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.]
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 Math Department chairman
Robyn Rosenthal (RRosenthal@pvschools.net) and two teacher colleagues. Paradise Valley Unified School District
expanded CIMM to more schools in subsequent years, saving much 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 . Robyn uses CIMM in 2012.
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 the Phoenix Union High School District, and thereafter at Hamilton High School in Chandler USD
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