Assessment of Science and Mathematics Learning:

The Case for Inclusive Classrooms



Daniel Nomishan

Bill Bourbeau

Marijah Tessier

Robert Pollock

Fitchburg State College

Fitchburg, MA 01420




Traditionally, the strategy for maximizing student achievement in both regular and special education environments has been direct instruction.  There is ample evidence to support such claims.  Teachers who use direct instruction are bound to identify specific target behavior they intend to teach.  Lesson delivery resources, skills to be taught and measurement of pupil performance are all based on behavior exhibited by students.  This is perhaps, contrary to the constructivist theory, which tends to be student-centered.  In a constructivist teaching and learning situation, a student is expected to make their own meaning from each concept or skill taught.  Authenticity of learning is measured through application of the concepts and skills in real life situations.


This presentation represents classroom research on teaching and learning.  The purpose of the research was to establish the constructivist approach as an alternative to teaching science and mathematics.  This involves going through what Henderson (1996) calls “plan-act-observe-evaluate cycle.” The students are encouraged to communicate extensively.  The communication could be verbal, in writing or silent interaction.  It would be between student and student, student and teacher, or student and the computer.  The use of the computer and other technology during the research period are considered sufficient tools for enhancing the learning of math and science.  Participants will examine student active-learning models.


Unlike the basic skill of mathematics, science is generally considered a content subject, and mastering the content is, therefore, embedded in the goal of the study of science.  We believe that the study of science also includes not only learning the process skills, but the application of the skills in learning concepts. For both math and science, focus was on the assessment of skills and the eventual remediation of any difficulties students might have.  Besides factual and conceptual knowledge, laboratory type skills, intellectual skills, and generic thinking skills were assessed (NCTM, 1989; NRA, 1995).





In this research, the researchers made observations during mathematics and science teaching situations.  Mathematical computation skills, and the difficulties elementary and middle school students experience in combining and manipulating numbers to solve problems were observed. The researchers also examined the critical thinking skills students used as they stated hypotheses, experimented, drew conclusions, and reflected on the conclusions in relation to the stated science problems.  Data were then gathered on science and mathematics readiness skills critical to a good foundation in future problem solving situations.  Possible problem behaviors were identified using inventories and other observational tools, to enable the researchers to devise corrective strategies (Enright, 1990).


Results and Analysis


Observations revealed that for primary grades, the special needs children exhibited higher problem behaviors than non-handicapped students as follows: understanding basic number concepts (SN=75%, NSN-32%) writing and summarizing numbers (SN=68%, NSN=18%).  Special needs students also were seen to exhibit problems in each of whole number operations, fractions, and decimals.  Special needs students were observed to more often forget their basic number parts, frequently using fingers to count or relying on a number line or needing the use of a manipulative for basic computation. However, both special needs and non-special needs students had problems seeking relationships between parts and the whole concept needed to solve problems involving fractions and decimals.  In science, observations showed that students with special needs characterized by behavioral and learning disabilities were nearly equally able to observe and describe directed experimentation, use the computer as a learning tool, and choose a correct instrument for taking simple measurements.  Non-special needs students, however, were seen to possess greater skills for distinguishing relevant features of an observation, accessing data via on-line and on-print sources, sorting and grouping data, and making inferences and describing relationships and patterns.


The research shows that special needs (SN) students differed from non-special needs (NSN) students in the way they process information, in the way they identify by commonalities, cause and effect, and in the way they combine information into a new whole.  Differences were also observed in planning of experiments (true inquiry) to test hypotheses and critiquing the worth of information and principles and of the logic of information and principles.



Evidence gathered from this study may not provide conclusive results. However, the study tends to show that there exists marked differences in the way special needs students and non-handicapped students learn mathematics and science.  The differences were seen where a deeper understanding and application of concepts were required.  Special needs students tended to take longer periods of time in solving conceptual and contextual problems that demanded higher order thinking skills.  This is particularly so when teaching strategies are mainly at the abstract, symbolic level.  When the constructivist approach was used, all students were able to make meanings of the concepts taught.  Student active-learning was present and there appeared to be an increase in conceptual knowledge because teachers knew when to use appropriate materials and approaches (Bruner, 1986; Carin & Bass, 2001; Ebenezer & Connor, 1998; Martin, 2000; Piaget, 1973; and Victor & Kellough, 2000).  The study also demonstrated the effectiveness of observational procedures in collecting data for assessment of learning problems that special needs students experience in science and mathematics (Turnbull, Turnbull, Shank, & Leal, 1999).


We do recognize that children may not display significant behaviors during observations.  The interpretation of certain behaviors may also at times not be clear or unbiased.  Though the study does not possess sufficient depth for broad generalizations to be made for effective teaching of math and science to students with special needs as well as those in regular classrooms, the following implications could be drawn from the study: (1) Language development is necessary to enhance mathematical and scientific thinking and processes (Vygotsky, 1962); (2) Students should be provided opportunities to use concepts and manipulative materials, including computers; (3) Provide plenty of practice that is appropriate to the age and learning levels of the children; (4) Use cues and prompts to facilitate the thinking and problem-solving process; and (5) Proceed from the simple to the complex procedures for learning concepts.




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