teaching practice

19 Nov 2003 19:36 AR AR207-PS55-25.tex AR207-PS55-25.sgm LaTeX2e(2002/01/18) P1: GCE10.1146/annurev.psych.55.082602.133124

Annu. Rev. Psychol. 2004. 55:71544doi: 10.1146/annurev.psych.55.082602.133124

Copyright c 2004 by Annual Reviews. All rights reservedFirst published online as a Review in Advance on September 22, 2003

TEACHING OF SUBJECT MATTER

Richard E. MayerDepartment of Psychology, University of California, Santa Barbara,California 93106-9660; email: [email protected]

Key Words educational psychology, cognitive psychology, learning, instruction,reading

n Abstract Psychology of subject matter refers to the scientific study of learningand instruction within school subjects. The growing research literature on teachingand learning of school subjects represents one of educational psychologys most pro-ductive accomplishments of the past two decades. The purpose of this chapter is toexamine representative advances in the psychology of subject matter, including howpeople learn to read words, comprehend printed passages, write compositions, solvearithmetic word problems, and understand how scientific systems work. The intro-duction provides a historical overview of how to promote transfer and is followed byreviews of representative research in learning and teaching of reading fluency, readingcomprehension, writing, mathematics, and science.

CONTENTS

INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 716Three Views of How to Promote Transfer : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 717

TEACHING OF READING FLUENCY: THE TASK OF READING APRINTED WORD : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 718

Being Aware of Sound Units: Insuring Phonological Awareness : : : : : : : : : : : : : : : 719Decoding Words: Building Automatic Phonics Processing : : : : : : : : : : : : : : : : : : : 721Accessing Word Meaning: Fostering a Rich Vocabulary : : : : : : : : : : : : : : : : : : : : : 722

TEACHING OF READING COMPREHENSION: THE TASK OFCOMPREHENDING A PASSAGE : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 723

Using Prior Knowledge: Teaching Readers to Integrate Knowledge : : : : : : : : : : : : 723Using Prose Structure: Teaching Readers to Select and Organize

Knowledge : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 724Making Inferences: Teaching Readers to Integrate and Organize

Knowledge : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 725Using Metacognitive Knowledge: Teaching Readers to Monitor

Processing : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 726TEACHING OF WRITING: THE TASK OF WRITING A

COMPOSITION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 726Planning: Teaching Writers to Find, Organize, and Adapt Material : : : : : : : : : : : : : 727Translating: Helping Writers Overcome Cognitive Load : : : : : : : : : : : : : : : : : : : : : 728

0066-4308/04/0204-0715$14.00 715

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19 Nov 2003 19:36 AR AR207-PS55-25.tex AR207-PS55-25.sgm LaTeX2e(2002/01/18) P1: GCE

716 MAYER

Reviewing: Helping Writers Detect and Correct Errors : : : : : : : : : : : : : : : : : : : : : : 729TEACHING OF MATHEMATICS: THE TASK OF SOLVING A

WORD PROBLEM : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 729Problem Translating: Teaching Students to Represent Sentences : : : : : : : : : : : : : : : 729Problem Integrating: Teaching Students to Use Problem Schemas : : : : : : : : : : : : : 730Solution Planning and Monitoring: Teaching Students to Devise

Solution Plans : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 732Solution Execution: Teaching Students to Carry Out Procedures : : : : : : : : : : : : : : : 733

TEACHING OF SCIENCE: THE TASK OF UNDERSTANDING HOWTHINGS WORK : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 734

Recognizing an Anomaly: Teaching by Confronting Misconceptions : : : : : : : : : : : 735Constructing a New Model: Teaching by Providing a Concrete Analogy : : : : : : : : 736Using a New Model: Teaching Students How to Test Hypotheses : : : : : : : : : : : : : : 736

CONCLUSION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 737AUTHOR NOTE : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 738

INTRODUCTION

Psychology of subject matter refers to the scientific study of learning and instruc-tion within specific school subjects such as reading, writing, mathematics, science,and history (Bruer 1993, Mayer 1999, Shulman & Quinlan 1996). The growingresearch literature on teaching and learning of school subjects represents one of ed-ucational psychologys most productive accomplishments of the past two decades(Mayer 2001a). The continuing development of psychologies of subject matter isconsistent with trends in cognitive science, including the focus on learning as (a)a change in knowledge rather than solely as a change in behavior, and (b) as adomain-specific rather than domain-general activity (Bruer 1993).

Advances in the psychology of subject matter have contributed to the creationof an educationally relevant science of learning and instruction (Bransford et al.1999, Lambert & McCombs 1998, Mayer 1999, Phye 1997). Importantly, researchon the psychology of subject matter shows the benefits of building a scienceof instruction that is contextualized in school subjects rather than presented asgeneral context-free principles. A review of research on teaching of subject mattercontributes to theory (by focusing on knowledge representation and cognitiveprocessing in specific domains), to methodology (by focusing on cognitive taskanalyses of realistic tasks), and to practice (by identifying effective instructionalprocedures).

The purpose of this chapter is to examine some representative advances in thepsychology of subject matter, including how people learn to read words, compre-hend printed passages, write compositions, solve arithmetic word problems, andunderstand how scientific systems work. The introduction provides a historicaloverview of how to promote transfer and is followed by reviews of representa-tive research in learning and teaching of reading fluency, reading comprehension,writing, mathematics, and science.

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TEACHING OF SUBJECT MATTER 717

Three Views of How to Promote Transfer

How can we help people learn so that they will be able to transfer what they havelearned to new situations? Transfer occurs when a learner applies what was learnedto new situations. Transfer is often cited as the major goal of education, and the con-cept of transfer is at the heart of the science of instruction (Bruer 1993, Mayer 2002,Mayer & Wittrock 1996, Shulman & Quinlan 1996). For more than 100 years, psy-chologists have sought to understand how best to promote transfer (Haskell 2001,Mayer 2002, Singley & Anderson 1989), resulting in three major views of transfer:general transfer, specific transfer, and specific transfer of general knowledge.

General transfer refers to the idea that it is possible to improve the mind ingeneral. For example, as the twentieth century began, the dominant theory oftransfer was the doctrine of formal discipline, namely, the idea that certain schoolsubjects such as Latin and geometry would produce proper habits of mind thatcould improve learning across all tasks. However, when educational psychologistssubjected the doctrine of formal discipline to careful empirical study in the early1900s, no evidence for general transfer was found (Thorndike 1913, Thorndike &Woodworth 1901).

Specific transfer refers to the idea that previous learning helps on a new taskonly if the new task requires exactly the same behavior as was learned. This is thetheory of transfer that Thorndike and others offeredunder the name transfer byidentical elementsas an alternative to the failed doctrine of formal discipline.More recently, Singley & Anderson (1989, p. 51) have proposed that skills can bepresented as production systems in which productions, once learned, can serve asthe identical elements of Thorndikes theory. Thus, transfer occurs to the extentthat productions required in a previously learned skill are the same as those requiredin a to-be-learned skill.

