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Presentation on theme: "Touch: http://www.youtube.com/watch?feature=fvwp&NR=1&v=lgw0CFD5SJg Fibonacci: http://www.youtube.com/watch?v=E9cX_14rf4g."— Presentation transcript:

1 Touch: http://www.youtube.com/watch?feature=fvwp&NR=1&v=lgw0CFD5SJg
Fibonacci:

2 Math Across the Curriculum
Rob Kimball

3 Or If we are not going to use it outside of math class, why do we have to learn it?

4 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.

5 It is everyone’s problem.
Or It is everyone’s problem. Innumeracy A term meant to convey a person's inability to make sense of the numbers that run their lives. Innumeracy was coined by cognitive scientist Douglas R Hofstadter in one of his Metamagical Thema columns for Scientific American in the early nineteen eighties. Later that decade mathematician John Allen Paulos published the book Innumeracy. In it he includes the notion of chance as well to that of numbers. Innumeracy : Mathematical Illiteracy and Its Consequences ... John Allen Paulos The book that made innumeracy a household word. This book was written with the hope of shining some light on this issue. Many numeracy concepts are explored and explained. Paulos speaks mainly of the dangers of mathematical innumeracy; that is, the common misconceptions of the layperson in regards to numbers, exploring the relationship between math and the human mind. Paulos discusses innumeracy with quirky anecdotes, scenarios and facts, encouraging readers in the end to look at their world in a more quantitative way.

6 The simple fact is that many students who enter college are innumerate.

7 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. Paulos’ list of the consequences of innumeracy include: Inaccurate media reporting and inability of the public to detect such inaccuracies Financial mismanagement (e.g., of debts), especially regarding the misunderstanding of compound interest Loss of money on gambling, in particular caused by gambler’s fallacy Belief in pseudoscience Distorted assessments of risks Limited job prospects These are bad consequences i

8 Innumeracy can make you poorer.
Couple’s numeracy skills linked to greater family wealth, study finds Couples who score well on a simple test of numeracy ability accumulate more wealth by middle age than couples who score poorly on such a test, according to a study of married couples in the United States.

9 Innumeracy can make you unhealthier.
Understanding Food Nutrition Labels Challenging For Many People In one of the most rigorous studies ever conducted to determine how well people comprehend the information provided on food nutrition labels, researchers have found that the reading and math skills of a significant number of people may not be sufficient to extract the needed information, according to an article published in the November issue of the American Journal of Preventive Medicine.

10 Innumeracy can make you misunderstand important information.
Numbers Are Just Numbers, But How You Grasp Them Fills In Details Which is a lower risk that you will get a disease: 1 in 1000; a 1% chance, or a 0.05% chance? Choosing the correct answer depends on a person’s numeracy — the ability to grasp and use math and probability concepts – according to a presentation at the annual meeting of the American Association for the Advancement of Science.

11 Innumeracy can be passed down through the generations
Parents should talk about math early and often with their children — even before preschool, report finds The amount of time parents spend talking about numbers has a much bigger impact on how young children learn mathematics than was previously known. For example, children whose parents talked more about numbers were much more likely to understand the number principle that states that the size of a set of objects is determined by the last number reached when counting the set.

12 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 Sample Questions The NAAL Test Questions Tool provides easy access to the questions and answers from the 1985, 1992, and 2003 assessments that are released to the public. There are now 146 questions available in this tool. Among the released items, 79 were administered in the 1985 YALS and again in the 1992 NALS. In addition, 56 items created for the 1992 NALS have been released, as well as 11 items developed for the 2003 NAAL. Items were used in more than one of the assessments in order to report trend information. Note that the questions in this tool do not represent complete coverage of the content, cognitive skills, and range of difficulty in the 1985, 1992, and 2003 assessments for a particular scale. Some unreleased items are being preserved for possible use in upcoming assessments, and released questions will not be used in future tests. The test questions utilize stimulus materials drawn from a variety of real-world situations. The questions and stimulus material may differ slightly from those that appeared in the assessment because they are formatted for the Web. Some question formats (e.g., multiple-choice, oral response) or stimulus materials were used in the 1985 and 1992 assessments but not in the main 2003 assessment. Where materials are copyrighted, permission to reproduce them on the Web has been obtained. ... to begin the Test Questions Tool.

13 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

14 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

15 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 If you order the “Onion Soup” and “The Lancaster Special” compute the 10% tip you should leave.

16 Mathematical Literacy requires Conceptual Understanding
Explaining MPG a recent YouTube video that went viral

17 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 mathematics students need to learn today is not the same mathematics that their parents and grandparents needed to learn. When today’s students become adults, they will face new demands for mathematical proficiency that school mathematics should attempt to anticipate. Moreover, mathematics is a realm no longer restricted to a select few. All young Americans must learn to think mathematically, and they must think mathematically to learn. All young Americans must learn to think mathematically, and they must think mathematically to learn.

