This resource was developed by CSMC faculty and doctoral students with support from the National Science Foundation under Grant No. ESI-0333879. The opinions and information provided do not necessarily reflect the views of the National Science

1
This resource was developed by CSMC faculty and
doctoral students with support from the National
Science Foundation under Grant No. ESI-0333879.
The opinions and information provided do not
necessarily reflect the views of the National
Science Foundation. 1-20-05
2

Committees and Reports that Have Influenced the
Changing Mathematics Curriculum
This set of PowerPoint slides is one of a series
of resources produced by the Center for the Study
of Mathematics Curriculum. These materials are
provided to facilitate greater understanding of
mathematics curriculum change and permission is
granted for their educational use.
Report of the National Institute of Education
Conference on Basic Mathematical Skills and
Learning Report 1975
http//www.mathcurriculumcenter.org
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Conference on Basic Mathematical Skills and
Learning
The Euclid Conference Euclid, Ohio October,
1975 The National Institute of Education (NIE)
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Background The 1970s

• Many questions remained about the effectiveness
  of the new mathematics curricula.
• Many believed the topics in the new curricula
  were too abstract and challenging for students
  and they also questioned the lack of
  applications.
• Strategies to effectively implement the new
  mathematics curricula were often absent or
  inadequate.
• The National Science Foundation significantly
  reduced funding for teacher enhancement programs
  and development of new curricula.
• There was a back to basics movement in
  mathematics. However, there was little agreement
  about the definition of basic skills among
  educators.
• The National Institute of Education (founded in
  1972) sponsored a 3-day conference in 1975 in
  Euclid, Ohio to discuss basic mathematical skills
  and learning.

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Steering Committee

• Gerald Rising, State University of New York at
  Buffalo
• Peter Hilton, Battelle Research Institute and
  Case Western Reserve University
• Edward Esty, National Institute of Education
• Ross Taylor, Minneapolis Public Schools
• Robert Davis, University of Illinois at Urbana
• Israel Scheffler, Harvard University
• James Wilson, University of Georgia at Athens

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May, 1975Dear _________,You are invited to
join us for a conference on basic mathematical
skills in Euclid, Ohio, this October. Please
draft a position paper on the following two
questions and send it to us before the
conference.1. What are basic mathematical
skills and learning?2. What are the major
problems related to childrens acquisition of
basic mathematical skills and learning, and what
role should the NIE play in addressing these
problems?We look forward to your
response.Sincerely,Gerald Rising and Peter
Hilton
(Adapted from Volume II, p. 2)
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Volume IContributed Position Papers
This volume contains the 33 position papers that
were commissioned before the conference. After
the conference, each author revised their paper
for publication. Edward Begle was the only
contributor who was not able to attend the
conference.
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Volume IIWorking Group Reports

• This volume describes the organization of the
  conference, includes reports of the working
  groups, and provides a summary.
• Four working Groups
• 1. Classroom Instruction and Teacher Education
• 2. Curriculum Development and Implementation
• 3. Goals for Basic Mathematical Skills and
  Learning
• 4. Research Priorities
• The last section of Volume II provided a summary
  of the entire conference by Peter Hilton and
  Gerald Rising.

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Classroom Instruction and Teacher Education
Recommendations focused on Developing
innovative teacher education programs that lay
emphasis on clinical methods to better understand
students mathematical comprehension, on
diagnosis of learning difficulties in
mathematics, and on development of
problem-solving teaching techniques.
Developing effective diagnostic tools and
appropriate remediation materials. They believed
that clinical centers should be established.
Developing instructional materials focused on
problem solving processes.
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Curriculum Development and Implementation
Proposals for Research and
Development Impact of calculators
and computers Integration of mathematics with
its areas of application Dissemination
and implementation strategies for new
curricula Creative methods for
teaching arithmetic and ratio/proportion Altern
ative treatments of topics in arithmetic Improv
ed assessment materials, including materials for
diagnosis and remediation

• Basic Issues and Policy Guidelines
• Study the impact of the
• behaviorist-humanist controversy
• Specify implementation plans for
• new curricula to support research,
• including replication
• Produce teacher guides and
• professional development plans to
• accompany new curricula
• Draw on research-proven materials
• and procedures in future
• curriculum work
• Involve members from all areas of
• mathematics education and related
• disciplines in the development of
• future curricula

