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Teaching and Learning The nature and context of instruction are what matter most in engaging students in learning. Although policies at the school level and beyond affect what goes on in classrooms, classroom instruction how and what teachers teach is the proximal and most powerful factor in student engagement and learning. In this chapter we discuss what is known about engaging teaching, with special attention to the needs of students in economically disadvantaged urban settings. Teaching at the high school level is challenging in part because students are expected to master discipline-specific knowledge that does not have obvious relevance to real-life settings. What does the reading of a John Donne poem or solving an algebraic equation have to do with adolescents' lives or even their anticipated roles as workers and parents in adulthood? The challenges are particularly daunting in low-income urban communi- ties, where many students enter high school with low skill levels and limited English proficiency, and lack stable resources in the form of family income, housing, or health care. Any of these risk factors can increase the likelihood that students will be unmotivated to engage productively in the intellectual demands of the high school curriculum. Research on teaching is vast, but concentrated on the elementary level. Consequently, although a fair amount is known about effective pedagogy for adolescents, the research base is meager compared to that which is focused on younger children. Concentrating on studies involving students in urban high schools limits the empirical base even further. Despite the relative scarcity of studies on subject-matter teaching at the 60 1 1 1 1 1
TEACHING AND LEARNING 6 high school level, there is evidence that can be used to guide instructional planning (Alvermann and Moore, 19911. We discuss in this chapter what is known about effective teaching in literacy and mathematics, focusing espe- cially on research involving urban low-income students and students of color. We selected these two subject areas because they are considered core and they are instrumental to learning other subject matter. In the final section of the chapter we discuss research on school organizational factors and conditions of teaching that best enable the kind of teaching that re- search suggests is most effective. LITERACY The teaching of reading, writing, and speaking at the high school level ideally takes place in every subject matter. Students are expected to read literature and write essays and creative pieces in English-language arts, and to read textbooks and occasionally primary source documents in history, social studies, and science. Although there tends to be little reading in mathematics, mathematical literacy is required to understand and evaluate public arguments (often in newspapers and magazines and on television programming) and forms of advertising where numerical data are used as evidence (Paulos, 1990, 19951. Many students come to high-poverty schools with poor proficiency in reading and writing, and few urban high schools are prepared to address the double challenge of meeting students' basic literacy needs while teaching them to tackle the complex reading and writ- ing tasks of the disciplines (Finders, 1998-1999; Jimerson, Egeland, and Teo, 1999; Roderick and Camburn, 19991. Gains have been made in mathematics achievement over the past de- cade, but not in reading. On the National Assessment of Educational Progress (NAEP), 17-year-olds today read no better than their counterparts a decade ago. Scholastic Aptitude Test (SAT) scores also have remained flat. Furthermore, huge gaps exist among different ethnic groups. African- American and Latino 17-year-olds taking the NAEP read about as well as and have vocabularies roughly equivalent to those of white 13-year-olds (NCES, l999b; Phillips, Crouse, and Ralph, 19981. Reading problems are particularly pronounced in the high schools of large urban districts in low- income communities (Campbell et al., 2000; Dreeben and Gamoran, 1986; Education Trust, 1999; Guiton and Oakes, 19951. In the 35 largest central cities in the country, more than half of entering 9th-grade students read at the 6th-grade level or below (Grosso de Leon, 20021. The poor progress in developing literacy skills may be explained in part by adolescents' low participation in literacy activities. Based on NAEP survey data, 25 percent of 17-year-olds currently report reading fewer than
62 ENGAGING SCHOOLS five pages per day for both schoolwork and homework (see Education Trust, 20011. What Is Involved in Reading?i Reading is a form of problem solving (Olshavsky, 1976-19771.2 When good readers first encounter a text, they search for clues about topic, theme, or perspective. They search their long-term memory for models or explana- tions that can provide a filter for understanding the rest of the text. For example, if the reader sees the word "bat" in the title or first sentence, she searches her prior knowledge and reads on to find out whether this story will be about baseball or animals that fly. An abundance of research in reading documents the powerful role that prior knowledge plays in reading comprehension. For example, if the title of a story has the word "sine," and the reader has no clue what a "sine" is, he will have difficulty making sense of the text. Readers need knowledge of topics, vocabulary, and the structure of words, sentences, paragraphs, and texts (e.g., stories versus expository texts). Stories may be structured as mysteries, science fiction, magical realism, or satire. The structure of ex- pository texts may be extended definition, comparison-contrast, or prob- lem-solution. Consideration of these kinds of prior knowledge that students bring from their lives inside and outside of school is crucial to teaching reading comprehension. Readers must actively construct their understanding of texts from word to word within sentences, from sentence to sentence, from paragraph to paragraph, from section to section, and even across texts. Whereas a liter- ary reading may emphasize searching for multiple, nuanced meanings of words, phrases, and whole texts, reading a scientific report does not involve such degrees of freedom. Knowledge in scientific writing may be communi- cated through words, mathematical formulas, graphs, or illustrations of patterns and cycles. Concepts are often communicated through technical vocabulary that has very specialized meaning in the particular scientific domain. For example, the word force may mean one thing in physics from the perspective of the Theory of Relativity and something qualitatively different from the perspective of Quantum Theory. Reading primary source documents in history requires the reader to question the potential biases of 1In order to address one area with some depth, we have elected to focus on reading, rather than on the challenges of teaching written composition or speaking. 2For thorough reviews of what research says about what is involved in the process of comprehending written texts, see the following: Kamil, Mosenthal, Pearson, and Barr (2000). For more succinct reviews of the research on reading comprehension, see the following: Fielding and Pearson (1994); Pearson and Dole (1987); Pressley (2000).
TEACHING AND LEARNING 63 the author and to search across multiple texts to find other perspectives. The structure of sentences in both historical documents (such as the Decla- ration of Independence, the Narrative of Frederick Douglass, the essays of Francis Bacon) and older literary works can be difficult to parse because they are long and complex. Very different evidence is required to make cogent arguments in support of Darwin's theory of evolution in contrast to the claim that the character of Sethe in Toni Morrison's novel Beloved was justified in killing her baby to keep the baby from being taken back into the horrors of the African Holocaust of Enslavement. These are just a few examples to illustrate the complexity of the task of reading in the disci- plines. The extraordinary access to information in this new information age also has important implications for our definition of literacy and the skills that need to be taught. The World Wide Web makes information available, including technical information, that nonspecialists previously could not easily access. But the information available on the Web is often not accurate or objective. More than ever, students need to be taught to critically evalu- ate information, consider its source and possible biases, and compare and contrast claims from various sources. A literate citizen must now have a higher level of critical and analytic skills than was true even a decade ago. These forms of critical evaluation, reasoning, and making sense of different kinds of texts in different subject matters should be the object of literacy study at the high school level. But most secondary teachers, regard- less of subject matter, have little formal training in the teaching of reading, nor specifically in the problems of reading in the subject matters they teach (Anders, Hoffman, and Duffy, 20001. Literacy skills are not taught in part because many teachers believe that they are teachers of subject matter not teachers of reading (Anders et al., 2000; O'Brien, Stewart, and Moje, 1995; Romaine, McKenna, and Robinson, 1996), or they assume that students with poor reading skills cannot tackle difficult texts. Rather than provide instruction on how to develop the skills students need, teachers often give them watered-down textbooks (Alvermann and Moore, 19911. Literacy needs to be taught in urban high schools, both to ensure that students have access to subject matter instruction and to develop their literacy skills in various subject matters. By implementing existing knowI- edge of motivation and effective pedagogy, we can provide instruction that engages students and helps them achieve high levels of literacy (Ol~father and DahI, 1995; father and McLaughlin, 1993; father and Thomas, 1998; Verhoeven and Snow, 20011. We summarize evidence on effective strategies for teaching reading, then illustrate these teaching principles by describing some exemplary programs.