18 The ability to perform some of the basic operations of mathematics is a necessary but not sufficient condition of quantitative 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. Solve x - y = -17 25x + 8y = 532 { The ability to perform some of the basic operations of mathematics is necessary for quantitative literacy, but even the ability to perform many of them is not sufficient. Anyone who has taught mathematics, or who has taught a subject requiring the mathematics students have learned in previous courses, is aware of this fact; they encounter students who are technically capable but unable to make reasonable decisions about which techniques to apply and how to apply them. Mathematicians and their colleagues in other departments share frustration at the fragility of what students learn in their mathematics classes. We hesitate to call literate a person who reads haltingly, picking out words one at a time with no appearance of understanding what is being read; yet too many of the students leaving mathematics courses use mathematics haltingly if at all—too many appear to be lacking in conceptual understanding. We make a distinction here between conceptual understanding and formal mathematical understanding. The latter refers to an ability to formulate precise mathematical arguments that are universal in the sense that they work for all numbers or all polynomials. Conceptual understanding is understanding of a less formal nature, more like what mathematicians sometimes call intuitive understanding. It refers to an ability to recognize underlying concepts in a variety of different representations and applications. For example, a student who understands the concept of rate knows that the velocity of a moving object, the slope of its position graph, and the coefficient of t in a formula giving its position as a function of time t, are all manifestations of the same underlying concept, and knows how to translate between them. Richardson and McCallum The Third R in Literacy

19 A goal for mathematics departments:

20 A goal for mathematics departments:
“Create a mathematically literate student.” Mathematical literacy is necessarily a goal of a mathematics department. The specific skills required are taught in math courses. However, to be literate in mathematics the courses can’t be constructed in the historically prevalent SILO design – isolated and not connected, neither with other disciplines nor within mathematics.

21 A goal for colleges:

22 “Create a quantitatively literate student.”
A goal for colleges: “Create a quantitatively literate student.” Who is responsible for ensuring that college graduates are quantitative literate? The responsibility of producing a QL person cannot lie totally within a math department. Faculty in other disciplines must be able to identify where mathematics is used as a tool and promote the conceptual understanding necessary to apply that mathematics appropriately.

23 Promote Math Across the Curriculum
Non SMET students SMET students CBMS 2010 (in progress) In fall 2010, over 1,150,000 students in Precollege courses (Arithmetic, Pre-algebra, Elementary and Intermediate Algebra, and Geometry) comprised over half (57%) of mathematics program enrollment. This percentage has been essentially stable at 57% since 1990. …Precalculus level courses (College Algebra, Trigonometry, College Algebra & Trigonometry, Introduction to Mathematical Modeling, Precalculus) accounted for 18% of 2010 enrollment, one percentage point down from enrollment reported in Precalculus courses, together with Precollege courses, accounted for 75% of mathematics and statistics enrollment at public two-year colleges in fall 2010. At 4-year colleges, Introductory Mathematics courses account for over 700,000 students while calculus-level courses account for around 600,000 students. Since most non-SMET student take only one math course and SMET students take several calculus courses, you can see the proportion of students is much greater than the numbers.

24 Quantitatively Literate
Teachers Politicians Business CEOs Voters Consumers The point is that including mathematics in courses for NON-SMET students needs to be emphasized much greater than for SMET students. The science and engineering courses SMET students are required to take ‘usually’ require students apply mathematics. How many math courses are required in NON-STAT majors? One or two. Attorneys

25 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. …For example, a person who knows calculus is not necessarily any more literate than one who knows only arithmetic. The person who knows calculus formally but cannot see the quantitative aspects of the surrounding world is probably not quantitatively literate, whereas the person who knows only arithmetic but sees quantitative arguments everywhere may be. Adopting this definition, those who know mathematics purely as algorithms to be memorized are clearly not quantitatively literate. Quantitative literacy insists on understanding. This understanding must be flexible enough to enable its owner to apply quantitative ideas in new contexts as well as in familiar contexts. Quantitative literacy is not about how much mathematics a person knows but about how well it can be used

26 Where is the Math? Measurement Geometry Estimation Reasonableness Rates and Proportions Density Data Analysis numeric, graphic Rate of Change Statistics sampling representations of data (numeric/graphic) variability Models Optimization Predicting Supporting numeracy: Math in vocations:

27 Dialogue Debate Problem Stating Problem Solving Investigating
Where is the Literacy? Reasoning Sense Making Connecting Bridging Inferring Dialogue Debate Problem Stating Problem Solving Investigating Supporting numeracy: Math in vocations:

28 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. What is striking about these reports is that even the Science, Math, Engineering, and Technology (SMET) disciplines feel the need to explicitly request conceptual understanding from mathematics courses preparing their students. All the more must we worry about the state of conceptual understanding in students who are not preparing for SMET disciplines, but simply need quantitative literacy as a basic life skill.

