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Constructivism vs. NCLB and MCAS – Pedagogy vs. Standards
Abstract
The establishment of the No Child Left Behind Act has catapulted standardized testing to the national forefront. At the same time, middle schools across Massachusetts are instituting math textbook programs that follow a constructivist methodology. Can the use of instructional approaches that center on co-constructivism and social constructivism meet standardized test requirements of MCAS? Key theories of constructivism are examined. The methodology behind construction of the math component of the Massachusetts Comprehensive Assessment System is then examined. Findings indicate that the design and implementation of the MCAS in response to NCLB is not in alignment with a constructivist methodology of teaching. This leads to a dichotomy of teaching the student versus teaching to the test.
John T. Crescitelli
Boise State University
Michael Fuller/EdTech 504
July 31, 2010
Constructivism vs. NCLB 2
Introduction
The deadline for alignment to the U.S. government’s No Child Left Behind Act of 2014
is fast approaching. At that point, all students in U.S. public schools must show proficiency in
all subject areas. The NCLB Act requires all states comply with national educational standards
and develop assessment systems to assure all students are making adequate yearly progress.
From Pennfeld, NY to Alpine School District in Utah, to Guilford ,CT, to Hamilton County,
TN, constructivist math text programs such as Investigations, Everyday Math, and Connected
Math are being challenged by parents and advocates who are against ‘reform mathematics’(Hu,
2007; Schultz, 2009; Shapira, 2008).
Is there a basis for this backlash against constructivist mathematics practices? I believe
there is. However, I do not believe a constructivist approach to teaching math in the middle
school is incorrect. I believe that the assessment systems set in place by individual states, and I
will use Massachusetts for my study, do not adequately assess learning in a manner that
compliments constructivist approaches to instruction. In fact, I believe that due to NCLB and
state testing requirements, constructivist texts such as Connected Math and Investigations cannot
succeed. The tests created by individual states to meet the requirements of NCLB do not align
with middle school math text series that follow constructivist practices.
The very foundations of how we look at assessment must be changed in order for
constructivist practices that place the learner as the central role to be successful (Brooks, 1999).
The focus on high-stakes accountability testing changes the focus of assessment from enhancing
student learning to that of managing comparative data of schools and learners. I am not
suggesting that students and teacher must not be held to standards. However, success on a high
Constructivism vs. NCLB 3
stakes, multiple choice test, does not necessarily hold anyone accountable for real learning
(McDermott, 1993).
The goal of the Department of Education must be to develop instructional technologies
that better assess learning for all students. That focus must move evaluation away from
computer, data driven analysis to a more holistic view of learning that allows for various forms
of assessments to better meet the needs of educational reform. Although performance-based
assessment would be challenging to monitor nationwide, allowing more autonomy to states to
determine adequate yearly progress might allow for more alternative assessment practices.
Key Principles of Constructivism and Math Instruction
Constructivist theories originate in the cognitive psychology studies of Jean Piaget. It
was Piaget’s belief that children develop understandings by assimilation and accommodation to
stimulus around them although the learning is an internal response (Piaget, 1955). Constructivist
theories contend that knowledge is not transmitted from teachers to students (Bjorklund, 1995,
Stager, 2001). Constructivism supports the idea that students construct knowledge “themselves
when they interact with the environment” (Ishii, n.d.; Nesmith 2008, p 2). This is a shift from
the behaviorist approach that all students learn the same concepts at the same time. Teachers
now facilitate lessons. This allows students to construct knowledge through social interactions
and to develop schema from surrounding information (Fosnot, 2005; Simon, 1995). Students
process new understandings in an effort to make accommodations (Dick, 1992; Piaget, 1955).
Investigations, Connected Math, Everyday Math, and Core Plus mathematics text
programs for middle school all fall into the realm of constructivist instruction. The
methodologies of each program center on process over memorization. Each program follows
protocols that follow co-constructivist and situated constructivist philosophies (Anderson &
Constructivism vs. NCLB 4
Kanuka, 1999). These math text programs are in use around the country (Association for the
Advancement of Science [AAAS], 2000). The AAAS ranks both Connected Math 2 and
Investigations with its highest ranking (AAAS, 2000).
Each of these constructivist math text programs center on situated group interaction.
Students are presented with a semi-authentic learning scenario in order to discover
understandings in small group situations. Students are then led through investigations that
explore the main topic(s) of the lessons. Students work in cooperative learning situations to
make discoveries about new learning and are asked to keep a journal of understandings,
reflections and questions for clarification. The programs are about discovery, not formulas and
computation. It is the responsibility to the learner to explore the mathematical concepts in order
to build understandings (Lerman, 1996).
