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Touch: http://www.youtube.com/watch?feature=fvwp&NR=1&v=lgw0CFD5SJg Fibonacci: http://www.youtube.com/watch?v=E9cX_14rf4g. Math Across the Curriculum. Rob Kimball. Or. If we are not going to use it outside of math class, why do we have to learn it?. Or.
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If we are not going to use it outside of math class, why do we have to learn it?
We downloaded some data to a spreadsheet, calculated some statistics, and used those statistics to support oral arguments….In my English class!That math stuff must really be important.
It is everyone’s problem.
The simple fact is that many students who enter college are innumerate.Judging from what is going on in our society, you have to wonder how many college graduates are as well.
Innumeracy can make you poorer.
If you order the “Onion Soup” and “The Lancaster Special” compute the 10% tip you should leave.
a recent YouTube video that went viral
Mathematics is also an intellectual achievement of great sophistication and beauty that epitomizes the power of deductive reasoning. For people to participate fully in society, they must know basic mathematics. Citizens who cannot reason mathematically are cut off from whole realms of human endeavor. Innumeracy deprives them not only of opportunity but also of competence in everyday tasks.
x - y = -17
25x + 8y = 532
Richardson and McCallumThe Third R in Literacy
…tests showing that the demand for the product is expected to decrease 3,125 units for every 1.00 increase in price from the current level of 31.5 thousand units. The supply is expected to increase 1,000 units for each 1.00 increase in price from the current 17,000 units.
Find the break-even point.
“Create a mathematically literate student.”
“Create a quantitatively literate student.”
Non SMET students
Quantitative literacy describes a habit of mind rather than a set of topics or a list of skills. It depends on the capacity to identify mathematical structure in context; it requires a mind searching for patterns rather than following instructions. A quantitatively literate person needs to know some mathematics, but literacy is not deﬁned by the mathematics known.
Statisticssamplingrepresentations of data (numeric/graphic)variability
Rates and ProportionsDensity
Data Analysisnumeric, graphic
Rate of Change
Population Densities (by county)
It is difficult to teach students to identify mathematics in context – and many teachers have no experience doing this.
It is much easier to teach an algorithm than the insight needed to identify quantitative structure.
Teaching in context poses a tremendous challenge.
Problems in mathematics courses can be contextualized – StatWay and QuantWay
Problems in other disciplines are already contextualized – we must help students identify the math.
Mathematical Literacy: “An individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned, and reflective citizen.”
More info on PISA: http://www.icme12.org/upload/submission/2001_F.pdf
Math Panel – A review of first year courses; “What are the quantitative skills used in the course?”
The first-year courses students often take, in addition to a math class, require little in the way of mathematical thinking – numeracy – quantitative reasoning.
Texts often focus on facts and procedures.
Tests are often even worse. They are often computer - generated multiple choice questions that don’t require reasoning or sense making.
(Rob’s review – not necessarily that of NCEE)
Impact Studies at Queensborough and Houston Community Colleges Feb, 2011
A new paradigm.”…individuals must be broadly trained so that they can understand and contribute to research that overlaps different fields .”
(National Research Council)
“Interdisciplinary learning is a 21st Century imperative. We are continually faced with societal and global challenges that require interdisciplinary thinking to identify suitable solutions, such as finding new energy sources, dealing with the effects of our changing climate, and ensuring populations across the globe have adequate food and healthy living environments.” Summary report from Project Kaleidoscope – “What Works in Facilitating Interdisciplinary Learning in Science and Mathematics”
Energy Conservation, The Influence of Television, Exploration of Space, Obesity Epidemic, The Changing Demographics of the U S, US Debt…
Math across the curriculum can occur in many directions and success can look very different at different institutions.
It takes a champion, or two, to make it happen.
In the increasingly complex, data-rich global environments of the 21st Century, successful students need to be equipped with flexible, adaptive analytical higher-order strategies.
Quantitative writing addresses the need for these higher-order thinking skills.
Most issues of public policy have a significant quantitative dimension. Whether deliberating about health care, energy usage, or immigration policy, effective citizens must be able to interpret and analyze numbers, read graphs, understand simple statistics, and recognize the ways that numerical data can be manipulated for rhetorical effect.
QW assignments help develop students for responsible citizenship.
Spreadsheets are used throughout industry.
Educators, and especially mathematics educators, seem reluctant to utilize this ubiquitous tool.
Criminal Justice – How long has the potato been dead?
Economics – Cost / Benefit Analysis of driving across town for cheaper gas
Medicine – Examining the effect of dose, time interval, and elimination rate on attaining a therapeutic drug level
Friendly Conspiracies – collaboration between mathematics faculty and faculty from other departments(Hughes Hallett, 2001)Gateway Testing – mathematics competency tests in courses across the university (Bauman and Martin, 1995; University of Nevada, Reno)Instructional Support – provide support (equipment, lessons, collaboration) for teachers (Dartmouth College, 2001)Workshops – face-to-face discussions that help faculty outside of mathematics understand QL (Project Kaleidoscope, PKAL 2002; CRAFTY (MAA) Haver & Ganter)Quantitative Reasoning Requirements – a set of courses designated to meet QR requirements for undergraduates
Mathematics is far more than just a tool for research. In fact, its most common uses – and the reason for its prominent place in school curricula – are routine applications that are now part of all kinds of jobs.
…If we look at these common uses of mathematics from the perspective of the school curriculum, we see that mathematics at work is very different from mathematics at school.
Predicting membership by grade using a historical model and the cohort survival ratio.
A Rock Used As A Doorstop Changed North Carolina
Numeracy Through North Carolina History Kimball, 2011
Numeracy Through Texas HistoryKimball 2011
Mathematical proficiency, as we see it, has five strands:
Number and OperationsAlgebraGeometryMeasurementData Analysis and Probability
Adding It Up
Some animals that dwell on grassy plains are safeguarded against attacks by their large size; others are so small that they can protect themselves by burrowing into the ground. Still others must count on speed to escape their enemies.An animal’s speed depends on its size and the frequency of its strides. The tarsal (foot) bone of a horse is lengthened, with each foot having been reduced to only one toe. One thick bone is stronger than a number of thin ones. This single toe is surrounded by a solid hoof, which protects the bone against jolts when the animal is galloping over hard ground. The powerful leg muscles are joined together at the top of the leg so that just a slight muscle movement at that point can freely move the slip lower leg.
The fastest sprinter in the world is the cheetah. Its legs are shorter than those of a horse, but it can reach a speed of more than 110 km/hr in 17 seconds and maintain that speed for more than 450 meters. The cheetah tires easily, however, whereas the horse, whose top speed is 70 km/hr, can maintain a speed of 50 km/hr for more than 6 km. A cheetah is awakened by a horse’s hooves. At the moment the cheetah decides to give chase, the horse has a lead of 200 meters. The horse, traveling at top speed, still has plenty of energy. Taking into consideration the data that has been provided, can the cheetah catch the horse? Assume the cheetah will need around 300 meters to reach its top speed. Provide graphs to support your conclusions letting the vertical axis represent distance and the horizontal axis time. (Kindt, 1979)
Student at the end of the semester: “Thank God I’ll never have to take another math course in my life!”
Arnold Packer: Quantitative literacy, in my judgment, can save the day, not by being added to the curriculum but by altering required mathematics.