29 Where is the math? The math found in other disciplines is often transparent – to students (and instructors?) What is striking about these reports is that even the Science, Math, Engineering, and Technology (SMET) disciplines feel the need to explicitly request conceptual understanding from mathematics courses preparing their students. All the more must we worry about the state of conceptual understanding in students who are not preparing for SMET disciplines, but simply need quantitative literacy as a basic life skill.

30 Population Densities (by county)
Persons Per Sq Mile 250-66,995 50-99 25-49 10-24 5-9 1-4 Population Densities (by county)

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34 Diagnostic Tool

35 Math in context means math is meaningful

36 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. One of the reasons that the level of quantitative literacy is low in the U.S. is that it is difficult to teach students to identify mathematics in context, and most mathematics teachers have no experience with this. It is much easier to teach an algorithm than the insight needed to identify quantitative structure. Most U.S. students have trouble applying the mathematics they know in “word problems” and this difficulty is greatly magnified if the context is novel. Teaching in context thus poses a tremendous challenge. The work of Erik De Corte, in Belgium, throws some light on what helps students to think in context. DeCorte investigated the circumstances under which students give unrealistic answers to mathematical questions. For example, consider the problem that asks for the number of buses needed to transport a given number of people; researchers find that a substantial number of students give a fractional answer, such 33 2/3 buses. DeCorte reported that if the context was made sufficiently realistic, for example, asking the students to write a letter to the bus company to order buses, many more students gave reasonable (non-fractional) answers. De Corte’s work suggests that many U.S. students think the word problems in mathematics courses are not realistic. (It is hard to disagree.) Mathematicians have a lot of work to do to convince students that they are teaching something useful. Having faculty outside mathematics include quantitative problems in their own courses is extremely important. These problems are much more likely to be considered realistic.  As another example, many calculus students are unaware that the derivative represents a rate of change, even if they know the definition. Asked to find a rate, these students do not know they are being asked for a derivative; yet, this interpretation of the derivative is key to its use in a scientific context. The practical issue, then, is how to develop the intuitive understanding necessary to apply calculus in context. Mathematicians have a natural tendency to try to help students who do not understand that the derivative is a rate by re-explaining the definition; however, the theoretical underpinning, although helping mathematicians understand a subject, often does not have the same illuminating effect for students. When students ask for “an explanation, not a proof,” they are asking for an intuitive understanding of a topic. Mathematicians often become mathematicians because they find proofs illuminating. Other people, however, often develop intuitive understanding separately from proofs and formal arguments. My own experience teaching calculus suggests that the realization that a derivative is a rate comes not from the definition but by talking through the interpretation of the derivative in a wide range of concrete examples. It is important to realize that any novel problem or context can be made “old” if students are taught a procedure to analyze it. Students’ success then depends on memorizing the procedure rather than on developing their ability to apply the central mathematical idea. There is a difficult balance to be maintained between providing experience with new contexts and overwhelming students by too many new contexts. Familiar contexts should be included—they are essential for developing confidence—but if the course stops there, quantitative literacy will not be enhanced. There is tremendous pressure on U.S. teachers to make unfamiliar contexts familiar and hence to make problems easy to do by applying memorized algorithms. Changing this will take a coordinated effort: both school and college teachers will need to be rewarded for breaking out of this mold.

37 Teaching Math In Context
Problems in mathematics courses can be contextualized – StatWay and QuantWay Problems in other disciplines are already contextualized – we must help students identify the math. What is the problem? Helping community college students succeed in developmental mathematics is a major priority of the Carnegie Foundation. This is because currently up to 60 percent of community college students who take the placement exam learn they must take at least one remedial course (also called developmental education) to build their basic academic skills. The vast majority of community college students referred to developmental mathematics do not successfully complete the current sequence of required courses and many leave college for good. Improving Developmental Math in Community Colleges Recognizing the grave consequences for individual opportunity and more generally for our economy and society, theCarnegie Statway ™and Quantway ™Networked Improvement Communities have embraced an audacious goal—to increase from 5 percent to 50 percent the percentage of students who achieve college math credit within one year of continuous enrollment. The Instructional System Version 1.0 of the Statway™ and Quantway™ lessons were created by The Charles A. Dana Center at The University of Texas at Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching, and are copyrighted by both organizations. Participants in both Carnegie’s Statway™ and Quantway™ Networked Improvement Communities are not using Version 1.0, but instead are using Version 1.5 of the lessons, which have been co-developed and improved by the Network. These materials are part of an Instructional System that includes: Ambitious learning goals leading to deep and long lasting understanding; Lessons and out-of-class materials to advance these goals; Formative and summative assessments, including end of module and end of course assessments; Productive Persistence — an evidence-based package of practical student activities and faculty actions integrated throughout the instructional system to increase student motivation, tenacity and skills for success; Language and literacy component which interweaves necessary supports in instructional materials and classroom activities so that learning is accessible to all; Advancing teaching component to provide instructors with the knowledge, skills and habits necessary to experience efficacy in initial use and develop increasing expertise over time. This dimension is essential in seeking to reduce the variability in outcomes; Analytics to support the continuous improvement of teaching and of the materials.

