SUMMER 2009 Vol. 20, No. 4

WISCONSIN CENTER FOR EDUCATION RESEARCH • SCHOOL OF EDUCATION • UNIVERSITY OF WISCONSIN–MADISON • WWW.WCER.WISC.EDU

Challenges and Opportunities in Math

“Mathematics for all” is a goal that has not been related professional development for teachers: realized, despite the attention and efforts of , Mathematics in many mathematics educators. Context, MathScape, and MathThematics. The 2008 Trends in International Mathematics Lessons learned from the Show-Me Project and Science Study (TIMSS) showed that are documented in the book, A Decade of mathematics learning opportunities for students Middle School Mathematics Curriculum in the U.S. are often shallow, compared to Implementation (Information Age many other countries. The curriculum, particu- Publishing, 2008). larly with the middle grades, is repetitive and How College Proximity Mathematics In Context lacks depth. And too often assessments do not 4 Influences Enrollment Mathematics in Context (MiC) was developed align with district frameworks and classroom and later revised at the Wisconsin Center Familism Helps and curriculum materials. That means students are for Education Research under the leader- 5 Hinders College Success either tested on mathematical content they ship of Thomas Romberg in collaboration have not had the opportunity to learn, or they with a group of curriculum designers at the Summer Institute to are tested on only a small part of what they 6 Improve University Freudenthal Institute in the Netherlands. MiC have learned. Science Teaching embodies the theory of Realistic Mathemat- The development of richer, more challenging ics Education (RME) proposed by Hans Evaluating a Core mathematics classroom environments and Freudenthal. Instead of seeing mathematics 7 Reading Program learning opportunities requires simultaneous as subject matter that has to be transmitted, renewal of curriculum, instruction, RME stresses the idea of mathematics as and assessment. a human activity, arising from the reality of The Show-Me Center Project (1997-2007) students. Education should give students the promoted the dissemination and implementa- "guided" opportunity to "re-invent" mathemat- tion of four comprehensive NSF-funded middle ics by doing it.

school mathematics curriculum programs and (continued on next page...) WCER RESEARCH highlights

