Edgardo José Avilés-Garay
C&I 430
Trends and Issues in Math Education
Spring 1999
White Paper #1
The topic of our last meeting was precisely about the curriculum and its
dimensions in education, principally the teaching and learning of school mathematics.
But what curriculum really means? What things are included in a curriculum?
First of all, there are many dimensions or focus about what curriculum is. Sometimes is
defined according with the view of Hilda Taba and Ralph Tyler: as a plan for action or a
written document that includes strategies for achieving desired goals or ends. Other
theorists have defined curriculum keeping in mind the experiences of the learner. This
last view implies the existence of school, although many other experiences can be outside
the school. According with Ornstein (1993), curriculum focuses in goals, objectives,
subject matter, and organization of instruction. Finally, Romberg has defined the concept
of curriculum from the mathematics education perspective. He said, “curriculum refers
to a course of study, its contents, and its organizations”. Romberg continues arguing that
“the calls for change imply that the mathematical content that society would like students
to have an opportunity to learn in schools has changed”.
The Curriculum and Evaluation Standards for School Mathematics (NCTM,
1989), interpreted curriculum as a multi-dimensional set where are included the
mathematics that students need to know, how students are to achieve mathematical goals,
what teachers need to do to help students develop their knowledge and the context in
which teaching and learning occur.
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To design and implement an academic program, particularly in schools,
curriculum policy-makers have to pay special attention to certain aspects to have a
successful product. Among this aspects, there are, students’ needs, objectives of school
mathematics, instructional strategies, evaluation and assessment tools, content and
process, and so on . As an example, one of the more important aims supported by the
National Council of Teachers of Mathematics (NCTM) is “mathematics for all students”.
It means, that all students must have equal opportunities to learn and do mathematics in
all levels. “All students should gain mathematical power – that is, the ability to explore,
conjecture, and reason logically as well as the ability to use a variety of mathematical
methods effectively to solve non-routine problems” (NCTM, 1989). To reach this goal is
essential an well-organized curriculum where all its dimensions be harmoniously
orchestrated. In this sense, Standards pointed out that is necessary the “assessment of
individual students, of the instructional environments, and all aspects of the instructional
system”.
The NCTM has recalled in many of its documents for changes in the views of
teaching and learning of mathematics, and therefore in school mathematics curricula.
But, why these changes are important? Which are the fundaments for implement these
changes? Romberg has addressed essential issues regarding this concern. He has
formulated important issues in this way, like: a) why change the content and organization
of mathematics curriculum? b) what are the salient features of the current mathematics
curriculum?; c) what content and organization are being advocated?; d) how is the
mathematical sciences education community planning to implement these changes; and e)
what are some of the issues and problems reformers will face? Undoubtedly, all of these
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desired changes in school curriculum, proposed by Romberg, imply significant and
careful reviews on it. Have been the objectives of the curriculum appropriately fulfilled?
Which is the level of satisfaction of each one of the curriculum participants? Romberg,
through each one of the questions introduced earlier, has suggested and argued which is
the current situation in mathematics school curriculum, what has happened on it, and over
all, why these calls for changes are important and necessaries.
Although some researchers have not widely emphasized the genuine and
particular relationship between education process and the environments where it takes
place, Norton & Wiburg (1998) have argued that one important instructional strategy is
precisely learning environments. The process of teaching and learning is one well
organized, sequential and logically structured where all its parts are in its respective
places. Also, this process takes place in a context with its own sense. It means that aims,
goals, instructional strategies and activities, teacher and students interactions, assessment
and evaluation techniques are not isolated and or fragmented one from another. These
authors have stated that “the design of that context, the learning environment, is an
important as the designs that teachers create for literacy, problem solving, knowledge,
community, and information use”. In this sense, learning environments, specifically,
physical facilities must be consistent and agreed with learning process.
Classrooms together with others physical facilities, should encourage students to
become effective learners. In other words, these kind of facilities are essential part of
learning. In its discussion draft of Principles and Standards for School Mathematics, the
NCTM argued that “mathematics classrooms are viewed as places where thinking about
and doing mathematics is the central focus”. In this classroom environment, students will
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be able to learn to value mathematics, become confident and sure in their own ability,
become mathematical problem solvers, learning to communicate mathematically, and
learning to reason mathematically.