64 Effective Pedagogy Literacy Teaching and Student Engagement ENGAGING SCHOOLS Few empirical studies explicitly link particular approaches to literacy instruction with stuclent engagement and even fewer studies inclucle large samples of ethnically diverse, low-income high school students (Verhoeven and Snow, 20011. Consistent with the general principles of motivation cliscusseci in Chapter 2, correlational studies reviewed by Guthrie and Wigfielci (2000) inclicate that students who believe they have some control over achievement outcomes and have a sense of competency are relatively more motivated to react. Furthermore, studies have shown that students who react outside of school become better reaclers (Anclerson, Wilson, and Fielcling, 1988; Fielcling, 1994; Guthrie, Schafer, Wang, and Afflerbach, 19951. Most of the latter studies, however, have been with elementary-ageci children. in one of the few large-scale studies of aclolescents, Cappella and Weinstein (2001) examined reacting resilience, using a cohort of 1,362 students in the National Eclucational Longituclinal Stucly (NELS) of 1988. Resilience was operationally clefineci as turning around low reacting achieve- ment in the 8th gracle by the 12th gracle. They clistinguisheci between distal risk factors (e.g., low socioeconomic status, single-parent househoici) and proximal risk factors (e.g., school environment, curriculum). By the 12th gracle, only 15 percent of the students who haci been at risk for continued low achievement in reacting in the 8th gracle haci acivanceci to intermediate or acivanceci reacting proficiency, so the resilient group was small. As has been founci in the achievement motivation studies cliscusseci in Chapter 2, students' beliefs preclicteci their resilience. Students who believed they haci the power to affect outcomes were more likely to show significant improve- ment in their reacting skills. In a similar vein, eighth-gracle eclucational expectations preclicteci resilience 4 years later, in conjunction with taking rigorous acac emlc courses. In the next section, we will describe the features of literacy instruction that appear to promote learning. Although the studies reviewed clo not assess engagement clirectly, it seems safe to assume that improved achieve- ment involveci increased engagement. The features cliscusseci inclucle forms of task structure, task complexity, grouping practices, evaluation tech- niques, motivational strategies, and quality of stuclent-teacher and stuclent- stuclent relationships. Features of Effective Pedagogies for Literacy The instructional approaches supported by research on literacy learn- ing are dramatically different from what is usually seen in low-performing
TEACHING AND LEARNING 65 urban high schools. The high school English-language arts curriculum usu- ally involves disconnected lists of books and readings of the same authors (Alvermann and Moore, 1991; Applebee, 1993,1996; Applebee and Purves, 1992), and teaching remains largely "frontal" lecturing (Applebee, Burroughs, and Stevens, 2000; Hillocks, 19991. Reading in the content areas tends to be limited to textbooks and is not characterized by strategy instruction (Alvermann and Moore, 1991; Bean, 2000~. Although more innovative instructional practices and uses of technology are being imple- mented in many schools, they are less common in urban high schools serving low-income students and students of color (Irvine, 1990; McDermott, 1987; Pillar, 1992~. Based on the accumulated research findings regarding the teaching of reading comprehension (Education Trust, 1999; Moore, Bean, Birdyshaw, and Rycik, 1999; National Reading Panel, 2000; Pressley, 2000; Roehier and Duffy, 1991; Snow, 2002), we abstract the following features of suc- cessful pedagogy in literacy: Personalized relationships Authentic tasks Capitalizing on cultural knowledge Use of multiple resources Rigorous and challenging instruction Explicit instruction Frequent feedback from assessments · Integrated curricula We elaborate on each of these features. As discussed in previous chapters, the term personalized relationships refers to the nature of relationships between and among adults and stu- dents. The nature of interpersonal relationships may be socialized through classroom structures such as small-group and whole-class instruction through the norms for who can talk and about what. In addition to facili- tating social connections, researchers have found that providing students with opportunities to interact with each other, such as by debating impor- tant ideas and working in small groups, increased the amount of reading and thinking about texts in which students engaged (Alvermann and Hynd, 1989; Guthrie et al., 19951. The task of creating personalized relationships between adults and adolescents can be more complex in low-income urban schools, where many adolescents carry out adult-like roles (as parents, caregivers for siblings, financial support for families) while expected to fulfill more child-like roles at school, but may be more important for these students than for more affluent students (Burton, Allison, and Obeidallah, 1995~.
66 ENGAGING SCHOOLS Authentic tasks involve reading and writing activities that have some meaning in the world outside of school. Students who have been disengaged from academic work often do not see why the reading and writing they are asked to do in school matters for their personal development, for their future adult roles, or for the communities in which they live. Authentic tasks that require the application of complex reasoning in real-worId set- tings are more motivating and produce higher academic achievement (Lee, Smith, and Croninger, 19951. Ideally, authentic tasks also must be funda- mentally linked to problems and modes of reasoning within the academic subject matter. Studies also suggest the value of capitalizing on students' cultural knowledge. All knowledge is cultural. The question is whose cultural knowI- edge is privileged or made accessible in instruction (Moll and Greenberg, 19901. The lack of congruence between students' life experiences and in- struction in most schools has been well documented, especially for low- income students, students of color, and English-language learners (Banks and Banks, 1993; Delpit, 1988; Gay, 1988; Hilliard, 1991-1992; Nieto, 1992; Philips, 19831. We also know that prior knowledge is crucial to all acts of learning and especially to reading. Students sometimes have diffi- culty understanding texts that are not related to their personal experiences and cultures because they lack the appropriate prior knowledge of the topic, or they do not know how to tap into relevant knowledge they do have. Lee (199Sa, l995b, 2001) addresses this challenge in her work with low-income African-American high school students with histories of low achievement in reading. She designed a framework for culturally responsive curriculum and instruction related to literature, although the framework is applicable to other reading and problem solving in other subject matters. Lee's Cultural Modeling Framework for teaching literature identifies cat- egories of problems in the high school literature curriculum that are consid- ered generative. These include recognizing symbolism, irony, satire, using unreliable narrators, and using specific strategies for rejecting a literal inter- pretation and reconstructing a figurative interpretation (Rabinowitz, 1987; Smith and Hillocks, 19881. The approach involves using students' cultural knowledge to learn technical literary concepts. For example, students learn figurative language by analyzing familiar literary forms, such as oral genres of African-American Vernacular English, rap lyrics, and film clips. Lee argues that speakers of African-American Vernacular English already have a tacit understanding of these language forms, but do not activate that knowledge in school-based contexts. Using culturally familiar material and a specially designed curriculum, Lee's intervention was successful in getting students with low standardized reading scores to tackle complex works of literature. The conventions for instructional talk in Cultural Modeling class-
TEACHING AND LEARNING 67 rooms included the productive use of African-American Vernacular English discourse norms. Similar approaches to discipline-specific and culturally responsive pedagogies in literacy have been reported elsewhere (Ball, 1992, l995b; Foster, 1987; Mahiri, 1998~. The value of allowing students to use multiple resources or sources of help to gain mastery was discussed recently by Gutierrez, Baquedano-Lopez, and Tejada (1999) and is supported by an abundance of research on learn- ing (see National Research Council, 19991. Such resources may include support from peers, from competencies in languages other than English, and from tools such as computers. Examples of drawing on multiple- language competencies include English-language learners using their knowI- edge of their first language to help them read and write in English, or using skills in African-American Vernacular English to interpret literary problems (Lee, 1993, 1997~. Other resources may include access to multiple modali- ties (reading, writing, speaking, drawing, performing) for problem solving or to represent knowledge (Gardner, 1993~. The value of being able to use a native language is suggested by a study by Timenez, Garcia, and Pearson (1996~. They examined the reading strat- egies of a small sample of sixth- and seventh-grade bilingual students who were successful English readers. These successful bilingual readers demon- strated substantial knowledge about similarities and differences in the struc- ture of English and Spanish. They actively used this knowledge, for ex- ample, in looking for Spanish cognates in English words to help infer word meanings. They also translated across languages as an aid in constructing meaning. Perhaps most importantly, these successful bilingual readers held a different conception of the purposes of reading than their less successful counterparts. Timenez (2000) reports that successful readers saw reading as a process of making sense of text, and they believed they could draw on multiple-language competencies to do this. Less successful bilingual stu- dents saw reading as saying the words correctly in English. Moll, Estrada, Diaz, and Lopes (1980) found that students demon- strated greater levels of participation in instructional talk as well as more complex thinking when the organization of classrooms encouraged stu- dents to draw on their competencies in both English and Spanish. Lucas, Henze, and Donato (1990) identified eight characteristics of high schools that are successful with language-minority students, all focusing on ways that the school systematically structures opportunities to help students use both languages as tools for their learning. A key idea is that what a student can do with support is always greater than what he or she can do alone (Cole, 1996; Rogoff, 1990; Vygotsky, 19811. The goal is to provide students with as many sources of support as possible. In some cases, the task is simply to encourage students to identify and use the resources they have. Students who work through problems of
68 ENGAGING SCHOOLS academic reading and writing while drawing on multiple sources of support should also develop confidence in their ability to learn (Alvermann, Hinchman, Moore, Phelps, and Waff, 1998~. The rigor and challenges of the literacy c?~rric?~?~m (across subject mat- ters, not just the English-language arts) refers to whether students are asked to learn new constructs from reading texts and writing about what they read (rather than simply to remember facts), whether they are asked to apply what they learn from reading and writing to novel tasks, and whether they are expected to make connections across bodies of readings. Box 3-1, taken from Applebee et al. (2000), provides an example of a rigorous assignment in English-language arts. The assignment illustrates a rigorous curriculum because: · it focuses attention on a portion of text that is central to understand- ing the internal state of a character and by extension to examining the themes of the work as a whole. · there are no simple right or wrong answers to the questions, but there are constraints on a warrantable response based on the text itself and the life experiences of the students. · it asks students to make connections between their own life experi- ences and those of a key character in ways that help to explicate the themes of the work as a whole. · it asks students to read, think critically, and communicate their . . . . reasoning In written form. Explicit attention to strategies for problem solving is another feature of
TEACHING AND LEARNING 69 effective literacy pedagogies (National Reading Panel, 2000; Pearson and Dole, 1987; Pressley, 2000; Snow, 20021. Although there is an abundance of research on the effectiveness of explicit teaching of reading comprehen- sion strategies in elementary school, much less attention is paid to this issue at the high school level. Strategies for teaching both reading comprehension and composing need to be different at the high school level from what is effective at the elementary level. In addition to generic reading, high school students need to know discipline-specific strategies for asking questions, making and test- ing predictions, summarizing, drawing inferences, using prior knowledge, and self-monitoring (Beck, McKeown, and Gromoll, 1989; Dole, Duffy, Roehier, and Pearson, 1991; Lemke, 1998; Rabinowitz, 1987; Wineburg, 1991; Wineburg and Wilson, 19911. Examples of discipline-specific reading skills include understanding symbolism in literature, reliability in primary source documents in history, and argumentation in the sciences. In addition to generic reading, most students need explicit instruction to achieve such competencies, as well as to fee! competent, which is a critical factor in engagement. Providing explicit supports for students to engage in complex reasoning that involves reading, writing and speaking, comprehending and critiquing difficult texts, and producing sophisticated texts are more effective than scripted lessons or decontextualized drills. Scripts and drills are useful for memorizing, but not for the complex reasoning required of reading in the content areas (National Research Council, 19991. Strategies for teaching discipline-specific literacy skills, however, have not been well studied. Finally, students need frequent feedback from assessments to be able to observe their progress and to self-correct. Feedback on progress toward mastery can contribute to students' sense of competence and control, and teachers need the feedback from assessments to plan instruction. Assess- ments at the most local level schools and classrooms generally give the most useful information because they are tailored to the curriculum and the skills of the students at hand. Classroom assessments have the power to be diagnostic and to provide students with immediate feedback on what they can do and what they need to learn. Assessments at the departmental or course level in high school provide opportunities for teachers to learn from their practice and to target larger issues of curriculum and instruction. The instructional approaches that teachers use can be facilitated or constrained by the curriculum, which is often defined at the school or even the district level. Applebee and colleagues (2000) describe curricula in which the content (for example, texts selected for reading) is disconnected and unrelated, and the relationships across texts are not well defined (for ex- ample, survey literature or history courses organized solely by chronology).
