Green Mathematics?
Gary Talsma
Mathematics and Statistics Department
Calvin College
Grand Rapids, MI 49546
()
CEA Convention South Bend, IN
October 22, 2009
Isn’t Math Teaching Neutral?
Simply put, teaching math in a neutral manner is not possible. No math teaching — no teaching of any kind, for that matter — is actually "neutral," although some teachers may be unaware of this.
For example: Let's say two teachers use word problems to teach double-digit multiplication and problem-solving skills. They each present a problem to their students. The first teacher presents this one:
A group of youth aged 14, 15, and 16 go to the store. Candy bars are on sale for 43¢ each. They buy a total of 12 candy bars. How much do they spend, not including tax?
The second teacher, meanwhile, offers a very different problem:
Factory workers aged 14, 15, and 16 in Honduras make McKids children's clothing for Wal-Mart. Each worker earns 43 cents an hour and works a 14-hour shift each day. How much does each worker make in one day, excluding fees deducted by employers?
While both problems are valid examples of applying multi-digit multiplication, each has more to say as well. The first example has a subtext of consumerism and unhealthy eating habits; the second has an explicit text of global awareness and empathy. Both are political, in that each highlights important social relations.
When teachers fail to include math problems that help students confront important global issues, or when they don't bring out the underlying implications of problems like the first example here, these are political choices, whether the teachers recognize them as such or not.
From Rethinking mathematics: Teaching social justice by the numbers, edited by Eric Gutstein and Bob Peterson, (Rethinking Schools Ltd., 2006), p. 6.
Simple linear regression results:
Dependent Variable: CO2 parts per million
Independent Variable: Year1
CO2 parts per million = -2231.1033 + 1.29954 Year1
Sample size: 59
R (correlation coefficient) = 0.987
R-sq = 0.9741981
World Oil Reserves and Oil Production
YEAR / Rsrvs(Gbbl) / Prod(Gbbl) / Yrs. Left1980 / 667 / 23.0 / 29.0
1981 / 688 / 21.7 / 31.6
1982 / 717 / 20.9 / 34.3
1983 / 727 / 20.7 / 35.2
1984 / 762 / 21.1 / 36.2
1985 / 771 / 21.0 / 36.8
1986 / 878 / 22.1 / 39.8
1987 / 910 / 22.2 / 41.0
1988 / 998 / 23.1 / 43.3
1989 / 1006 / 23.4 / 43.0
1990 / 1003 / 23.9 / 42.0
1991 / 1008 / 23.8 / 42.3
1992 / 1013 / 24.0 / 42.2
1993 / 1014 / 24.1 / 42.1
1994 / 1019 / 24.5 / 41.6
1995 / 1029 / 24.9 / 41.4
1996 / 1051 / 25.5 / 41.2
1997 / 1069 / 26.3 / 40.6
1998 / 1069 / 26.8 / 39.8
1999 / 1089 / 26.4 / 41.2
2000 / 1104 / 27.3 / 40.4
2001 / 1133 / 27.3 / 41.5
2002 / 1180 / 27.2 / 43.4
2003 / 1206 / 28.1 / 42.9
2004 / 1211 / 29.3 / 41.4
2005 / 1220 / 29.6 / 41.2
2006 / 1241 / 29.7 / 41.7
2007 / 1261 / 29.7 / 42.4
2008 / 1258 / 29.9 / 42.1
Whales, Models, and Peak Oil
To fit models to data, I used an online applet at I used a “2D Gaussian Peak” model, i.e., a normal curve, to fit the data with a symmetric bell-shaped curve characteristic of production levels of a non-renewable resource over time. The equation for the model is , where A is the maximum height of the curve, x = B is the axis of symmetry of the curve, and C determines the width of the curve (in the sense that the curve’s inflection points occur C units to left and right of x = B).
A = 11973.2A = 15346.6
B = 1845.8B = 1853.6
C = 13.98C = 17.38
R2 = .89R2 = .86
Using annual world oil production data for 1960-2008, we can compute a Gaussian model for world oil production.