Conventional middle grades mathematics curricula have FROM THE generally portrayed learning sequences in terms of INTERIM DIRECTOR related abstract representations to develop procedures and algorithms. In contrast, MiC instructional sequences are A new generation of scholars is conceived as “learning lines” in which starting points elicit undertaking rigorous research informal, often concrete, representations. These concrete on pressing problems of policy representations help students make sense of important mathematical abstractions. and practice in education. WCER will continue to prepare The Show-Me Project Beth Graue them for their careers through Show-Me Project Director for MiC and WCER assistant WCER’s Interdisciplinary Training Program for scientist Margaret Meyer says the project supported change in teachers' practice by targeting curricular change. The Predoctoral Research in the Education Sciences. project's goals included: To date the program has attracted 32 high- (a) supporting the awareness, examination, and implementa- caliber students who have worked on a rich array tion of comprehensive standards-based middle school of education research projects, produced 32 mathematics curricula; publications (including several articles in leading (b) designing, developing, and supporting professional journals), made 91 conference presentations development opportunities for middle grade teachers (including the major disciplinary and education and administrators; conferences), and launched its first 5 graduates into (c) providing communication networks for middle school teachers and their district teams who implement new research careers. Challenges remain Another new challenge was the 2006 publication of the curricular and instructional techniques designed to advance Despite the success of these reform mathematics National Council of Teachers of Mathematics (NCTM) Three new faculty-led experimental studies of student understanding and achievement in mathematics; and curricula, and of the Show-Me Project, challenges Focal Points. The Focal Points identify the curricular education policy interventions have involved scores (d) providing information and professional development remain, Meyer says. These challenges face mathematics content focus of specific grades. If these recom- of schools and thousands of students, and have to mathematics educators and mathematicians in higher teachers, district leaders, teacher educators, and future mendations are followed, there will be problems with helped us provide training in every phase of large- education who prepare future generations of middle grades mathematics curriculum developers over the Show-Me Project curricula. That’s because they focus mathematics teachers. scale randomized trials. next decade. on well-articulated learning trajectories of content to be developed over several grades. The formalization Changes in teaching Challenge 1: Students in many parts of the country have The program will train another 30 fellows over 5 years of concepts is not always the first goal at a particular Since the publication of the 1989 NCTM Standards and not had the opportunity to learn mathematics using with disciplinary homes in sociology, economics, grade level in which the content is taught. the publication of the standards-based curricula, it has quality standards-based mathematics curricula. psychology, political science, and social welfare. been clear that teachers are being asked to teach different Challenge 2: The four NSF-funded curricula were Next steps mathematics (than they learned) in different ways (than The ITP includes developed in response to the 1989 NCTM Standards. Meyer says future curricula development will continue they were taught) and this demands significant professional At that time, few states and fewer districts had a to be influenced by the research-based efforts of the ◾◾course work in students’ disciplines, in development. mathematics curriculum framework. The landscape has authors of the Show Me Project family of materials. education, and in advanced statistics, changed drastically since: Most states and districts have For example, when using MiC, teachers encounter a tension The lessons learned from this project cut across the including courses in experimental design and their own standards or frameworks. Expectations for between (a) teaching for student recall of common algo- four curriculum programs and share commonalities measurement; students vary widely by state and district. Students meet- rithms and (b) teaching for student understanding through with standards-based curriculum reform at any level, ing proficiency standards in one state can be considered ◾◾a weekly interdisciplinary seminar; guided reinvention using mathematical models (including, for Meyer says. She believes that documenting these below proficient in another. What happens then? example, percent bars and ratio tables). The teacher sup- lessons learned will be one of the legacies of the ◾ certification in a minor in education sciences; ◾ ports students’ guided reinvention with these models through Challenge 3: Curriculum publishing is a business, and Show-Me Project. the use of questions, examples, and counterexamples that publishers must keep an eye on the bottom line. If a ◾◾a research practicum on randomized trials in clarify how the models could be used. curriculum does not sell, the publisher will not continue education; As a result, MiC emphasizes that teachers’ professional to support it. Curriculum developers and publishers need ◾◾an intensive internship in randomized field development experiences should address: to continue cooperating to ensure the educational and trials; and commercial viability of the curriculum materials. a. the function of problem contexts, ◾ ongoing experience in faculty-led research Challenge 4: Over the course of the 10 years of the ◾ b. the rationale for various mathematical models projects that address practical problems Show-Me Project, the four sets of curriculum materials and tools, in education. evolved in response to several outside forces. One c. the sequencing of activities to promote progressive effect of the standards movement has been to push the Margaret Meyer Beth Graue formalization of the mathematics, and first-year algebra course down into the middle school. Professor of Curriculum & Instruction At issue is agreement about what constitutes a first-year d. a multi-dimensional approach to assessing Interim Director, WCER algebra course. student understanding.

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How College Proximity Influences Enrollment Familism Helps and Hinders Hispanic College Success

