Math Standards-KCTM Presentation

Report
Standards
1
WHERE WE CAME FROM AND WHERE WE
ARE GOING
Function of Standards
f(st) = c2
DR. BRENNON SAPP
OCTOBER 2010 KCTM
Let’s Start with a Math Problem
(worthy of the new standards)
2
Compare the following sets of equations when
x1+x2+x3+x4+x5+x6+x7+x8 =1 :
a) f(x) = 0x1 + 0.13 x2 + 0.26x3 + 0.4x4 + 0.6x5 +
0.8x6+ x7 +1.4x8
b) f(x) = 0(x1 + x2 + x3 + x4 + x5 + x6) + (x7 + x8)
How might we go about maximizing f(x) for each
equation?
Why Change?
3
In 2004, the unemployment rate for recent high
school graduates who had not enrolled in college
in the fall of 2004 was 20 percent.
The unemployment rate for young people who
dropped out of high school between October 2003
and October 2004 was 40 percent.
Why Change?
5
There will never ever be another
time when we can’t get information.
In fact we have too much
information and we don’t know how
to judge if it is right, wrong, useful,
or useless.
6
7
Greatest Accomplishment In Mathematics?
8
 Counting
 Discovery of Zero
9
We have to Teach Students to
Think
10
WHAT DO YOU DO WHEN
YOU DON’T KNOW WHAT TO
DO?
11
To Quote an Authority
12
“Give a man a fish. . . .blah blah blah”
“Teach a man to fish . . . blah blah blah”
According to the Professionals
13
“We are living in a world without borders. To meet the
realities of the 21st century global economy and
maintain America’s competitive edge into the future,
we need students who are prepared to compete not
only with their American peers, but with students from
all across the globe for the jobs of tomorrow.”
CCSSO
According to the Professionals
14
“Governors recognize that new economic realities
mean it no longer matters how one U.S. state
compares to another on a national test; what matters
is how a state’s students compare to those in countries
around the globe”
NGA
Do you? Or are you still comparing your students
success to the next school over? The next county over?
The state average (do you know what Kentucky is rated
Nationally/Internationally?)
Let’s Put it Another Way
15
“Stop GPS-ing student’s learning”
“Teach them to read a map”
Dr. Ann Shannon
Gates Consultant
First Standards
16
 The most ancient mathematical texts available are
Plimpton 322 (Babylonian, 1900 BC)
 The Rhind Mathematical Papyrus (Egyptian
mathematics c. 2000-1800 BC)
 Moscow Mathematical Papyrus (Egyptian
mathematics c. 1890 BC).
All of these texts concern the so-called Pythagorean
theorem, which seems to be the most ancient and
widespread mathematical development after basic
arithmetic and geometry.
Pimpton 322
17
A Listing of Pythagorean Triples
Rhind Mathematical Papyrus
18
“Accurate reckoning for inquiring into
things, and the knowledge of all things,
mysteries...all secrets.”
Rhind Mathematical Papyrus
19
The first part consists of reference tables and a
collection of 40 algebraic problems
 simple fractional expressions
 completion (sekhem) problems
 linear equations (aha problems).
Moscow Mathematical Papyrus
20
Moscow Mathematical Papyrus
21
 Ship’s part problems. . .problems like calculations for the
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length of a ship’s rudder or the length of a ship’s mast given
that it is 1/3 + 1/5 of the length of a cedar log originally 30
cubits long
Aha problems-involve finding unknown quantities if the
sum of the quantity and part(s) of it are given.
Pefsu Problems-ratios for figuring the strength of beer or
bread
Baku problems-to calculate the output of workers
Geometry Problems-area, surface area, and volume
Earliest Chinese Math Text
22
The Suàn shù shū (筭數書), or the Writings on
Reckoning . . . .
Earliest Chinese Math Text
23
24
Earliest Chinese Math Text (Book)
25
 69 mathematical problems from a variety of sources.