A = 25.31
B = 2004.7
C = 34.19
R2 = .86
Note that this model indicates that peak production has already occurred, that oil production will drop to 1960 levels (about a third of current levels) by 2050, and that oil production will essentially cease by the end of this century.
Oil Consumption and Population
World / US / World / USProd / Cnsmp / Pop / Pop
YEAR / (Gbbl) / (Gbbl) / (Gppl) / (Gppl)
1965 / * / 4.2 / 3.35 / 0.19
1966 / * / 4.4 / 3.42 / 0.20
1967 / * / 4.6 / 3.49 / 0.20
1968 / * / 4.9 / 3.56 / 0.20
1969 / * / 5.2 / 3.64 / 0.20
1970 / * / 5.4 / 3.71 / 0.21
1971 / * / 5.6 / 3.79 / 0.21
1972 / * / 6.0 / 3.87 / 0.21
1973 / * / 6.3 / 3.94 / 0.21
1974 / * / 6.1 / 4.02 / 0.21
1975 / * / 6.0 / 4.09 / 0.22
1976 / * / 6.4 / 4.16 / 0.22
1977 / * / 6.7 / 4.23 / 0.22
1978 / * / 6.8 / 4.30 / 0.22
1979 / * / 6.7 / 4.38 / 0.23
1980 / 23.0 / 6.2 / 4.45 / 0.23
1981 / 21.7 / 5.9 / 4.53 / 0.23
1982 / 20.9 / 5.6 / 4.61 / 0.23
1983 / 20.7 / 5.6 / 4.69 / 0.23
1984 / 21.1 / 5.7 / 4.77 / 0.24
1985 / 21.0 / 5.7 / 4.85 / 0.24
1986 / 22.1 / 5.9 / 4.94 / 0.24
1987 / 22.2 / 6.1 / 5.02 / 0.24
1988 / 23.1 / 6.3 / 5.11 / 0.25
1989 / 23.4 / 6.3 / 5.19 / 0.25
1990 / 23.9 / 6.2 / 5.28 / 0.25
1991 / 23.8 / 6.1 / 5.37 / 0.25
1992 / 24.0 / 6.2 / 5.45 / 0.26
1993 / 24.1 / 6.3 / 5.53 / 0.26
1994 / 24.5 / 6.5 / 5.61 / 0.26
1995 / 24.9 / 6.5 / 5.69 / 0.27
1996 / 25.5 / 6.7 / 5.77 / 0.27
1997 / 26.3 / 6.8 / 5.85 / 0.27
1998 / 26.8 / 6.9 / 5.93 / 0.28
1999 / 26.4 / 7.1 / 6.01 / 0.28
2000 / 27.3 / 7.2 / 6.09 / 0.28
2001 / 27.3 / 7.2 / 6.16 / 0.29
2002 / 27.2 / 7.2 / 6.24 / 0.29
2003 / 28.1 / 7.3 / 6.31 / 0.29
2004 / 29.3 / 7.6 / 6.39 / 0.29
2005 / 29.6 / 7.6 / 6.46 / 0.30
2006 / 29.7 / 7.6 / 6.54 / 0.30
2007 / 29.7 / 7.5 / 6.61 / 0.30
2008 / 29.9 / 7.1 / 6.69 / 0.30
Simple linear regression results:
USCnsmp(Gbbl) = 0.97239995 + 21.572496 USPop(Gppl)
Sample size: 44
R (correlation coefficient) = 0.853
R-sq = 0.72761065
Simple linear regression results:
Where: Year > 1979
WrldProd(Gbbl) = 1.5658209 + 4.206804 WrldPop(Gppl)
Sample size: 29
R (correlation coefficient) = 0.9694
R-sq = 0.93975747
Prod / Cnsmp / Pop / Pop / Pop / Cnsmp / Cnsmp / Cnsmp
YEAR / (Gbbl) / (Gbbl) / (Gppl) / (Gppl) / Pct / Pct / Per Person / Per Person
1965 / * / 4.2 / 3.35 / 0.19 / 5.8 / * / * / 21.6
1966 / * / 4.4 / 3.42 / 0.20 / 5.7 / * / * / 22.5
1967 / * / 4.6 / 3.49 / 0.20 / 5.7 / * / * / 23.1
1968 / * / 4.9 / 3.56 / 0.20 / 5.6 / * / * / 24.4
1969 / * / 5.2 / 3.64 / 0.20 / 5.6 / * / * / 25.5
1970 / * / 5.4 / 3.71 / 0.21 / 5.5 / * / * / 26.2
1971 / * / 5.6 / 3.79 / 0.21 / 5.5 / * / * / 26.8
