item Math A series of options from which to choose
correct response(s) Grade 3: 1-3 minutes per item Grades 4-11: 1-2
minutes per item
Slide 49
Constructed Response (CR/ER) www.ELATestPrep.com Student
EvidenceMaximum Time Requirement Items may require test-takers to
enter a single word, phrase, sentence, number, or set of numbers.
2-10 minutes
Slide 50
Technology Enhanced (TE) www.ELATestPrep.com Student
EvidenceMaximum Time Requirement Items will take advantage of drag-
and-drop, hot spot, drawing, graphing, gridded-response items, and
simulation technologies. Time will vary depending on the task.
Slide 51
Performance Task (PT) www.ELATestPrep.com Test Item TypeStudent
EvidenceMaximum Time Requirement Performance Task (PT) Requires
analytical thinking, evaluations, and support of students own
responses across multiple content standards. ELA Students will
produce either a full written text or present a speech Math
Integrate knowledge and skills to formulate a problem, create a
model, evaluate data, and interpret results. Grades 3-8: 105
minutes (over 2-3 days) High School: 120 minutes (over 2-3
days)
Slide 52
Lets go to the SBAC site and take a look at some of their
sample items for math:
http://sampleitems.smarterbalanced.org/itempreview/sbac/index.htm
www.ELATestPrep.com
Webbs Definition of DOK (Hess, 2009) DOK-1 (Recall &
Reproduction) Recall of a fact, term, principle, concept; perform a
routine procedure; locate details DOK-2 (Basic Application of
Skills/Concepts) Use of information; conceptual knowledge; select
appropriate procedures for a given task; two or more steps with
decision points along the way; routine problems; organize/display
data; interpret/use simple graphs; summarize; identify main idea;
explain relationships; make predictions DOK-3 (Strategic Thinking)
Requires reasoning, or developing a plan or sequence of steps to
approach the problem; requires decision making or justification;
abstract, complex, or non-routine; often more than one possible
answer; support solutions or judgments with text evidence DOK-4
(Extended Thinking) An investigation or application to real world;
requires time to research, problem solve, and process multiple
conditions of the problem or task; noun-routine manipulations;
synthesize information across disciplines/content areas/multiple
sources source: SBCOE www.ELATestPrep.com
Slide 55
Complexity Does NOT refer to difficulty, but rather to the
cognitive steps a test-taker must go through to arrive at a correct
answer. source: SBCOE www.ELATestPrep.com
Slide 56
Source: Webb, Norman L. and others. Webb Alignment Tool
Wisconsin Center of Educational Research
http://www.wcer.wisc.edu/WAT/index.aspx www.ELATestPrep.com
Slide 57
Student Task Usually 1 Right Answer Recall / Simple Calculation
DOK 1 Acting on Knowledge DOK 2 Multiple Answers/Multiple Pathways
One ConceptDOK 3 Many Different Concepts DOK 4
www.ELATestPrep.com
Slide 58
www.corestandards.org Mission Statement: The Common Core State
Standards provide a consistent, clear understanding of what
students are expected to learn, so teachers and parents know what
they need to do to help them. The standards are designed to be
robust and relevant to the real world, reflecting the knowledge and
skills that our young people need for success in college and
careers. With American students fully prepared for the future, our
communities will be best positioned to compete successfully in the
global economy. www.ELATestPrep.com
Slide 59
CCSS Math Standards address the problem of a curriculum that is
a mile wide and an inch deep. stress conceptual understanding. do
NOT dictate curriculum or teaching methods. are NOT new names for
old ways of doing business. www.ELATestPrep.com
Slide 60
How to read the grade level standards: Domain Number and
Operations in Base Ten 3.NBT Use place value understanding and
properties of operations to perform multi-digit arithmetic. 1.Use
place value understanding to round whole numbers to the nearest 10
or 100. 2.Fluently add and subtract within 1000 using strategies
and algorithms based on place value.... 3.Multiply one-digit whole
numbers by multiples of 10 in the... Standard Cluster
www.ELATestPrep.com
Slide 61
Possible Challenges Were still accountable to the STAR CST
until 2014-15, but we need to transition to CCSS now. No
curriculum/resources aligned with CCSS (and the bridge materials
dont seem to be very good at this point) Huge shift in
instructional strategies Technology www.ELATestPrep.com
Slide 62
Possible Solutions / Next Steps We need to be the experts! Be
positive; this is a rare do-over opportunity! Examine the CCSS for
my grade level Use the CA97 to CCSS springboard template/document
to help us transition Design lesson(s) which take a CA97
standard(s) DOK-1 and add complexity so it is CCSS DOK-2, 3, or 4.
GATE Icons of depth & complexity may be the key to creating
DOK2-4 activities. Explore interdisciplinary approach with math,
science, and ELA Communicate and collaborate Share ideas and work
with colleagues Invite observation and feedback
www.ELATestPrep.com
Slide 63
Acknowledgements/ Permissions Much of the information in this
ppt was learned from the Common Core Institute and from various
trainings conducted by the San Bernardino County Office of
Education (SBCOE). The training by SBCOE is highly informative, and
I strongly recommend it for those seeking more information about
CCSS. SBAC-www.smarterbalanced.orgwww.smarterbalanced.org Common
Core State Standards Initiative- www.corestandards.org
www.corestandards.org The SBAC logo and Common Core logo were
included within this ppt for educational purposes only. They are
the property of SBAC and Common Core. Neither of these entities
were involved with the making of this ppt, nor have they endorsed
it in any way. Permission to freely use this ppt is granted under
the following conditions: It is for educational purposes only, and
there is no fee associated with viewing it. It is not altered in
any way. The Comprehensive Strategic Intervention logo and
www.ELATestPrep.com footer must remain in
place.www.ELATestPrep.com
