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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 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. Or Innumeracy It is everyone’s problem. The simple fact is that many students who enter college are innumerate. 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 Innumeracy can make you poorer. Couple’s numeracy skills linked to greater family wealth, study finds Innumeracy Innumeracy can make you unhealthier. Understanding Food Nutrition Labels Challenging For Many People Innumeracy Innumeracy can make you misunderstand important information. Numbers Are Just Numbers, But How You Grasp Them Fills In Details Innumeracy Innumeracy can be passed down through the generations Parents should talk about math early and often with their children — even before preschool, report finds National Center for Educational Statistics • 78% of adults cannot explain how to compute the interest paid on a loan • 71% cannot calculate miles per gallon on a trip • 58% cannot calculate a 10% tip for a lunch bill National Center for Educational Statistics • 78% of adults cannot explain how to compute the interest paid on a loan • 71% cannot calculate miles per gallon on a trip • 58% cannot calculate a 10% tip for a lunch bill National Center for Educational Statistics • 78% of adults cannot explain how to compute the interest paid on a loan • 71% cannot calculate miles per gallon on a trip • 58% cannot calculate a 10% tip for a lunch bill National Center for Educational Statistics • 78% of adults cannot explain how to compute the interest paid on a loan • 71% cannot calculate miles per gallon on a trip • 58% cannot calculate a 10% tip for a If you order the “Onion Soup” and “The Lancaster lunch bill Special” compute the 10% tip you should leave. Mathematical Literacy requires Conceptual Understanding Explaining MPG a recent YouTube video that went viral Adding It Up: Helping Children Learn Mathematics, 2001 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. The ability to perform some of the basic operations of mathematics is a necessary but not sufficient condition of quantitative literacy. Solve { x - y = -17 25x + 8y = 532 …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. Richardson and McCallum The Third R in Literacy A goal for mathematics departments: A goal for mathematics departments: “Create a mathematically literate student.” A goal for colleges: A goal for colleges: “Create a quantitatively literate student.” Promote Math Across the Curriculum Non SMET students SMET students Quantitatively Literate Teachers Politicians Business CEOs Voters Consumers Attorneys QL: A habit of mind 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. Where is the Math? Measurement Statistics Geometry sampling representations of Estimation data (numeric/graphic) Reasonableness Rates and Proportions variability Models Density Optimization Data Analysis Predicting numeric, graphic Rate of Change Where is the Literacy? Dialogue Debate Problem Stating Problem Solving Investigating Reasoning Sense Making Connecting Bridging Inferring Curriculum Foundations Report (CRAFTY) Life Sciences …the definition of mastery of a mathematical concept recognizes the importance of both conceptual understanding at the level of definition and understanding in terms of use, implementation, and/or computation. Business …help prepare business students by stressing conceptual understanding of quantitative reasoning and enhancing critical thinking skills. http://academic.bowdoin.edu/faculty/B/barker/dissemination/Curriculum_Foundations/ Where is the math? The math found in other disciplines is often transparent – to students (and instructors?) Persons Per Sq Mile 250-66,995 100-249 50-99 25-49 10-24 5-9 1-4 Population Densities (by county) Diagnostic Tool Math in context means math is meaningful Teaching Math In Context 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. Teaching Math In Context Problems in mathematics courses can be contextualized – StatWay and QuantWay http://www.carnegiefoundation.org/developmental-math Problems in other disciplines are already contextualized – we must help students identify the math. Programme for International Student Assessment (PISA, 2000) 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 A P P L Y t h e Other disciplines M A T H National Center On Education and the Economy Math Panel – A review of first year courses; “What are the quantitative skills used in the course?” Missing Math 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) Math Across the Curriculum Or Interdisciplinary Studies Models Learning Communities American History College Algebra English Learning Communities English Arithmetic Study Skills Impact Studies at Queensborough and Houston Community Colleges Feb, 2011 Aligned Interdisciplinary Studies Communications Psychology Statistics 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” Themed Studies American History Calculus Economics Energy Conservation, The Influence of Television, Exploration of Space, Obesity Epidemic, The Changing Demographics of the U S, US Debt… Even in English Class 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. Quantitative Writing 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. http://serc.carleton.edu/sp/carl_ltc/quantitative_writing/why.html QW 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 ACROSS THE CURRICULUM Spreadsheets are used throughout industry. Educators, and especially mathematics educators, seem reluctant to utilize this ubiquitous tool. http://www.serc.carleton.edu/sp/ssac_home SPREADSHEETS ACROSS THE CURRICULUM 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 Math Across the Curriculum HOW? 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 WHAT? Lynn Steen 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. Operations Research Laboratory for Education (OREd) Predicting membership by grade using a historical model and the cohort survival ratio. Challenges to MAC • Time – the density of the syllabus • Ability – using mathematics may be outside the comfort zone of some • Effort – it is extra work to find/write projects that use and promote quantitative literacy • What is Mathematics – too many people characterize mathematics as computation History A Rock Used As A Doorstop Changed North Carolina Numeracy Through North Carolina History Kimball, 2011 History San Marcos Numeracy Through Texas History Kimball 2011 Adding It Up Mathematical proficiency, as we see it, has five strands: • conceptual understanding—comprehension of mathematical concepts, operations, and relations • procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately • strategic competence—ability to formulate, represent, and solve mathematical problems • adaptive reasoning—capacity for logical thought, reflection, explanation, and justification • productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. Standards For School Mathematics (NCTM) Number and Operations Algebra Geometry Measurement Data Analysis and Probability Adding It Up Change and Relationships 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) Supporting Mathematics Across the Curriculum What should it mean for the math curriculum? 1. The mathematics that is taught should be embedded in the real world of the students. 2. Mathematical literacy will lead to different curricula in different cultures. 3. The content of the mathematics curricula will have to be modernized at least every ten years. Reforming a Failing Curriculum 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. Specific Recommendations 1. QL has a strong partner and advocate in the science community. (Science for All Americans (Project 2061 1989) 2. Consider engaging the social sciences in the quest for QL. 3. Adopt detailed and specific goals with benchmarks for progress. 4. Coordinate QL across disciplines by making QL part of faculty development. 5. Promote changes (improvements) in pedagogy advanced by national organizations. 6. Develop reliable and valid assessments of experiments in curriculum and instruction that target QL and publish the results. Resources • http://www.math.dartmouth.edu/~mqed/eBo okshelf/ • http://www.mac3.amatyc.org • http://www.therightstuff.amatyc.org • http://www.maa.org/cupm/crafty