Using Applications to Enhance Student Interest and Achievement in Mathematics:. Examples, Rationale, and Evidence Rosalie A. Dance, University of the Virgin Islands [email protected]
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Examples, Rationale, and Evidence
Rosalie A. Dance, University of the Virgin Islands
We easily succeed in teaching two kinds of students:
• those who are just like us, and
If teachers provide mathematics investigations in a variety of contexts in schools, students are steeped in the relevance of mathematics to their own intellectual pursuits.
Biological and models of their worldenvironmental contextsversions available from (1) Comap in the Consortium Pull-out sections (2) http://www9.georgetown.edu/faculty/sandefur/handsonmath/ (3) www.uvi.edu/sites/uvi/pages/imsa-home.aspx username: imsa-uvi password: mathincontext (4) [email protected] (on request)
Recursion equations and equilibrium
c/(k+a) → 0 as a Horizontal asymptote
ca/(k+a)→ c asa Horizontal asymptote
a=kd/(c-d)→infinity asd→cVertical asymptote.
Effective investigation of rates of change. Students see that a horizontal asymptote occurs where
dy/dx → 0 as x →infinity ;
a vertical asymptote occurs where
dy/dx →infinityas x → c, for some constant c.
130(0.87)^t, t Є [0, 1.5)
f(t) = 145(0.87)^(t-1.5), t Є [1.5, 7)
233(0.87)^(t-7), t Є [7, 24)
Lead in child’s bloodstream: half-life ~45 days
Lead in a child’s bones: half-life about 19 yrs.
Cadmium in adult body: half-life ranges from 9 to 47 years.
r = ap + gi, where a and gi, are determined from data.
◊ Determine population carrying capacity
◊ Determine what value of p maximizes population growth
◊ Where harvest size is a linear function of population size, h(p),
determine h(p) – g(p) from a graph of the functions.
◊ Determine harvest size that maintains population size
◊ Analyze effects of varying harvest rates on population size
Calories burned during physical workouts depend on weight and intensity of exercise.
c=6.55w+6.50h-7.06a+980.9 (women, age > 15)
c=9.3w+19h-10.2a+105.5 (men, age > 15)
Business contexts models of their worldand Social Sciencesversions available from (1) www.uvi.edu/sites/uvi/pages/imsa-home.aspxusername:imsa-uvipassword:mathincontext(2)Comap, in Consortium Pull-out sections(3) http://www9.georgetown.edu/faculty/sandefur/handsonmath/(4) [email protected] (on request)
See “Herbal Business” IMSA-UVI
See “How long can we expect to live?” at http://www.uvi.edu/sites/uvi/Documents/SciMath/IMSA-RDance/20.pdf
See Consortium website, www.comap.com/product
Opportunity to review history of this theorem before the
and for “looking at an iguana vs. looking at a fish” context, http://www.uvi.edu/sites/uvi/Documents/SciMath/IMSA-RDance/22.pdf
With contexts of interest to students and a mathematics classroom culture that supports the development of a learning community, we can supply two critical factors that support mathematics learning in traditionally underserved populations of students:
◊ A sense of community,
◊ An atmosphere of challenge.
Research suggests that these two, in combination, are powerful contributors to student persistence:
Albury, A. (1992). Social orientations, learning conditions and learning outcomes among low-income Black and White school children. Unpublished doctoral dissertation. Howard University, Washington, DC.
Boaler, J. (2002). Experiencing school mathematics. Mahwah, NJ: Lawrence Erlbaum Associates.
Cobb, P., Yackel, E. & McClain, K. (1999). Symbolizing and communicating in mathematics classrooms. Hillsdale, NJ: Lawrence Erlbaum Associates.
Heath, S.B. (1981). Questioning at home and at school: A comparative study. In G. Spindles (Ed.), Doing ethnography: Educational anthropology in action. New York: Holt, Rinehart & Winston.
Mehan, H. (1979). What time is it, Denise? Asking known information questions in classroom practice. Theory into Practice, 18(4), 285-294.
Piaget, J. (1952). The origins of intelligence in children. New York: International Universities Press.
Sinclair, J. & Coulthard, M. (1975). Towards an analysis of discourse: The language of teachers and pupils. London: Oxford University Press.
Treisman, P.U. (1992). Studying students studying calculus: A look at the lives of minority students in college. The College Mathematics Journal, 23 (5), 362.
Sandefur, J. and Dance, R. Hands-on Activities for Algebra at College. http://www9.georgetown.edu/faculty/sandefur/handsonmath/
Kaahwa, Janet. The role of culture in mathematics teaching and learning. In press.