A History of Research in Mathematics Education

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A History of Research in Mathematics Education

• By Jeremy Kilpatrick

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The history of education.

• Education was not considered a discipline to be
  studied.
• Germany (1779) and Sweden (1804) were the first
  countries to chair departments of education.
• In the U.S., New York University (1832), Brown
  University (1850) and University of Michigan
  (1860) led the way.
• Mathematics education programs began to develop
  at the end of the 19th century.

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Influences from the Disciplines

• Mathematics
• Mathematicians were curious about how math was
  created.
• Observations of their childrens and
  grandchildrens mathematical helped develop and
  improve programs.
• Psychology
• Empirical studies were used to observe patterns
  in cognitive development of school aged children.

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Pioneer in Mathematics

• Feliz Klein
• Professor of mathematics at Erlanger (1872)
• Famous for his Erlanger Programm
• Believed that mathematics should fall between
  humanistic and scientific education
• Served as president of the International
  Commission on the Teaching of Mathematics, which
  reported on state of mathematics teaching around
  the world.
• The comparisons were descriptive rather than
  analytical.
• Reports were generated from data collected from
  surveys

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Pioneer in Psychology

• Alfred Binet
• Director of the first French psychological
  laboratory
• Sought to gather precise data by scientifically
  training teachers and allowing them to practice
  experimental pedogogy in their classrooms
• Believed that questionnaires, observation and
  experiment were the best means for gathering this
  information
• Originator of intelligence testing
• Believed that intelligence testing should be used
  for diagnosis rather than ranking
• Basis for IQ test

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Research on Thinking

• Jean Piaget studied the processes children used
  to obtain their answers. His assessment of
  reasoning processes led to the clinical method.
• Psychological laboratories were established all
  over the world, including one at Johns Hopkins
  University in 1883.
• At JHU, G. Stanley Hall brought experimental
  pedagogy to the U.S. by launching a child study
  movement.

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More research on thinking.

• University of Wurzburgs Otto Selz concentrated
  his studies on problem solving and influenced a
  generation of psychologists.
• Karl Dunker authored and influential monograph
  that analyzed the processes of solving problems
• Lev Vygotsky formulated a thoery of mental growth
  where development is guided by instruction

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Studies of Teaching and Learning

• Teaching is taken as a treatment and learning as
  an effect.
• The basic technique for analyzing such effects
  within the compass of a single investigation is
  analysis of variance, developed by Ronald A.
  Fisher.

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Connectionism

• Phrase coined by Edward Thorndike to describe his
  behaviorist studies in 1900.
• Thorndike and Robert Woodward attempted to show
  the limitations of transfer of training.
• For example, they found that practicing
  estimating the sizes of rectangles did not
  improve ones ability to estimate the sizes of
  triangles.
• However, Thorndike did not say that transfer of
  training was impossible but only that transfer
  cannot be assumed to occur, that it is rarely
  automatics, and that direct teaching for desired
  outcomes is usually more efficient and economical
  than are hoped-for, spill-over effects

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Charles H Judd

• His studies disproved connectionism.
• Fifth and sixth graders that were taught the
  principle of refraction did better shooting darts
  at a moving underwater target than pupil who were
  not familiar with refraction.
• Believed that arithmetic is a general mode of
  thinking.

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The Testing Movement

• Started in Boston in 1845 to prove to the state
  board how well their students were performing
  (backfired)
• Detailed work done by reformer Joseph Mayer Rice
  in the 1890s.
• His studies concluded that by setting standards
  and administering exams, school districts could
  get the results they wanted.

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Child Study

• G. Stanley Hall and Maria Montessori published
  findings on the use of activities and materials
  in teaching mathematics to young children.
• Because child study usually involves pre-school
  children, it has not produced much worthwhile in
  the area of mathematic education.

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The Measurement Movement

• Cliff W. Stone conducted a study on 3000 students
  to measure achievement in reasoning and
  fundamentals.
• Stone wanted to standardize the administration
  and scoring of the test in order to extract
  relationships between other factors.
• Introduction of the concept of efficiency of
  instruction-ratio linking achievement to time
  spent in instruction

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The Social Utility Movement

• What does business want?
• Mental calculations
• Does the curriculum have too much fluff?
• Yes. Too many excessive requirements and too
  much time spent on arithmetic.
• What arithmetic do people use?
• Simple calculations, using numbers under 1000
• Calculations for buying and selling
• Simple fractions with numerator of 1

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A Reaction to Reductionism

• Critics argue that curriculum cannot be based on
  frequency of adult usage
• Shall we say that 60 of the teaching of the
  schools in spelling and language should be
  devoted to the 100 word of the most frequent
  occurrenceto the, and, but, to, be, etc?

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Incidental Learning and Readiness

• Incidental learning-children learn arithmetic
  better if it is not systematically taught
• IL was the precursor for readiness
  theory-concepts are better taught to a child once
  he/she is mature enough to understand it.
• Louis Benezet, a superintendent in New Hampshire,
  conducted a study that didnt teach arithmetic
  until after grade 7. After a years instruction,
  these students tested at the same level of
  students that had been taught in a traditional
  manner.

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Responses to Curriculum Issues

• Though most agreed on the importance of knowing
  arithmetic, required math courses in high school
  was challenges in the 1920s and 1930s.
• Educators started evaluating individual
  differences and whether or not all students would
  benefit from studying math.
• Other studies dealt with unified mathematics.
• Eight Year Study-allowed secondary schools to
  experiment with innovative curricula without
  risking graduates chances of admission to college

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The search continues.

• Math educators still didnt know where they fit
  in.
• Mathematicians were busy arguing mathematical
  minutiae.
• Psychologist often debated issues that were
  irrelevant to math education.

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The Golden Age-early to mid 1950s

• American school were under attack for graduating
  young adults that were not prepared for college
  or the working world.
• Three gatherings of mathematicians and educators
  to analyze and/or solve the problem
• 1962-conference that brought together
  psychologists, mathematicians nad mathematics
  educators to discuss the problems of mathematical
  learning.
• 1967-more diverse and marked the beginning of
  true interdisciplinary and community among
  researchers in math education
• 1968-mainly mathematicians and educators called
  together to identify topics for projects, thesis
  and postdoctoral research in mathematics
  education.

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Organized and progressive research

• Journal-Vol.1 No.1 Journal for Research in
  Mathematics Education (January 1970)
• About 85 of the research was being conducted in
  the U.S.
• New doctoral programs in math education

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Realistic approach

• European researchers explored activity theory
  developed in the Soviet Union.
• Mathematics is viewed as a human activity arising
  out of real situations that ask the students to
  learn from investigating problems theyve
  formulated
• What does this sound like???

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Conclusion

• Has the lack of depth in mathematics education
  research contributed to the disputes over math
  reform?
• Are TERCs and Everyday Math considered studies
  for research in math education?
• Whats next??