38 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: This paper reports on the work done in preparation for the OECD 2012 Programme for International Student Assessment (PISA) survey of mathematical literacy. PISA surveys are conducted every three years. The first was in 2000, so that the 2012 survey is the fifth in the series. As well as making inter-country comparisons and linking achievement data to information on schools and teaching, it is now possible to examine trends in achievement over about a decade. In each cycle, the major focus of the survey rotates through reading literacy, scientific literacy and mathematical literacy. The 2012 survey focuses on mathematical literacy, for the first time since Because of this focus, a large number of new mathematical literacy items have been created and trialled for 2012, the Framework which specifies the nature of the assessment has been revised and an optional additional computer-based assessment has been developed. The questionnaires for students and schools will emphasise mathematics. In 2012, at least 67 countries (including all 33 of the OECD member countries) will participate in the main survey, with many undertaking the optional components, including computer-based assessment of mathematical literacy (CBAM), general problem solving, financial literacy, parent and teacher questionnaires and a student questionnaire on familiarity with ICT. The first results from the 2012 survey should appear near the end of the year.

39 Providing information to assist policymakers, researchers, educators, and the public obtain a
comprehensive picture of how U.S. students perform in key subject areas is an important objective of the National Center for Education Statistics (NCES). In the United States, nationallevel data on student achievement comes primarily from two sources: the National Assessment of Educational Progress (NAEP)—also known as the “Nation’s Report Card”—and the United States’ participation and collaboration in international assessments, such as the Trends in International Mathematics and Science Study (TIMSS) and the Program for International Student Assessment (PISA). 1 NAEP measures fourth-, eighth-, and twelfth-grade students’ performance, most frequently in reading, mathematics, and science, with assessments designed specifically for national and state information needs. Alternatively, the international assessments allow the United States to benchmark its performance to that of other countries—in fourth- and eighth-grade mathematics and science in TIMSS and in 15-year-olds’ reading, mathematical, and scientific literacy in PISA. All three assessments are conducted regularly to allow the monitoring of student outcomes over time. 2 While these different assessments may appear to have significant similarities, such as the age or grade of students or content areas studied, each was designed to serve a different purpose and each is based on a separate and unique framework and set of items. Thus, not surprisingly, there may be differences in results for a given year or in trend estimates among the studies, each giving a slightly different view into U.S. students’ performance in these subjects. NCES released results from the 2003 administrations of TIMSS and PISA in December 2004. Results from the 2003 administration of NAEP Mathematics were released in late 2003; and results from the 2000 administration of NAEP Science also are available.

40 Mathematical Literacy in PISA
Mathematical literacy entails the use of mathematical competencies at several levels, ranging from performance of standard mathematical operations to mathematical thinking and insight. It also requires the knowledge and application of a range of mathematical content. PISA assesses mathematical literacy in three dimensions: First, the content of mathematics, as defined mainly in terms of broad mathematical concepts underlying mathematical thinking (such as chance, change and growth, space and shape, reasoning, uncertainty and dependency relationships), and only secondarily in relation to "curricular strands" (such as numbers, algebra and geometry). The PISA 2000 assessment, in which mathematics is a minor domain, focuses on two concepts: change and growth, and space and shape. These two areas allow a wide representation of aspects of the curriculum without giving undue weight to number skills. Second, the process of mathematics as defined by general mathematical competencies. These include the use of mathematical language, modelling and problem-solving skills. The idea is not, however, to separate out such skills in different test items, since it is assumed that a range of competencies will be needed to perform any given mathematical task. Rather, questions are organized in terms of three "competency classes" defining the type of thinking skill needed. The first class of mathematical competency consists of simple computations or definitions of the type most familiar in conventional mathematics assessments. The second class requires connections to be made to solve straightforward problems. The third competency class consists of mathematical thinking, generalization and insight, and requires students to engage in analysis, to identify the mathematical elements in a situation and to pose their own problems. Third, the situations in which mathematics is used, ranging from private contexts to those relating to wider scientific and public issues.

41 APPLY the MATH Other disciplines

42 National Center On Education and the Economy
Math Panel – A review of first year courses; “What are the quantitative skills used in the course?”