 Each problem has a question, an answer, followed by
a method.
 conversion between units
 elementary arithmetic
 Fractions
 inverse proportion
 false position method for
¶= 3
finding roots
 factorization of numbers
 geometric progressions
 interest rate calculations
 extraction of approximate
square roots
 volume of various 3-d shapes
 relative dimensions of a
square and its inscribed circle
First Calculators?
26
First Calculators?
27
Exponential Time Jump
28
When was the first time
“We” got standards?
29
KENTUCKY EDUCATION
REFORM ACT
(KERA)
Kentucky Education Reform Act
30
In 1990, the Kentucky General Assembly passed the
Kentucky Education Reform Act (KERA) in response
to a ruling the previous year by the Kentucky
Supreme Court that the commonwealth's education
system was unconstitutional
Kentucky Program of Studies
31
Which is still by law what we are responsible to teach to
each and every student
 Goal 1 (Basic Communication and mathematics Skills)
 Goal 2 (Application of Core Concepts)
 Goal 3 (Developing Self-Sufficiency)*
 Goal 4 (Responsible Group Membership)*
 Goal 5 (Think and Solve Problems)
 Goal 6 (Connect and Integrate Knowledge)
*Not to be assessed by state testing
KIRIS
32
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The Kentucky Instructional Results Information
Service (KIRIS) was used from 1992 to 1998, and
included
open-response items
performance events
on-demand writing prompts
mathematics portfolios
KIRIS
33
It was during this time we received:
Transformations:
Kentucky’s Curriculum
Framework, (1995).
Transformations (Vol. I)
34
 (1) definitions of the academic expectations which
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indicate student progress toward the outcome;
(2) ideas for making connections to real-life
situations;
(3) samples of topics and processes within content
areas
(4) teaching and assessment strategies
(5) ideas for incorporating community resources
(6) activities to involve students
(7) reflections on academic expectations.
Transformations (Vol. 2)
35
 (1) transforming the learning environment to foster
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change
(2) alternative uses of school time to address
curricular needs
(3) local curriculum development guide
(4) teachers' questions about implementation
(5) resources which identify teaching and assessment
strategies, sources, models, and key readings.
Core Content
36
?.?
CATS
37
1998 legislation replaced KIRIS with the
C o m m o n w e a l t h A c c o u n t a b i l i t y Te s t i n g
S ys t e m , u s i n g o p e n - r e s p o n s e a n d m u l t i p l e choice items, an on-demand writing prompt,
A writing portfolio, and the terranova
national norm-referenced test.
CATS
38
 Testing was divided across grades to limit the burden
on teachers and students in any single grade
 Mathematics portfolios, which have been part of
KIRIS in grades five, eight, and twelve, were
suspended
 NRT?
Commonwealth Accountability Testing System
39
Major changes in CATS were made in 2007
 revisions to the content being tested
 years each subject is tested
 relative weight given to different topics
 relative weight given to multiple-choice and openresponse questions
 the national norm-referenced test included in school
scores
 “cut points” used to convert students’ numerical
scores to performance levels
Senate Bill 1
40
FEBRUARY 10, 2009
Did KERA/KIRIS/CATS Work?
41
 Money in the state is distributed more fairly
 According to teachers-they receive more support and
direction on good instruction
 According to administrators schools focus more on
instruction and quality teaching in more sought after
and valued
 According to Kentucky data, elementary schools
would have surpassed the 2014 goal, middle schools
would have reached the 2014 goal, but high schools
would have not reached the 2014 goal of proficiency
Did KERA/KIRIS/CATS Work?
42
 According to many experts and professional organizations
“The nation follows Kentucky on educational reform.”
