crescitelli - edtech 504 - synthesis paper

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


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 &


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


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.


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


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


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).


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


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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