a uthentic i ntegration of m athematics and s cience (aims) – a model for integrating m athematics...
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AUTHENTIC INTEGRATION AUTHENTIC INTEGRATION OF MATHEMATICS AND OF MATHEMATICS AND
SCIENCE (AIMS)SCIENCE (AIMS)
– – A MODEL FOR INTEGRATING MATHEMATICS A MODEL FOR INTEGRATING MATHEMATICS AND SCIENCEAND SCIENCE
Presented by Páraic Treacy (NCE-MSTL, University of Limerick, Ireland)
Difficulties Facing Irish Mathematics Difficulties Facing Irish Mathematics Education SystemEducation 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)
Difficulties Facing UK Difficulties Facing UK Mathematics Education SystemMathematics 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)
Difficulties Facing UK Difficulties Facing UK Mathematics Education Mathematics Education
SystemSystem
“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)
Criticisms of Mathematics Criticisms of Mathematics and Science Tuitionand 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)
How does this affect 3How does this affect 3rdrd Level? 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.
O’Donoghue (2004)
How Can How Can TheseThese Issues Be Issues Be Resolved?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)
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 Benefits of Integrating Mathematics and ScienceMathematics and Science
Approach to IntegrationApproach 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)
Authentic Instruction Authentic Instruction BenefitsBenefits
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)
Authentic Integration of Authentic Integration of Mathematics and Science Mathematics and Science
(AIMS)(AIMS)
How Does AIMS work?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.
Authentic Integration of Authentic Integration of Mathematics and Science Mathematics and Science
(AIMS)(AIMS)
Genetics and Probability - Genetics and Probability - DiscussionDiscussion
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 Huntington’s Disease.
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 - Genetics and Probability - DiscussionDiscussion
How could the task be How could the task be improved?improved?
Increase interest by using examples of celebrities and the traits their offspring might have…
Research carried out…Research carried out…
6 Maths-Science Integration lessons developed.
Implemented in 4 Irish 2nd Level Schools.
90 students participated.
Teachers that applied the Teachers that applied the modelmodel“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 I’d normally teach. The students really responded well to it.”
Teachers that applied the Teachers that applied the modelmodel“This approach seems to make complete sense to me, where you would bring the mathematical concepts along with the scientific concepts…
I definitely think it’s a model that more teachers should use”
Teachers that applied the Teachers that applied the modelmodel
“Very positive opinion of the teaching model employed. I think the tasks were absolutely fantastic”
Thanks for listening…Thanks for listening…
Information on the AIMS model and lesson plans based on this model are available by request.
Contact: [email protected]
ReferencesReferencesBoaler, 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: Today’s Standards for Teaching and Learning in America’s 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.
ReferencesReferencesJudson, 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%206209.pdf [accessed 10th April 2010].
ReferencesReferencesNewmann, 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.