Thorndikes theory of transfer by identical elements, and the updated versionsstill in use today, have been challenged not on the grounds that specific trans-fer theory is incorrect but rather that it is incomplete. In the early 1900s, Judd(1908) demonstrated learning a general principle about light refraction could pro-mote transfer of how to shoot at underwater targets at various depths. Similarly,Wertheimer (1959) demonstrated that learning a general principle about the struc-ture of parallelograms enabled students to transfer their learning of how to computethe area of a parallelogram to unusual shapes. Instead of specific transfer of specificresponses, these researchers proposed what can be called specific transfer of gen-eral knowledgethe idea that students can apply a general principle or conceptionto new tasks that require the same principle or conception. This specific-transfer-of-general-knowledge approach underlines advances in cognitive strategy instruction(Pressley 1990) as well as the teaching of subject matter.

Like Goldilockss search for a place to rest, psychologys search for a theoryof transfer has taken it to three placesfirst to general transfer theories whichwere too soft, then to specific transfer theories which were too hard, and finallyto a hybrid theory of specific transfer of general knowledge which seems to be

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718 MAYER

just right. Thus psychology enters the new millennium equipped with a potentiallypowerful conception of transfer, and one that drives the successful new field ofpsychology of subject matter. In particular, the search for what to teach has movedfrom general habits to specific responses, and finally to general principles andconceptions that apply to a particular domain. For example, in arithmetic insteadof teaching Latin or geometry as a way to discipline the mind (i.e., general trans-fer), or solely memorizing arithmetic facts or procedures (i.e., specific transfer),instruction includes a focus on underlying concepts such as a mental number linethat helps students understand a wide array of addition and subtraction problems(i.e., specific transfer of general knowledge).

Cognitive task analysis is the primary tool of researchers in the field of psychol-ogy of subject matter. The goal is to identify the cognitive processes and knowledgerequired to accomplish basic academic tasks. Once the underlying processes, con-ceptions, principles, or strategies have been pinpointed, the goal of instruction isto insure they develop in the minds of learners. In the remainer of this chapter,several representative academic tasks and the cognitive processes underlying themare examined.

TEACHING OF READING FLUENCY:THE TASK OF READING A PRINTED WORD

Learning to read is generally recognized as the single most important task forstudents in the primary grades. Although interest in learning to read has a longhistory dating back to the seminal work of Huey (1908/1968), the pace and fruit-fulness of reading research has blossomed in the past two decades. In this section Iexplore the issue of how a person accomplishes the task of reading a printed word.In short, what does someone need to know in order to read a printed word? Thestarting point in answering this question is to conduct a cognitive task analysisthat is, a description of the cognitive processes that a person would need to gothrough in order to accomplish the task. I review research on three componentprocesses in word reading as shown in Table 1being aware of sound units inwords (i.e., phonological awareness), translating printed words into spoken words(i.e., decoding), and determining the meaning of words (i.e., meaning access).

TABLE 1 Component processes in reading a word

Name Definition

Being aware of sound units Recognizing, producing, and manipulating phonemesDecoding words Converting a printed word into soundAccessing word meaning Finding a mental representation of the words meaning in

ones memory

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Being Aware of Sound Units: Insuring Phonological Awareness

The English language consists of approximately 42 sound units ranging from /a/as in say to /z/ as in zoo. Phonological awareness refers to the processes ofrecognizing, producing, and manipulating the sound units of a language. Examplesof phonological awareness include segmentationthat is, given a spoken wordsuch ascat, the student can produce the three constituent sounds /c/, /a/, and/t/and blendingthat is, given some spoken sounds such as /n/, /i/, and /s/ thestudent can combine them into a spoken word, nice. Other examples includedeletion of the first phoneme (for the spoken word top say it without the /t/),deletion of the last phoneme (for the spoken word same say it without the/m/), substitution of the first phoneme (for the spoken word ball change thebeginning sound from /b/ to /k/), and substitution of the last phoneme (for thespoken word park change the last sound from /k/ into /t/). In sum, as a firststep in word reading, students need to know that words are composed of soundunits (or phonemes), and students need to be able to hear, produce, and manipulatethem.

Children tend to develop phonological awareness through the primary grades.This observation can be called the phonological development hypothesis, which hasbeen examined in a variety of studies. One way to test this hypothesis is to conductcross-sectional studies of the phonological awareness performance of students atvarious ages. For example, when children were asked to segment spoken wordsinto constituent phonemes, almost none of the four-year-olds succeeded whereasmost of the six-year-olds did (Liberman et al. 1974). Similarly, when childrenwere asked to segment spoken words in constituent syllables, approximately halfof the four-year-olds succeeded whereas almost all six-year-olds did (Libermanet al. 1974).

Another way to test the phonological development hypothesis is to conduct lon-gitudinal studies, examining the phonological awareness performance of studentsat various points in their childhood. For example, Juel et al. (1986) gave a batteryof phonological awareness tests to a group of children at several points acrosstheir primary grades, including segmentation, blending, deletion of first phoneme,deletion of last phoneme, substitution of first phoneme, and substitution of lastphoneme. Upon entering first grade, they averaged 35% correct on the phonologi-cal awareness tests, and by the end of first grade they averaged 73% correct. Uponentering second grade, they averaged 83% correct, and by the end of second gradethey averaged 86% correct.

Phonological awareness is a prerequisite to learning to read. This statementcan be called the phonological awareness hypothesis, which has been tested innumerous studies. One way of testing the phonological awareness hypothesis isto compare the phonological awareness performance of good and poor readers.For example, Bradley & Bryant (1978) found that younger good readers per-formed better than older poor readers on tests of phonological awareness such asidentifying which of four words lacked a sound contained in the other four words

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720 MAYER

(e.g., answering that rag is the odd word among sun, sea, sock, rag). Similarly,students who have difficulty learning to read tend to lack phonological awareness(Stanovich 1991).

A second way of testing the phonological awareness hypothesis is to conductlongitudinal studies comparing a childs phonological awareness early in schoolingwith the childs reading performance several years later. For example, Bradley &Bryant (1985) found a strong correlation (r D 0.5) between the scores of four- andfive-year-olds on a phonological awareness test with their scores on a standardizedtest of reading achievement given three years later. In a similar study, childrensphonological awareness scores taken at the beginning of first grade correlatedstrongly with their scores on pronouncing printed words (r D 0.5) or writingspoken words (r D 0.6) at the end of second grade (Juel et al. 1986).

In a review of longitudinal studies testing the phonological awareness hypothe-sis, Wagner & Torgesen (1987) reported 20 cases in which childrens performanceon tests of phonological awareness at an early age correlated strongly with theirperformance on tests of reading achievement at a later age, even when the ef-fects of cognitive ability were controlled. Consistent with the phonological aware-ness hypothesis, Wagner & Torgesen (1987, p. 202) concluded that phonologicalawareness and reading are related independent of general cognitive ability.

