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: paraic.treacy@ul.ie

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.