Transcript Workshop 4 - Washington Educational Research Association

Making Sense of the Math
Revisions
George W. Bright, Ph.D.
Special Assistant to the Superintendent
OSPI
[email protected]
1
Overview of the Session
• National Mathematics Advisory Panel
• Legislative Actions & Graduation Requirements
• Revised Mathematics Standards: Feb 29 version
Platter Review and Recommendations
Digging into the Revised Standards
2
National Mathematics Advisory Panel
Final Report released on March 13, 2008.
45 Recommendations and Findings
Major Topics of School Algebra
Critical Foundations of Algebra
Benchmarks for the Critical Foundations
3
National Mathematics Advisory Panel
K-8 Curriculum
“The mathematics curriculum in Grades PreK–8
should be streamlined and should emphasize a welldefined set of the most critical topics in the early
grades.”
4
National Mathematics Advisory Panel
Instruction
“Instructional practice should be informed by highquality research, when available, and by the best
professional judgment and experience of
accomplished classroom teachers. High-quality
research does not support the contention that
instruction should be either entirely “student centered”
or “teacher directed.” Research indicates that some
forms of particular instructional practices can have a
positive impact under specified conditions.”
5
National Mathematics Advisory Panel
Teachers
“Our citizens and their educational leadership should
recognize mathematically knowledgeable classroom
teachers as having a central role in mathematics
education and should encourage rigorously evaluated
initiatives for attracting and appropriately preparing
prospective teachers, and for evaluating and retaining
effective teachers.”
6
National Mathematics Advisory Panel
Effort
“Use should be made of what is clearly known from
rigorous research about how children learn, especially
by recognizing a) the advantages for children in
having a strong start; b) the mutually reinforcing
benefits of conceptual understanding, procedural
fluency, and automatic (i.e., quick and effortless)
recall of facts; and c) that effort, not just inherent
talent, counts in mathematical achievement.”
7
National Mathematics Advisory Panel
Assessment
“NAEP and state assessments should be improved in
quality and should carry increased emphasis on the
most critical knowledge and skills leading to Algebra.”
8
National Mathematics Advisory Panel
Research
“The nation must continue to build capacity for more
rigorous research in education so that it can inform
policy and practice more effectively.”
9
Major Topics of School Algebra (1 and 2)
Symbols and Expressions
Polynomial expressions, Rational expressions, Arithmetic and finite geometric series
Linear Equations
Real numbers as points on the number line, Linear equations and their graphs, Solving
problems with linear equations, Linear inequalities and their graphs, Graphing and
solving systems of simultaneous linear equations
Quadratic Equations
Factors and factoring of quadratic polynomials with integer coefficients, Completing the
square in quadratic expressions, Quadratic formula and factoring of general quadratic
polynomials, Using the quadratic formula to solve equations
10
Major Topics of School Algebra (1 and 2)
Functions
Linear functions, Quadratic functions—word problems involving quadratic functions,
Graphs of quadratic functions and completing the square, Polynomial functions (including
graphs of basic functions), Simple nonlinear functions (e.g., square and cube root
functions; absolute value; rational functions; step functions), Rational exponents, radical
expressions, and exponential functions, Logarithmic functions, Trigonometric functions,
Fitting simple mathematical models to data
Algebra of Polynomials
Roots and factorization of polynomials, Complex numbers and operations, Fundamental
theorem of algebra, Binomial coefficients (and Pascal’s Triangle), Mathematical induction
and the binomial theorem
Combinatorics and Finite Probability
Combinations and permutations
11
Critical Foundations of Algebra
• Fluency with Whole Numbers
• Fluency with Fractions
• Particular Aspects of Geometry and
Measurement
12
\
National Mathematics Advisory Panel
Benchmarks: Whole Numbers
1) By the end of Grade 3, students should be
proficient with the addition and subtraction of
whole numbers.
2) By the end of Grade 5, students should be
proficient with multiplication and division of
whole numbers.
13
National Mathematics Advisory Panel
Benchmarks: Fractions
1) By the end of Grade 4, students should be able to identify and
represent fractions and decimals, and compare them on a
number line or with other common representations of
fractions and decimals.
