Authentic Integration of Mathematics and Science (AIMS) – A model for integrating Mathematics and Science

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Authentic Integration of Mathematics and Science
(AIMS) A model for integrating Mathematics
and Science

• Presented by Páraic Treacy
• (NCE-MSTL, University of Limerick, Ireland)

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Difficulties Facing Irish Mathematics Education
System

• 40 of adults struggle with everyday mathematics
  problems.
• Only 16 of students sat the higher-level Leaving
  Cert maths paper in 2011.
• (RTE, 2010 State Examinations Commision, 2011)

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Difficulties Facing UK Mathematics Education
System

• More than a third of 16-year-olds almost
  200,000 failed to gain at least a C grade in
  GCSE maths in 2011.
• About 13 of students took A-levels in the
  subject in England, Wales and Northern Ireland.
  In Scotland, numbers reached around 25.
• The Telegraph (2012)

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Difficulties Facing UK Mathematics Education
System

• Prof Stephen Sparks said few pupils took maths
  beyond the age of 16 after being put off by
  test-driven lessons in primary and secondary
  school.
• He said classes often focused on the dry
  procedures behind sums to make sure children
  pass exams instead of passing on a well-rounded
  understanding of the subject.
• The Telegraph (2012)

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Criticisms of Mathematics and Science Tuition

• Little or no emphasis placed on the explanation
  of concepts
• Few opportunities to apply Mathematics learning
  in everyday contexts
• Pupils fail to see the meaningfulness behind
  the tasks they are completing.
• (Lyons et al., 2003 Boaler, 1994)

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How does this affect 3rd Level?

• Students enter 3rd Level lacking the numerate
  skills to cope with everyday life and demonstrate
  large gaps in their knowledge.
• Students unable to solve problems depend on
  translation algorithms that work for textbook
  problems.
• ODonoghue (2004)

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How Can These Issues Be Resolved?

• Students should recognize and apply
  mathematics in contexts outside mathematics.
  Students need experiences applying mathematics
  concepts and representations to describe and
  predict events in almost all academic
  disciplines, as well as in the workplace as we
  develop a fully informed citizenry.
• - NCTM (2009, p.3)

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Benefits of Integrating Mathematics and Science

• Integration can improve students scientific and
  mathematical conceptual learning.
• Integration can enhance students ability to
  think critically, apply information, motivation
  and interest.
• Judson and Sawada (2000) Hurley (2001)
  Venville et al (2004)

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Approach to Integration

• Contextually-based, hands-on, cooperative group
  work involving plenty of discussion and inquiry
  comes highly recommended when designing
  integrative lessons for Mathematics and Science.
• (Furner Kumar, 2007 Frykholm Glasson, 2005
  Miller Davison, 1999 Daniels, Hyde, and
  Zemelman, 2005)

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Authentic Instruction Benefits

• Authentic Instruction positively affects pupil
  performance in
• Authentic Intellectual Work.
• Knowledge retention.
• Execution of basic skills and algorithms.
• (Lee et al, 1995 Newmann et al, 1996 Newmann et
  al, 1998 Newmann et al, 2001)

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Authentic Integration of Mathematics and Science
(AIMS)
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How Does AIMS work?

• Example combining Genetics and Probability
  through a single task.
• Use knowledge of trait alleles of a mother and
  father to determine the traits their offspring
  are likely to inherit.
• Apply Punnett squares to aid this process.

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Authentic Integration of Mathematics and Science
(AIMS)
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Genetics and Probability - Discussion

• Can this be used to predict anything else that
  the offspring may inherit?
• Could this be used to aid decision making in the
  IVF process? What are the implications?
• Discussions on how inheritance affects
  probability of developing cancer or heart
  ailments as well as inheriting diseases such as
  Cystic Fibrosis and Huntingtons Disease.

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Genetics and Probability - Discussion

• Combinations of probabilities what is the
  probability of one of the offspring having
  freckles and short eyelashes?
• Are these probabilities independent of one
  another?

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How could the task be improved?

