High School Mathematics
Department Chairpersons Meeting
November 17, 2011
Presented by the Office of Curriculum, Instruction and Student Support
Dewey Gottlieb
Educational Specialist for Mathematics
Stacie Kaichi-Imamura
Mathematics Resource Teacher
My Intentions
• Inform
• Learn
• Stimulate
• Provoke
• Plan
• Inspire
HIDOE’s Strategic Plan
July 2011 – June 2018
RTTT Action Plan
Systems of Support to enable schools to do their best work
Common Core Standards
Career & College Ready Diploma
Standards-based instruction
Formative Assessments
Interim Assessments
Summative Assessments
STEM
Data for School Improvement
Longitudinal Data System
Using data to inform instruction
SMARTER Balanced
Assessment Consortium
HIDOE is working collaboratively with 30 other
states to design and implement an assessment
system aligned to the Common Core State
Standards
SY 2014-2015: SBAC assessments to be
administered for grades 3-8 and 11.
HIDOE’s transition plan for implementing the
CCSS was developed in response to SBAC’s work
plan and timelines
Implications for High
School Mathematics
• BOE Policy 4540
– Class of 2016: 3 credits of mathematics
(Algebra I and Geometry required)
• High school mathematics courses
– Modeling Our World I & II
– Review of ACCN to recommend addition or
deletion of courses.
Modeling Our World
Courses
• MOW IA/IB
– Supplement to Algebra I (intent is for
students to enroll concurrently)
– Content based on the CCSS for High School
Mathematics (focus on MODELING)
» Not a replacement of pre-algebra or a
basic skills review course
– Counts toward one of the 3 mathematics
credits required for a diploma
Modeling Our World
Courses
• MOW IIA/IIB
– A “Bridge to Algebra II” course
– Content based on the CCSS for High School
Mathematics (focus on MODELING)
– Counts toward one of the 3 mathematics
credits required for a diploma
Fundamental Beliefs
All children, regardless of differences in
ethnic background and socioeconomic status
have the capacity to learn and succeed at
high levels. Mathematics classrooms should
be characterized by a caring environment,
active engagement, inquiry, and a culture
that promotes dialogue and a willingness to
learn from one’s mistakes.
Fundamental Beliefs
It is the responsibility of all mathematics
teachers to ensure that students are provided
with meaningful learning opportunities that
promote academic success, self-efficacy,
personal growth, and an appreciation for the
utility and beauty of mathematics that will
inspire students to view the continued study of
mathematics as a worthwhile pursuit.
Who did this for you?
Transition from HCPS III
to the Common Core
August 2011 – June 2014
NON-tested grade levels
• Grades K-2 & Algebra II
Instruction aligned to the CCSS
• Algebra II to continue to use
the ADP standards
• Instruction and the HSA blueprint
aligned to HCPS III
Tested grade levels
• Grades 3-8, Algebra I and
• Incorporation of the CCSS into
Geometry
classroom instruction and SBAC
field test
All Grade Levels
CCSS Mathematical Practices
The Standards for
Mathematical Practices
“Encouraging these practices in students of all ages
should be as much a goal of the mathematics curriculum
as the learning of specific content” (CCSS, 2010).
1.
2.
3.
4.
5.
6.
7.
8.
Make sense 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 use of structure.
Look for and express regularity in repeated reasoning.
Standards for
Mathematical Practice
Reasoning
and
Explaining
Modeling
and
Using Tools
Seeing Structure
and
Generalizing
#1: Mathematically
Proficient Students …
Make sense of problems and persevere in solving them.










Explain the meaning of the problem to themselves
Look for entry points
Analyze givens, constraints, relationships, goals
Make conjectures about the solution
Plan a solution pathway
Consider analogous problems
Try special cases and similar forms
Monitor and evaluate progress, and change course if necessary
Check their answer to problems using a different method
Continually ask themselves “Does this make sense?”
Gather
Information
Make a
plan
Anticipate
possible
solutions
Continuously
evaluate
progress
Check
results
Question
sense of
solutions
#2: Mathematically
Proficient Students …
Reason abstractly and quantitatively.
Decontextualize
Represent as symbols, abstract the situation
5
½
Mathematical
Problem
P
x x x x
Contextualize
Pause as needed to refer back to situation
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education).
Presentation to the CCSSO Mathematics SCASS, November 2011.
#3: Mathematically
Proficient Students …
Construct viable arguments and critique the
reasoning of others.
Make a conjecture
Build a logical progression of
statements to explore the
conjecture
Analyze situations by breaking
them into cases
Recognize and use counter
examples
Whitesides, E. (2011). The CCSS Mathematical Practices. Presentation at the CCSSO Mathematics SCASS meeting, November 2011).
#4: Mathematically
Proficient Students …
Model with mathematics.
Problems in
everyday life…
…reasoned using
mathematical methods
Mathematically proficient students
• make assumptions and approximations to simplify a
situation, realizing these may need revision later
• interpret mathematical results in the context of the
situation and reflect on whether they make sense
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education).
Presentation to the CCSSO Mathematics SCASS, November 2011.
#5: Mathematically
Proficient Students …
Use appropriate tools strategically.
Proficient students
•
are sufficiently familiar with
appropriate tools to decide
when each tool is helpful,
knowing both the benefit
and limitations
•
detect possible errors
•
identify relevant external
mathematical resources,
and use them to pose or
solve problems
#6: Mathematically
Proficient Students …
Attend to precision.