The physical environment can not be passive or static. It one must provide sense,
direction and support to curriculum, and therefore, to education process itself.
Classrooms must reflect diverse kind of activities, experiences, showing in other words
that mathematics learning is an enjoyable task.
In this sense, Weiss has argued that facilities wrong planned or developed could
be obstacles to effective mathematics teaching. “While the teacher is the key to much of
what goes on in mathematics classrooms, a number of external influences can also affect
the quality of instruction”, she said. Through her thoughts, she has given particular
attention to the facilities and their relations with learning. She mentioned that not only
architectural resources are important, also, equipment and supplies to complement and
enrich the classrooms are essential.
In addition, maybe implicitly, Weiss has introduced an important and “hot” issue
in mathematics education, the professionalization of mathematics teaching. Noddings
(1992) has stated that professionalization of teaching is part of the current efforts of
reform. But, Weiss focused in the lack of appropriate learning facilities as one of the
reasons because teachers are so far from reach professional standards. “Teaching is
considered a “profession”, but the working conditions most teachers face are not in
keeping with professional standards”, she argued.
Returning to our earlier discussion, a forced question in this discussion is which is
the role of technology in these learning environments? Is evident that mathematics
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teaching and learning process can not take place isolated and still using “old-fashion”
techniques and methods. The Standards said that “mathematical instructional programs
should use technology to help all students understand mathematics and should prepare
them to use mathematics in an increasingly technological word” (NCTM, The
Technology Principle, 1998). The use of technology represented by calculators,
computers, softwares, and during the last years, through the World Wide Web, engage
students in mathematics activities where they can learn in different and innovative ways.
In addition, students can value mathematics through appropriate applications toward
other fields using technology. The diversity that the Internet offers, allow students to
investigate, express their ideas mathematically, and overall, permit make conclusions or
evaluate situations objectively.
How must be the mathematics classroom organized to enhance and enrich the
students’ learning? Norton & Wiburg (1998) stated that the arrangement of furniture and
materials, the kinds of tools available to students, and the use of time influence student
learning. In the same way, these factors have a particular influence in the relationships
between students among themselves and teacher. The classroom organization must
satisfy students’ particular needs, offering equal opportunities to discover, reach and
learn. As educator, the style that gathers all of these requirements is a laboratory
classroom, where students can have the availability to use technology, of course,
supervised by teacher and with a clear objective in mind. Also, classrooms must provide
space to pay attention to students with learning difficulties where teacher can meet with
them individually or in small groups.
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This discussion has showed that learning environments has its particular place in
curriculum design and planning. It suggest that curriculum policy-makers, administrators,
teachers and students have to pay more attention to improve and enrich the educational
settings and its dimensions where learning take place every day.
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References
Brubaker, D.L. (1982). Basic concepts central to an understanding of curriculum
planning. Curriculum Planning: The Dynamics of Theory and Practice. Glenview,
Illinois: Scott, Foresman and Company.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation
Standards for School Mathematics. Richmond, Virginia. NCTM.
National Council of Teachers of Mathematics. (1998). Principles and Standards
for School Mathematics: Discussion Draft. Standards 2000. Richmond, Virginia. NCTM.
Noddings, N. (1992). Professionalization and mathematics teaching. In D.A.
Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 197208). Richmond, VA: National Council of Teachers of Mathematics.
Norton, P., & Wiburg, K.M. (1998). Designing learning environments. Teaching
with Technology (pp. 248-274). Harcourt Brace College Publishers.
Ornstein, A.C., & Hunkins, F. (1993). The field of curriculum. Curriculum:
Foundations, Principles, and Theory. Second Edition. Allyn and Bacon.
Romberg, T.A. (xxxx). Questions about the mathematics curricula for grades K12. University of Wisconsin-Madison.
Weiss, I.R. (xxxx). The context of science and mathematics in-service education
programs. Horizon Research, Inc.