Each of these text programs integrates modern uses of technology into the curricula to
enhance activities and motivate learners. From interactive online games, to homework and
parental help lines, to project extensions, each of these math programs allow the student
opportunities to expand understandings through the use of current technology. The computer
integration is not geared toward drill and practice, however. Because of this, they do not collect
nor monitor student data nor compare them to a standard similar to the state mandated
assessment systems.
These reform oriented curricula follow constructivist perspectives and are endorsed by
the NCTM and the AAAS (Nesmith, 2008). In Social Constructivism as a Philosophy in
Mathematics, Paul Ernest believes that math knowledge is influenced by human activity. The
application and how that application applies from generation to generation is a higher level
socio-constructivist path that we follow to learn math (Ernest, 1998; Nesmith, 2008). A
Constructivism vs. NCLB 5
constructivist view of learning is that knowledge is personal and idiosyncratic in nature (Duffy &
Jonassen, 1992; Merill, 1991). Emphasis is not on memorization of formulas nor is it focusing
on standard algorithm understandings. A student constructs his/her own knowledge based on the
ability to assimilate new information into past understandings (Piaget, 1955; Schifter & Simon,
1991). The design and implementation of Investigations, Connected Math, Everyday Math, and
Core Plus mathematics text programs follow this educational structure.
Massachusetts Math MCAS design and administration
In an effort to help states develop comprehensive assessment systems, the US
Department of Education has set strict criteria that individual states must follow when creating a
standardized assessment. The goal is to collect accurate and valid data that will hold districts
accountable for student achievement against national learning standards. The U.S. Department
of Education (USDOE, 2007) legislation states
NCLB requires states to develop a single statewide system of assessments. All public school students must participate in this assessment system, including those with disabilities and those who are not yet proficient in English. (p. 29)
All students in the same grade are expected to carry the same understandings and be able to show
equal competency in all subject areas regardless of background or ability.
To streamline the assessment process and make the process of evaluation manageable by
the U.S. Department of Education, the government guidelines require that all assessments and
data be of high technical quality so as to aggregate easily for state and national assessments
(USDOE, p. 39). The purpose of aggregated assessment is to rank and grade students, teachers,
and districts against a national standard. In order to meet the needs of aggregate data sorting, test
of this nature are designed in the form of multiple choice and short answer.
Constructivism vs. NCLB 6
The national requirements dictate that all states submit an accountability plan, outlining
the academic assessments and how they address the national standards. This plan must also
include an accountability system for students, teachers, and school systems. In an assessment of
the Massachusetts accountability plan as submitted to the federal government, it was found that
the state plan met or exceeded all national standards for a comprehensive assessment system
(USDOE, 2001).
An examination of recent math MCAS assessment surveys shows a design with
predominance toward multiple choice examples (MA department of elementary and secondary
education [MADOE], test blueprints by grade, 2010). In middle school math MCAS
assessments for 2005-2010 (grades six, seven, and eight), each test consisted of 32 multiple
choice questions, six short answer, and four open response questions. The state is also specific
about content. Percentage alignments are as follows: 26% number sense and operations, 28%
patterns, relations and algebra, 13% geometry, 13% measurement, and 20% data analysis,
statistics and probability (MADOE, 2010).
On testing days, students are tested at the same time, under similar conditions, without
guidance or speaking of any kind. The only help students are allowed comes from a math
formula sheet provided by the state. Students are expected to complete the exam in a certain
time period, though extending time is allowed. Although certain special education students may
be allowed a smaller testing environment or perhaps a scribe, no other help is allowed, be it
instructional technologies or teacher aide. This is the model that the U.S. Department of
Education finds exemplary (USDOE, 2001).
Although the technology behind the evaluation of standardized testing is more
sophisticated, allowing for more aggregate assessments and cross references to assure all
Constructivism vs. NCLB 7
students are making adequate yearly progress, the technological advancements are not making
strides to assess broader understandings associated with constructivist learning in mathematics
classrooms (Brooks, 2009). Testing success centers on the ability to accurately perform
calculations and make explicit determinations about specific math problems. This testing
structure does not allow for performance based assessments or other assessments more
appropriate for a constructivist math classroom.
