Integrated vs. Traditional Pathway

Integrated (International)
Math Pathway
vs
Traditional Math Pathway
What Do They Look Like?
TRADITIONAL
REGULAR
HONORS
8th Grade
8th Grade Math
Algebra I
Freshmen
Algebra I
H.Algebra II
Sophomores
Algebra II
H.Geom
Juniors
Geometry
H.PreCalc
Seniors
PreCalc
AP Calculus
(Stats)
AP Stats
(Comp.Science)
(Applied-Financial Algebra)
INTEGRATED
REGULAR
HONORS
8th Grade
8th Grade Math
H. Math I
Freshmen
Math I
H. Math II
Sophomores
Math II
H. Math III
Juniors
Math III
H.PreCalc
Seniors
PreCalc
AP Calculus
(Stats)
AP Stats
(Comp.Science)
(Applied-Financial Algebra)
(Math IV)
How Do They Differ?
TRADITIONAL
 Objectives presented as
separate concepts
 Taught via rules,
procedures, and
memorization
 Lecture based, teacher
directed
 Continuous practice of
procedures
INTERGRATED
 Objectives from algebra,
geometry, functions,
math modeling, and
probability and statistics,
are interwoven
 Real world problems are
investigated via lab-type
experiences
 Teacher serves as
facilitator and coach
 Collaborative learning
 Practice with a purpose
How Do Those Attributes Align with CCSS?
Common Core Attributes
 Focus and coherence
 Balance of Concepts and
Skills
 College and Career Readiness
 Mathematical Practices
1.
2.
3.
4.
5.
6.
7.
8.
Mathematical Practices
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments and
critique 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
FACTS TO CONSIDER
 Although the percentage of US high school students enrolled in
integrated mathematics courses is pretty small, the worldwide
percentage of students enrolled in integrated mathematics courses
would be about 99%. In the US K-8 mathematics is integrated, and
in the rest of the world, K-12 mathematics is integrated. So about 12
million US students in Algebra I, Geometry, or Algebra II would be
about 1% of more than 1 billion school-aged children worldwide.
 In college, in the workplace, and in everyday life, problems do not
come labeled “Algebra” or “Geometry”. Thus, for success in college
and careers, high school graduates need opportunities to bring
together their understandings of number, algebra, geometry, and
statistics. In other words, whatever the names of the courses,
mathematics curriculum and instruction should provide
opportunities for integrated learning.
DATA POINTS
From a paper prepared for the National Academies Board
on Science Education and Board on Testing and
Assessment for “Highly Successful STEM Schools”…
COSMIC Study Results
(Comparing Options in Secondary Mathematics
:Investigating Curriculum)
Tarr, Ross, McNaught, Chavez, Grouws, Reys, Sears and
Taylan, 2010
Results as measured on three tests – two created
specifically for the study and one standardized –
measuring content, reasoning and problem solving
• Gain Scores (Posttest – Pretest) were positively correlated on
three tests in favor of integrated curricula compared to traditional
curricula.
• When controlling for %FRL (Free and Reduced Lunch), the
magnitude of the correlation between Curriculum Type and
student outcomes become significantly different than 0 in favor of
the integrated curricula.
• Opportunity to Learn (OTL) was significantly and positively
correlated with higher performance on all three outcome
measures.
• OTL and %FRL are closely related. In other words, the findings
suggest that using integrated math with students of poverty is a
promising option.
Much has been written about how to close the achievement gap.
Most educational gurus agree that students who take more
rigorous coursework learn more, perform better on tests, and
reach higher levels of post-secondary education.
ADVANCED MATH ENROLLMENT (BEYOND THREE YEARS) IN ONE NORTH
CAROLINA SCHOOL AFTER INSTITUTING INTEGRATED MATH CURRICULUM
20012000-01
2002-03 2003-04 2004-05
2005-06
02
Prob/Stats
39
Discrete
40
Stat/Disc
108
110
111
77
AFM
Advanced Functions and Modeling
Precalc
54
103
188
IM4
Integrated Math 4
193
171
170
110
131
16
75
69
147
166
AP Stats
61
62
81
104
88
80
AP Calc
63
74
61
84
81
97
TOTALS
391 455 499 504 510 631
Most Recent Information from PARCC
December 21st, 2012
 PARCC high school assessments will include course-based tests
in Algebra I, Algebra II and Geometry as well as equivalent
integrated courses Mathematics I, II, and III.
 For the first three years of testing, the math will be based on an
enhanced version of the final mathematics assessment (Algebra
II or Math III) that include two additional performance based
tests that draw on students’ knowledge of key concepts and skills
from earlier high school math courses.
 Since Integrated Math series incorporate all topics of math
content each year, at progressively high levels; it stands to reason
that students might have better retention of previously learned
material than in isolated content curriculum of traditional
pathways.
Math Common Core Pathway Update
December 18th, 2012
 Public Act 097-0704 that was passed in June of 2012, charged ISBE to
“…coordinate the acquisition, adaptation, and development of middle and
high school mathematics curriculum models to aid school districts and
teachers in implementing standards for all students.”
Public Act
http://www.ilga.gov/../legislation/publicists/fulltext.asp?Name=097-0704
 Model to be presented by March 1, 2013
 “We have recently confirmed with the group of stakeholders that is creating
the model mathematics curriculum that the curriculum will follow the
INTEGRATED PATHWAY at the secondary level (which will also impact
middle school math curriculum for those who offer a compressed or
accelerated math trajectory for 6-8th grade students.” (Anji Garza –
Director of Professional Development Lee/Ogle ROE#47)
 Illinois has decided that districts will have this INTEGRATED model
curriculum that they can either adopt or adapt.
 “It has been our understanding, however, that the developed “model
curriculum” will drive the assessment that will be ordered from the PARCC
assessment consortium”. (Anji Garza)