A computer-based strategy for personalizing verbal problems in teaching mathematics

A Computer-Based Strategy for Personalizing Verbal Problems in Teaching Mathematics

Steven M. Ross Padma G. Anand

Steven M. Ross is Professor, Foundatums, at Memphis State University, Mem~is, TN 38152 and Padma G. Anand is Assistant Professor, Educational Psychology, Slippery Rock State University, Slippery Rock, PA 1605Z

The purpose of this study was to evaluate o computer-based strategy for personalizing verbal problems used in mathematics instruction. Personalization was achieved through a computer program that incorporated names of familiar people and events, such as the student's friends and birth date, into print copies of lesson examples. In two control treotments, concrete (nonadaptive) contexts and abstract contexts were employed. Subjects were 54 fifth- and sixth- graders studying a lesson on dMsion of fractions. Results showed the personalized-context treatment to be advantageous relative to one or both control treatments for (a) solving conventional word problems, Co) soMng transfer problems. (c) recognizing rule procedures, and (d) developing favorable ulliludes toward materials. Theoretical interpretations of these effect~ are discussed, along with considerations about the practicality and effectiveness of the present application using print materials compared to an earlier one using CAl.

ECTJ, VOI_ 35, NO. 3, PAGES 151-62 ISSN 0148-5806

An important potential advantage of computer-assisted instruction (CAI) over traditional teaching methodologies lies in its powerful capabilities for adapting instruction to individuals (Hannafin, 1984; Tenny- son, 1984). Exemplary strategies have im- proved learning by individualizing the quantity of instructional support presented (Hanson, Ross, & Rakow, 1977; Tennyson & Rothen, 1977; 1979), the incentive values of tasks within a lesson (Hansen et aI., 1977), the contexts of mathematical problems (An- and & Ross, 1987), the types of examples presented in concept learning (Park, 1984; Park & Tennyson, 1986), and exposure time of lesson frames (BeUand, Taylor, Canelos, Dwyer, & Baker, 1985; Tennyson, Welsh, Christensen, & Hajovy, 1985). These strategies systematically generate and deliver instructional resources in a manner that would be impossible or impractical to achieve in textbook or lecture presentations.

The focus of the present study was varying the contexts of verbal math problems to increase their meaningfulness to individuals. The rationale was based on the well- documented research evidence (National Assessment of Educational Progress, 1979) and frequent observation of math teachers (Knifong & Burton, 1985) that many students perform poorly in solving verbally stated problems. Several factors probably contribute to this outcome, among which are low reading skills (Marshall, 1984) and inexperience with the problem structures presented (Mayer, 1982; Rosen, 1984). Of

152 EGTJ FALL. 1987

additional importance, it would seem, is the relatedness of the contexts or themes of problems to individual s tudents ' back- grounds and interests. Prior studies have shown context to have strong influences on learning (Bower, 1981; Bransford & Mc- Carrell, 1974; Di Vesta & Ross, 1978; Schwaneflugel & Shoben, 1983), especially by novice problem-solvers (Chi, Glaser, & Rees, 1982; Owen & Sweller, 1985). Accord- ingly, verbal math problems featuring abstract, unrealistic, or highly technical contexts may hinder learning by requiring the translation of unfamiliar vocabulary and problem applications. A direct contrast is when students spontaneously employ math concepts in everyday activities, such as in using percentages to calculate savings in purchasing discounted merchandise or interest earned in a bank account.

To explore these assumptions, studies by Ross and associates (Ross, 1983; Ross & Bush, 1980; Ross, McCormick, & Krisak, 1986) examined the effectiveness of adapt- Lug the contexts of examples presented in a statistics unit to college students' academic majors. Nursing students performed best when the contexts concerned medical applications, whereas education students performed best when the contexts concerned teaching. In an extension of this research, Anand and Ross (1987) developed a computer model designed to increase the flexi- bility and practicality of the adaptive strategy by: (a) constructing personalized contexts for each student, Co) orienting the contexts to everyday interests and background variables, and (c) automating the tasks of lesson preparation and administrat ion. Their model was applied to a division-of-fractions unit taught to elementary-school students. In the adaptive treatment, information obtained from students about their personal experiences and interests were incorporated into the math problems by the CAI program. Relative to concrete and abstract contexts, the personalized contexts proved superior on measures of problem solving, formula recognition, and attitudes.