Conflicting Principles
NCLB implies that all students the same age should have exactly the same mental
capacities and capabilities. Each student in the country at a certain age should know and be able
to do exactly the same things (Hiebert, 2003; McDermott, 1993). It does not allow for
individuality, individualized learning styles, and learning abilities. It does not account for
special needs, learning disabled, and those with limited English proficiency (Hoover, n.d.;
Stager, 2001). It doesn’t allow for savants and those of other gifted natures.
The complexity of the learning process cannot be overlooked. The classroom is a
complex configuration of curriculum, teacher methodology, and the diverse learning needs of
twenty plus students. Evaluating the growth of individual learners with a simple multiple choice
tests limits individual teaching methodologies and eliminates individuality. Schools eventually
change instructional practices to teach to the test (Brooks, 1999; McDermott, 1993). In a
constructivist classroom, multiple realities are allowed to exits. In a constructivist classroom,
each learner is expected to make his/her individual meaning from an investigation (Lerman,
1989, von Glasersfeld, 1991). It is not intended that each child in the math class memorize
information based on that activity. However, in MCAS standardized testing formats, a
Constructivism vs. NCLB 8
constructivist interpretation of mathematics assessment is not supported. Answers and
understandings are predetermined.
By focusing on memorization rather than meaning, standardized tests eliminate any
viability to a constructivist mathematics program. If students are asked to calculate answers
based on a list of presented formulas, then a constructivist perspective is less effective than
traditional drill and practice methods (Fosnot, 2005; Ishii, n.d.). The testing design follows a
behaviorist view of knowledge transfer compared to one of knowledge construction (Jaworski,
1996).
In order for states to properly aggregate student data for the national database, technology
needs to be streamlined into a data driven format. That does not allow for differentiated analysis
of student success plans. Although students may engage in activities in the classroom that
promote higher order thinking including the use of technology, the empirical/analytic model of
the state assessment survey subjects students to an assessment system that is too limited in
approach to effectively evaluate learning. “Direct teaching produced appreciable gains in
achievement on standardized tests, at the cost of developing detrimental attitudes toward
mathematics” (Helmke, Schneider, & Weinert, 1986, p. 10). This conflicts directly with the
NCTM recommendations that math should foster a view of mathematics as a meaningful activity
that explores alternative methods of instruction and assessment (1987, p. 158). NCTM
reinforces that the “emphasis should be on establishing a climate that places critical thinking at
the heart of instruction” (Cobb, Nichols, & Patashnick, 1990, p. 11).
Thirty-two multiple choice questions and six short answer questions do not amount to
critical thinking. Memorization of facts and the ability plug in formulas is only a true
assessment tool for those students who learn that way (Hiebert, 2003, Nesmith, 2008).
Constructivism vs. NCLB 9
Conclusion
A mix between traditional and constructivist ideas and methods might be the compromise
and the solution (Merrill, 1992). Teachers do it all the time. However, until the assessment
system is more inclusive to individual learning styles and more receptive to alternative
assessment strategies, use of a constructivist math text program in middle school will be
prohibitive to meeting national standards.
The teacher’s role in a traditional setting is to “provide clear, step-by-step demonstrations
and provide opportunities for practice” (Smith 1996, 390-391). This behaviorist perspective to
teaching and learning will adequately provide for standards-based testing, but is in direct
opposition to constructivist approaches to teaching and learning math. Teaching practices
designed to prepare students for mandated tests do not enable students to think critically and
extend learning to other situations (McDermott, 1993, Merrill, 1991). It simply prepares a
student to imitate learned behavior.
If we remain on course to meet the requirements of NCLB, tests like Massachusetts
MCAS test will continue down a path that conflicts with a constructivist classroom approach
(Brooks, 1999). Memorization of facts and the ability to plug in formulas will lead to successful
representation on standardized tests as dictated by NCLB mandates, but it will conflict with the
constructivist philosophical perspective of the NCTM (NCTM, 1987).
As long as national assessment strategies for NCLB center on standardized test scores
and the ability to aggregate data concerning standards, behaviorist math instruction will be a
stronger method to meet those needs. Only when the US Department of Education develops
educational technologies and testing protocols that allow for greater flexibility in how learning is
assessed will constructivist math texts like Investigation, Connected Math, Everyday Math, and
Constructivism vs. NCLB 10
Core Plus be effective teaching methodologies. The use of technology to carry out performance-
based assessments may not be easy to conduct and monitor to assess adequately yearly progress
in all students nationwide. However, without stronger technological advancements in
aggregating assessment protocols, and without a more sophisticated way to manage assessment,
constructivist math text programs will continue to struggle to meet the needs of NCLB.
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