Transcript Math Standards for School Administrators

Integrated School
Mathematics:
Pitfalls, Products,
and Predictions for
the Peach State
Keary Howard Ph.D.,
SUNY Fredonia
[email protected]
Some 60 Minute Objectives
• Define integrated mathematics via a
few good hooks.
• Put you in a New York State of mind.
• Discover the real Dana TeCroney.
• Tell the fortune of Georgia school
mathematics.
• Get you ready for some SEC football.
A truly integrated mathematics curriculum relies on rich
problems that:
1. Prompt solutions between and within fundamental
mathematical content areas.
2. Foster multiple representations.
3. Make you wanna solve ‘em.
Hook: How many solutions are there to the equation:
x
2 =x
2
Some NYS School Math Fast Facts
• NYS is home to some the largest school districts (New York City
School District), smallest school districts (Clymer Central School
District), and the richest (the Hamptons).
• It’s called the Empire state for a reason. Driving time from
Clymer to the Hamptons is approximately the same as it is from
Clymer to Columbia, SC or from Clymer to Knoxville, TN.
• Since the 1950s, all school districts in NYS have been united by a
common high school mathematics curriculum.
• Since the 1920s, common assessments (Regents Exams) have
been a staple of the secondary school exam.
• An Integrated Mathematics Curriculum at the high school level
was first piloted 30 years ago. Although significant revisions have
been made to the curriculum on at least two occasions, Integrated
Mathematics remains firmly in place in NYS.
Riddle me this…
• Rank order the following three
artifacts from greatest to least on
their influence on the ‘taught’
curriculum.
A. State Standards Document
B. National Textbooks
C. State-Mandated Exit Exams
Integrated Mathematics Revisited Via a
Clymer Pirate
•
9th-11th grade mathematics takes on weird and blatantly non-descriptive
names such as Course I, II, and III or Sequential Math I, II, or III.
•
The topics taught are expansive and often re-examined from year to year.
In the 1990s typical NYS freshmen and sophomores were exposed to:
logic, transformational geometry, combinatorics, as well as more
traditional curricular material such as algebra and Euclidean Geometry.
•
Texts needed to be created specifically for NYS students, since the
curriculum was so different from those in other states. They varied from
the traditional to very progressive. Each school district is free to choose
its text. The decision often rests with the department chair or a
committee headed by the department chair.
•
While schools are free to choose texts, all schools must give the same exit
exam. Course I, II, and III exams are created by teams of teachers,
secured, and administered at the same date each year. The exam serves
as the ‘final’ for each student and scores (both individual and district) are
reported to a state clearinghouse
Some Examples of 1990s Integrated
Math Regents Exams in NYS
•
•
You can trace the history of NYS Integrated math through its exit exams:
http://www.nysl.nysed.gov/regentsexams.htm
Course I Sample 10 Point Questions
Some Basic Theory on Curriculum
Implementation
Posner’s Five Concurrent Curricula:
–
–
–
–
–
1.
2.
3.
4.
5.
Official Curriculum
Operational Curriculum (Taught and Tested)
Hidden Curriculum
Null Curriculum
Extra Curriculum
Posner, G. (1992). Analyzing the Curriculum. McGraw-Hill.
Four
– 1.
– 2.
– 3.
– 4.
Critical Tasks of Teachers:
Content Coverage (Breadth)
Content Mastery (Depth)
Classroom Management
Positive Affect
“Teachers will adapt or transform an unsuitable curriculum in
such a way that they can make the curriculum fit the
classroom realities.” (Posner, p.187)
NYS Integrated Math, NCTM Standards, and
NCLB = Bad Date
• The last decade has been one of critical and significant change in
NYS school mathematics.
• Now all students would be required to pass the new statemandated Math A exam to receive a high school diploma. These
new exit exams would eliminate the high school level Integrated
Mathematics Course I, II, and III offered annually in June. Now
two exams (Math A and Math B) would cover the material of
three.
• Three critical changes were made that affected the curriculum:
– Standards were raised requiring all students to pass the Integrated
Math A exam.
– The exams moved from criterion referenced to norm-referenced.
– Choice was eliminated in what questions student could answer. In
addition, much more emphasis was placed on open-ended constructed
response problems
Take the ‘L’ Out of Lover ‘Cause That’s What We
Are: An Integrated Math A Exit Exam Fiasco
• In June of 2003 a Math A Regents Exam produced the
greatest uproar of any NYS exam to date.
• Two thirds of all students failed the exam, many of whom
planned to graduate.
• The exam was poorly written, verbose, and some thought
overly difficult.
• State ed commissioner Richard Mills immediately voided the
exam results and established a panel to review the exam
and provide direction for the future.
• The Math A panel quickly produced a list of
recommendations for Commissioner Mills. These included
the development of a new exam, new piloting procedures,
and (most importantly) the establishment of new
mathematics standards with specific grade
performance indicators.
Two Samples from the 35-Question,
Four-Part, 20-Page Exam
A ‘Honey Do’ List for Georgia’s Best
Math Educators
• Do work hard to establish a set of math-specific standards
and content performance indicators for each grade level.
• Do create state-wide curricular material that can be used in
the creation of Georgia-specific texts.
• Do entrust your teachers with the creation of high-quality
exit exams that accurately reflect your curricular content
and philosophy.
• Do look to the GCTM for leadership in professional
development and oversight of curricular materials,
curricular implementation, and exam creation.
• I do like your chances – you’ve got great students,
teachers, schools, and universities.
In the process, please don’t sacrifice your mathematical soul.
Remember, a truly integrated mathematics curriculum relies
on rich problems that:
1. Prompt solutions between and within fundamental
mathematical content areas.
2. Foster multiple representations.
3. Make you wanna solve ‘em.
I Challenged the Goliath
Following ‘Fright Night’ at SFOG and a midnight
run on the Goliath, you ask yourself a simple
question: Are the tallest coasters, the fastest?
Another McGyver Miracle?
McGyver claims that he can find the height of any object
with only a protractor and mirror, while never leaving the
ground. Describe, in theory, how this is possible. Use
diagrams and your understanding of geometry, similarity,
and proportion to provide a detailed explanation of the
mirror mystery.
SEC Showdown: Defense Wins Championships
The legendary Vince Dooley has a question for you: How
many points does it take to guarantee a win in SEC
football? Suppose that winning 75% of SEC divisional
games is typically the benchmark for big-time bowl
eligibility.
Closure: Helmet Sticker Quiz
x
• Q1: How many solutions are there to the equation: 2 = x
2
• Q1 Answer: 3
• Q2: What curricular product is likely to have the greatest impact
on the ‘taught’ curriculum?
• Q2 Answer: State-Mandated Exit Exams
• Q3: Posner argues that teachers will adapt the official curriculum
to fit the needs of four critical teaching tasks which include
coverage, mastery, positive affect, and what fourth critical
component?
• Q3 Answer: Classroom Management
• Bonus: What’s the greatest ‘Break-Up’ Line of all time?
• Bonus Answer: Take the ‘L’ out of ‘Lover’ ‘cause that’s
what we are…