Solving the math problem: AIMS math test gains
due to Modeling Instruction and CIMM
by Jane
Jackson (interview of Denis Lawton in summer 2007)
Solving
the math problem is crucial. Toward this end, below is solid evidence for great
effectiveness in math achievement of Modeling Instruction and Cognitive
Instruction in Mathematical Modeling (CIMM) for middle school students in urban
public low income schools.
Use of
Modeling Instruction and CIMM can improve the high school graduation rate,
contribute to economic development; and enhance the wellbeing of our culture
by producing a populace who can think, reason, and understand.
Denis Lawton is an experienced and highly regarded 8^{th}
grade mathematics teacher in an urban Phoenix elementary school in a
povertystricken neighborhood. He is the only 8^{th} grade teacher in
his school. In 20062007, his class consisted of regular to lowlevel
students; all but one were Hispanic, onehalf were ELL, ten were SPED with
learning disabilities.
Denis reports a huge improvement in the pass rate in the
ÒArizona Instrument to Measure SuccessÓ (AIMS) 8^{th} grade math test
in spring 2007, the year after he took our graduate course, PHS534: ÒMethods of
Physical Science Teaching.Ó Twothirds of his students, 65%,passed the AIMS math test, compared to only half
(48%) in the year before he took our course. Results were equally good in the
next year, 2008.
He reports that his 2007 students started out
worseprepared than the previous year's group, which makes their math
achievement even greater than the test scores indicate.
He states as chief reasons for his improved AIMS pass rate that he implemented his course learning from summer 2006 at ASU. Specifically, he did oneweek modeling cycles eight or nine times during the year in his prealgebra sections.
Causes of success were, he said in a phone interview,
"a deliberate focus on what concepts mean; repetition; modeling; kids having to verbalize and
describe in whiteboard presentations, and me as the teacher going into the
cycle with a crystal clear vision of what I wanted the students to produce at
the end."
He began each modeling cycle with an activity in
mathematical modeling that he learned in the course (modeling workshop); among
them were measurement activities using Cognitive Instruction in Mathematical
Modeling (CIMM) developed by Dr. Robert MacDuff, formerly a Postdoctoral
Associate in the Modeling Instruction Program at Arizona State University, and
adapted by workshop leaders Patricia Burr and S. Lee Rodgers. He taught slope
in connection with graphing and linear equations for the first time to his
prealgebra students.
Students prepared whiteboards and gave presentations for a
couple of days in each cycle. He said, "Doing the math was only part of
it; kids thought deeply when preparing
whiteboards about what questions I'd ask them. They prepped one another for
this."
Denis gathered evidence showing the progress of the 66
students (out of 90) in his 8^{th} grade math classes who had also
taken the 7^{th} grade AIMS test at his school (from a different
teacher). SPED students are included in the 66, he said. He wrote, "I looked at data
analysis, algebra, and measurement  the items we repeatedly explored in
modeling." Here is a summary of some of his results. The number of those
66 students who got higher than 65% correct in each topic are:
AIMS
test TOPIC 
%
CORRECT 
7^{TH}
grade AIMS Test 
8^{th}
grade AIMS test 
gain 