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45 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)

46 Math Across the Curriculum Or Interdisciplinary Studies
Models

47 Learning Communities American English History College Algebra
Faculty teams share a group of students and tie the subject matter together with common projects. Elon College has taken this to a new level, even putting these teams together in the same residence halls. Learning communities seem to have grown in number, in particular, in pre-college courses. These students often need support and encouragement as they learn how “TO DO COLLEGE”. The NCTM Standards emphasize the importance of developing mathematical language and communication in order to understand concepts rather than merely following a sequence of procedures. Math Expressions seeks to build a community of learners who have frequent opportunities to explain their mathematical thinking through Math Talk and thereby develop their understanding. children are asked to solve problems, explain their solutions, answer questions, and justify their answers. They use proof drawings as a reference for their explanations. The dialogue that takes place helps everyone understand math concepts more deeply, and it helps children to increase their competence in using mathematical and everyday language. While children engage in dialogue, the teacher acts as a guide to maintain the focus of the discussion and to clarify when necessary College Algebra

48 Learning Communities English Arithmetic Study Skills
 Both Queensborough and Houston began by implementing a basic model of a one semester developmental math learning community; the programs strengthened over the course of the demonstration by including more curricular integration and some connections to student support services.  Learning community students attempted and passed their developmental math class at higher rates at both colleges.  In the semesters following students’ participation in the program, impacts on developmental math progress were far less evident. By the end of the study period (three semesters total at Queensborough and two at Houston), control group members at both colleges had largely caught up with learning community students in the developmental math sequence.  On average, neither college’s learning communities program had an impact on persistence in college or cumulative credits earned Learning Communities for Students in Developmental Reading An Impact Study at Hillsborough Community College NCPR, Michael J. Weiss, Mary G. Visher, Heather Wathington, with Jed Teres, Emily Schneider. Scaling Up Learning Communities The Experience of Six Community Colleges NCPR, Mary G. Visher, Emily Schneider, Heather Wathington, Herbert Collado. Case Studies of Three Community Colleges The Policy and Practice of Assessing and Placing Students in Developmental Education Courses An NCPR Working Paper (National Center for Postsecondary Research) NCPR, Stephanie Safran, Mary G. Visher. The Learning Communities Demonstration Rationale, Sites, and Research Design NCPR, Mary G. Visher, Heather Wathington, Lashawn Richburg-Hayes, Emily Schneider, with Oscar Cerna, Christine Sansone, Michelle Ware. A Good Start Two-Year Effects of a Freshmen Learning Community Program at Kingsborough Community College MDRC, Susan Scrivener, Dan Bloom, Allen LeBlanc, Christina Paxson, Cecilia Elena Rouse, Colleen Sommo. Building Learning Communities Early Results from the Opening Doors Demonstration at Kingsborough Community College MDRC, Dan Bloom, Colleen Sommo. Learning Communities and Student Success in Postsecondary Education: A Background Paper. MDRC, Derek V. Price, Malisa Lee. Impact Studies at Queensborough and Houston Community Colleges Feb, 2011

49 Aligned Interdisciplinary Studies
Communications Psychology Statistics …training areas as basic biomedical, behavioral, and clinical. This is obviously an oversimplification. There are many disciplines within each of these areas and significant overlap in and between these three major groupings. In point of fact, some of the most significant research occurs at the interfaces between traditional research areas. This is even more likely to be true in the future because the solution to complex biological and health care problems will require experts and expertise in many different disciplines—and increasingly expertise in more than one field. Consequently, it is important to encourage such research. If this research is to be successful, individuals must be broadly trained so that they can understand and contribute to research that overlaps different fields.National Research Council, 2004  In considering these issues, it is important to remember that today's interdisciplinary research often ends up as tomorrow's “traditional” discipline. A new paradigm. ”…individuals must be broadly trained so that they can understand and contribute to research that overlaps different fields .” (National Research Council)

50 “Interdisciplinary learning is a 21st Century imperative
“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” Multidisciplinarity is a process in which scholars from disparate fields work independently or sequentially, periodically coming together to share their individual perspectives for purposes of achieving broader-gauged analyses of common research problems. Participants in multidisciplinary teams remain firmly anchored in the concepts and methods of their respective fields. Interdisciplinarity is a more robust approach to scientific integration in the sense that team members not only combine or juxtapose concepts and methods drawn from their different fields, but also work more intensively to integrate their divergent perspectives, even while remaining anchored in their own respective fields. Stokols, D., K.L. Hall, B.K. Taylor, and R.P. Moser The science of team science: Overview of the field and introduction to the supplement. American Journal of Preventive Medicine 35 (2S): S77–89.

51 Themed Studies American History Calculus Economics
The idea is simple.  Connect the "discipline silos" in education by relating every discipline, at least a few times, to a common theme.  This academic year, we have six themes.  Each theme lasts for approximately four weeks. As students see commonalities between their classes, we hope they will begin to see how the disciplines connect, while at the same time learning about modern issues that might normally be addressed in upper-level topic-oriented courses or Freshman seminars. Economics Energy Conservation, The Influence of Television, Exploration of Space, Obesity Epidemic, The Changing Demographics of the U S, US Debt…

52 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.

53 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. Economics Diet planning/research Demographic data Performance analysis Psychology – data from experiments

54 Q W 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.

55 Spreadsheets Across the Curriculum
Spreadsheets are used throughout industry. Educators, and especially mathematics educators, seem reluctant to utilize this ubiquitous tool.

56 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

57 Math Across the Curriculum

58 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

59 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.

60 Operations Research Laboratory for Education (OREd)
Predicting membership by grade using a historical model and the cohort survival ratio.

