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A UTHENTIC I NTEGRATION OF M ATHEMATICS AND S CIENCE (AIMS) – A MODEL FOR INTEGRATING M ATHEMATICS AND S CIENCE 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? How does this affect 3 rd Level? Students enter 3 rd 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? [S]tudents 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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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) Benefits of Integrating Mathematics and Science

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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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Combinations of probabilities: what is the probability of one of the offspring having freckles and short eyelashes? Are these probabilities independent of one another? Genetics and Probability - Discussion

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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 2 nd 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@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/NCTM%20Guiding%20Principles%20620 9.pdf [accessed 10th April 2010]. http://www.nctm.org/uploadedFiles/Math_Standards/NCTM%20Guiding%20Principles%20620 9.pdf

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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.

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