70 ENGAGING SCHOOLS The kinds of instructional strategies described in this chapter are most likely to be found in schools that implement what Applebee and colleagues call "integrated c?~rric?~," in which students continuously revisit the core questions of the discipline across lessons and units of instruction within a year as well as across years. (See Box 3-2 for an example.) We turn now to four studies of literacy instruction at the middle and high school levels to illustrate the implementation of these features of effec- tive literacy pedagogies. The studies were conducted in urban communities where students had very low skills when they entered high school. Three of the four examples examine whole-school approaches to literacy instruction across multiple sites; all four include schools in urban districts with ethni- cally diverse and low-income student populations. Each reflects some na- tional effort, either through an intervention that is national in scope or through analysis by a national or regional research center. Furthermore, all four include a large sample size and provide empirical data regarding stu- dent outcomes in reading (at least) as well as process data regarding how each feature was enacted. The findings of these studies are also corrobo- rated by many smaller studies of individual or small clusters of classrooms or teachers. Although an evaluation of these four programs is limited by possible selection biases (of students, staff, or both), the major finding across these studies is that the implementation of literacy pedagogies can- not be limited to specific instructional activities. Instead, they require a coherent adherence to a core set of principles.
TEACHING AND LEARNING Effective Literacy Programs Literacy Instruction in High-Performing Schools in Low-Income Communities 71 Under the direction of Langer (2001), the Center for English Learning and Achievement (CELA) conducted a groundbreaking study of middle and high schools across the nation that "beat the odds" in terms of indicators of achievement in reading. A total of 24 schools were selected from Florida, New York, Texas, and California based on district-level high-stakes assess- ments. Fifty-eight percent of the schools had 45 to 84 percent of students who received free or reduced-price lunches. Over a 2-year period, CELA researchers studied 44 teachers working in 25 schools involving 2,640 students, with 528 students as student informants. They observed class- rooms, shadowed and interviewed teachers across their various profes- sional activities in the school, interviewed case study students, and analyzed classroom and school-level documents. Based on classroom and school-level data, teachers were placed into one of three categories: (1) exemplary teachers in high-achieving schools; (2) exemplary teachers in schools that were typical for their districts; and (3) typical teachers in typically performing schools. Langer and her col- leagues found common features in the instructional practices of exemplary teachers in both exemplary and typical schools that are similar to those we have described. Successful teachers gave explicit instructions in reading and writing and they created opportunities for students to learn and practice skills in the context of authentic reading and writing tasks. In contrast, teachers in at least half of the typically performing schools taught skills in isolated lessons that were not connected to larger units of instruction. High-achieving schools integrated test preparation into the routines of classroom instruction across the school year, rather than providing test preparation as an isolated activity apart from the curriculum. High-achiev- ing teachers and schools tended to analyze the demands of high-stakes assessments and to structure units of instruction so that students had mul- tiple opportunities over time to develop conceptual understanding and skills as well as test-taking competencies. They used their analyses of test perfor- mance and of student work to make adjustments in the curriculum. Exemplary teachers created connections within and across lessons. They also created connections between school learning and students' experiences outside of school. By contrast, teachers with lower rates of achievement had disconnected and uncoordinated lessons; they focused on an initial level of mastery of a given skill and moved on to the next skill, without giving
72 ENGAGING SCHOOLS students an opportunity to integrate and apply skills and knowledge they had developed. All of the exemplary teachers explicitly taught the skills and strategies students needed to comprehend and compose complex texts across genres. They developed rubrics that made explicit the criteria for evaluation of both the processes that students employed and the quality of the products that students produced. Explicit instruction in strategies, skills, and con- cepts helped students develop both procedural knowledge (how to do it) and meta-cognitive knowledge (how to monitor one's understanding and self-repair when comprehension breaks down). By contrast, 83 percent of typical teachers in lower achieving schools asked students to analyze text or create a composition without any instruction in how to accomplish these difficult tasks. Successful teachers also helped students develop deep conceptual un- derstanding. To promote this level of understanding, students were asked to apply concepts and strategies across multiple texts. Whole-class instruc- tion was often used, but students were also encouraged to work together in groups to explore and evaluate problems from multiple perspectives. These peer interactions often involved rich discussions in which students initiated and elaborated on one another's ideas. Nystrand (Nystrand, 1997; Nystrand and Gamoran, 1997) found similarly that successful teachers engaged stu- dents in authentic discussions, with students asking questions that required conceptual analysis. Although some of the instructional practices we have described were found in lower achieving schools, their presence was intermittent. This study shows that individual exemplary teachers can make a difference, even in schools that do not support schoolwide productive practices and profes- sional development. For students who enter high school already signifi- cantly behind, however, sporadically excellent teachers are not sufficient to overcome their risks for continued underachievement. Coalition Campus Schools Project The second large-scale study involves the Coalition Campus Schools Project (CCSP), the collaboration between the New York City Board of Education and the Center for Collaborative Education. This study (Dar- ling-Hammond, Ancess, and Ort, 2002) involved 11 small schools that replaced 2 large high schools in New York City. Curriculum in these small schools was structured on the model of New York alternative schools serving low-income students, which have achieved success far surpassing district-level averages (see Chapter 5, this volume). The first cohort of six small schools began during the 1993-1994 school year. There is good objective evidence of their success in engaging students
TEACHING AND LEARNING 73 in learning. Although they enrolled larger percentages of low-income stu- dents and English-language learners than city averages, these high schools had higher graduation rates, higher attendance rates, and fewer rates of discipline problems than city school averages. In the area of reading achieve- ment, based on both SAT and New York Regents exams, results were mixed for the first several years. However, by 1996-1997, llth-grade gen- eral education students in three of the schools substantially outperformed similar schools on the New York State Regents exams in reading and writing. Consistent with other findings, these data collected by Darling- Hammond and colleagues support the proposition that changing school instructional cultures is difficult (all of the schools did not show strong positive effects) and takes time (it took several years for positive effects to show). The instructional practices used in the Coalition schools correspond closely to what other lines of research, described earlier, have shown to be effective. Personalized relationships were achieved by reducing teaching loads for teachers and creating longer instructional blocks of time. Intellec- tual rigor was achieved by encouraging complex reasoning across subject matters. In all core subjects (with a possible exception of mathematics), this necessitated extended reading and writing of complex texts. For example, students read works across national and cultural boundaries by authors such as Isabel Allende, Bertolt Brecht, Henrik Ibsen, Gabriel Marquez, Toni Morrison, William Shakespeare, and Richard Wright. Students studied com- plex topics in the social studies and the sciences. Portfolios requiring in- depth study and evaluations of the quality of student understanding con- tributed to the level of intellectual rigor in these schools. Authentic tasks were evident across sites. Projects, portfolios, and internships outside of school involved reading, writing, and research. Structured opportunities to help students reflect on and evaluate their work in these authentic experi- ences were also characteristic across sites. Students were asked to identify problems, make plans, do field work, and write up their conclusions. For example, in one class project, students identified tree samples for Central Park rangers, who were understaffed. Explicit instruction in strategies was given and incorporated into evaluation procedures, which included detailed rubrics that made public the criteria by which students' works were judged. Students had access to multiple resources for learning through collaborative projects, internships outside the school, and seminars and assignments that involved reflections on what and how they were learning. Multiple sup- ports also included tutoring before and after school that involved peers and adult mentors. Finally, a flexible and responsive assessment system required students to think deeply during complex, authentic tasks as well as to take more traditional tests. Students were encouraged to reflect on their learning and they were given feedback and supports to bolster areas of weakness. As