•
•
•
•
•
•
communicate precisely to others; use clear definitions
state the meaning of the symbols they use
specify units of measurement
label the axes to clarify correspondence with problem
calculate accurately and efficiently
Express answers with an appropriate degree of precision
Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819
#7: Mathematically
Proficient Students …
Look for and make use of structure.
•
•
•
look closely to discern a pattern or structure
step back for an overview and shift perspective
see complicated things as single objects, or as
composed of several objects
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education).
Presentation to the CCSSO Mathematics SCASS, November 2011.
#8: Mathematically
Proficient Students …
Look for and express regularity in repeated reasoning.
•
•
•
notice if calculations are repeated and look both for general
methods and for shortcuts
maintain oversight of the process while attending to the details,
as they work to solve a problem
continually evaluate the reasonableness of their intermediate
results
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education).
Presentation to the CCSSO Mathematics SCASS, November 2011.
Let’s do some math!
• Please take about the next 13π
minutes to complete the
mathematical tasks.
• Pay close attention to and note your
own mathematical thinking as you
work.
Focus Group Interviews:
We want your thoughts
• In order to create meaningful courses that
teachers will be excited to teach and
students will be engaged, let’s think about.
•
What are barriers to success in Algebra I?
•
How can we better prepare and motivate
students to be successful beyond Algebra I?
• Your feedback will inform the development
of the MOW courses.
My Intentions
• Inform
• Learn
• Stimulate
• Provoke
• Plan
• Inspire
A shift in perspective
The CCSS for Mathematics compel a
change in the culture of traditional
mathematics classroom.
In the typical mathematics classroom
students are “too busy covering content”
to be engaged with mathematics.
A shift in perspective
Mediocre mathematics achievement
and unacceptably stark achievement
gaps are the symptoms – not the
problem.
If we conceive of it as an
“achievement” gap, then it’s THEIR
problem or fault.
--Steve Leinwand
(Presentation at the Association of State Supervisors of Mathematics, April 2011)
A shift in perspective
Alternatively, it is a system failure, the heart
of which is modal instruction that fails to
provide adequate opportunity to learn, that is
the problem.
If we conceive of it as an “instruction” gap,
then it’s OUR problem or fault.
And OUR responsibility to fix!
--Steve Leinwand
(Presentation at the Association of State Supervisors of Mathematics, April 2011)
Let’s be clear
We’re being asked to do what has never
been done before:
• Make math work for nearly ALL kids and
get nearly ALL kids ready for college.
• There is no existence proof, no road
map, and it’s not widely believed to be
possible.
--Steve Leinwand
(Presentation at the Association of State Supervisors of Mathematics, April 2011)
Let’s be clearer
When most of our efforts work for
only 30% - 40% of our students …
We’ve got work to do!
--Steve Leinwand
(Presentation at the Association of State Supervisors of Mathematics, April 2011)
A shift in perspective
Number of
HS Grads
Enrolled at
UHCCs
Number Enrolled in
Developmental or
Remedial
Mathematics
Percent Enrolled in
Developmental or
Remedial Mathematics
2008
3,379
1,680
49.7%
2007
2,208
1,409
50.2%
2006
2,589
1,251
48.3%
Year
3,379
2008
1,680
49.7%
HIDOE Grads Enrolled at UHCCs
2007
2,808
50.2%
1,409
2,589
2006
48.3%
Number enrolled in DEV or REM
mathematics
1,251
Source: University of Hawai`i Institutional Research Office, “Hawaii Public High School Graduates Enrolled in
Remedial and/or Developmental Classes at the University of Hawai`i Community Colleges” (February 2009)
A shift in perspective
100%
90%
Percent of Hawaii
DOE Graduates
Enrolled in
Remediation-level
Courses in the
University of
Hawaii system*
80%
70%
60%
2008
50%
2009
49%
50%
2010
40%
30%
38% 36%
35% 33%
20%
10%
0%
Remedial Math
Remedial English
*Source: Hawaii P-20 Partnerships for Education “College and Career Indicators Report”
Another perspective
• Dr. Mitchel Anderson, UH-Hilo
• Dr. Diane Barrett, UH-Hilo
• Dr. Monique Chyba, UH-Manoa
Promoting the
Mathematical Practices
Mathematics as a tool
for making informed,
well-reasoned decisions.
What does this mean for the
grades that I teach?
• Let’s discuss MP #3 and MP #4 a little
more deeply.
• If the MP is the effect that we want to
bring about (i.e., see students
exhibiting), what must we consider
when designing learning experiences
to cause that result?
Additional Updates
• Algebra II End-of-Course Exam
• Testing
window: May 7-13, 2012
• Standards Toolkit Website
• Resources and
webinars
• Good Idea Grant
•
www.hsta.org/upload/goodideagrant_app.pdf
Additional Updates
• Presidential Awards for Excellence in
Mathematics and Science Teaching
(PAEMST)
• www.paemst.org
• Nominate an
teacher
outstanding grades K-6
Additional Updates
Upcoming PD opportunities:
•
ADP Algebra II EOC Exam (Pearson trainers)
• Workshops scheduled January 9-13, 2012.
•
Diane Barrett, Mitch Anderson, Bob Pelayo (UHHilo)
• Workshops to be planned in spring and
summer focusing on Algebra II and the CCSS
Additional Updates
Upcoming PD opportunity:
•
Dan Meyer
• March 26-27
• End of June
• End of July
 Video: “Math Class Needs a Makeover”
http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html