1972 / * / 6.0 / 3.87 / 0.21 / 5.4 / * / * / 28.5
1973 / * / 6.3 / 3.94 / 0.21 / 5.4 / * / * / 29.8
1974 / * / 6.1 / 4.02 / 0.21 / 5.3 / * / * / 28.4
1975 / * / 6.0 / 4.09 / 0.22 / 5.3 / * / * / 27.6
1976 / * / 6.4 / 4.16 / 0.22 / 5.2 / * / * / 29.2
1977 / * / 6.7 / 4.23 / 0.22 / 5.2 / * / * / 30.6
1978 / * / 6.8 / 4.30 / 0.22 / 5.2 / * / * / 30.8
1979 / * / 6.7 / 4.38 / 0.23 / 5.1 / * / * / 29.9
1980 / 23.0 / 6.2 / 4.45 / 0.23 / 5.1 / 27.1 / 5.2 / 27.3
1981 / 21.7 / 5.9 / 4.53 / 0.23 / 5.1 / 27.0 / 4.8 / 25.5
1982 / 20.9 / 5.6 / 4.61 / 0.23 / 5.0 / 26.7 / 4.5 / 24.0
1983 / 20.7 / 5.6 / 4.69 / 0.23 / 5.0 / 26.9 / 4.4 / 23.7
1984 / 21.1 / 5.7 / 4.77 / 0.24 / 5.0 / 27.3 / 4.4 / 24.3
1985 / 21.0 / 5.7 / 4.85 / 0.24 / 4.9 / 27.4 / 4.3 / 24.1
1986 / 22.1 / 5.9 / 4.94 / 0.24 / 4.9 / 26.9 / 4.5 / 24.7
1987 / 22.2 / 6.1 / 5.02 / 0.24 / 4.8 / 27.4 / 4.4 / 25.1
1988 / 23.1 / 6.3 / 5.11 / 0.25 / 4.8 / 27.4 / 4.5 / 25.7
1989 / 23.4 / 6.3 / 5.19 / 0.25 / 4.8 / 27.1 / 4.5 / 25.6
1990 / 23.9 / 6.2 / 5.28 / 0.25 / 4.7 / 26.0 / 4.5 / 24.8
1991 / 23.8 / 6.1 / 5.37 / 0.25 / 4.7 / 25.6 / 4.4 / 24.1
1992 / 24.0 / 6.2 / 5.45 / 0.26 / 4.7 / 25.9 / 4.4 / 24.2
1993 / 24.1 / 6.3 / 5.53 / 0.26 / 4.7 / 26.1 / 4.4 / 24.2
1994 / 24.5 / 6.5 / 5.61 / 0.26 / 4.7 / 26.4 / 4.4 / 24.5
1995 / 24.9 / 6.5 / 5.69 / 0.27 / 4.7 / 26.0 / 4.4 / 24.3
1996 / 25.5 / 6.7 / 5.77 / 0.27 / 4.7 / 26.2 / 4.4 / 24.8
1997 / 26.3 / 6.8 / 5.85 / 0.27 / 4.7 / 25.8 / 4.5 / 24.9
1998 / 26.8 / 6.9 / 5.93 / 0.28 / 4.7 / 25.7 / 4.5 / 25.0
1999 / 26.4 / 7.1 / 6.01 / 0.28 / 4.6 / 27.0 / 4.4 / 25.5
2000 / 27.3 / 7.2 / 6.09 / 0.28 / 4.6 / 26.3 / 4.5 / 25.5
2001 / 27.3 / 7.2 / 6.16 / 0.29 / 4.6 / 26.3 / 4.4 / 25.2
2002 / 27.2 / 7.2 / 6.24 / 0.29 / 4.6 / 26.5 / 4.4 / 25.1
2003 / 28.1 / 7.3 / 6.31 / 0.29 / 4.6 / 26.0 / 4.5 / 25.2
2004 / 29.3 / 7.6 / 6.39 / 0.29 / 4.6 / 25.8 / 4.6 / 25.8
2005 / 29.6 / 7.6 / 6.46 / 0.30 / 4.6 / 25.7 / 4.6 / 25.7
2006 / 29.7 / 7.6 / 6.54 / 0.30 / 4.6 / 25.4 / 4.5 / 25.3
2007 / 29.7 / 7.5 / 6.61 / 0.30 / 4.6 / 25.4 / 4.5 / 25.1
2008 / 29.9 / 7.1 / 6.69 / 0.30 / 4.5 / 23.7 / 4.5 / 23.3
Then he [Jesus] said to them, "Watch out! Be on your guard against all kinds of greed; a man's life does not consist in the abundance of his possessions." Luke 12:15
References
Kuyers Mathematics - http://www.calvin.edu/kuyers/math/index.html
Kuyers Mathematics is a mathematics curriculum resource funded by the Kuyers Institute for Christian Teaching and Learning at Calvin College. The site contains units intended to supplement and enrich a high school mathematics curriculum. Each unit contains a number of lessons integrating a Christian approach, “using mathematics to think about and better understand God, his creation, and our place and calling in the world.” Several of the units have themes related to environmental or social justice issues.