74 ENGAGING SCHOOLS was found for effective teachers in the CELA study, students were not given isolated lessons on test preparation, but rather assessment was integrated into the instructional routines across the school year. Strategic Literacy Project The third set of examples comes from the Strategic Literacy Project (SLP) with a home base at the West Ed Lab (Greenicaf, Schoenbach, Cziko, and Mueller, 2001; Schoenbach, Greenicaf, Cziko, and Hurwitz, 19991. The Strategic Literacy Project takes on the challenge of teaching reading at the middle and high school levels. The project attends to reading across subject matters, addressing the social dimensions of learning, the personal dimensions of students' identities as readers, the cognitive dimensions of reading strategies that characterize better readers, and a knowledge-build- ing dimension that involves expanding repertoires in knowledge of topics, vocabulary, genres, and text structure that readers need as resources for constructing meaning while reading. A study of 9th graders in a high school serving a substantial population of low-income students and students of color (including those in special education and English-language learners) showed significantly greater than a year's growth at the 9th-grade level. Rates of growth did not vary as a function of the teacher, or by the students' ethnicity or language back- ground. This study involved a specially designed freshman course in aca- demic literacy, preparing students for the demands of reading across content areas (Greenicaf et al., 2001~.3 Descriptions of classroom interactions document how students were able to draw on multiple resources to support learning, rigorous authentic work, assessments that provided students with timely and useful feedback, personalized relationships among all participants, and explicit attention to modeling and scaffolding strategies. In relation to the motivational poten- tial of this work, the researchers also surveyed students before and after the freshman course regarding their conceptions about reading as a process and about themselves as readers. Students reported doubling the number of books they read over the year. In the postsurvey, students described explic- itly an array of strategies available to them to make sense of what they read. 3Although this reported rate of growth is laudable, it must be noted that in order for students who are significantly behind in reading to "catch up," they must achieve greater than a year's growth for a year of instruction. Although there is evidence of such rates of growth at the elementary school levels, there are few examples, especially of any large scale, of such rates of growth at the high school level. This may be due, in part, to the increased demands of subject matter reading required at the high school level.
TEACHING AND LEARNING School Achievement Structure 75 The School Achievement Structure (SAS) was founded by Dr. Barbara Sizemore as a mode! for whole-school reform based on her earlier work in low-income schools in the Pittsburgh Public Schools. The Ten Routines of SAS (Sizemore, 1995) are consistent with the pedagogical principles we have outlined. SAS is based on the Effective Schools Models (Edmonds, 1979; Sizemore, 1985) and emphasizes the reorganization of the whole- schoo! climate. Consistent with the pedagogical principles described in this chapter, SAS emphasizes 5-week assessment routines that are aligned with standards to which schools are accountable. Schools identify concepts and strategies to be mastered and pace instruction so that skills are distributed across the school year. Students are grouped flexibly so that individual student needs are addressed. Data-driven decisions about reteaching, re- grouping, and retesting are made by teachers across the school year. De- signing literacy instruction to be culturally responsive to students' prior knowledge and experiences is also central to SAS routines. SAS has worked since 1992 with a number of schools in Chicago placed on academic probation, including 14 high schools with long histo- ries of very low achievement. Before the intervention began in 1993, SAS high schools had 17.2 percent of their students reading at or above national norms. The number increased in SAS high schools to 37.2 percent in 2000. Another indicator of the value of this mode! is the percentage of students scoring in the bottom quartile in reading comprehension: in 1994, 73 per- cent; in 2000, 38 percent. These figures are particularly important because SAS schools involve no selection biases in terms of staffing or students (Sizemore, 19951. Although the research is not extensive, what is available provides per- suasive evidence that it is possible to engage and increase the literacy skills of urban youth. Looking across studies, the evidence reveals considerable overlap in the instructional approaches that appear to have been most effective. We turn now to mathematics, where the research provides addi- tional evidence for the value of similar strategies. MATHEMATICS Achievement in mathematics has serious consequences for life opportu- nities, earning potential, and the ability to participate fully in society. On a daily basis, people encounter information (e.g., election results, interest rates, unemployment trends, weather reports, medical risks) that they need to interpret. With the increasing use of technology in the workforce, people who cannot manipulate symbols and the language of computers will be at a significant disadvantage.
76 ENGAGING SCHOOLS The evidence is clear that students in urban schools are not faring well in mathematics. In 2000, 40 percent of 12th graders in central cities scored "below basic" on the National Assessment of Educational Progress (Na- tional Center for Education Statistics, 2001a), compared to 32 percent in urban fringe (suburban) and large towns and 35 percent in rural and small towns. The picture is actually worse than these data suggest because the proportion of students who have dropped out by the 12th grade is much higher in urban than in suburban schools (see Chapter 1, this volume). The gap between students of color, who are disproportionately in urban schools serving low-income youth, and white students remains substantial. As was found for reading, in 1999 African-American and Latino 17-year-olds scored about the same on the NAEP math test as did white 13-year-olds (NCES, l999b). Gender differences on standardized tests in mathematics also have been found, but they are modest compared to the gender differences found in the beliefs that mediate engagement discussed in Chapter 2. Compared to males, on average females typically rate their math competencies lower (even though they often get higher grades), have lower expectations for success, and consider math less relevant to their future. Perhaps not coincidentally, females are less likely to persist in the mathematics curriculum or to aspire to mathematics or science-related careers (Eccles, 1984, 1994; Eccles et al., 1983; Eccles, Barber, and Tozefowicz, 19981. Because most studies that examine gender do not also look at race, we do not know whether the gender differences found apply to all ethnic groups. Contributing to the relatively poor performance of urban high school students is their poor access to high-quality mathematics teachers. Many studies suggest the value of both a solid background in mathematics and teacher training for student learning (e.g., Darling-Hammond, 1996, 1999; Ferguson, 1991; Ferguson and Ladd, 1996; National Commission on Math- ematics and Science Teaching for the 21st Century, 20001. A national survey found that in schools where 60 percent or more of the students served were eligible for free lunches, approximately one-third of the math- ematics teachers and nearly 20 percent of the science teachers did not hold an undergraduate or graduate major or minor in their main teaching field (National Center for Education Statistics, l999c). Oakes ~1990) reports huge differences in the qualifications of teachers in schools serving non- white students compared to those serving white students. White students had a 69-percent chance of getting a math or science teacher with a college degree in the subject, whereas nonwhite students had only a 42 percent chance. White students had an 86-percent chance of having a teacher certi- fied to teach math or science; the comparable figure for nonwhite students was 42 percent According to data gathered by the National Commission on Teaching and America's Future (1996), 40 percent of students in high-
TEACHING AND LEARNING 77 poverty schools (greater than 49 percent eligible for free lunch) had math teachers who had not even minored in mathematics. Having a strong background in mathematics does not ensure effective teaching, but a deep knowledge of the subject matter is necessary for teach- ers to engage students in activities that go beyond rules and procedures (Ball, 1992; Ma, 19991. Not knowing mathematics can severely limit the repertoire of instructional strategies on which teachers can draw. The lack of a strong mathematics background, common among teachers in urban schools, may thus contribute to the frequent use of textbooks, worksheets, urilis, and teaching that emphasizes disconnected rules as opposed to a web of interrelated concepts (National Research Council, 20011. What Mathematics Involves Most people think of mathematics as procedures that children need to develop fluency in applying. But much more is involved. Mathematics is the science of patterns, including mental or visual, static or dynamic, quantita- tive or qualitative, practical or recreational, real or imagined (Dehacne, 1997; Deviin, 20001. Balance in the architecture of buildings, the repeat nature of limb branching in trees, and even the dispersion of milk poured into a cup of coffee reflect mathematical properties. Doing mathematics requires being able to see similarities in features of problems that allow one to apply previously proven rules. Educational researchers and mathematicians define mathematical pro- ficiency as having five components: (1) conceptual ?~n~erstan~ing (compre- henuing mathematical concepts, operations, and relations); (2) Grocer patency (being able to carry out procedures flexibly, accurately, efficiently, and appropriately); (3) strategic competence (being able to formulate, rep- resent, and solve mathematical problems); (4) adaptive reasoning (being able to think logically, reflect, explain, and justify); and (5) productive disposition (being inclined to see mathematics as sensible and useful, while also believing in diligence and one's own efficacy; National Research Coun- cil, 20001. Consistent with this multidimensional definition of mathematics profi- ciency, the National Council of Teachers of Mathematics (NCTM, 2000), the leading professional organization for researchers and practitioners con- cerneu with mathematics education, stipulates that students should unuer- . . . . . . . .. .. . stand mathematics trom a number ot perspectives and be able to communl- cate that knowledge in a number of ways. Consider, for example, the simple linear function: y = 3x + 9. Rather than expecting students to merely plug numbers into algebraic equations to get answers (the traui- tional two-column chart), students should be able to understand that the notation represents a relationship between two objects (X and Y). They