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66 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

67 A Rock Used As A Doorstop Changed North Carolina
History A Rock Used As A Doorstop Changed North Carolina 3.0 A Rock Used as a Doorstop Changed North Carolina John Reed left the British army and settled near fellow Germans in the lower Piedmont of NC. His farm was near Midlands just east of what is now Charlotte. The family lived off what they got from the land, mostly grain crops. The story goes that Reed’s son, in 1799, found a large yellow rock in the creek on their property. It was unusual and shiny so they kept it and used it as a doorstop for three years. A Fayetteville jeweler identified the seventeen pound rock as gold and paid Reed’s asking price of $3.60. Later, Reed and the jeweler agreed on $1000 settlement. Reed’s son was the first documented gold find in the US. Reflect: A thousand dollars can buy a lot today! Think what it might have purchased in 1799. Reed formed a partnership and began mining operations in the off season, giving their crops first priority. Later that year, a 28-pound nugget was found. The news spread fast and other Piedmont farmers began exploring their creeks and finding gold. The lure of gold drew miners from as far as England to western NC in what is known as the NC Gold Rush. Reflect: Find an object that weighs in the neighborhood of 28 pounds? Lure: anything that attracts, as in a fishing lure Piedmont: a plateau region that between the Atlantic Coastal Plain and the Appalachian Mountains. The piedmont region in the eastern US stretches from New Jersey through NC and into GA. At first, mining was only done above ground in creek beds. By 1825, the metal was discovered to exist in veins of white quartz. Work underground began at the Reed mine in Reed died a wealthy man in The mine was sold several times and the last nugget, 23 pounds, was found there in Underground mining ended in 1912 when the cost of digging was more than the value of gold being found. Reflect: What makes gold so valuable? Gold coins were used as far back as 2700 BC. A $ double eagle gold coin was sold in 2002 for over $7 million. Gold mining was a major industry in many NC counties. From 1800 to the Civil War, gold mining employed more North Carolinians than any other occupation other than farming. At its peak in the 1830s and 1840s, there were as many as 56 mines operating simultaneously in NC. The NC Gold Rush attracted free-spirited pioneers from other states and from Europe. New ideas and more advanced manufacturing procedures came along with them. This diversity was never clearer in the election of 1860 and in the turmoil leading up to secession. NC was the largest producer of gold until surpassed by California in Because all of the gold being used in coins was coming from NC, the US opened a mint in Charlotte in The Bechtler family operated a private mint from 1831 until The Bechtler mint produced more than a million coins in denominations of $1.00, $2.50, and $ Bechtler’s precision and the reliable gold content of his coins earned him a spotless reputation that allowed him to prevail against other producers. He died in Rutherfordton and his coins are prizes for collectors to this day. Reflect: A coin made from pure gold is certainly worth more than one made from a mixture of gold and some other metal of lesser value. Knowing coins were pure was important. Read more about the Bechtler Mint at The news of gold in NC brought many notables to the State. Among them was the designer of the US Capitol, William Thornton. He purchased 35,000 acres of land in what is now Stanly County and formed the NC Gold Mine Company. Investors included a former Governor and the Treasurer of the US. Europeans came as well, bringing skills and techniques already proven elsewhere. Steam technology began to be employed in the search for gold and soon spread to the textile mills that were just emerging, especially around Greensboro. It was there, in 1828, that the first ever steam-powered cotton mill was built. This marked the beginning of Greensboro’s status as a major textile manufacturing center. Reflect: Mechanizing industry required power. The use of steam to generate power was relatively short-lived. What replaced it? The influence of the immigrants who came to NC to mine for gold changed the state. No longer would it be called “The Rip Van Winkle State.” The technology shared by the miners, especially the Cornish from Great Britain, was to make NC into a leading manufacturing state throughout the early 19th century. Today, leaders in banking, research, and industry have indirectly benefited from the foreign miners and investors in the nation’s first gold rush. The prominence of Charlotte in the banking industry can be attributed to the gold rush in NC. (3.1) The price of gold is constantly changing. For our purposes, let’s say that gold is now being sold for $1,400 per ounce. Find today’s price of the 17 pound nugget Conrad Reed found in 1799. (3.2) The coins at the Bechtler mint were of different karats. Karat weight is a unit of fineness for gold equal to 1/24 part of pure gold in an alloy. Pure gold, 24 karats, is 1000 fine; 100% gold. 23 karat gold is 23/24 gold or fine. 18 karat gold is 18/24 gold or fine. How many karats would a gold coin be if it were fine? (3.3) You may visit the Reed gold mine in NC for free. However, you must pay $2 to pan for gold. If you went there each day for a year, how many ounces of gold, at $1400 per ounce, would you need to find to pay your admission fees for the year? (3.4) The price of gold fluctuates continuously. The chart shows the price of gold in U S dollars per ounce on March 25, 2011 from midnight to 5:15 p.m. What was the price per ounce at 10 a.m. and then at about 12:45 p.m. when it bottomed out? What was the percent change during that time period? The chart shows that the price of gold, at 17:15 EST was $ /ounce, down $16.45/ounce for the day. What was the percent change from midnight until 17:15 EST? Sources: ils.unc.edu/nclibs/davidson/Davidson%20County%20Mining.htm, en.wikipedia.org/wiki/Christopher_Bechtler, dboitnott.home.mindspring.com/Articles/nc_gold_rush.html, ncmuseumofhistory.org/collateral/articles/s06.gold.rush.pdf Numeracy Through North Carolina History Kimball, 2011