 Based on the center’s National Education Index, Kentucky’s
ranking has gone from 43rd in 1992 to 35th in 2007, a
finding consistent with Education Week’s “Quality Counts
2008” Achievement Index, which ranks Kentucky 40th,
and the Morgan Quitno 2006-07 Smartest State Index,
which ranks Kentucky 31st
 The center also notes that “Only two states that were in the
bottom ten in 1992 managed to climb out of that group:
Kentucky and North Carolina
C OMMON C ORE S TATE
S TANDARDS I NITIATIVE
Who Else is at the Table?
44
Work groups comprised of representatives from higher
education, K-12 education, teachers, and researchers
drafted the Common Core State Standards. The work
groups consulted educators, administrators,
community and parent organizations, higher
education representatives, the business community,
researchers, civil rights groups. . .
A list of work groups and expert members is available
at www.corestandards.org.
Focus
45
The point of the state-led effort to create common
academic standards is simple: improving teaching and
learning to ensure that high school graduates in every
part of the nation have the knowledge and skills they
need for college or a career. The process is designed to
produce standards that are research and evidencebased as well as internationally benchmarked. If
students meet these new rigorous and clear standards,
they will have better choices in their lives and the
nation will be more competitive in today’s global
economy.
Overview of the Initiative
State-led and developed common core
standards for K-12 in English/language
arts and mathematics
Focus on learning expectations for
students, not how students get there.
Why Now?
 Disparate standards across states
 Student mobility
 Global competition
 Today’s jobs require different skills
Why is This Important for
Students, Teachers, and Parents?
 Prepares students with the knowledge and
skills they need to succeed in college and
work
 Ensures consistent expectations
regardless of a student’s zip code
 Provides educators, parents, and students
with clear, focused guideposts
What Momentum is There for the Initiative?
48 states, the District of
Columbia, and two territories
have signed on to the Common
Core State Standards Initiative
Criteria for the Standards
 Fewer, clearer, and higher
 Aligned with college and work expectations
 Include rigorous content and application of knowledge
through high-order skills
 Build upon strengths and lessons of current state
standards
 Internationally benchmarked, so that all students are
prepared to succeed in our global economy and society
 Based on evidence and research not professional
opinion
Standards Development Process
 College and career readiness standards
developed in summer 2009
 Based on the college and career readiness
standards, K-12 learning progressions
developed
 Multiple rounds of feedback from states,
teachers, and feedback group and validation
committee.
 Public comment period on K-12 standards ends
April 2.
Validation Committee
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National and International Experts (as a separate
entity) were used to determined that the standardsdevelopment principles were adhered to by examining
the standards for:
 evidence of the knowledge and skills students need
to be college- and career-ready,
 a proper level of clarity and specificity,
 evidence that the standards are comparable with
other leading countries’ expectations, and
 a grounding in available evidence and research.
Nearly 10,000 People Provided Feedback
53
 K-12 teachers (48 percent);
 •parents (20 percent);
 •school administrators (6 percent);
 •post secondary faculty members or researchers (5
percent);
 •students (2 percent); and
 •other (2 percent).
Math Standards Advances
 Focuses on core conceptual understandings and procedures
starting in the early grades.
 In grades K-5 students gain a solid foundation in whole
numbers, addition, subtraction, multiplication, division,
fractions, and decimals. For example, students in
Kindergarten focus on the number core in order to prepare
them for addition and subtraction.
 In the middle grades, students build upon the strong
foundation in grades K-5 through hands on learning in
geometry, algebra, probability, and statistics.
 The high school standards call on students to practice
applying mathematical ways of thinking to real world issues
and challenges and emphasize mathematical modeling.
Difference Now?
55
 Vertically aligned (a k-12 package)
 Developmentally appropriate according to research
 A continuum of basics to higher level thinking
 More specifics
 Internationally benchmarked
Moses was a Math
Teacher
56
Opinion?
57
 A majority of educators agree or strongly agree that
the College- and Career-Readiness Standards
accurately portray the characteristics exhibited by a
student ready for success after high school.
 Twenty-five percent of respondents who disagree
that the standards are set at the appropriate level of
rigor, do so for a variety of reasons but are split
between whether they are too high or too low.