A third way of testing the phonological awareness hypothesis is to determinewhether instruction in phonological awareness helps students learn to read. Forexample, some five- and six-year-olds received phonological awareness trainingin 40 ten-minute sessions spread over a two-year period (Bradley & Bryant 1985,1991). In a typical training session, the child was given a picture of a bus andthen asked to pick out the picture starting with the same sound from a group ofpictures. Other students (control group), received 40 ten-minute sessions involvingthe same words but without phonological tasks. When tested at the end of thetwo-year instructional period, students who had received phonological awarenesstraining scored nearly one year ahead of control students on a standardized test ofreaching achievement. When tested five years later, the trained group still scoredhigher than the control group on reading achievement.

In another study, some kindergarteners received 28 twenty-minute sessions onphonological awareness over a seven-week period whereas other kindergarteners(control group) received no phonological awareness training beyond regular class-room activities (Bradley & Bryant 1985). Although both groups scored about thesame on a pretest of phonological awareness, the trained group showed a largegain on a posttest of phonological awareness compared to almost no gain for thecontrol group. Importantly, by the end of the school year 35% of the phonologicalawareness trained group were classified as readers, compared to 7% of the controlgroup.

Other researchers have also found that providing direct instruction in phono-logical awareness (sometimes called phonemic awareness) can help improve laterreading achievement (Bus & van IJzendoorn 1999, Ehri et al. 2001). For example,in a review of 36 published studies, Bus & van IJzendoorn (1999, p. 411) foundconsistent evidence that phonological training reliably enhances phonological

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and reading skills. Similarly, in a review of 52 published studies, Ehri et al.(2001, p. 260) found consistent evidence that phonemic awareness instructionis effective: : : in helping children acquire phonemic awareness and in facilitatingtransfer of phonemic awareness skills to reading.

The study of phonological awareness represents one of the landmark successstories in the annals of psychologies of subject matter. Within the past 20 years,researchers have succeeded in identifying phonological awareness as a prerequisiteskill for learning to read. Goswami & Bryant (1992, p. 49) summarize the story asfollows:

There can be little doubt that phonological awareness plays an important rolein reading. The results of a large number of studies amply demonstrate astrong (and consistent) relationship between childrens ability to disentangleand to assemble the sounds of words and their progress in learning to read: : : .There is also evidence that successful training in phonological awareness helpschildren learn to read: : : . However, it is only the first step.

What happens if students do not build sufficient phonological awareness skillswithin their first few years of primary school? Stanovich (1986, p. 364) describes acausal chain of escalating negative effects in which students with poor phonolog-ical skills have reduced opportunities to develop automaticity in decoding, whichin turn causes them to have to pay more attention to the process of word decoding,leaving less capacity for comprehending what they are reading. Thus, they windup with a more limited vocabulary and knowledge base, both of which are neededfor reading comprehension. Phonological awareness trainingeven as little as 5to 18 hours of direct instructionattempts to break this chain and give students achance to become proficient readers.

Decoding Words: Building Automatic Phonics Processing

The English language consists of 26 letters that, in various ways, are related to 42sounds. Decoding refers to the process of converting a printed word into a sound.Thus, decoding consists of pronouncing printed words but does not necessarilyinvolve knowing what the words mean. Examples include giving a student a printedword (such as CAT) and asking the student to read it aloud (such as sayingcat) or giving the student a printed pseudoword (such as BLUD) and askingthe student to read it aloud (such as saying blood).

Development of automatic decoding processing (i.e., being able to decode wordswithout using conscious mental effort) is a prerequisite for success in reading. Thiscan be called the decoding hypothesis, and is based on the idea that attentionalcapacity is limited. When it must be used to decode words, it cannot be used tomake sense of the material. Consistent with the decoding hypothesis, third- andfifth-grade students who scored high on a standardized test of reading compre-hension were much faster in pronouncing pseudowords or unfamiliar words thanwere students who scored low on reading comprehension (Perfetti & Hogaboam1975).

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A second way of testing the decoding hypothesis is to teach students how todecode so the decoding process becomes automatic. For example, asking studentsto read and reread a passage aloud until they make no errors (i.e., the methodof repeated reading) is a useful way to build decoding automaticity (Dowhower1994, Koskinen & Blum 1986, Samuels 1979). Overall, the preponderance ofresearch shows that children need to develop fast and automatic word decodingprocesses before they can become proficient in reading comprehension (Mayer2003). Even in learning a second language, decoding skill in ones native languageis a major predictor of decoding skill in ones second language, which in turn isa major predictor of reading comprehension in ones second language (Meschyan& Hernandez 2002).

Perhaps the most contentious debate in the field of reading instruction concernswhether to use a phonics or a whole-word approach for teaching students howto decode words (Adams 1990; Chall 1983, 2000; Pressley 1998). In the phon-ics approach, children learn to produce the sounds for individual letters or lettergroups and to blend those sounds together to form a word. In the whole-wordapproach, children learn to pronounce a word as a single unit, which can be calledsight-reading. Fortunately, the great debate has been subjected to a great amountof careful research, and the results clearly show that some instruction in phon-ics is needed for the development of reading achievement (Adams 1990; Chall1983, 2000; Pressley 1998). Almost all observers call for a balanced approach thatincludes aspects of phonics and whole-word instruction (Pressley 1998).

The study of decoding represents another success story in the annals of psy-chologies of subject matter. Within the past 20 years, researchers have reachedconsensus that balanced instruction including phonics promotes decoding auto-maticity, which is needed for success in reading.

Accessing Word Meaning: Fostering a Rich Vocabulary

The third component process in word reading is meaning access, which refersto finding a mental representation of the meaning of a word in ones memory.Meaning access depends on having a rich vocabulary, such as knowing that catrefers to a four-legged furry creature that purrs.

Less-skilled readers are more likely to rely on the sentence context when readinga word than are more-skilled readers (West & Stanovich 1978). In short, skilledreaders have automatized their meaning access processing so that when they reada word they effortlessly know what it means without having to use context cues tofigure it out. When meaning access does not require attentional capacity, readerscan use all of their attention for making sense of the passage.

The vocabulary hypothesis is that having a strong vocabularywhich allowsreaders to access word meaning effortlesslypromotes performance on tests ofreading comprehension. In support of this hypothesis, Anderson & Freebody(1981) reported that children who have better vocabularies perform better ontests of reading comprehension, and Meschyan & Hernandez (2002) report a high

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correlation between vocabulary test score and reading comprehension test score.Similarly, students perform better on tests of reading comprehension when unfa-miliar words are replaced with more familiar synonyms (Marks et al. 1974).

It is estimated that young readers need to increase their vocabularies by at least2000 words per year (Nagy & Scott 2000). What is the best way to promote arich vocabularythat is, fast and effortless word recognition? On the one hand,direct instruction involves teaching the definitions of a core set of words, whereason the other hand immersion involves asking students to engage in many literateactivities such as reading. Direct instruction is most effective when students areencouraged to use the words in familiar contexts and improves reading comprehen-sion only in passages that include the newly learned words (Beck et al. 1982, Stahl& Fairbanks 1986). Yet, according to Nagy & Herman (1987), it is not possiblefor students to achieve the full vocabulary growth they need each year solely viadirect instruction, so immersion is the only reasonable alternative. According tothis view, students must learn the bulk of new vocabulary words through reading,listening to, or producing prose. Less research has been conducted on vocabu-lary learning than on processes in the foregoing sections, so continued work isneeded.