2) By the end of Grade 5, students should be proficient with
comparing fractions and decimals and common percents,
and with addition and subtraction of fractions and decimals.
3) By the end of Grade 6, students should be proficient with
multiplication and division of fractions and decimals.
14
National Mathematics Advisory Panel
Benchmarks: Fractions
4) By the end of Grade 6, students should be proficient with all
operations involving positive and negative integers.
5) By the end of Grade 7, students should be proficient with all
operations involving positive and negative fractions.
6) By the end of Grade 7, students should be able to solve
problems involving percent, ratio, and rate and extend this
work to proportionality.
15
National Mathematics Advisory Panel
Benchmarks: Geometry and Measurement
1) By the end of Grade 5, students should be able to solve
problems involving perimeter and area of triangles and all
quadrilaterals having at least one pair of parallel sides (i.e.,
trapezoids).
2) By the end of Grade 6, students should be able to analyze the
properties of two-dimensional shapes and solve problems
involving perimeter and area, and analyze the properties of
three-dimensional shapes and solve problems involving
surface area and volume.
3) By the end of Grade 7, students should be familiar with the
relationship between similar triangles and the concept of the
slope of a line.
16
Reflection on the NMAP Final Report
• Which of the findings and recommendations
strike you as unusual or particularly
important?
• How might the findings and recommendations
of the National Mathematics Advisory Panel
affect discussions and decisions about
standards, curriculum, and testing in WA?
17
Legislative Actions in 2008
• Legislative actions were completed prior to the
release of the Final Report of the National
Mathematics Advisory Panel.
• Implementation of these actions may be influenced
by that Final Report.
18
Status of Legislation: Standards (Bill 6534)
By May 15
• receive report of national consultant’s review of Feb 29
version of Standards
• consult WA Mathematics Panel about the consultant’s
recommendations
• hold public hearing
• direct modifications to consultant’s report
• forward final report and recommendations to OSPI for
implementation
19
Status of Legislation: Standards (Bill 6534)
By July 01
• OSPI shall “revise the mathematics standards to conform
precisely to and incorporate each of the
recommendations of the State Board of Education”
By July 31
• “approve adoption” of the standards
OR
• develop a plan to do this by September
20
Probable Schedule: Standards
By April 17
• SBE approves K-8 standards
By May 15
• SBE approves standards for Algebra 1, Geometry,
Integrated Mathematics 1, Integrated Mathematics 2
By July 15
• SBE approves standards for Algebra 2, Integrated
Mathematics 3
21
Status of Legislation: WASL (Bill 3166)
• shorten the tests for grades 3-8
• create diagnostic tools (NOTE: “diagnostic” is not defined)
• by 2010 create end-of-course tests for Algebra 1 and
Integrated Mathematics 1
• by 2011 create end-of-course tests for Geometry and
Integrated Mathematics 2
• in 2013 end-of-course tests may substitute for 10th grade
WASL
• in 2014 end-of-course tests replace the 10th grade WASL
22
Issues of Scheduling: WASL
• In order to have end-of-course tests ready for use in
Spring 2010, the standards for Algebra 1 and Integrated
Mathematics 1 must be approved by May 15.
• Any delay beyond that date would put new creation of
new tests in jeopardy.
• This puts some urgency into the discussion of standards
by the State Board of Education.
23
Graduation Requirements:
State Board of Education
• 3rd mathematics credit required for graduation in
2013
• The State Board of Education will determine the
list of permissible courses.
• The expectation is that these decisions will be
made in July 2008.
24
Revised K-12 Mathematics Standards
Feb 29 version: Organization
K-8: organized by grade
Core Content, Additional Key Content, Core
Processes
High School: organized by courses
Algebra 1, Geometry, Algebra 2
Mathematics 1, Mathematics 2, Mathematics 3
also, topics for possible 4th year courses
25
Review of the Feb 29 Version
• The State Board of Education asked Linda Plattner
to review the Feb 29 version of the Revised K-12
Mathematics Standards. Report submitted to
Legislature on March 10, 2008.
• Linda Plattner reviewed the GLEs in Summer 2007 and the
Jan 21 version of the Revised K-12 Mathematics Standards.
