Bernard L. Madison

Evolution of Numeracy and the National Numeracy Network

The National Numeracy Network grew from heightened awareness of the complex and sophisticated nature of quantitative literacy and the resulting need for interdisciplinary attention to education for quantitative literacy in schools and colleges. This complexity and sophistication applies especially to the US where it is fueled by an agile economy and the needs of a democratic society. This paper describes the environment surrounding the National Numeracy Network’s establishment, some of its activities, and some complementary and synergistic actions by other professional societies. The paper concludes with a sample of quantitative literacy programs in colleges and universities

Quantitative Reasoning in the Contemporary World, 1: The Course and Its Challenges:

The authors describe successes and challenges in developing a QL-friendly course at the University of Arkansas. This work is part of a three-year NSF project Quantitative Reasoning in the Contemporary World (QRCW) that supported the expansion of the course. The course, MATH 2183, began experimentally in Fall 2004 as a section of finite mathematics known informally as “News Math” for 26 students from arts and humanities disciplines. Over the past six years, the course has evolved and now MATH 2183 is approved to satisfy the College of Arts and Sciences mathematics requirement for the Bachelor of Arts degree. In 2009-2010, it was offered in 16 sections to about 500 students. The course,, which is designed so that students work collaboratively in groups of three to four to discuss and answer questions related to quantitative information found in newspaper and other media articles, has encountered a variety of challenges that exemplify broader questions confronting interactive teaching of mathematics in context. Many students possess deeply held views regarding mathematics and struggle with the departure from traditional, lecture-driven mathematics classes. Available curricular materials that engage undergraduate students to reason in real-world settings are limited. Solving new problems on quizzes and examinations is challenging and uncomfortable for students, but necessary as QL requires “authentic” tasks. The variety of contexts in which QR is needed tests the instructor’s flexibility and knowledge. Many of the challenges have been ameliorated by putting together Case Studies for Quantitative Reasoning: A Casebook of Media Articles which bases sets of questions upon quantitative content derived from media articles. Learning gains measured by preand post-course tests are modest (two percentage points for the mean), but still larger than in other control groups. Faculty advisors’ attitudes about the course are overall positive. Persistence beyond the course, as measured by a survey of 300 former students, seems positive; for example, 29 of the 42 respondents state that their confidence with QR had increased since the course. Similar courses are being taught at Central Washington University and Hollins University by Stuart Boersma and Caren Diefenderfer, respectively, who are also co-PIs on the NSF QRCW project.

Quantitative Reasoning in the Contemporary World, 2: Focus Questions for the Numeracy Community

Numerous questions about student learning of quantitative reasoning arose as we developed, taught and assessed the Quantitative Reasoning in the Contemporary World course described in the companion paper in this issue of Numeracy. In this paper, we present some of those questions and describe the context in which they arose. They fall into eight general problem areas: learning that is context-bound and does not easily transfer (i.e., situated learning); the need for a productive disposition regarding mathematics; the connection between QL and mathematical proficiency; the persistence of students, despite our efforts, for using the wrong base for percents; the inconsistent and sometimes incorrect language in media articles on percent and percent change; the need for students to possess quantitative benchmarks in order to comprehend the size of large quantities and to know when their answers are unreasonable; students’ avoidance of using the algebra they learned in the prerequisite course; and conflation of “bigger” and “better”. We offer these questions as products of our experience with this course in order to encourage future research on issues that affect teaching similar courses that develop QR skills in undergraduate students.

Quantitative Reasoning in the Contemporary World, 3: Assessing Student Learning

In this third paper in a series describing the Quantitative Reasoning in the Contemporary World course, the authors provide an adaptation of the Association of American Colleges and Universities quantitative literacy VALUE rubric. Describing achievement levels in six core competencies (interpretation, representation, calculation, analysis/synthesis, and communication), the resulting Quantitative Literacy Assessment Rubric (QLAR) is applicable to grading student work and has exhibited a high degree of reliability in two separate scoring tests (97% and 88% respectively). The distribution of the six core competencies across the 24 case studies in the authors’ quantitative reasoning casebook shows that interpretation, calculation, and analysis/ synthesis were present in most all of the case studies. In addition to acting as a reliable scoring tool, the QLAR can improve teaching, learning, and curricular materials.