TEACHING OF READING COMPREHENSION:THE TASK OF COMPREHENDING A PASSAGE

The previous section focused on learning to read (reading fluency); this section fo-cuses on reading to learn (reading comprehension). Reading comprehension is theprocess of making sense out of a text passage, that is, building a meaningful mentalrepresentation of the text. This process of active learning occurs when a reader (a)selects relevant information from a text passage, (b) organizes the incoming mate-rial into a coherent mental representation, and (c) integrates the incoming materialwith existing knowledge. What does someone need to know in order to understanda passage, that is, engage in active learning? Four cognitive processes are involvedin reading comprehension: using prior knowledge (which involves the process ofintegrating), using prose structure (which involves the processes of selecting andorganizing), making inferences (which involves the processes of integrating andorganizing), and using metacognitive knowledge (which involves the monitoringof cognitive processing). These processes are summarized in Table 2.

Using Prior Knowledge: Teaching Readersto Integrate Knowledge

The readers prior knowledgeincluding his or her storehouse of schemasconstitutes the single most important factor underlying individual differences inreading comprehension. According to schema theory, reading comprehension isa process of assimilating presented information to existing knowledge, so the

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TABLE 2 Component processes in comprehending a passage

Name Definition

Using prior knowledge Activating and assimilating to existing schemasUsing prose structure Distinguishing important and unimportant material

Organizing material into a coherent structureMaking inferences Adding appropriate inferences to the materialUsing metacognitive knowledge Determining whether the passage makes sense

outcome of learning depends both on what was presented and the readers existingknowledge. Thus, in order to make sense of a passage, a reader must possess anduse relevant schemas.

For example, in Bartletts (1932) classic study, students who recalled an unfa-miliar folk story they had read tended to leave out many details (leveling), embellishparticularly distinctive details (sharpening), and reorganize the story on the basisof a theme such as a war battle or hunting accident (rationalization). Accordingto Bartlett, students dropped all references to a spirit world because these didnot fit their existing schemas and students reorganized the story so it would fitwith an existing schema. Classic cognitive studies have confirmed that studentsperform more poorly on reading comprehension tests when they lack appropriateprior knowledge (Bransford & Johnson 1972) and that different material is learneddepending on the prior knowledge used by the reader (Pichert & Anderson 1977).

In spite of their skill in reading fluency, young readers often lack appropriateschemas to understand prose (Gernsbacher 1990). For example, American ele-mentary school children had difficulty in reading about the history of the Frenchand Indian War (Beck et al. 1991). However, when the passage was reframed asa conflict in which both France and England claimed the same piece of land, stu-dents could use a familiar schema (i.e., a fight between two sides that both wantthe same thing) to make sense of the passage. Students learned much more fromthe passage if they read the reframed version (Beck et al. 1991) or received someequivalent background information before reading the original passage (McKeownet al. 1992). A major theme of research on prior knowledge is that reading materialshould be appropriate for the interests and experience of the reader.

Using Prose Structure: Teaching Readers to Selectand Organize Knowledge

The second process in Table 2 is the ability to use prose structure (e.g., the hierarchi-cal organization of ideas), including recognizing the difference between importantideas and minor details. Beginning readers often lack sensitivity to prose structure.When asked to read and recall material from a text passage, younger readersand less-skilled readers tend to remember important and unimportant information

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equally well whereas older and more-skilled readers tend to remember importantinformation better than unimportant information (Brown & Smiley 1977, Taylor1980). Similarly, older readers and more-skilled readers spend more time readingsentences with topic shiftsusually the first sentence in a passage or sectionthando younger or less-skilled readers (Gernsbacher 1990, Hyona 1994).

Can readers be taught to use prose structure during reading? One technique is toteach students how to outline or summarize passages. For example, Chmielewski& Dansereau (1998) taught some students how to outline a passage as a conceptmapconsisting of nodes and linkswhereas other students received no training.On a subsequent reading task in which no note taking was allowed, the mappinggroup performed much better on a retention test than did the control group. Sim-ilarly, Cook & Mayer (1988) taught students how to outline textbook paragraphsbased on prose structures such as classification (e.g., breaks material into cate-gories as in a hierarchy), sequence (e.g., describes a step-by-step process as ina flow chart), and comparison (e.g., compares two or more things along severaldimensions as in a matrix). Students who received structure training performedbetter on understanding new text passages than did control students. Finally, stu-dents who were told to take notes by filling in a compare/contrast matrix learnedmore from a lecture than students who were told to take conventional notes (Kiewraet al. 1991). Overall, less-skilled readers benefit from direct instruction in how toorganize incoming material.

Making Inferences: Teaching Readers to Integrateand Organize Knowledge

The third process in Table 2 is inference-making. Weaver & Kintsch (1991) esti-mate that readers may need to make as many as a dozen inferences to understanda sentence in a passage. Although researchers recognize that the ability to makeinferences is a cornerstone of reading competence (Winne et al. 1993, p. 53),young readers are notoriously poor at making inferences during reading (Oakhill& Yuill 1996). For example, kindergarteners are less likely than are fourth gradersto make inferences while listening to sentences, such as inferring that a key wasused for the sentence, Our neighbors unlocked the door (Paris & Lindauer 1976).Similarly, in reading a story about a boy reaching for a heavy cookie jar that was ona high shelf just as the door opened, older readers were more likely than youngerreaders to infer that the boy was caught in the act of doing something he was notsupposed to do (Paris & Upton 1976).

Can students be taught to make appropriate inferences while reading? In aseries of classroom studies, practice in making inferences about text passagesspread over five weeks improved the reading comprehension of second gradersand poor-reading fourth graders but not good-reading fourth graders (Hansen 1981,Hansen & Pearson 1983). In a similar study, primary grade children received seven30-minute training sessions on inference making such as generating questions thatcould be answered by a text (Oakhill & Yuill 1996). For poor readers, the trained

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group showed an improvement in reading comprehension as compared to a controlgroup, but for good readers the training had no effect. Finally, Winne et al. (1993)provided nine sessions of inference training to poor comprehenders in grades 4through 6, including asking students to answer inference questions about a passageand then providing correct answers. The trained group showed improvements inreading as compared to other groups. Overall, there is encouraging evidence thatstudents can learn to improve their inference-making skills.

Using Metacognitive Knowledge: Teaching Readersto Monitor Processing

The final process listed in Table 2 is using metacognitive knowledge, that is, knowl-edge of ones cognitive processing. The most important metacognitive process inreading is comprehension monitoringthe process of recognizing when a passagedoes not make sensebut elementary school children are not good at it. Markman(1979) found that elementary school children in grades 3, 5, and 6 did not recog-nize inconsistencies in passages, such as that there is no light at the bottom ofthe ocean and fish that live at the bottom of the ocean can see the color of theirfood. Similarly, most third graders did not recognize inconsistencies in a passagesuch as statements about a strainer that water passes through the holes and thespaghetti stays in the strainer and the spaghetti passed through the holes in thestrainer into the bowl and the water stayed in the strainer (Vosniadou et al. 1988).