• The Legislature delayed action until after Linda
Plattner’s review of the Feb 29 version.
26
Revised K-12 Mathematics Standards
Feb 29 version: Plattner Review
“We first want to commend the substantial work of
Washington educators and community leaders, OSPI,
and the Dana Center. Washington has broken new
ground in its approach to organizing grade level
content by priorities rather than mathematical strands.
The writing teams were inclusive, the stakeholder
feedback extensive. The document clearly is
thoughtful and written with mathematical expertise.”
27
Revised K-12 Mathematics Standards
Feb 29 version: Plattner Review
“Standards inherently involve tensions. They are goal
statements about which different people, even
different experts, will have varied opinions. They
require negotiations, and represent compromises
among varied legitimate participants and groups.”
Confrey, Jere, “Tracing the Evolution of Mathematics Content Standards in the United States: Looking Back and Projecting
Forward towards National Standards,” a paper prepared for the Conference on K–12 Mathematics Curriculum Standards,
sponsored by CSMC, NCTM, Achieve, College Board, MAA, ASA (February 2007).
28
Revised K-12 Mathematics Standards
Feb 29 version: Plattner Review
“The new mathematics standards for grades
K–8 are very close to excellent. These
standards do compare favorably with the best
in the nation and the world. The Performance
Expectations are specific, measurable,
important mathematical topics that are both
focused at particular grades and developed
across grade levels.”
29
Revised K-12 Mathematics Standards
Feb 29 version: Plattner Review
“While they [the high school standards] are
much improved from OSPIʼs January version,
further revision is needed. Some areas, such
as occasional imprecision of language, is
similar to grades K–8 and just as easily fixed.
Other areas, such as missing content and
content organization, are more problematic.”
30
Revised K-12 Mathematics Standards
Feb 29 version: Plattner Recommendations
1. An exemplar review of the OSPI February standards K–8 and 9–12, similar
to last yearʼs comparison to other states, countries and national frameworks using
the nine criteria to provide external validation that these are the best standards. In
order to compress the timeline … we suggest fewer grade levels and fewer
documents.
2. Substantive edit for grades K–8. The content is very good; language is
almost ready. These standards are so close that work could be completely very
quickly.
3. A revision of the high school standards. The core content of the
subjects is in the document and many of the examples are excellent. The language
needs to be tightened and there is some more work to be done on the content. This
means it will take slightly longer than the grade K–8 work.
31
The Substance of the Revised Standards
Given the pivotal role of standards in testing,
curriculum review, and instruction, let’s turn
our attention to what mathematics
Washington educators have said is important
for students to learn.
Attend first to K-8 standards.
32
Depth of Content
Where is the first mention of each of the following
ideas? Where is the last mention?
• multiplication of whole numbers
• mean of a set of data
• area formulas for triangles
What do you notice about the range of grades for
these topics?
33
Debriefing Depth of Content
multiplication of whole numbers
mean of a set of data
area formulas for triangles
34
Grade Band Discussions: K-2, 3-5, 6-8
What key mathematics would students in your
grade band learn for each of the following?
operations, geometry, data
How do the main ideas develop across your grade
band for each of the following?
operations, geometry, data
35
Debriefing Grade Band Discussions
operations
geometry
data
36
Student Learning
What is the image of mathematics that the
Standards for this grade band
communicate?
What is the “residual learning” that
students will have as they leave this grade
band?
37
Debriefing Student Learning
image of mathematics
“residual learning”
38
High School Standards
• If Algebra 2 is for ALL students, what content
should it include?
• If Algebra 2 is for COLLEGE-BOUND
students, what content should it include?
• What options to Algebra 2 should there be?
39
Revised High School Standards
• How well do the High School Revised
Mathematics Standards reflect what students
should know?
• Tentatively, Algebra 2 standards should be
approved about July 2008.
40
Closing Comments
• Share this information with colleagues.
• Communicate with Legislators and members of
the State Board of Education about what should
be in Washington State’s Revised K-12
Mathematics Standards.
• Support local teachers as they learn about the
revised standards and begin to implement them.
41