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69 History San Marcos Numeracy Through Texas History Kimball 2011
Lyndon Baines Johnson, the 36th President of the United States ( ) and the 37th Vice President of the United States ( ), was born in Stonewall, Texas in His ancestors include a Baptist pastor who was also the President of Baylor University. After graduating from Southwest Texas State Teachers’ College (now Texas State University – San Marcos), he taught public speaking at Sam Houston H S in Houston. Johnson’s Presidency could be remembered for numerous reasons, but most people associate him with Vietnam. It was he who began America’s direct involvement in the ground war in Vietnam. By 1968, over 550,000 American soldiers were inside Vietnam and being killed at the rate of over one thousand per month. LBJ, as he was known, died at his home in 1973 at the age of 64, one day before a ceasefire was signed in Vietnam. 11.0 San Marcos Reflect: Who was President of the United States before and after LBJ? Reflect: How could LBJ be the 37th VP and the 36th President? Johnson married Claudia Alta Taylor (Ladybird) in 1934 at St. Mark’s Episcopal Church in San Antonio ten weeks after their first date, during which LBJ proposed. Ladybird was instrumental in LBJ’s career. It was she who funded his first campaign for Congress and she who provided the financial means for LBJ to act the part of the Texas Rancher. In 1943, Ladybird purchased KTBC, an Austin radio station that was in debt, for $17,500. Through the years, she expanded her holdings to include other radio stations as well as TV stations. Her initial investments turned into more than $150 million in assets. The Johnson Ranch in Stonewall is still an active ranch. It includes the airport runway LBJ used and the cattle barns that were designed so LBJ could chauffeur his guests through the barns to examine his prize herd of Longhorns. You, just like the many dignitaries LBJ escorted around the ranch in his big Cadillac, can drive through the property today. The student center at Texas State University is named after LBJ. Texas State is the only University in the state with an alumnus who became President of the US. Texas State is also the home of the fictional TV series, Friday Night Lights. Texas State University’s main campus in San Marcos is about 60 miles southeast of LBJ’s ranch situated just off I-35 between Austin and San Antonio. The main campus consists of 457 acres. The university also owns and manages 5,038 additional acres used for recreation, an instructional farm, and ranch land. Part of those holdings include Sewell Park, on the banks of the spring fed San Marcos River. The school serves 32,000 students, most of whom commute, as only 17% live on campus. The school offers 12,421 parking spaces surrounding its 225 main campus buildings.1 Students of the university enjoy swimming and tubing in the outflow from the Edwards Aquifer in San Marcos Springs. As you enjoy your meal at a local steak house, you can watch as students jump off the rocks into the spring fed, warm water just beneath one of the spillways that take the discharge from the springs and form the San Marcos River. Aquifer: a wet underground layer of water-bearing permeable rock (or gravel) from which groundwater can be extracted. Archaeologists believe the area around the springs is the oldest continually inhabited site in North America. Remains indicate that humans lived in the area as many as 11,500 years ago. Fresh water, in an otherwise barren environment, has attracted people to this area for many years. The Cantona Indians called the springs Canocanayesatetlo, meaning “warm water.” Europeans first visited the springs in 1691. In 1845, General Edward Burleson, a native of North Carolina, acquired the land around the headwaters of the river. He built a two-room cabin overlooking the springs where he built a dam across the river to operate a gristmill. The dam inundated the springs and formed Spring Lake. Burleson’s dam provided water pressure to run the gristmill. The dam also protected the archaeological artifacts that lay at its bottom for over one hundred years. Some of the artifacts recovered from the lake bed are on display now at the site. Gristmill: Wheat is ground to make flour. Maize is ground to make corn meal. Before electricity, water was used to turn large stones which ground the initial ingredients to the desired texture. The building in which this was done was called a gristmill. In most farming communities, there was a mill where local farmers brought their own grain. The miller would grind the ingredients and give the farmer back the ground meal or flour, keeping a percentage called the “miller’s toll.” History does not record a time when the San Marcos Springs ceased to flow! The lowest recorded flow rate was 46 cubic feet per second in 1956 (August). The chart below shows the seasonal fluctuation in flow as monitored by the USGS Water Resources Division in San Antonio. The Edwards Aquifer is a geological feature in central Texas that has allowed the Hill Country area, including Austin and San Antonio, to grow steadily without worrying about the availability of drinking water. Even though the region is semi-arid and adjacent to the Chihuahuan desert, this unique groundwater system produces enough water to serve the needs of almost two million users in south central Texas. Rain in the Hill Country, about 30 inches per year, seeps through the surface until it reaches a relatively impermeable layer of limestone. The water runs along the top of this layer until it reaches the Balcones Fault Zone where cracks in the surface limestone allow the water to seep deeper into more porous limestone. The Edwards Limestone acts as a filter as well as duct system carrying the water underground for miles and miles. However, the space in which the water is stored is confined. As more water enters, the water level rises, and pressure pushes water up to the surface. In areas like San Marcos and Comal Springs, the water is discharged abundantly and naturally at the surface. Porous: having a surface that contains pores or a body that contains cavities, easy to penetrate The growth in the population of the area and the continuing increase in the demand for water have prompted several studies to find alternative sources of water, promote conservation, and manage existing resources. One of the events that brought the region’s water issues to a fore in the 1990’s was a well drilled in southwest Bexar County. At the time, it was the largest well in the world. When it blew, it blew out rocks the size of basketballs 20 feet into the air.2 11.1 During the two years of 1967 and 1968, American soldiers were being killed in Vietnam at the rate of about 1,000 per month. The population of the U S was about 200,000,000 at that time. If each soldier that was killed had an extended family of six other people, on average, what percentage of US citizens were directly affected (within the extended family of someone killed) by deaths in Vietnam during those two years? 11.2 Ladybird Johnson began investing in radio and TV stations in south central Texas in Her investments grew to more than $105 million in assets by 2003 when they were sold to Emmis Comm. Inc. (http://www.statesman.com/news/content/shared/news/stories/ladybird/07/16/ 0716ladybiz.html) What initial amount would have to be deposited in an account that earned 5% simple interest over 60 years in order to have $105 million? About how many of the students at Texas State commute (do not live on campus)? 11.4 Estimate the number of acres Texas State has dedicated to providing parking spaces. 11.5 The lowest recorded rate of flow for the San Marcos Springs was 46 cubic feet per second. At that rate, how many gallons of water flowed out of the springs in one day? (1 cubic foot = US gallons) 11.6 The “Daily Flow Volume” chart shows the amount of water flowing from San Marcos Springs from October 1994 through August Estimate the average daily flow during this time. 11.7 According to edwardsaquifer.net, there are about 1,250 square miles of area in the “recharge zone” of the Edwards Aquifer. That means that the rain in the area of the recharge zone that does not evaporate will likely end up underground. If the area making up the recharge zone gets 30 inches of rain each year, how many acre-feet of water is collected by the aquifer if 80% of the rain water gets to the aquifer? (An “acre-foot” is a unit of volume commonly used in the US in reference to large-scale water resources. You see the amount of water in a reservoir, or in sewer flow capacities, commonly measured using this unit. It is defined by the volume of one acre of surface area to a depth of one foot.) Source: LBJ library and ranch (personal visit) Source: San Marcos Springs Aquifer (personal visit) 1 2 Numeracy Through Texas History Kimball 2011