Can students be taught to monitor their comprehension? There is encouragingevidence that students can learn to improve their comprehension monitoring skills.For example, Rubman & Waters (2000) asked students to represent a passage byplacing figures on a magnetic board or to simply read the passage. Low-skill thirdand sixth graders in the storyboard construction group were much more likely torecognize inconsistencies than those in the read-only group, and weaker effectswere found for the high-skill third and sixth graders. Similarly, Markman & Gorin(1981) found that 8- and 10-year-olds were better able to recognize inconsistenciesin a passage after being shown examples in other passages. In addition, third graderswho received examples as well as direct instruction in how to use comprehension-monitoring strategies performed particularly well on recognizing inconsistenciesin passages as compared to nontrained students (Elliot-Faust & Pressley 1986).

TEACHING OF WRITING: THE TASK OF WRITINGA COMPOSITION

What are the cognitive processes involved in writing a composition? In order toanswer this question, Hayes & Flower (1980) asked students to think aloud as theywrote an essay on a topic such as How I spent my summer vacation. In analyzingthe writers thinking-aloud protocols, Hayes & Flower identified three cognitiveprocesses in writing: planning, in which the writer remembers or finds relevantinformation, decides how to organize it, and sets goals for how to communicate

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TABLE 3 Component processes in writing a composition

Name Definition

Planning Remembering or finding relevant information,deciding how to organize it, and setting goalsfor communicating with the audience

Translating Producing printed text on paper or screenReviewing Detecting and correcting errors in the text

with the audience; translating, in which the writer produces text; and reviewing, inwhich the writer detects and corrects errors in the text. This analysis is similar toothers (Gould 1980, Kellogg 1994), including a revised model by Hayes (1996),and is summarized in Table 3.

Planning: Teaching Writers to Find, Organize,and Adapt Material

A major cognitive process in writing an essay is planning, which includes thesubprocesses of generating (i.e., recalling relevant information from ones memoryor locating relevant information from external sources), organizing (i.e., figuringout how to organize the material in a coherent way), and goal setting (i.e., evaluatingthe material against criteria such as appropriateness for the audience).

Gould (1980) found that adults who were asked to write a short business letterspent about two thirds of their time in pausesgenerally after long clauses orsentenceswhich suggests that most of the time was spent in local planning. InGoulds study the writers did not show long pauses before they startedindicatinga lack of global planningand did not spend much time revising what they hadwritten. Matsuhashi (1982) obtained similar results in watching high school stu-dents write essays. Apparently, when the task is very simple or the writers areinexperienced, there is not much global planning.

Bereiter & Scardamalia (1987) identified a developmental trend in planningactivities for writing in which children entering elementary school dont gener-ate many ideas, older elementary school children generate many ideas but failto organize or evaluate them (i.e., knowledge telling), and older high school stu-dents generate a lot of ideas that they also evaluate and organize (i.e., knowledgetransforming).

Can students be taught to engage in prewriting activities that foster appropriateplanning processes? Kellogg (1994) asked college students to write an essay ona given issue. Before starting to write the essay, they were told to write as manyideas as they could think of (generating group), to write a list of important ideas(listing group), to produce a hierarchical outline (outline group), or were given noinstructions (no prewriting activity group). Students in the outline group producedhigher quality essays than students in any of the other groups. When students are

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instructed to engage in planning processesincluding generating, evaluating, andorganizing ideasthey write better essays.

Another way to foster the planning process is to ask students to write aboutfamiliar topics. For example, Caccamise (1987) reported that students producedmore ideas when planning to write about a familiar topic than an unfamiliar one.Overall, students need to have access to material that they have organized andthought about.

Translating: Helping Writers Overcome Cognitive Load

In the process of translating, the writer carries out the writing plan by producingwritten text. Writers tend to alternate between cognitive processes such as planningand translating, by generating a plan, writing a little bit, then checking the plan,and so on (Hayes & Flower 1980).

Translating demands conscious attention. According to Nystrand (1982), thewritten text should be legible, grammatical, meaningful, coherent, and appropriatefor the intended audience. If writers focus their attention on lower level aspectsof translatingsuch as writing legible and grammatical sentencesthey may nothave sufficient remaining attentional capacity to handle higher level aspects oftranslatingsuch as writing an essay that makes sense and influences the reader.One way to remove low-level constraints on translating is to allow students todictate an essay. For example, fourth- and sixth-grade students who were asked todictate an essay generated more words and slightly better essays than students whowere asked to write an essay by hand (Bereiter & Scardamalia 1987). Consistentwith the constraint removal idea, Read (1981) has shown that even six-year-oldscan writing interesting stories when they are told to not worry about spelling,punctuation, or grammar.

In a related study, students were asked to write a preliminary draft followed bya final draft (Glynn et al. 1982). Students who were told to write a polished prelim-inary draft (i.e., paying attention to spelling, punctuation, and grammar) generatedlower quality final drafts than did students who were told to write unpolished pre-liminary drafts (i.e., not paying attention to spelling, punctuation, and grammar).Apparently, students in the unpolished draft group could devote more attentionto writing a powerful essay because they did not have to focus their attention onlow-level aspects of translating.

Using a word processor may be another way to remove low-level constraintson translating. For example, students generated higher quality essays when theyused a word processor than when they wrote in longhand, but only if they wereexperienced in using the word processor (Kellogg & Mueller 1993). In a review,Bangert-Drowns (1993) found that the advantage for word processors was greaterfor younger writers who were experienced with using word processors. However,for more experienced writers, the quality of essays was generally equivalent withword processors or pens (Bangert-Drowns 1993, Kellogg 1994). Apparently, whenthe output device (handwriting or word processing) requires undue attention andthe writing task itself is demanding, the quality of the final product can suffer.

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Reviewing: Helping Writers Detect and Correct Errors

Reviewing refers to detecting errors in a written text and correcting them. Whenasked to write an essay, college freshmen spent less than 10% of their time onreading or revising what they wrote (Pianko 1979). Similarly, when asked to writea one-page business letter, managers also spent less than 10% of their time readingor revising what they wrote (Gould 1980). Most of the corrections students makeare surface and mechanical revisions rather than improvements in the organizationor effectiveness of the text (Fitzgerald 1987). Even when middle school studentsare required to revise their essays, they fail to detect most of their mechanicalsyntax errors (e.g., subject-verb disagreement) and referent errors (e.g., misuseof a pronoun) and fail to correct most of the errors they detect (Bartlett 1982).Overall, there is clear and compelling evidence that students could benefit fromtraining in how to revise their essays.

Revision training focuses on helping students become more effective in thereviewing process. McCutchen et al. (1997, McCutchen 2000) reported that sev-enth graders were more successful in correcting errors in meaning from an essayon a familiar topic (e.g., Christopher Columbus) than an unfamiliar topic (e.g.,Margaret Mead). When the teacher highlighted sentences with mechanical errors,seventh graders focused more on mechanical errors and less on errors in mean-ing. Apparently, young writers are easily distracted from the task of detecting andcorrecting errors in meaning.