Reflections on the Tenth Anniversary of Mathematics and Democracy

Two independent reflections by early proponents of quantitative literacy connect todays numeracy initiative with its origin in concern about school tests, its impact on students today, and the challenges of democracy. Even as interest in QL grows in many places, evidence of need also grows. Moreover, well-meaning programs with other goals—especially at the K-12 level—often channel education in directions that fail to advance numeracy. Examples show that both students and teachers are enthusiastic when offered QL opportunities, but that individual beliefs and public decisions often belie the goals of QL.

Confronting Challenges, Overcoming Obstacles: A Conversation about Quantitative Literacy

An edited transcript of the opening session of a workshop on quantitative literacy held Oct. 10-12, 2008 at Carleton College, Northfield, Minnesota. The workshop, which brought together interdisciplinary teams from two dozen colleges and universities, was sponsored by the Quantitative Inquiry, Reasoning, and Knowledge (QuIRK) Initiative at Carleton and the Washington-based Project Kaleidoscope. Two mathematicians in the forefront of quantitative literacy initiatives over the period 1997-2008, Lynn Arthur Steen and Bernard L. Madison, converse about attitudes, obstacles, changes and accomplishments. The conversation, structured as an interview, begins with the relationship between mathematics and quantitative literacy and moves through issues central to effective education in quantitative reasoning to the relationship of such reasoning to the US financial crises of 2008.

If Only Math Majors Could Write...

This text of the opening plenary address to the 2011 Summit of the Appalachian College Association and the meeting of the National Numeracy Network makes an argument that quantitative reasoning and writing should be taught together. The argument is set up by noting that humanists have historically banished quantitative issues from their study of the liberal arts and that science, engineering, and mathematics education suffers from lack of approaches to learning that promote complex, deeper understanding, most notably integrative and reflective learning. Therefore, everyone would profit from combining writing and quantitative reasoning. Five more specific reasons are discussed, drawing evidence from numerous sources among the twenty-nine references. The reasons given for combining quantitative constructs and language are: (1) To strengthen academic arguments; (2) To strengthen quantitative literacy/reasoning; (3) To interpret and improve public discourse; (4) To encourage quantitative reasoning across the curriculum; and (5) To prepare for the workplace. Underlying the basic argument and the reasons discussed are clear indications that, in present circumstances, teaching quantitative reasoning rests to a large extent on colleges and universities.

A Study of Placement and Grade Prediction in First College Mathematics Courses

Abstract A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test results were reasonably consistent with the ACT Math benchmark score of 22 for college readiness. Analysis of ACT Math scores, basic algebra scores, calculus readiness scores, and course grades indicated that basic algebra scores are reasonable predictors of grades in College Algebra, whether traditional or modeling-based.

How Does One Design or Evaluate a Course in Quantitative Reasoning

In the absence of generally accepted content standards and with little evidence on the learning for long-term retrieval and transfer, how does one design or evaluate a course in quantitative reasoning (QR)? This is a report on one way to do so. The subject QR course, which has college algebra as a prerequisite and has been taught for 8 years, is being modified slightly to be offered as an alternative to college algebra. One modification is adding a significant formal writing component. As the modification occurs, the current course and the modified one are judged according to six sets of criteria: the six core competencies of the Association of American Colleges and Universities rubric on quantitative literacy; the five mathematical competencies from the National Research Council (NRC) study report, Adding It Up; the eight practice standards from the Common Core State Standards for Mathematics; the five elements of effective thinking as articulated by Edward Burger and Michael Starbird, the summary research findings on human cognition from the NRC study report, How People Learn; and the ten principles gleaned from applying the science of learning to university teaching. The QR course, as described by ten design principles, is determined to be generally well aligned with most of the overlapping criteria of the six sets, providing cogent evidence of high educational value.

Quantitative Literacy and the Common Core State Standards in Mathematics

How supportive of quantitative literacy (QL) are the Common Core State Standards in Mathematics (CCSSM)? The answer is tentative and conditional. There are some QL-supportive features including a strong probability and statistics strand in grade 6 through high school; a measurements and data strand in K-5; ratio and proportional reasoning standards in grades 6 and 7; and a comprehensive and coherent approach to algebraic reasoning and logical argument. However, the standards are weak in supporting reasoning and interpretation, and there are indications that the applications in CCSSM – mostly unspecified – will not include many QL contextual situations. Early indicators of assessment items follow a similar path. Except for statistics, most of the high school standards are aimed at development of algebra and precalculus topics, and there will likely be little room for more sophisticated applications of the QL-friendly mathematics of grades 6-8. The experience with CCSSM is limited at this point, leaving several crucial results uncertain, including assessments, emphases on statistics, and kinds of modeling and other applications.