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Goals for Basic Mathematical Skills and Learning
General Goal Mathematics education should help
students improve their ability to think, to
reason, and to make sense of problems and
situations they face in their lives.
Basic Goals Students should have
appropriate computational skills be able
to relate mathematical ideas and physical
situations be able to make reasonable
estimations and approximate calculations
be able to organize and interpret numerical data,
including using graphs be able to measure
length, distance, angles, weight, area, volume,
and temperature be able to judge the
reasonableness of results have a
qualitative understanding of drawing inferences
from functions and rates of change be able
to interpret chance situations and apply ideas of
probability have an understanding of the
capabilities and limitations of computers
be able to apply general problem-solving
techniques.
Further Desirable Goals Students should
recognize the internal considerations of the
discipline of mathematics be able to
reason abstractly and construct arguments and
proofs be familiar with cultural
contributions of mathematics be familiar
with common mathematical notations
understand the basic idea of mathematical
modeling. Problem solving was considered as a
unifying goal that interrelates the general,
basic, and further desirable goals.
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Report on Research Priorities

• This working group addressed concerns in regards
  to policy issues and research priorities, as well
  as developing a set of research questions
• Recommendation 1 Support of research that
  relates to the learning and teaching of
  mathematics should be increased.
• Recommendation 2 Research resources should
  support a sequence of related studies including
  those of interest to mathematicians, mathematics
  educators, psychologists, classroom teachers, and
  the public.
• Recommendation 3 Research methods that were
  successful in other areas should be investigated,
  to expand the variety of methods used in
  mathematics education research.
• Recommendation 4 Information should be gathered
  and synthesized from prior research studies.
• Recommendation 5 Research to produce better
  assessment tools and evaluation methods in
  mathematics education should be supported.

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Report on Research Priorities

• Recommendation 6 A balance between
  investigations regarding resolving issues of
  immediate practical urgency and understanding
  learning and teaching should be pursued.
• Recommendation 7 Mathematics education research
  should focus on
• (a) identification and clarification of specific
  aspects of research problems
• (b) the development of attitudes, concepts,
  skills, and processes
• (c) instruction (d) school context (e)
  political and social context of the school (f)
  methodologies of research, development, and
  evaluation and (g) teacher education.
• Recommendation 8 Studies that reflect a balance
  among different levels of mathematical skills
  (manipulation, quantitative and spatial
  comprehension, and problem solving) should be
  supported.

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NCSM Position Paper on Basic Mathematical Skills

• After reviewing the Euclid Conference report at a
  special session of the 1976 NCSM Annual Meeting,
  the NCSM issued a position paper on basic
  mathematical skills in 1977.
• Ten Basic Skill Areas
• 1. Problem Solving
• 2. Applying Mathematics to Everyday Situations
• 3. Alertness to the Reasonableness of Results
• 4. Estimation and Approximation
• 5. Appropriate Computational Skills
• 6. Geometry
• 7. Measurement
• 8. Reading, Interpreting, and Constructing
  Tables, Charts, and Graphs
• 9. Using Mathematics to Predict
• 10. Computer Literacy
• These 10 areas mirrored most of the
  recommendations in the Euclid Conference Vol. II
  document. This influence could be attributed to
  the fact that three participants of the Euclid
  Conference, Dorothy Strong, Ross Taylor, and
  Edward Esty, were also members of the NCSMs Task
  Force. Taylor and Esty were specifically involved
  with the third working group.
• NCSM Position Paper on Basic Mathematical
  Skills

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Significance of the Report of the National
Institute of Education Conferenceon Basic
Mathematical Skills and Learning
Provided possible new directions for the school
mathematics curriculum, particularly in the
areas of quantitative reasoning and skills in
light of increasing computer and
calculator capabilities. Influenced the
National Council of Supervisors of Mathematics
(NCSM) 1977 position paper on basic
skills. Influenced the National Council of
Teachers of Mathematics planning group for An
Agenda for Action.

16

• References
• Grouws, D. A., Cebulla, K. J. (2000).
  Elementary and middle school mathematics at the
• crossroads. American education Yesterday,
  today, and tomorrow. Chicago The National
• Society for the Study of Education.
• Jones, P. S. (1970). A history of mathematics
  education in the United States and Canada.
• Reston, VA National Council of Teachers of
  Mathematics.
• Klein, D. (2003). A brief history of American
  K12 mathematics education in the 20th
• century. In J. Royer (Ed.), Mathematical
  cognition. Greenwich, CT Information Age
• Publishing.
• National Institute of Education. (1975).
  Conference on Basic Mathematical Skills. Vol. 1,
• Contributed position papers, Euclid, OH.
  Washington, DC Author.
• National Institute of Education. (1975).
  Conference on Basic Mathematical Skills. Vol. 2,
• Working group reports, Euclid, OH. Washington,
  DC Author.