In an exemplary study, Fitzgerald & Markman (1987) gave sixth graders a se-ries of thirteen 45-minute sessions on how to make additions, deletions, substitu-tions, and rearrangements in compositions (i.e., revision training). On a subsequentwriting assignment, students who had received direct instruction in these revisionactivities made more revisions and produced higher quality written products thandid untrained sixth-grade students who spent an equivalent amount of time readingfine literature.

TEACHING OF MATHEMATICS: THE TASKOF SOLVING A WORD PROBLEM

What does someone need to know in order to solve an arithmetic word problemsuch as: At Lucky, butter costs 65 cents per stick. Butter at Vons costs 2 cents lessper stick than butter at Lucky. If you need to buy 4 sticks of butter, how much willyou pay at Vons? Table 4 lists four cognitive processes in mathematical problemsolving: translating, integrating, planning, and executing (Mayer 1992).

Problem Translating: Teaching Students toRepresent Sentences

In translating, the problem solver converts each sentence into an internal mentalrepresentation. This process requires linguistic knowledge (such as knowing thatVons and Lucky are proper nouns) and factual knowledge (such as knowing that

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TABLE 4 Component processes in solving an arithmetic word problem

Name Definition

Translating Converting each sentence into an internal mental representationIntegrating Building a coherent mental representation of the problem situationPlanning/monitoring Devising a solution plan and keeping track of how well it worksExecuting Carrying out a solution plan

there are 100 cents in a dollar). For example, the first sentence can be mentallyrepresented as Lucky D 0.65, the second sentence as Vons D Lucky 0.02,and the third as Total Cost D 4 Vons. Research shows that people have aparticularly difficult time in translating relational statements, that is, sentences thatexpress a quantitative relation between two variables (such as the second sentence).For example, when primary grade children were asked to listen to and repeat backa problem such as Joe has three marbles. Tom has five more marbles than Joe.How many marbles does Tom have? they sometimes recalled the problem as Joehas three marbles. Tom has five marbles. How many marbles does Tom have?(Riley et al. 1982). Similar results were found when college students were asked toread and recall a list of eight word problems (Mayer 1982). When college studentswere asked to write an equation to represent relational sentences such as There aresix times as many students as professors at this university, they wrote the wrongequation (e.g., 6S D P) about one third of the time (Soloway et al. 1982). Hegartyet al. (1995) found that poor problem solvers were particularly prone to errors inremembering relational statements as compared to successful problem solvers.

These results demonstrate that students need instruction in how to representthe sentences in word problems, particularly relational sentences. In an exemplarytraining study, college students who had difficulty in solving word problems re-ceived two 30-minute training sessions in how to represent the sentences in wordproblems on a number line (Lewis 1989). As a result, their error rates on solvingword problems fell dramatically as compared to students who had not received thetraining. In a school-based study, middle school students participated in a 20-dayprealgebra unit that emphasized translating relational sentences into tables, graphs,equations, and their own words (Brenner et al. 1997). Students who participatedshowed larger gains in solving word problems than did students who receivedconventional instruction.

Problem Integrating: Teaching Students to UseProblem Schemas

A sentence-by-sentence translation of each sentence in a word problem is a goodfirst step, but the ultimate goal in understanding a problem is to build a situationmodelthat is, a mental representation of the situation being described in the

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problem (Kintsch & Greeno 1985, Mayer & Hegarty 1996, Nathan et al. 1992).Problem integrating occurs when a problem solver builds a mental representation ofthe situation described in the problem. The process of integrating requires that theproblem solver select relevant information from the problem statement, organizeit into a coherent representation, and make necessary inferences (Mayer 1992).Integrating depends on schematic knowledgethat is, knowledge of problem types(such as knowing that the butter problem is a total cost problem in which totalcost D unit cost number of units).

When high school students were asked to sort word problems into categories,they showed high levels of agreement and were quite fast in their decisions (Hinsleyet al. 1977). Overall, 18 categories were created, such as distance-rate-time prob-lems, work problems, and area problems, which suggests that the students haddeveloped schemas for common types of word problems. In a related study, Mayer(1981) identified approximately 100 types of word problems in some commonlyused middle-school mathematics textbooks, including varieties of the categoriesfound by Hinsley et al. (1977). When students were asked to read and then recall alist of eight word problems, they made more errors in recalling rare problem types(i.e., those appearing infrequently in textbooks) than common problem types (i.e.,those appearing frequently in textbooks) (Mayer 1982).

Experts and novices differ in the way they sort word problems. For example,Quilici & Mayer (1996) found that students who lacked experience in statisticstended to sort statistics word problems based on cover story (such as grouping allproblems about rainfall) whereas students who had taken several statistics coursestended to sort statistics word problems based on the type of statistical test involved(such as grouping all t-test problems). Similarly, seventh graders who are poorproblem solvers tend to sort problems on the basis of the cover story (such asputting together all problems about money) whereas good problem solvers tend tosort problems on the basis of the underlying mathematical structure (Silver 1981).

Successful and unsuccessful problem solvers tend to engage in different cog-nitive processes while reading word problems (Lewis & Mayer 1987, Verschaffelet al. 1992). Unsuccessful problem solvers tend to focus on the numbers in theproblem and to use the keywords in the problem to determine what operation toapply (e.g., less than primes subtraction). For example, in the following problemthe keyword less than primes the incorrect arithmetic operation of subtracting 2from 65: At Lucky, butter costs 65 cents per stick. This is 2 cents less per stickthan butter at Vons. If you need to buy 4 sticks of butter, how much will you pay atVons? Unsuccessful problem solvers are more likely to give the incorrect answer,(0.65 0.02) 4 D 2.52, for this version of the problem, but they tend to givethe correct answer for a version in which the keyword primes the correct arithmeticoperation (e.g., At Lucky, butter costs 65 cents per stick. Butter at Vons costs 2cents less per stick than butter at Lucky. If you need to buy 4 sticks of butter, howmuch will you pay at Vons?). In contrast, successful problem solvers give thecorrect answer for both versions of the problem (Hegarty et al. 1995, Mayer &Hegarty 1996, Verschaffel et al. 1992). Eye movement studies (Hegarty et al. 1995)

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show that unsuccessful problem solvers spend more time looking at the numbersand keywords (e.g., 65, 2, less than, 4, how much) in a word problem whereassuccessful problem solvers spend more time looking at the variable names (e.g.,Lucky, Vons). The unsuccessful problem solvers appear to be engaging in a processof number grabbing or direct translation whereas the successful problem solversappear to be building a situation model (Mayer & Hegarty 1996). Consistent withthis distinction, Low & Over (1989) found that problem solving scores correlatedhighly with students scores on detecting missing or irrelevant information in wordproblems.

There appears to be a developmental trend in which students create more dif-ferentiated problem schemas as they gain more experience. For example, kinder-garteners seem to know cause/change problems (Pete has two marbles. Tim giveshim three more marbles. How many marbles does Pete have now?), but as childrengain more experience over the next few years, they distinguish other types, such ascombination problems (Pete has two marbles. Tim has three marbles. How manydo they have altogether?) and comparison problems (Pete has two marbles. Timhas three more marbles than Pete. How many marbles does Tim have?) (Rileyet al. 1982).