As U.S. high school students consider attending college, Having colleges nearby may affect a student’s chances In 1980, only 8% of college graduates were Hispanic, and that They’re willing to leave home, if the best education requires it. At the same time, another impulse encourages them the ability to attend a college close to home is often a very of going to college in two ways. Having local colleges percentage rose a mere two points by 2000, a paltry increase important consideration. may influence local students’ propensity to strive for to stay at home and uphold family ties that help shape given the rapid demographic growth of Hispanic youth over the a college education (the predisposition mechanism). their identity. It’s especially important for students from minority and Second, living close to a college may increase the odds of last two decades. low-income families. In a study of high school seniors, López Turley found that going to college simply because it makes the transition to America’s preoccupation with illegal immigration and the Hispanics are the most likely to say it’s important to live One study estimates that about 54% of U.S. high school college easier logistically, financially, and emotionally (the growing Hispanic population has fueled anti-immigrant at home during college, even those with college-educated seniors had parents who said it was important for their convenience mechanism). and anti-Hispanic sentiment. Like black students, Hispanic parents. But students who say it is important to stay home children to live at home while attending college. The main difference between these mechanisms is that students often face prejudice in school. But that raises the are significantly less likely to apply to college, especially to UW–Madison sociology professor Ruth López Turley says the first is associated with an increased likelihood of going question: Why are Hispanic students’ college application selective institutions. researchers should stop treating the college-choice process to any college, while the second is associated with an rates so much lower than those of black students, even Her recent study used data from the Texas Higher as though it were independent of location. It’s important to increased likelihood of going to a nearby college. though both groups are affected by the racial climate? Education Opportunity Project. The study sample included situate this process within its geographic context. 13,803 seniors attending 96 Texas public high schools in Students from low-income families have significantly lower Only 22% of Hispanics between the ages of 18 and 24 spring 2002. Living near colleges may be associated with a greater odds of applying to and enrolling in college in general. enrolled in a postsecondary institution in 2000, compared to likelihood of going to college, says López Turley. Residents But they have significantly higher odds of applying to and 39% of whites and 31% of blacks in this age bracket. Compared to whites and blacks, Hispanic high school of counties with postsecondary institutions have higher enrolling in a nearby college, which corresponds with the Family income level, parental education, school quality, and seniors were significantly less likely to apply to: rates of college enrollment than those without convenience explanation. immigrant status all affect Hispanic students’ educational postsecondary institutions. ◾◾ a selective college (14% versus 31% of whites and López Turley notes a couple of limitations: Although success. But these cannot fully account for Hispanic 19% of blacks). López Turley investigated the effect of college proximity underachievement, says UW–Madison sociology professor the number of colleges within commuting distance is ◾◾ a four-year college (42% versus 55% of whites and on high school seniors’ college application and enrollment associated with higher odds of applying to college, it’s Ruth López Turley. Many studies have concluded that 56% of blacks) and decisions. Using a national sample, she measured proximity not necessarily associated with enrolling 2 years after familism is especially pronounced in Hispanic culture, and ◾ any college (54% versus 66% for whites and 70% by the number of colleges within commuting distance. The that it both helps and hinders Hispanic students. ◾ completing high school. The study also suggests that of blacks). study addressed these questions: although the effect of college proximity is statistically López Turley and co-author Matthew Desmond define significant, it is smaller than the effect of other factors, It’s important for educators to better understand Hispanic ◾◾ How are colleges distributed (by type) in relation to familism as a social pattern whereby one’s individual such as test scores, race/ethnicity, and parents’ education. students’ desire to live at home during college, and the where students live? interests, decisions, and actions are conditioned by a consequences of this decision on educational outcomes, network of relatives that takes priority over the individual. ◾◾ Are more colleges nearby associated with higher odds says López Turley. Living away from home cultivates of enrolling in college? Hispanics, and Mexican-Americans in particular, live in students’ independence and establishes bonds of mutual respect between parents and children. By comparison, ◾ By what mechanism does college proximity affect larger and denser kinship networks than whites. Hispanic ◾ students who stay home while attending school obtain students’ college choices? adults and adolescents value interdependence and family obligations more so than whites. lower levels of educational attainment. Living at home often Many high school seniors have a range of colleges within whittles away students’ aspirations where family-related Some college-bound Hispanic students find themselves responsibilities confront them. commuting distance, but distribution varies widely. Students Ruth López Turley in the East tend to have the most colleges nearby, while pulled in two directions: They want to cultivate themselves. students in the South tend to have the fewest. (continued on next page...)