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71 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.

72 Standards For School Mathematics (NCTM)
Number and Operations Algebra Geometry Measurement Data Analysis and Probability Adding It Up

73 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.

74 The fastest sprinter in the world is the cheetah
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)

75 Supporting Mathematics Across the Curriculum What should it mean for the math curriculum?
The mathematics that is taught should be embedded in the real world of the students. Mathematical literacy will lead to different curricula in different cultures. The content of the mathematics curricula will have to be modernized at least every ten years. U.S. mathematics curricula, both in high school and college, fail badly in meeting de Lange’s criteria. Although high school and introductory college mathematics do include some so-called real- world problems, these very often are not embedded in the world of any student. Some national needs are cited as reasons for stronger mathematics education, but the duties of citizenship in a democracy—perhaps the most fundamental need of the country—are rarely considered when teaching mathematics. The school curriculum may have been modernized once in the past 50 years, depending on the interpretation of “modernize,” and introductory college mathematics currently may be undergoing some reform, but there is no systematic way to modernize college offerings. Every five to 10 years seems beyond the pale. Beyond a lack of connection to real-world applications, there is an additional mismatch between the mathematics curriculum and available jobs. According to Carnevale and Desrochers, “too many people do not have enough basic mathematical literacy to make a decent living even while many more people take courses such as geometry, algebra, and calculus than will ever actually use the mathematical procedures taught in these courses in high school”

76 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.

77 Specific Recommendations
QL has a strong partner and advocate in the science community. (Science for All Americans (Project ) Consider engaging the social sciences in the quest for QL. Adopt detailed and specific goals with benchmarks for progress. Coordinate QL across disciplines by making QL part of faculty development. Promote changes (improvements) in pedagogy advanced by national organizations. Develop reliable and valid assessments of experiments in curriculum and instruction that target QL and publish the results.

78 Resources http://www.math.dartmouth.edu/~mqed/eBookshelf/


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