Students can learn to build situation models, that is, coherent representations ofthe situation described in the problem. For example, Low (1989) taught students todetect whether word problems contained irrelevant information, needed additionalinformation, or neithera task that requires students to build a coherent situationmodel of the problem. Students who received training showed large improvementsin their word problem solving performance as compared to students who receivedno instruction. In another training study, students who received training in how touse a computer program to represent a word problem as an on-screen animationperformed better on a subsequent word problem solving test than did students whopracticed solving word problems (Nathan et al. 1992). In short, students benefitfrom training aimed at helping them learn to translate a word problem into asituation model.

Solution Planning and Monitoring: Teaching Studentsto Devise Solution Plans

The third cognitive process in Table 4 is planning and monitoring, in which thestudent devises a solution plan and keeps track of how well it works during problemsolving. Planning is based on strategic knowledge, that is, general strategies suchas finding a related problem, restating the problem in a different way, and breakingthe problem into subgoals (Mayer 1992, Schoenfeld 1985). When students receiveinstruction and practice in how to carry out planning strategies such as these,they perform better on a subsequent word problem-solving test than subjects whosimply practice solving the problems (Schoenfeld 1985).

Worked-out examples are step-by-step descriptions of how to solve exampleproblems and are commonly found in mathematics textbooks (Mayer et al. 1995).

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Reed (1999) has shown that students need support in how to use worked-out exam-ples, including verbal explanations for each step and instructions for when to use aparticular worked-out example. Catrambone (1995) has shown that students benefitwhen each subgoal is explicitly labeled and explained in worked-out examples.

Students attitudes can influence their problem-solving strategies. Some stu-dents believe that word problems are solved by applying meaningless procedures,which can be stated as follows: Ordinary students cannot expect to understandmathematics; they expect simply to memorize it and apply what they have learnedmechanically and without understanding (Schoenfeld, 1992, p. 359). For exam-ple, many third-grade students believe that all story problems can be solved byapplying the operations suggested by the key words present in the story, e.g., in allsuggests addition, left suggests subtraction, share suggests division (Lester et al.1989, p. 84). A recent national survey of U.S. mathematics students revealed that54% of the fourth graders and 40% of the eighth graders thought that the bulk ofmathematics learning consists of memorizing rules (Silver & Kenney 2000).

Verschaffel et al. (2000) have shown how mathematics students from all overthe world often solve math word problems by manipulating symbols without un-derstanding what they are doing. They seek to carry out an arithmetic computationwithout trying to make sense of the problem, a strategy that Schoenfeld (1991, p.316) calls suspension of sense-making. In contrast, a key to successful problemsolving is the development of what can be called a productive disposition, thatis, an inclination to see mathematics as sensible, useful, and worthwhile, coupledwith a belief in diligence and ones self-efficacy (Kilpatrick et al. 2001, p. 5).

Students can learn productive planning strategies by working on realistic mathproblems in authentic settings. For example, in the Jasper project, students view avideo that describes an adventure story in which some decisions need to be madebased on mathematical computations (Bransford et al. 1996, Van Haneghan et al.1992). Students who received practice in developing strategies for solving theJasper problems showed larger gains in solving word problems than did matchedstudents who received regular classroom instruction.

Solution Execution: Teaching Students to CarryOut Procedures

The fourth process in Table 4 is solution-executing, that is, carrying out a solutionprocedure. Solution executing requires procedural knowledge, that is, algorithmssuch as how to add, subtract, multiply, and divide (Mayer 1992).

Fuson (1992) has described how childrens skill in solving simple additionproblems (such as 2 C 4 D 6) develops from counting-all procedures (such ascounting 1, 2, pause, 3, 4, 5, 6), to counting-on procedures (such as starting with2 and then counting on 3, 4, 5, 6), to derived facts procedures (such as I cantake 1 from the 4 and give it to the 2, and I know 3 plus 3 is 6), to known facts(such as memorizing that 2 plus 4 is 6). For example, Groen & Parkman (1972)used a reaction-time paradigm to find that most first graders use a counting-on

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procedure for simple addition. Siegler & Jenkins (1989) have shown that primary-grade children have a variety of procedures available for simple addition problemsand select the one that best fits any particular problem. Brown & Burton (1978)found that students errors in solving three-column subtraction problems occurbecause students are correctly applying an incorrect procedurea procedure thathas one or more bugs (incorrect steps) in it.

Students can learn procedures as a meaningless sequence of steps. To helpthem understand what they are doing, students need to see how procedures arerelated to concrete situations and concepts. For example, concrete manipulativesare concrete objects used to represent steps in arithmetic procedures, such as usingsticks bundled by tens (English 1997, Resnick & Ford 1981). In a research re-view, Hiebert & Carpenter (1992, p. 70) concluded the effectiveness of concretematerials in classrooms have yielded mixed results. More recently, Moreno &Mayer (1999) found that childrens learning of addition and subtraction of signednumbers was improved when they played with an educational game that repre-sented the steps visually as a bunny moving along a number line. Schwartz et al.(1996) found similar improvements in students skills on addition and subtractionof signed numbers when they practiced using a computer-based image of a trainof various lengths along a number line.

Case and his colleagues (Case & Okamoto 1996; Griffin et al. 1994, 1995) haveshown that skill in applying arithmetic procedures (such as solving the problem2 C 4 D 6) is linked to the childs conceptual understanding of a mental numberline (as measured by telling which of two numbers is larger, moving a tokenalong a number line for a specified count, and so on). For example, about 50%of the students in Cases studies entered school without adequate knowledge of amental number line. When students were given 40 short lessons involving explicitinstruction in using a mental number line (such as moving a token along a path for aspecified number of steps in a board game), they showed a great improvement bothin their ability to a use a mental number line (which can be called number sense)and in their ability to learn arithmetic. In a review, Bruer (1993, p. 90) concludesfor mathematics to be meaningful, conceptual knowledge and procedural skillshave to be interrelated in instruction.

TEACHING OF SCIENCE: THE TASK OFUNDERSTANDING HOW THINGS WORK

What are the cognitive processes involved in scientific reasoning? According to thetraditional view, science learning involves adding knowledge to memory. In con-trast, according to the conceptual change view, science learning involves changingones mental model of how something works (Limon & Mason 2002, Posner et al.1982). A mental model is a cognitive representation of the functional parts of a sys-tem and the cause-and-effect relations showing how a change in the state of one partaffects a change in the next one (Gentner & Stevens 1983, Halsford 1993, Mayer

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TABLE 5 Component processes in understanding how a scientific system works

Name Definition

Recognizing an anomaly Realizing that ones mental model is flawedCreating a new model Mentally constructing a new mental modelUsing a new model Using a mental model to test hypotheses in research

1992). Three important steps in conceptual change are: (a) recognizing an anomaly(i.e., realizing that ones current mental model is not able to explain the observablefacts), (b) constructing a new model (i.e., creating a model that is able to explain theobservable facts), and (c) using a new model (i.e., making and testing predictionsof the model in new situations). These three processes are summarized in Table 5.