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(...continued from previous page) Summer Institute to Improve University Science Teaching Compared to Hispanics, blacks are nearly Every week seems to bring a new breakthrough in science. We twice as likely to complete college; whites are live in a state of warp speed exploration, whether in deep-sea over three times as likely. By one estimate, trenches or stellar nurseries billions of light years distant. 49% of Asians, 30% of whites, and 16% of blacks enrolled in kindergarten today will College students will tell you, however, that introductory science courses often disappoint. Teaching practices have grow up to earn a bachelor’s degree. Only not changed along with advances in scientific research. 6% of Hispanics will. Hispanic students Somehow, large, anonymous classrooms are supposed to are falling through the cracks even as the excite undergraduates about research and scientific ways Hispanic population is rising at a pace that is of thinking. fundamentally altering the American landscape. But some high-enrollment undergraduate courses are The Hispanic population currently constitutes being transformed into more effective, learner-centered about 12% of the total U.S. population, an environments, thanks to the work of WCER researchers increase of about 57% between 1990 and 2000, Christine Pfund, Christine Pribbenow and colleagues from compared to a 13% growth for the total U.S. across the nation. An annual summer institute hosted at UW– Evaluating a Core Reading Program population during that time period. If current Madison http://academiessummerinstitute.org/ encourages biology instructors to experiment with their teaching and to levels of educational disadvantage continue adopt more effective techniques. If you’re a fourth-grader you could be the victim of an Borman’s final sample included 5 schools, from which as the Hispanic population expands, then an achievement gap equivalent to nearly 3 years of learning, 49 Grade 1–5 classrooms and 917 to 923 students increasing fraction of the U.S. population will Since 2004 the National Academies Summer Institute on depending on whether you are African-American, participated. (Sample and data attrition claimed some of the be insufficiently prepared for work and civic life. Undergraduate Education in Biology has welcomed five Hispanic, White, poor, or non-poor (U.S. Department of control students, the treatment students, and participating cohorts of educators representing 64 U.S. institutions in 36 Education, 2005). classrooms.) states. They include faculty and instructional staff from public and private institutions. The University of Wisconsin-Madison Despite many efforts to close this gap, early elementary The study findings should prove significant for curriculum partners with the National Academies and the Howard Hughes literacy instruction and learning still fails many of America’s leaders, literacy leaders, researchers, and policymakers. Familism should not be thought of monochromatically, says Medical Institute to implement the program. poor and minority students. Curriculum and literacy leaders: Borman’s study deter- López Turley. Familism may help bring about an array of In a recent issue of Science, Pfund and colleagues show Educators are trying. But they can’t find all they need in the mined that the average student from an OCR classroom positive outcomes as well as an equally impressive array that alumni of the Summer Institute report significant learning professional literature on core reading programs. UW– outperformed nearly 58% of the students in classrooms that of negative consequences. Likewise, familism can exert gains in scientific teaching. Most alumni reported increased Madison education professor Geoffrey Borman finds that were not assigned to OCR. Overall, students from OCR simultaneously mixed effects on similar outcomes: A stable confidence in their ability to implement these strategies and current published research offers few studies that examine classrooms scored from 12% to 19% of 1 standard devia- family life can encourage academic success even as it expressed their intentions to do so. Two years after attending the impact of these programs on children’s reading skills. tion higher on reading assessments. (The effect sizes for attenuates students’ horizon of postsecondary possibilities. the Institute, 98% of those responding to a survey said they OCR are essentially equivalent to the impact for class-size Finally, familism within one community may look nothing To help remedy this shortcoming, Borman and colleagues were still experimenting to improve their teaching. Specific reductions found through the Tennessee Student-Teacher like familism in another and, therefore, may exhibit very Maritza Dowling and Carrie Schneck evaluated and changes in teaching activities include using case studies, Achievement Ratio [STAR] study.) different effects. reported on one such program, Open Court Reading (OCR). clickers, and cooperative groups. Alumni reported substantial OCR is a -based K–6 curriculum grounded in Researchers and policymakers: Cluster randomized field increases in their use of learner-centered classroom activities, research-based practices. It has been widely used since trials (like this one) involving widely replicated school-based measuring student learning and teaching effectiveness, and the 1960s. interventions (like OCR) are both possible and desirable employing diversity-aware teaching strategies. Nearly 70% for producing unbiased estimates of the effects of educa- But despite its widespread use, OCR had not been evalu- of participants reported using these methods in at least half tional treatments. of their class sessions. ated rigorously. Borman and Dowling initiated a study to answer two questions: These outcomes provide evidence of the promising Changing one’s teaching is not easy. 1-year effects of OCR on students’ reading outcomes, Among their major challenges, alumni ◾◾Is it possible or desirable to use randomized field trials to measure widely used core reading programs? and, Borman says. They also Ruth López Turley reported time pressures, balancing suggest that these effects may responsibilities, and lack of recogni- ◾◾How effective is OCR in particular? be replicated across varying tion for their teaching efforts. How- contexts with rather consistent ever, some alumni commented that During the 2005–06 school year Borman and Dowling and positive results. The following agencies supported this research: The attending the Institute helped them to studied elementary school classrooms from Grades 1 Ford Foundation, Mellon Foundation, Hewlett Foundation, negotiate change. through 5. This was a randomized controlled trial: Some Spencer Foundation, National Science Foundation, The classrooms were assigned to use OCR, the others were not. The question was, compared with traditional classrooms, do National Institute of Child Health and Human Development, Christine Pfund Geoffrey Borman and Princeton’s Office of Population Research. the OCR curricular and professional development materials improve literacy outcomes for elementary students?

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WCER RESEARCH highlights

Interim Director Beth Graue Editor Paul Baker Editorial Consultants Rebecca Holmes & Cathy Loeb Production Media Education Resources & Information Technology

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