78 ENGAGING SCHOOLS should also be able to represent the equation in graphical and verbal forms and understand the relationship between these forms. Students should be able to describe in everyday words what the function looks like (e.g., a straight line increasing from left to right, like a ramp on a loading dock), what some of its properties are (e.g., linear), and how the graphical version relates to the symbols used to represent the function in the equation shown (e.g., noting that the slope is represented by the number 3 and the point at which it crosses the y-axis is when x equals 0, or where the ramp would enter the ground if it continued). To gain a deeper understanding of concepts, students need to be able to move back and forth between different representations of data and ways of proving conjectures, not just completing exercises. For example, if students are never asked to relate the abstract symbols of math to something in their real world, they are deprived of the resources (e.g., real contexts, personal experiences) for problem solving. In this case, math remains a disconnected set of facts rather than an intricate web of concepts. Students should be expected to understand the following: What shifts the function upward and downward on the y-axis (as if the floor on which the ramp rests was raised or lowered)? What shifts the function left and right on the x-axis (as if the ramp could be pulled in one direction or another across the floor)? What increases or decreases the slope of the function (the angle of the incline of the ramp)? What other groups of functions share similar properties? Tech- nology (e.g., graphing calculators) can make this learning more efficient by visually modeling changes in the function without students having to de- velop a separate table of values and then a graph for every trial set of points they decide to pursue. With the help of lava applets, students have the ability to change two variables at the same time and watch how they affect the shape and other properties of the function. Features of Effective Pedagogy NCTM has grappled with the task of defining strategies for making mathematics instruction engaging to students. The framework NCTM (2000) developed on the basis of research in mathematics learning provides us with a vision for what mathematics instruction should look like: PStudents] draw on knowledge from a wide variety of mathematical top- ics, sometimes approaching the same problem from different mathemati- cal perspectives or representing the mathematics in different ways until they find methods that enable them to make progress. Teachers help stu- dents make, refine, and explore conjectures on the basis of evidence and use a variety of reasoning and proof techniques to confirm or disprove those conjectures.... Alone or in groups and with access to technology, Pstudents] work productively and reflectively, with the skilled guidance of
TEACHING AND LEARNING their teachers. Orally and in writing, students communicate their ideas and results effectively. (p. 3 ~ 79 This vision of school mathematics differs considerably from what many of us experienced (and were uninspired by) as high school students, when we learned equations and rules that the teacher wrote on the chalkboard, and practiced their application on sets of similarly formatted problems. Traditional math instruction has not typically engaged students actively in mathematical thinking and problem solving. The active grappling with math ideas described in the NCTM standards, in contrast, is consis- tent with what motivation researchers have found to engage students (see Chapter 2, this volume). Although educators and researchers continue to debate the best ap- proaches to teaching (e.g., "direct instruction" versus "inquiry oriented," "teacher centered" versus "student centered," "traditional" versus "re- form"), quality mathematics education is more complex than can be cap- tured in simple dichotomies. For example, effective teachers are student centered in the sense that they build on student's understanding, engage them in active problem solving, and connect math learning to their experi- ence outside of school. They are also directive in the sense that they deter- mine the mathematical concepts to be learned, select most (although not all) of the problems students work on, guide students' thinking, assess their knowledge, and create opportunities for them to practice their understand- ings and to develop fluency. Notwithstanding some dispute about the value of particular practices, there is a fairly good body of research supporting some practices over others, to which we now turn. Because engagement, as it is defined in Chapter 2, is usually not measured in studies of math teaching, we focus on three indirect indicators of student engagement: (1) participation in the school mathematics sequence (taking a relatively large number of math- ematics courses usually more than three during high school); (2) partici- pation in advanced levels of school mathematics (e.g., trigonometry, precal- culus, discrete/finite mathematics, statistics, calculus); and (3) mathematics achievement on standardized tests. The three indicators are interrelated. For example, both the number of courses taken in high school mathematics and participation in advanced levels of mathematics are associated with higher achievement scores (Lee, Croninger, and Smith, 1997; National Cen- ter for Education Statistics, 2001a; Rock and Pollack, 1995~. Caution is called for in interpreting the effects of instruction on stan- dardized achievement tests because the tests often do not match the school curriculum (Stake, 1995; Zevenbergen, 2000~. For example, mathematics teaching that emphasizes understanding over memorizing does not always produce increased scores on tests of basic skills, but does appear to in-
80 ENGAGING SCHOOLS crease scores on tests that also emphasize mathematical concepts (Carpen- ter, Fennema, and Franke, 19961. Incleeci, stanciarclizeci tests in mathemat- ics rarely match the forms of instruction most researchers finci to be effec- tive. For example, most students are not tested on problem solving or reasoning, but rather on their ability to identify the appropriate rule and apply it to achieve a correct answer. Few tests inclucle open-encleci ques- tions, instead relying on multiple-choice answers that reinforce students' belief that getting the correct answer is more important than the strategy behind solutions. The tests used also can underestimate some students' competencies. When Boater (2002b) altered the content on a mathematics test to eliminate confusing contexts and language for word problems, low-income Latino students were able to demonstrate significantly higher levels of mathemat- ics unclerstancling than their stanciarclizeci test scores suggested. Looking across studies, we see support for the features of engaging and effective practices in mathematics that are listed below. The features founci to be effective in research on teaching mathematics are remarkably similar to the features of engaging literacy instruction, although they are chucked into slightly different categories. As was true for literacy, it is clifficult to identify in studies the specific practices that enhance engagement. More likely, sets of practices work synergistically either to promote or undermine stuclent engagement and learning. The features of effective instruction are as follows: · Personally relevant · Access to native language · Authentic, open-encleci problems and involvement in mathematical . c .lscusslons feedback · Peer collaboration · Rigorous and challenging instruction with frequent assessment and · Access to technology The value of making mathematics personally relevant is suggested by a stucly of nine high school mathematics departments (Gutierrez, 2000b). In schools where students showed significant gains in mathematics achieve- ment between gracles 9 and 12 and where they took more mathematics and higher levels of mathematics than their peers, teachers were more likely to report using activities that drew on the everyday knowledge and interests of their students (e.g., National Basketball Association stanclings, African- American voter registration in southern states, and ages of actors and ac- tresses when nominated for Academy Awarcis) to provicle a context for mathematical concepts and representations of data. Teachers in these effec-
TEACHING AND LEARNING 8 tive settings were also more likely to offer students some choice in topics for . . . . projects or activities. As has been found in research on literacy teaching at the high school level, studies have demonstrated the value of giving students access to their native language in mathematics courses. Mathematics is a language unto itself. Therefore, although everyone who learns math must negotiate the translations between everyday language and formal mathematics, students whose native language is not English encounter greater cognitive demands in making sense of mathematical terms. Although most of the research conducted is at the elementary level, there is good evidence that effective mathematics teachers of English-language learners show respect for their students' culture and language, and encourage students to draw on their native language to master mathematical concepts (Gutierrez, 2002a; Moses and Cobb, 20011. Studies also suggest the value of allowing students to work and collaborate with each other in their native language, and provid- ing materials for them in their primary language (Khisty and Viego, 1999; Silver, Smith, and Nelson, 19951. Explaining or teaching something to someone else consolidates and deepens the understanding of the subject matter by the person in the teach- ing role. This is one of the reasons why experts in mathematics instruction recommend that students be given authentic open-ended problems and op- portunities to be involved in mathematical discussions, such as by asking them to discuss and justify the strategies they use to solve problems. In one national study, 12th-grace students who reported talking with others about how to solve mathematics problems at least weekly scored higher than those students who reported talking with other students monthly or never4 (National Center for Education Statistics, 2001a). Moreover, in both na- tional (e.g., Moses and Cobb, 2001; Silver et al., 1995; Somerton, Smith, Finnell, and Fuller, 1994) and small-scale studies (e.g., Gutierrez, 2002b), students who were active in mathematical discussions tended to persist in the mathematics sequence or score higher on mathematical exams. Boaler (2002b) compared the instruction in British classrooms in which students were highly engaged and claimed to be enthusiastic about math to classrooms in which students claimed to be mostly bored and didn't par- ticularly like math. One of the most prominent differences between the engaging and boring classrooms was the nature of the problems students were asked to solve. In the engaging classroom students were given open- ended problems that had multiple solutions or strategies and that allowed students to take initiative and be creative. (See Box 3-3 for an example.) 4This trend was true in both 1996 and 2000; however, only in 1996 was this difference shown statistically.