Recognizing an Anomaly: Teaching byConfronting Misconceptions

The first step in conceptual change is to recognize that ones conception of howsomething works does not square with the available data. In short, rather than start-ing as blank slates, people enter the science classroom with mental models of howthe world works, and often their mental models are incorrect. For example, manypeople harbor misconceptions (or preconceptions) about the laws of motion, suchas predicting that a ball shot through a curved tube will continue to curve once itexits from the tube (McCloskey et al. 1980), an object traveling at a constant speedover a cliff will continue moving horizontally and then fall straight down (Kaiseret al. 1985, McCloskey 1983), or that a ball dropped by a running person willfall straight down (McCloskey 1983). In short, many people believe in impetustheorythe idea that an object moves only when a force is acting on italthoughschool-taught Newtonian theory is that an object continues moving unless a forceacts on it.

Can students be taught to recognize their misconceptions? Clement (1982)found that a conventional course in physics did little to eliminate students miscon-ceptions. However, Chi (2000) asked some students to engage in self-explanationsas they read a text on how the human heart worksthat is, they explained the textaloud as they read it. Most students began with a flawed mental model of the heartthat Chi calls the single-loop model, i.e., the idea that the arteries carry blood fromthe heart to the body (where oxygen is collected and waste is deposited) and veinscarry blood from the body to the heart (where it is cleaned and reoxygenated). Stu-dents who engaged in self-explanations were more likely to recognize that theirmental model conflicted with the information presented in the text, such as theright side pumps blood to the lungs and the left side pumps blood to other parts ofthe body.

In a classroom study, fifth and sixth graders were asked to make predictions,then take measurements, and explain why the measurements conflicted with their

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predictions (Vosniadou et al. 2001). For example, after trying to pull a heavy ta-ble that they could not move, students concluded that no force was acting on thetableconsistent with impetus theory. However, when they used a dynamometer,they measured a considerable force being exerted on the table by their pulling. Inthe ensuing classroom discussion, students had to reconcile the conflicting infor-mation that an object can be nonmoving and still have a force exerted on it. Studentswho participated in these kinds of cognitive conflict episodes showed greater im-provements in solving physics problems than did nontrained students. Overall,research on recognizing misconceptions shows that cognitive conflict seems tobe the starting point in the process of conceptual change (Limon 2001, p. 373).

Constructing a New Model: Teaching by Providinga Concrete Analogy

Once learners recognize that their models are flawed, the next step is to build anew model (as shown in the second process in Table 5). According to the Posneret al. (1982) the new model should be intelligible (i.e., the learner understands it),plausible (i.e., the learner can reconcile the model with the available data and otherknowledge), and fruitful (i.e., the learner can use the model in new situations).Gentner (1989) proposed that students understand how a new system works byrelating it to a familiar system. For example, Gentner & Gentner (1983) found thatsome students understand an electrical circuit is like a water-flow system in whichthe wires are like pipes, the electrons are like water, the battery is like a pump, andthe resistor is like a constriction in a pipe.

One way to foster the process of model construction in students is to provideconcrete representations of the model. For example, adding pictorial models totextbook passages or animated models to online narration helps students under-stand how various systems work, such as brakes, pumps, lungs, and lightningstorms (Mayer 1989, 2001). In a focused set of studies, students learned Newtonslaws of motion by playing various video games in which a ball could be kickedin any direction using a joystick (White 1993, White & Frederiksen 1998). In themicroworld called ThinkerTools, the balls behaved in line with the laws of mo-tion, and students were asked to discuss the validity of various possible ways todescribe the laws. Students who participated in the ThinkerTools microworld fordaily 45-minute sessions over a two-month period showed fewer misconceptionsabout the physics of motion than did control students. Overall, experience withfamiliar, concrete models can help students replace their incorrect mental models.

Using a New Model: Teaching Students Howto Test Hypotheses

The third process in conceptual change is using a new model to make predic-tions in a new situation (as listed in the third line of Table 5). There is consistentevidence that high school students have substantial difficulty in two important

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aspects of scientific reasoninggenerating theories and interpreting data. For ex-ample, Klahr (2000) asked students to figure out what the RPT button did on aprogrammable toy vehicle called BigTrack. They could press any sequence ofbuttons on the control panel and then see what the vehicle did. Most childrenonly considered one theory, ignored conflicting results, and just kept testing thesame theory repeatedly. In a computer-based simulation of a biology experiment(Dunbar 1993), most students began with a theory and ran experiments intendedto confirm the theory (i.e., they engaged in confirmation bias). When the result-ing data conflicted with their theory, most students tended to ignore the resultsand they continued to seek to confirm their theory. Kuhn et al. (1988) found thatstudents were unable to judge whether a piece of data refuted a theory. Otherresearchers have shown that most high school students do not systematically testhypotheses in a way consistent with Piagets formal operations, which is the level ofthinking required for scientific reasoning (Karplus et al. 1979, Lawson & Snitgen1982).

What can be done to improve students skill in testing hypotheses? WhenLawson & Snitgen (1982) provided direct instruction in how to test hypothesesfor biological theories, students showed substantial improvements in their scoreson tests of scientific thinking. In an exemplary study (Carey et al. 1989), seventhgraders participated in a three-week science unit focusing on scientific thinking,including intensive investigations on topics such as Why do yeast, flour, sugar,salt, and warm water produce a gas? Students who participated showed substan-tial improvements in their beliefs about science and scientific research. Overall,there is growing evidence that scientific reasoning can be taught (Halpern 1992,Linn & Hsi 2000).

CONCLUSION

This chapter provides an overview of recent advances in the psychology of subjectmatter. The first step is to clearly define a subject matter domain (such as readingfluency, reading comprehension, writing, mathematics, or science) and within thedomain clearly specify a target task (such as reading a word aloud, comprehending aparagraph, writing an essay, solving an arithmetic word problem, or understandinghow something works). The next step is to conduct a cognitive task analysis,specifying the major cognitive processes required to accomplish the task (such aslisted in Tables 1 through 5). Finally, research is needed to determine how peoplelearn each of the needed cognitive processes, including how to help them learn.

Although the grand learning theories of the early twentieth century have fadedaway (Mayer 2001b), researchers have made progress in understanding how peoplelearn in specific subject areas (Mayer 2002). Research on the psychology of subjectmatter is a prime example of the shift from domain-general cognitive theories todomain-specific cognitive theories. Research on the psychology of subject matteralso exemplifies a shift in research methods for studying how people perform on

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decontextualized sterile laboratory tasks to how people perform on contextualizedrealistic tasks. Finally, research on the psychology of subject matter representsone of educational psychologys greatest success stories. In short, research on howpeople learn subject matter has yielded progress in understanding human learningand cognition.

In closing, I share Shulman & Quinlans (1996, p. 420421) recent assessmentof the field: As we approach the 21st century, we can anticipate the return of thepsychology of school subjects to its former centrality in educational psychology.However, unlike earlier attempts to study the teaching of school subjects, psychol-ogy comes equipped with techniques for analyzing and describing the knowledgeunderlying academic performance (Anderson et al. 2001).

AUTHOR NOTE

For an expanded review of this material, see Mayer 2003.

The Annual Review of Psychology is online at http://psych.annualreviews.org

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