Opinion?
58
 Educators embrace the idea of fewer topics. Many are
relieved that they will be responsible for fewer standards
and be able to spend the time necessary to teach a topic
well.
 Elementary teachers are most alarmed that “patterning” is
missing.
 Middle School comments revealed tension within the
mathematics education community around the amount and
type of statistics and probability that should be included
and disagreements about when it should be taught, but
none of them agreed with each other
Opinion?
59
 High School teachers did not have common threads of
complaints about the standards
Opinion?
60
The respondents who teach at the college level indicated that
the standards lack key content, including
 solutions of systems of linear equations with two or more variables
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using determinants
solutions of systems of quadratic equations
 trigonometric functions and
exponential equations
identities
logarithms
 analytic geometry
solution of polynomial equations
 analytic geometry
binomial theorem
 parametric and polar equations
permutations and combinations
 conic sections
 complex numbers
Adoption Requirements for States
State adopts 100% of the common core K-12
standards in ELA and mathematics (word for word),
with option of adding up to an additional 15% of
standards on top of the core.
Adoption in Kentucky
62
 Kentucky agreed to completely adopt these
standards before they were ever finished
 Kentucky began breaking down the standards before
they were finished
 Now that the standards are official, Kentucky calls
them the Kentucky Core Academic Standards
(KCAS)
Official adoption currently is in the 30’s with 48 states
promising
Common Standards: The First Step
Standards are essential, but inadequate. Along with
standards,
•
Educators must be given resources, tools, and time to
adjust classroom practice.
•
Instructional materials needed that align to the
standards.
•
Assessments must be developed to measure student
progress.
•
Federal, state, and district policies will need to be
reexamined to ensure they support alignment of the
common core state standards with student achievement.
Math Problem Time
(New Standards)
64
 Compare the following data:
631,000 students at $6493 per student
76,600,ooo students at $7679 per student
Math Problem Time
(Old Standards)
65
Kentucky had 631,000 students in 2004 and we spent an
average of $6493 per student for education. The United states
has 76,600,ooo students and spent on average $7679 per
student.
a)What was the total revenue available for a company to
leverage from KY schools?
b)What was the total revenue available for a company to
leverage from US schools?
c)Use a ration to compare the amount of money available in
KY schools to US schools.
d)Construct a bar graph which shows how the two revenues
above compare?
Comparisons
66
631,000 1% $6,493
$4,097,083,000
% Expenditure
Available
Expenditures
/Student
KY
% of Students
Students
Total
Expenditures
1%
US 76,600,000 99% $7,679 $588,211,400,000 99%
Other Steps for NGA and CCSSO
 Leverage states’ collective influence to ensure that
textbooks, digital media. . .
 Revise state policies for recruiting, preparing,
developing, and supporting teachers and school leaders
 Hold schools and systems accountable through
monitoring, interventions, and support to ensure
consistently high performance
 Measure state-level education performance globally by
examining student achievement and attainment in an
international context to ensure that, over time, students
are receiving the education they need to compete
Let’s Start with a Math Problem
(worthy of the new standards)
68
Compare the following sets of equations when
x1+x2+x3+x4+x5+x6+x7+x8 =1 :
a) f(x) = 0x1 + 0.13 x2 + 0.26x3 + 0.4x4 + 0.6x5 +
0.8x6+ x7 +1.4x8
b) f(x) = 0(x1 + x2 + x3 + x4 + x5 + x6) + (x7 + x8)
This was and is how your school is evaluated:
 f(x) is your Index
x1 = %low novice, x2=%med novice. . . . .
x7= %proficient & x8= % distinguished
69
More Information
 Visit www.corestandards.org
 Sign up for Common Core State Standards updates:
www.ccsso.org/whats_new/newsletters/commoncoreupdates.html
 Dr. Brennon Sapp
bsapp.com

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