82 ENGAGING SCHOOLS Students had to use what they knew about mathematics in novel contexts, often deriving the rule from their own efforts rather than being told the rule before they began the problem. Students in the boring classrooms worked primarily from textbooks, learning rules and procedures to use on sets of similar problems. When students encountered difficult or multidimensional problems, teachers often broke them down into small pieces that could be solved by applying a learned procedure. A related teaching strategy that appears to promote engagement in mathematics is peer collaboration. Treisman (1990) found that when Afri- can-American and Latino students were taught to work with others to
TEACHING AND LEARNING 83 complete homework assignments or to study (a strategy that was spontane- ously adopted consistently by Asian students), they scored better on course exams and standardized tests. Similar success was seen by a college profes- sor who used group work to teach mathematics to African-American col- lege students. The opportunity appeared to promote interest in more math- ematics coursework and mathematics-related careers (Anderson, 19901. To be sure, merely "talking" with classmates does not ensure math- ematical engagement or learning. The emphasis on reasoning (about par- ticular strategies for solving problems) and developing justifications for arguments seems to be most fruitful (Boater, 2002b). Moreover, some stu- dents (e.g., English-language learners) may be less inclined to participate in a discussion-oriented format than in traditional paper-pencil tasks (DeAvila, 1988; Moschkovich, 1999; Secada, 19961. Students who are not confident in their abilities may also have difficulty with such formats, especially in a competitive classroom context. Murrell (1999) studied 12 urban middle school students and found that open-ended, discussion-oriented classes did not increase African-American male students' understanding of mathemati- cal concepts. These students participated in the conversation, but they shied away from substantial engagement with mathematics for fear of making mistakes. This pattern aligns with other studies of African-American stu- dents who, when put in the spotlight, may perceive a threat of fulfilling a stereotype (e.g., that African Americans are intellectually inferior to other groups) and show reduced performance on measures of achievement (Steele, 19991. Opportunities to talk about mathematical problems with others appears to benefit students only when the teacher skillfully focuses the discourse squarely on mathematics, establishing norms that uncertainty is good and is a prerequisite for complex reasoning (see Boater, 2002b). Students are more engaged in mathematics when they receive challeng- ing, rigorous instruction (Gutierrez, 1996; Lee and Smith, 19951. Research- ers have attributed the relatively high standardized test scores among stu- dents in Catholic schools, controlling as best as possible for potential confounds, to the college preparatory courses all students take (Bryk et al., 1993; Lee et al., 19931. In contrast, the mathematics curriculum in most public urban high schools is composed substantially of lower track and lower level mathematics courses (e.g., business math, consumer math, math explorations, preaigebra), with students having little access to calculus, which is an important gate to college majors in mathematics and science (Mullis, Jenkins, and Johnson, 1994; Oakes, 19901. Further evidence that students in urban schools often get less than rigorous instruction comes from a study of urban schools in California and New York conducted by Gamoran, Porter, Smithson, and White (19971. They describe low-track courses in which "instruction is weak and growth is shallow" courses that serve as a "dead end for students' mathematical careers" (p. 3331.
84 ENGAGING SCHOOLS Frequent assessment of student understanding is a critical accompani- ment to rigorous instruction. Black and Wiliam (1998) reviewed 250 re- search studies and concluded that student learning (especially that of low achievers) is promoted by teachers who focus on formative assessment when making judgments about teaching and learning. Although formal paper-and-pencil assessments are useful strategies for gauging student learn- ing, they provide limited information. Because students exhibit what they know differently under different conditions, teachers also need to gather information about their students (both procedural skills and conceptual understanding) frequently and using varied techniques, such as observa- tions, conversations, interactive journals, and careful examination of stu- dent work making sure not to confound judgments about students' math- ematical knowledge with their language skills or writing ability. This kind of information gathered and considered collectively by teachers can help them make critical decisions about when to review material, when to move on, how to revisit a difficult concept, and how to adapt tasks for struggling students or enrich tasks for students who have mastered the material. Finally, evidence suggests that urban youth may be more engaged in mathematics when their teachers employ technology to help convey con- cepts (Dildine, 2000; Gutierrez, 1996; Moses and Cobb, 20011. For ex- ample, in a study of nine U.S. high schools by Gutierrez (1996, 2000b), graphing calculators and computers were used on a regular basis in the schools in which students actively participated in the mathematics curricu- lum, took more advanced mathematics courses such as precalculus and calculus, and scored better than predicted on standardized tests. Specifi- cally, students used algebra and geometry software and graphing calcula- tors to collect and represent data in different forms. In one analysis of NAEP data, 12th-grade students who reported using graphing calculators regularly scored higher on standardized tests than those students who re- ported using them less frequently (National Center for Education Statistics, 2001a). The direction of causality cannot be determined from existing studies, but they suggest the value of further investigation. Consideration also must be given to how technology is used. Research on motivation suggests that using technology to simulate or to apply math- ematics concepts to real-worId problems is likely to engage students' inter- est. But studies of the use of technology suggest that this is not how technol- ogy is typically used in urban schools. A recent report indicated that although approximately the same proportion of white students reported using computers primarily for simulations and applications (31 percent) as for drills and practice (30 percent), far more African-American students used computers primarily for drills and practice (52 percent, compared to 14 percent for simulations and applications; Wenglinsky, 19981. The differ- ence was also strong when comparisons were based on student poverty.
TEACHING AND LEARNING 85 Students in Title 1 schools were much less likely to use computers primarily for simulations and applications (13 percent) than students in schools that did not receive Title 1 funds (30 percent). The practices described in this section can be implemented in any set- ting, but it is difficult, as we will explain later, for an individual teacher to use these ambitious approaches to teaching mathematics without a great deal of training and ongoing support. Professional development programs and support systems have been developed to meet this need. Next we pro- vide examples of comprehensive programs that are based on the general principles of effective instruction that we have summarized and include support for teachers. Effective Mathematics Programs Using the three measures of student engagement in mathematics men- tioned earlier, we highlight three programs designed specifically to engage low-income urban students in mathematics. All three of these programs promote practices that are consistent with the findings from the achieve- ment motivation literature reviewed in Chapter 2. They are based on the belief that learning is maximized when it involves meaningful relationships with caring adults who have high expectations, where students work with others, where the focus is clearly on mathematics, and where connections are made to adolescents' knowledge and personal experiences. The Algebra Project In 1982 Robert Moses developed The Algebra Project to engage Afri- can-American inner-city and rural youth in mathematics (Checkley, 2001; Moses, Kamii, Swap, and Howard, 1989; Moses and Cobb, 20011. To date, more than 22 sites involve students in grades 7, 8, and 9 in 13 states, in cities such as Chicago, Milwaukee, Oakland, Atlanta, Indianapolis, San Francisco, and Los Angeles. Some key features of the program are providing professional develop- ment to teachers so they can come to see themselves as learners (focusing on joint learning with students and other teachers); employing adults who have enough contact with adolescents inside and outside of school to de- velop meaningful relationships; abolishing ability grouping and getting stu- dents to work effectively in both individual and small-group learning situa- tions; using curricular materials that focus on the way people create and use mathematics in the real world; and letting students experience a cultural event (e.g., riding the subway) that generates data to be used in exploring mathematical concepts. A key premise of The Algebra Project is that learning must be tied to
86 ENGAGING SCHOOLS students' personal experiences. Therefore, students learn to translate every- day life experiences into the symbolic language of mathematics. Four key components of the curriculum that teachers follow are 1. Physical Events (e.g., students take a trip a ride on a metropolitan transit system, a bus tour, or a walking tour of their community) 2. Pictorial Representation/Modeling (students are asked to draw pic- tures that visually mode! the event) 3. Intuitive Language/"People Talk" (students are asked to discuss and write about the physical event in their own language) 4. Structured Language/"Feature Talk" (students isolate features of the event such as start, finish, direction, distance on which they can build mathematics) The Algebra Project takes seriously the NCTM claim that students need to be able to represent and communicate data in a variety of forms (algebraic/symbolic, graphical, verbal, tabular). Thus, when students are asked to represent the physical trip with a picture, it is similar to graphing. When they are asked to use "people talk," they are being asked for a verbal description of their graph. When they seek features of the event that can be translated into structured mathematics language, they are being encouraged to use mathematics as symbols. Unfortunately this approach has not been rigorously evaluated. The evidence suggests, however, that the approach has some value. The first group of students who graduated from the project enrolled in high school in geometry and many have gone on to medical school and other graduate schools. In Arkansas, 7 out of the 11 cohorts of students that were followed showed at least a 10-point increase in mean scaled scores on the SAT-9 a year after being in the program. In all 12 Arkansas sites, there was a greater than 10 percent increase in the number of students scoring at or above proficiency on the state exam, whereas students at 8 out of the 9 control sites stayed at their previous levels or declined (West and Baumann, 20021. MESA Program A comprehensive outreach program, Mathematics Engineering Science Achievement (MESA), has been engaging Latino (primarily Mexican-Ameri- can) and African-American students throughout California since 1970 (Somerton et al., 19941. The program is outside of the students' regular school curriculum, but nevertheless provides evidence of the value of par- ticular approaches to engaging urban youth in mathematics. Students sign up for the program if they are enrolled in or willing to take algebra in 9th grade, and they continue to take rigorous mathematics courses throughout