data
analysis 
66%
& higher 
35
students (53%) 
49
students (74%) 
20% 

algebra
 overall 
66% &
higher 
23
students (35%) 
42
students (64%) 
30% 

geom.
 measurement 
70%
& higher 
24
students (36%) 
36
students (55%) 
20% 

He wrote about these data, "I found that we were
hitting almost onehalf of the eighth grade standards with each modeling cycle.
I have no other explanation
[than modeling instruction] for the incredible growth we saw."
Another way of looking at it is, for the 66 students who
took both tests while at his school, their AIMS math scores in standard format
are:
AIMS
math test 
7^{th}
grade 
8^{th}
grade 
Falls
far below 
14 
11 
Approaches 
21 
10 
Meets 
31 
41 
Exceeds 
0 
4 
This
shows a huge improvement in individual studentsÕ math achievement from grade 7
to grade 8.
Denis
was the only eighth grade math teacher in his school. He said that he hoped
that his district wouldn't revert to more traditional 'drill and kill' methods;
he wanted to use his evidence to convince his district that Modeling
Instruction is a better way. (He gave written permission to use his name.)
[Update
in 2009: He could not convince his colleagues; they chose a traditional math
curriculum. The school district was failing, and the staterequired consultant
from West Ed insisted that teachers use direct instruction. Denis moved to the
University Charter School in urban Phoenix. In 2016 he was Student Achievement Strategist for K8 Mathematics in Isaac
Elementary School District, in urban Phoenix. ]
Commentary
and further evidence:
More evidence of great success is provided by Ms. Robin
Inskeep, an eighth grade science teacher
at Porfirio Gonzales School in Tolleson Elementary School District. She wrote,
Date: Fri, 01 Oct 2004
From: "Inskeep, Robin" <RINSKEEP@tesd.k12.az.us>
I truly believe that the two
modeling classes that I have taken, Methods of Teaching Physical Science and
CASTLE [electricity], have greatly improved my teaching methods, which have
resulted in the students having a deeper understanding of the concepts being
taught. Last year was the first year that this method was implemented with the
entire 8th grade. Without a doubt, the skills that I learned through the
modeling courses were the major reason that this class' scores for math
approximately doubled in the 'meets and exceeds' category on the AIMS test spring of 2004. You have my permission to quote anything that I have said.
An
expansion of Modeling pedagogy to mathematics, Cognitive Instruction in
Mathematical Modeling (CIMM), was piloted with tremendous success in remedial
algebra at Paradise Valley High School in 20062007 by then Math Department
chairman Robyn Rosenthal and two teacher colleagues. Paradise Valley Unified School District expanded CIMM to
more schools in subsequent years, saving money by reducing the dropout rate
– and empowering students to think, reason, and understand. Data and a
principal's letter are at
http://modeling.asu.edu/CIMM.html . [Update in2016: When Robyn Rosenthal
retired in 2015, Paradise Valley High School discontinued prealgebra and CIMM.
Robyn wrote in 2016, ÒI would love to teach CIMM!Ó In 2016 she taught at Pinnacle HS: robynrosenthal@yahoo.com]
The need is urgent. CIMM and Modeling Instruction are a solution to the math problem  and the science problem. These problems go together. Schools are smart if they make concerted efforts to have teachers learn Modeling Instruction and CIMM.
Appendix:
the modeling workshop at ASU
Denis Lawton took PHS 534/MTE 598: Methods of Physical Science Teaching (Physical Science with Math Modeling Workshop). The course provides 8th and 9^{th} grade teachers of science and mathematics with education in Arizona standardsbased content and instructional strategies. Participants are introduced to the Modeling Method as a systematic approach to the design of curriculum and instruction. The name Modeling Instruction expresses an emphasis on making and using conceptual models of physical phenomena as central to learning and doing science. Mathematics instruction is integrated seamlessly throughout the entire course by an emphasis on mathematical modeling. Anticipated student outcomes include improved understanding in geometrical and physical properties of matter, mathematics and reasoning skills such as algebraic proportions, independent & dependent variables, relation between graphs and equations, and measurement & estimations; energy and states of matter. The course was taught by Patricia Burr and S. Lee Rodgers, teachers of ninth grade physical science until 2011 at South Mountain High School in Phoenix UHSD, then at Hamilton High School in Chandler USD. As of 2015, Patricia Burr is at Mountain Pointe High School in Tempe Union High School District.
For information: http://modeling.asu.edu/MNS/MNS.html
For an introduction to CIMM, visit http://modeling.asu.edu/CIMM.html .
Contact Dr. Jane Jackson, CoDirector, Modeling Instruction Program, Department of Physics, Arizona State University. 4809658438 or 4803141522, jane.jackson@asu.edu