Integrated Science and Mathematics Models

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Integrated Science and Mathematics Models

• Natalka Kosacz
• Adam White

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Organizations stressing the need to integrate the
curriculum

• National Council of Teachers of English (NCTE)
• National Council of Teachers Mathematics (NCTM)
• National Council for the Social Studies (NCSS)
• National Science Teachers Association (NSTA)
• School Science and Mathematics Association

3
An integrated curriculum focuses on the following
instructional views

• Learner-centered
• Students as active participants
• Students construct knowledge
• Teacher as facilitator

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Models of Integration

• Integrated different subject matters are
  blended such that the separate parts are not
  recognizable.
• - The Berlin-White Integrated Science and
  Mathematics Model (BWISM)
• Example Bouncing a light wave off a mirror and
  observing its incidence. (Science) The equation
  that explains that. (Math)

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Models of Integration

• 2. Interdisciplinary the integrity of the
  various academic disciplines remain clear.
• Example Discussing the scientific qualities of
  water purification. (Science) Analyzing the
  amount of purification materials required for a
  specific amount of water. (Math) Research and
  write a report regarding different purification
  facilities water purification procedures.
  (Language Arts)

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Models of Integrations

• 3. Thematic pertains to unifying commonalities
  among subjects or topics.

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Models of Integration

• 4. Continuum Model developed by Lonning
  DeFranco based on the notion of what and to
  what extent each subject is being integrated.

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Ten Views
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Connected

• Within each subject area, course content is
  connected topic to topic and relates ideas
  explicitly.

• Example
• Instructor relates the concept of fractions to
  decimals, which in turn relates to money and
  chemistry experiments

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Nested

• Within each subject area, the instructor targets
  multiple skills

• Example
• Instructor designs a unit on photosynthesis to
  simultaneously target equal-solving skills and
  the life cycle of a plant.

11
Sequenced

• Topics or units of study are rearranged and
  sequenced to coincide with one another. A concept
  that reinforces learning and abstract thinking.

• Example
• Teacher presents a study of water filtration
  systems while also looking at the chemic nature
  of fluoride and chlorine.

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Shared

• Shared planning and teaching takes place in two
  disciplines in which overlapping ideas emerge as
  organized elements.

• Example
• Science and Math teachers use data collection,
  charting and graphing as shared concepts that can
  be taught

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Webbed

• A theme is webbed to curricular contents and
  disciplines subjects use theme to sift out
  appropriate concepts and ideas.

• Example
• Instructors present a simple topical theme such
  as water and web it to the subject areas. i.e
  Students could review the chemical make up of
  water.

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Threaded

• Threads thinking skills, social skills, multiple
  intelligences technology and study skills through
  various disciplines.

• Example
• Science teachers target prediction in science
  labs while math teachers target prediction in
  equation solving.

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Integrated

• This approach matches subjects for overlaps in
  topics and concepts with some team teaching in an
  authentic integrated model.

• Example
• In all subjects instructors look for patterning
  models and approach content through patterns
  e.g. results mathematical evidence

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Immersed

• The disciplines become part of the learners lens
  of expertise the leaner filters all content
  through this lens and becomes immersed in ones
  own experience.

• Example
• Student has one area he or she excels at and
  tackles all problems from that perspective. E.g.
  students who are good at math handle everything
  from a mathematical paradigm. Poetry can be
  synthesized through numeric measure.

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Networked

• Learner filters all learning through the experts
  eye and makes internal connections that lead to
  external networks or experts in related fields.

• Example
• While this would primarily apply to older
  students, middle school children who enjoy
  astronomy can expand his/her knowledge base by
  meeting astronomers.

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Fragmented

• Traditional role keeps things separate, but can
  be tweaked to allow for some integration.

• Example
• Even though math and science are kept separate,
  teacher can make sure students know how to add
  and subtract before delving into the minutiae of
  a specific science problem.

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National Projects that demonstrate integration

• AIMS (Activities Integrating Mathematics and
  Science)
• - lesson plans and worksheets for K-9
• - curricular content for both mathematics and
  science are minimal
• - highly structured activities
• GEMS (Great Expectations in Math and Science)
• - created by Lawrence Hall of Science at the
  University of California at Berkley
• - activities designed for grades 4-8
• - activities based on integration of individual
  disciplines

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National Projects that demonstrate integration

• TIMS (Teaching Integrated Mathematics and
  Science)
• - created by the University of Chicago
• - activities designed for grades 1-6
• - lessons based on understanding mathematical
  concepts with applications to science and
  language arts
• TOPS
• - produced by TOPS Learning Systems in Canby,
  Oregon
• - activities designed for grades K-8
• - activities are based on science processes with
  mathematic components enhancing science

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Issues of Integration

• Definition of integration
• Lack of integrated curriculum materials
• Time and structure of the school day
• Lack of preservice teacher instruction
• Assessment (stardardized tests)
• Standards for individual disciplines remain
  separate

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Resources

• Berlin, Donna F. White, Arthur L. (1994). The
  Berlin-White Integration Science and Mathematics
  Model. School Science Mathematics, 94 (1), 12
  14.
• Czerniak, Charlene M. McDonald, Jacqueline.
  (1994). Developing Interdisciplinary Units
  Strategies and Examples. School Science
  Mathematics, 94 (1), 5 10.
• Czerniak, Charlene M. Weber, William B Jr
  Sandmann, Alexa Ahern, John. (1999). A
  literature review of science and mathematics
  integration. School Science Mathematics, 99
  (8), 421 430.
• Kepler, Lynne. (1995). See How Science Math Go
  Together. Instructor, 42 46.
• Lederman, Norman G. Niess, Margaret L. (1997).
  Integrated, interdisciplinary, or thematic
  instruction? Is this a question or is it
  questionable semantics? School Science
  Mathematics, 97 (2), 57 58.
• Lonning, Robert A. DeFranco, Thomas C. (1997).
  Integration of science and mathematics A
  theoretical model. School Science Mathematics,
  97 (4), 212 215.
• Lonning, Robert A. DeFranco, Thomas C.
  Weinland, Thomas P. (1998). Development of
  Theme-based, Interdisciplinary, Integrated
  Curriculum A Theoretical Model. School Science
  Mathematics, 98 (6), 312 319.
• Integration in the Elementary Curriculum.
  (1999). Phi Delta Kappa Fastbacks, 444, 7 35.
• Ten Views for Integrating the Curricula Design
  Options. http//web.usf.edu/lc/lcfaculty/integra
  te.html.