TEACHING AND LEARNING 87 high school. Most students earn average grades when they start, but they . . . . . . cave an Interest In careers In science or engineering. Currently, MESA helps prepare nearly 20,000 students of color each year for mathematics- and science-based careers. More recently expanded to include sites throughout the nation, MESA takes regular mathematics and science teachers and turns them into advisors who offer courses along- side the traditional mathematics/science curriculum offered by schools. In addition, 6-week summer enrichment programs and Saturday academies help students deepen their understanding and prepare for college courses in mathematics and science. MESA is founded on the idea of partnering with parents, business professionals, and community members to provide additional role models and to mentor students. Using hands-on instruction (e.g., where students build models of mathematical structures and processes), adults and older students in the MESA program become resources for adolescents, helping them mode! and visualize mathematics and science in ways that build a solid foundation for college instruction. The MESA curriculum focuses on themes that cut across disciplines (e.g., probability, measurement, matter, environment), with the goal of preparing adolescents for a rapidly changing environment. Students are also given leadership roles to develop their skills in obtaining summer internships and jobs in the field. As an incentive, the program pays a small stipend to students who earn a 3.0 or greater grade point average while in high school. MESA high school students are remarkably successful on traditional measures of achievement, including SAT scores and college attendance (Somerton et al., 1994), although it is not possible to ascertain to what degree these positive outcomes are a result of the program itself. There is clearly a selection bias in who enters the program, and research with an appropriate control group would provide much clearer evidence of the program effects. The achievement of the students in the program, however, is so remarkable that it is highly unlikely that participating students would have done as well without it. Although the program is designed as an adjunct to the regular high school, most components of the program could be implemented in the regular mathematics curriculum. The QUASAR Project The Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) Project is designed for middle school students. Since the fall of 1989 the QUASAR Project has been implemented in six economi- cally disadvantaged communities in California, Georgia, Massachusetts, Oregon, Pennsylvania, and Wisconsin (Doty, Mercer, and Henningsen, 1999; Silver et al., 19951.
88 ENGAGING SCHOOLS Key components of the project are curriculum development and modi- fication (e.g., developing activities for particular classes); staff development and ongoing teacher support (e.g., opportunities for teachers to continue to learn mathematics); classroom and school-based assessment design (e.g., focusing on students' thought processes, not just the answers they produce); and outreach to parents and the school district at large. With respect to pedagogy, a classroom emphasis is placed on building communities of learn- ers (cooperative groups, supporting mathematical thinking and collabora- tion); learning to question and coming to understand others; building com- munities of linguistically diverse learners; and enhancing the relevance of school mathematics (building on students' experiences, relating mathemat- ics to students' interests, and connecting mathematics to students' cultural heritage). To try to connect mathematics to cultural knowledge, for ex- ample, students in the QUASAR Project are encouraged to tell stories that mode! the mathematics they are learning (fitting the oral tradition of some cultural groups). In sites with a substantial African-American population, students have been asked to write essays on Egyptian numerals and the life of Benjamin Banneker. Mathematical discussions are promoted by asking students to debate mathematical assertions and use mathematical argumen- tation to support differing positions. The evidence suggests that these strategies increase student engagement and learning. In schools across the nation, the QUASAR Project has seen significant gains in student engagement in classroom discussions and in standardized achievement scores (tests of basic skills as well as conceptual understanding; Silver and Lane, 19951. As was found for literacy, a fair amount is known about the qualities of instruction that engage high school students, and evidence from a few programs suggests that these strategies might be applied effectively in urban schools. There is still much to learn, particularly about implementing pro- grams at scale in urban high schools. But the existing evidence provides no support for the traditional textbook and worksheet instruction seen in most schools serving low-income students and students of color. SPECIAL NEEDS OF URBAN YOUTH Our conclusions about effective teaching in literacy and mathematics are based in part on studies conducted in urban high school settings, giving us some confidence in their applicability to the students of concern in this volume. There are, however, particular circumstances related to teaching in schools that serve economically disadvantaged students, which need to be considered in any effort to increase students' engagement in learning. We have discussed the importance of connecting new knowledge in literacy and mathematics to students' own interests, experiences, and cul-
TEACHING AND LEARNING 89 sure. In urban low-income communities, effective pedagogy also requires attention and sensitivity to the out-of-school challenges that many students face including racism, homelessness, violence, and lack of sufficient re- sources to address mental and physical health problems. (See Chapter 7 for an extended discussion of this topic.) At the core of The Algebra Project (Moses and Cobb, 2001) and Lee's Cultural Modeling (Lee, C.D., 2000) is the goal of attending "holistically to the developmental, cognitive, and emotional needs of students. These models address the complex agenda that Ladson-Billings (1997, 2001) ar- ticulates in her call for culturally responsive pedagogy. They require atten- tion to the very real risks and challenges faced by urban adolescents. In the MESA program, for example, students are given opportunities to develop their skills in dealing with foreign and sometimes hostile environments (e.g., summer jobs in scientific laboratories where personnel are not accus- tomed to people of color). In addition to helping students cope with the challenges they face in urban environments, teachers can empower students by helping them de- velop leadership roles to promote change (Spencer, 1991, 1995, 1999; Spencer, Cross, Harpalani, and Goss, in press; Spencer, Noll, Stoltzfus, and Harpalani, 20011. Ladson-Billings (1994) writes eloquently on the impor- tance of encouraging activism and political awareness in any effort to en- gage low-income urban students in school. What we are recommending expands the role of the teacher substan- tially, from someone who focuses just on subject matter to someone who focuses on students, including the larger context in which they live (Foster, 19941. This requires a commitment to addressing social injustices (Hilliard, 1991, 19951. Teachers' philosophy related to their role may be as impor- tant as their lessons or the curriculum (Bartolome, 1994; Beaubocuf- Lafontant, 1999; Gustein, Lipman, Hernandez, and de los Reyes, 1997; Ladson-Billings, 1995; Lee, 1994; Shujaa, 19941. There is some evidence that teachers who are philosophically committed to equity and racial justice are less likely to have low expectations and more willing to adjust their instruction to meet the needs of their students while maintaining academic rigor (Ball, l995b, 2000a, 2000b; Lightfoot, 1973; Stodolsky and Grossman, 20001. Although no studies have shown the independent effects of a social justice orientation, there is evidence that suggests its possible value. In an evaluation of his National Science Foundation-supported (Mathematics in Context) curriculum supplemented with units on social justice, Gutstein (in press) found that 18 of his 24 7th-grade Latino urban students passed city entrance exams for competitive magnet schools and all went on to take algebra in 9th grade. His students averaged a gain of 1 month's grade equivalent in mathematics for every month they spent in his class. Similar
9o ENGAGING SCHOOLS success of students persisting in the mathematics sequence or enjoying math- ematics has been found by mathematics professors who hold a strong social justice stance (Anderson, 1990; Frankenstein, 1990, 19951. Another challenge that is especially prominent in urban schools serv- ing low-income youth is the low level of skills with which many students enter high school. Although there is good evidence that even students who are far behind when they begin high school can master the high school curriculum and achieve high standards, these students are the exception. The programs described in this chapter were all designed for students in schools serving predominantly low-income students and students of color, and they show promise of improving on traditional remedial methods. (See also Chapter 5.) In summary, it is important to acknowledge that teaching in economi- cally disadvantaged urban schools involves special challenges; it is equally important not to fall into a trap of low expectations, which often breed formulaic teaching and restricted conceptions of subject matter (Boater, 2002b). There are far too few examples of urban high schools that hold their students to challenging standards and engage them in mastering diffi- cult disciplinary concepts and strategies, but such schools exist, and provide the proof that schools can become such institutions. Complexity is no excuse for retreat. SUPPORTING TEACHERS Teachers in urban schools face students who are trying to cope with an array of challenges in their lives outside of school and struggling to learn the skills assumed by most high school curricula. These teachers also often face difficult working conditions large class sizes, little preparation time, scarce resources, and now, pressure from high-stakes tests that are often not aligned with their instructional program and goals. Teachers also have to confront their own stereotypes related to race and social class. Given these conditions and challenges, it is not surprising that the kind of ambi- tious pedagogy described in this chapter has not taken root in most urban schools. This kind of teaching requires considerable skill and sustained support. Because of the sheer complexity of teaching and the special chal- lenges of urban schools, the need for strong professional communities of teachers is critical. Indeed, building teacher capacity and providing teachers with ongoing, expert support may be the most critical factor in creating urban high schools that engage all students in learning. The same motivation principles that apply to student engagement are relevant to teachers as well. For example, just as self-efficacy promotes engagement in students, Stodolsky and Grossman (2000) saw relationships between teacher' sense of efficacy and their willingness to adapt to the