• Increase interest by using examples of
  celebrities and the traits their offspring might
  have

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Research carried out

• 6 Maths-Science Integration lessons developed.
• Implemented in 4 Irish 2nd Level Schools.
• 90 students participated.

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Teachers that applied the model

• They (the students) really enjoyed it. After
  completing the lessons, they were really enjoying
  it and were saying why is it over? to the
  extent that I was having to make my lessons so
  much more active because it was such a difference
  to the way Id normally teach. The students
  really responded well to it.

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Teachers that applied the model

• This approach seems to make complete sense to
  me, where you would bring the mathematical
  concepts along with the scientific concepts
• I definitely think its a model that more
  teachers should use

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Teachers that applied the model

• Very positive opinion of the teaching model
  employed. I think the tasks were absolutely
  fantastic

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Thanks for listening

• Information on the AIMS model and lesson plans
  based on this model are available by request.
• Contact paraic.treacy_at_ul.ie

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References

• Boaler, J. (1994) 'When Do Girls Prefer Football
  to Fashion? An Analysis of Female
  Underachievement in Relation to realistic
  Mathematic Contexts', British Educational
  Research Journal, 20(5), 551-564.
• Childs, P. (2006) 'The Problems with Science
  Education The more things change, the more they
  are the same', in SMEC, St. Patrick's College,
  Dublin, 18th September 2006, Dublin DCU, 6-27.
• Daniels, H., Hyde, A. and Zemelman, S. (2005)
  Best Practice Todays Standards for Teaching and
  Learning in Americas Schools, Portsmouth, NH
  Heinemann.
• Frykholm, J. and Glasson, G. (2005) 'Connecting
  Science and Mathematics Instruction Pedagogical
  Context Knowledge for Teachers', School Science
  and Mathematics, 105(3), 127-141.
•  
• Furner, J. and Kumar, D. (2007) 'The Mathematics
  and Science Integration Argument A stand for
  Teacher Education', Eurasia Journal of
  Mathematics, Science Technology Education,
  3(3), 185-189.

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References

• Judson, E. and Sawada, D. (2000) 'Examining the
  Effects of a Reformed Junior High School Science
  Class on Students' Mathematics achievement',
  School Science and Mathematics, 100(8), 419-425.
• Lee, V. E. and Smith, J. B. (1995) 'Effects of
  high school restructuring and size on early gains
  in achievement and engagement', Sociology of
  Education, 68(4), 241-270.
• Lyons, M., Lynch, K., Sheerin, E., Close, S. and
  Boland, P. (2003) Inside Classrooms a Study of
  Teaching and Learning, Dublin Institute of
  Public Administration.
• McBride, J. W., Silverman, F. L. (1991).
  Integrating elementary/middle school science and
  mathematics. School Science and Mathematics(91),
  285-292.
• Miller, K. W. and Davison, D. M. (1999)
  'Paradigms and Praxis The Role of Science and
  Mathematics Integration', Science Educator, 8(1),
  25-29.
• National Council of Teachers of Mathematics
  (2009) 'Guiding Principles for Mathematics
  Curriculum and Assessment', 1-5, available
  http//www.nctm.org/uploadedFiles/Math_Standards/N
  CTM20Guiding20Principles206209.pdf accessed
  10th April 2010.

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References

• Newmann, F. M. (1996) Authentic achievement
  Restructuring schools for intellectual quality,
  San Francisco Jossey-Bass.
• Newmann, F. M., Bryk, A. S. and Nagaoka, J. K.
  (2001) Authentic Intellectual Work and
  Standardized Tests Conflict or Coexistence?,
  Chicago Consortium on Chicago School Research.
• Newmann, F. M., Lopez, G. and Bryk, A. S. (1998)
  The quality of intellectual work in Chicago
  schools A baseline report, Chicago Consortium
  on Chicago School Research. 
• O'Donoghue, J. (2004) An Irish Perspective on the
  "Mathematics Problem", translated by University
  College Dublin.
• Venville, G., Rennie, L., Wallace, J. (2004).
  Decision making and sources of knowledge How
  students tackle integrated tasks in science,
  technology and mathematics. Research in science
  Education, 34(2), 115-135.