BP Statistical Review of World Energy June 2009 -
This site contains all kinds of interesting information about oil, natural gas, coal, nuclear energy, hydroelectricity, and “primary energy consumption.” Spreadsheets containing historical data about all of these energy sources can be downloaded from the site.
Tom Pfaff’s Sustainability Page - http://www.ithaca.edu/tpfaff/sustainability.htm
According to the creator of this webpage, it contains “data sets, example worksheets, and the background information you need to incorporate a sustainability theme into your Calculus I course … There are also links for further reading for you or your students.” Although the worksheets are targeted at calculus concepts, many of the activities can be modified for use in other classes. The site contains lots of data in Excel worksheets, and there are links to many thought-provoking articles. (This is where I originally ran across the whale data.)
RadicalMath -
“RadicalMath is a resource for educators interested in integrating issues of social and economic justice into their math classes and curriculum. On this website you will find links to access and download over 700 lesson plans, articles, charts, graphs, data sets, maps, books, and websites to help you bring these issues into your classroom.” The perspective here is probably best characterized as “secular humanist”, but the issues ought to be of interest to us as Christian mathematics teachers.
Rethinking Mathematics -
This is a website for a book with the same title (the book’s subtitle is Teaching Social Justice by the Numbers). Many excerpts from the book are available online; the book’s introduction provides much food for thought. Again, this site does not represent a Christian viewpoint, but shouldn’t Christians be committed to doing justice and loving mercy? Can mathematics be used to help with this?
Plan B 3.0: Mobilizing to Save Civilization-
This is a “data repository” website for a book by Lester Brown. There are dozens of Excel files that can be downloaded, dealing with many aspects of sustainability. (The entire book is available for download at a related website.)
http://www.calvin.edu/~tals/m143/cea.data contains data files I used in preparing this presentation. Most appear in two formats: Excel files (.xls suffix) and comma-separated text files (.csv suffix).