TEACHING AND LEARNING 9 needs of their students. Ball (199Sa, 2000a, 2000b) has developed an effec- tive program to help groups of teachers grapple with their assumptions about diversity and about what it means to learn. Collaboration and group work are most likely necessary for teachers to develop both the commit- ment and the sense of efficacy to pursue rigorous standards in the often difficult circumstances of urban school teaching. Many studies have shown the value of a culture of collaboration in fostering effective teaching practices (e.g., Coburn, 2001; Desimone, Por- ter, Garet, Yon, and Birman, 2002; Hiebert, Gallimore, and Stigler, 20021. For example, Louis, Marks, and Kruse (1996) found that teachers in schools that had a strong teaching professional community (defined by a shared sense of purpose, collaborative activity, collective focus on student learn- ing, and reflective dialogue) engaged in higher quality teaching, and their students performed higher on NAEP mathematics and reading assessments when compared to teachers in schools with weak professional communi- ties. (See also Louis and Marks, 1998.) Some mathematics experts tout the value of "lesson study," a strategy used in Japan for teacher collaboration. Stigler and Hiebert (1999) suggest that mathematics achievement in the United States might be raised by giv- ing teachers time and support to form teacher workgroups to plan, experi- ment with, analyze, and revise lessons. For example, teachers can videotape and analyze lessons they have planned together. The approach has been introduced in some U.S. elementary and middle schools, and might be adapted to be useful at the high school level as well. In the area of literacy, there are many excellent examples of local professional communities of teachers working in urban districts. Perhaps the longest existing national mode! is the National Writing Project, which promotes collaboration among individual teachers across school sites. Or- ganized, funded projects, such as QUASAR, The Algebra Project, and MESA, provide the practical training and social support required to imple- ment effective and engaging mathematics teaching (Gutierrez, 2000a). There are also many examples of strategies implemented at the city, district, school, and department levels to develop the kind of sustained, professional communities that support effective teaching. Many studies point to the importance of the subject matter department in high school teachers' ability to teach and to adapt to the needs of their students (Gutierrez, 1996; Lieberman and Miller, 2001; Little, 1993; McLaughlin, 1993; McLaughlin and Talbert, 1993, 2001; Siskin, 1994; Talbert and McLaughlin, 1994~. Effective subject matter departments in- volve teachers in collective goal setting; in aligning curriculum, pedagogy, and assessment; in engaging particular students in certain content; and in finding ways of addressing students' overall needs. These collaborative efforts at the department level are associated with positive learning and
92 ENGAGING SCHOOLS achievement for students (Ancess, 2000; Freedman, Simons, Kainin, Casareno, and the M-Class Teams, 1999; Greenicaf and Schoenbach, 1999; Lee, 20011. Gutierrez (1996, 1999, 2000b, 2002b) has studied successful urban high school mathematics departments and found that certain forms of struc- tural organization and normative cultures (including beliefs) are associated with teachers' willingness and ability to engage diverse learners. She found that mathematics departments whose teachers did not view mathematics as a static subject, used a rigorous mathematics curriculum, discussed lesson plans and students, rotated course assignments, had a commitment to eq- uity, and observed each other teaching tended to have students who were actively engaged in the mathematics curriculum and scored well on stan- dardized tests. Although they do not report data on student outcomes, Stodolsky and Grossman (2000) likewise found in their survey of teachers in 16 U.S. high schools that mathematics and English teachers who experi- mented with the curriculum in order to engage diverse learners in the classroom tended to work in departments that were collaborative and fo- cused on professional development (see also Coburn, 2001; McLaughlin and Talbert, 20011. A strong sense of community at the department level may also diminish the alienation that teachers often experience in large, urban, bureaucratic schools. Talbert (1995) proposes that collaboration among teachers can serve as a catalyst for increasing a school's commitment to meeting the needs of students who otherwise have low priority (also see Wehiage et al., 19891. Talbert and McLaughlin (1994) found in their analysis of survey data for 253 teachers in 36 academic departments in 8 public high schools that teachers' participation in a collaborative, innovative profes- sional community predicted their expectations for student achievement and their caring for students, controlling for their subject preparation and over- all job satisfaction. Gutierrez (1996, 1999, 2000b, 2002b) and Stodolsky and Grossman (2000) observed further that the teachers who engaged stu- dents best were in professional communities committed to equity. Thus, a teacher's workplace setting is critically important in supporting the kinds of practices that engage students in learning. Practices in schools and the broader community are also important. For example, Valerie Lee (2000) found that high schools that had a communal focus (reformed instruction, shared authority, collective commitment to the personal development of students) produced considerable gains in student achievement and nearly eliminated social class differences between stu- dents. The school community is so critical to successful mathematics teach- ing that in choosing its sites, the QUASAR Project requires a school climate that supports teacher innovation. Schools also have norms regarding what it means to teach and to learn,
TEACHING AND LEARNING 93 which can have powerful effects on instruction in classrooms and student engagement. Researchers have examined, for example, norms for instruc- tional conversations: "the kinds of questions to be asked . . ., the concepts to be explored, the vocabulary through which these concepts were ex- pressed, the relevance of personal knowledge and experience, and the na- ture of acceptable argument and evidence" (Applebee et al., 2000, pp.413- 414; see Camden, 1988,2001; Lee, C.D., 2000; Marshall, Smagorinsky, and Smith, 1995; Mehan, 1979; Nystrand and Gamoran, 1991, 1992; Tharp and Gallimore, 19881. These norms often vary for different tracks. Studies show that the students in lower track classes have significantly fewer op- portunities to elaborate on ideas, to weigh evidence from multiple and sometimes conflicting points of view, or to generate propositions (McDermott, 1987; Nystrand and Gamoran, 1997; Oakes, 1985) the kind of active participation in rigorous learning experiences that motivation researchers have found to be most engaging. As Rosa, a 9th-grade student from the Strategic Literacy Project (Greenicaf et al., 2001, p. 101), de- scribes: Um, usually in like a regular history class, like the one I had last year? Which was just pretty much all writing? Okay, "read from page so-n-so to so-n-so, answer the red square questions and the unit questions and turn them in." And he corrects them and says, "You did this wrong, you did this right. Okay, here you go." And that was pretty much the basic way every single day has gone. So, from day one to the end of the year, that's pretty much all we did. Answer the red square questions. And pret- ty much it's been like that since I got to middle school...." Urban schools serving low-income students are capable of much more, as is illustrated in a real instructional dialogue that reflected disciplined norms for reasoning in response to literature (see Box 3-4~. As efforts are made to improve the support and circumstances teachers encounter in urban high schools, parallel efforts need to be made to recruit teachers with expertise in their subject matter. The best of circumstances will not overcome deficiencies in knowledge of subject matter, of how people learn, and of the developmental needs of adolescents. Realistically, the kind of teaching described in this chapter is not likely to be imple- mented on a large scale until teaching is made more attractive in terms of working conditions that support career-long professional development, es- pecially in urban schools. Equally important are improvements in preservice teacher education that address preparation for the quality of teaching that this chapter has described. Teacher training is beyond the scope of this volume, but it is clearly a critical piece of any effort to improve teaching in urban high schools.
94 ENGAGING SCHOOLS CONCLUSIONS The findings from research on effective teaching of literacy and math- ematics are strikingly similar. The evidence suggests that the instructional program must be challenging and focused on disciplinary knowledge and conceptual understanding. It needs to be relevant to and build on students' cultural backgrounds and personal experiences, and provide opportunities for students to engage in authentic tasks that have meaning in the world outside of school. Engaging instruction gives students multiple learning
TEACHING AND LEARNING 95 modalities to master material and represent their knowledge, and allows them to draw on their native language and other resources. This kind of teaching is not possible if teachers do not have a deep understanding of their subject matter, of how people learn, and of how to address students' developmental needs. In addition, teachers need opportu- nities to collaborate with colleagues, and access to ongoing, expert guid- ance to advance their own knowledge and skills. Effective pedagogy also needs to be supported by a coherent school curriculum and school norms
96 ENGAGING SCHOOLS that support student inquiry and active involvement in their learning, inter- est in students as individuals, and respect for their cultural backgrounds. Our intent is not to argue that simply providing "good" pedagogy is sufficient. Our point is that "good" pedagogy is engaging and motivating. We do not assume that if you offer rigor students will come. We are confident, however, that if schools offer rigor and explicit supports for learning that are responsive to the developmental needs and cultural back- grounds of students, the majority of students will enter the academic game.