These uses of personalized materials of- fer practical suggestions for applied instructional design (Berliner, 1986), while supporting contemporary cognitive theories that stress the importance to schema devel-

opment and meaningful learning of relating new information to s tudents ' existing knowledge (Anderson, 1980; Ausubel, 1968; Mayer, 1975; Rumelhart & Ortony, 1977). Interpretations regarding the efficacy of CAI for such adaptations, however, would be unjustified from the evidence obtained. That is, simply because CAI is used to present learning materials does not necessarily imply that performance outcomes are due to some specific attributes or qualities of that medium (Clark, 1983; 1984; 1985; Salo- mon& Gardner, 1986). If the instructional theory underlying a teaching strategy is valid, learning benefits should be indepen- dent of the delivery medium employed. Should benefits be restricted to CAI, however, one might therefore search for some unique contribution that CAI makes to change the strategy's impact (Clark, 1984).

The present study was designed to ex- tend previous research on personalizing math instruction by evalua~ng a variation of Anand and Ross' (1987) model. Specifi- cally in contrast to the CAI approach used in the latter study, microcomputers were employed to generate printed copies of personalized lessons. This approach elimi- nates the need for one-to-one student con- tacts with computers during learning, an important practical advantage. The research design consisted of comparing effects on student learning and attitudes of personalized contexts relative to concrete (nonadaptive) and abstract contexts. It was hypothesized that personalized contexts would improve performance on achievement measures by increasing motivation and facilitating assimilation of the information taught with existing knowledge. Based on the authors' research experiences with the print and CAI (Anand & Ross, 1987) models, an additional, informal part of this paper addresses possible differences in how uses of these modes influence treatment administration in learning experi- ments.

METHOD

Subjects and Design Subjects were 54 fifth-grade (n =31) and sixth-grade (n =23) students attending a

PERSC)NAUZ1NG VERBAL PROBLEMS 153

university-affiliated elementary school. All had completed prerequisite units on addi- tion, subtraction, and multiplication of fractions. The school employs a modified Indi- vidually Guided Education (IGE) model in which fifth- and sixth-grade students attend classes together, but progress through course materials on an individual basis. Subjects were randomly assigned to abstract, concrete, and personalized context groups in learning a division-of-fractions unit. Major dependent variables were (a) posttest scores on context problems, transfer problems, and recognition-of-formula items; Co) task attitudes; and (c) lesson completion time.

Instrumentation and Learning Materials

Materials used in the study were adapted from those used by Anand and Ross (1987). Descriptions of the materials follow.

Biogra~ical Questionnaire. Students were asked to provide background information about themselves on a biographical questionnaire. Among the categories included were homeroom teacher's name, birth date, favorite relative, household pets, family's supermarket, favorite food, favorite restau- rant, friends' names, and favorite television show and stars. The last section of the questionnaire contained a two-item pretest on the division-of-fractions unit. The entire questionnaire required about 30 minutes to administer.

Instructional Unit. The instructional unit dealt with procedures for dividing fractions. It began with a review of prerequisite math facts which students could reference whenever desired while learning. The next section introduced the rule for dividing fractions and demonstrated its application to an example problem. The following four- step solution was taught: (a) identify the dividend and divisor, (b) write the whole number as a fraction, (c) invert the divisor to obtain its reciprocal, and (d) multiply the dividend by the reciprocal of the divisor to obtain the answer. The rule application was then repeated for four additional problems, all containing an integer numerator and fraction divisor. The lesson was pro- grammed in BASIC for use with an Apple [Ie

or compatible microcomputer. When exe- cuted, the program produced print copies of the lesson for individualized study.

Treatments were manipulated by varying the referents and background themes of the five example problems, while keeping the numerical values and types of measure- ment involved (i.e, objects, quantity, l~ne, and fluids) constant. Abstract contexts involved the use of general referents in problem statements, such as "quantity, .... fluid," "liquid," and so forth, without association to a meaningful background theme. Con- crete contexts used hypothetical concrete referents, such as "Mary, .... English," "an art- ist," and so forth to convey more realistic and specific applications. Parallel abstract and concrete versions of the sample problem are shown in Table 1.

TABLE 1 Parallel Examples from the Abstract and Concrete Contexts

Abstract There are 6 peckx:ls of time. We divide ti'~at time into ~/4 time periods. How many time periods would there be in all?

Concrete Mrs. Jones teaches English for 6 hours. She divides that time into periods of 3/4 hours. How many periods does Mrs. Jones have to teach English?

Personalized contexts were developed by re- placing abstract and concrete terms with personally familiar items obtained from the biographical questionnaire. The personalized information for a given student was entered using program DATA statements in a prescribed order, so that, for example, Value 1 was always birth date, Value 2 was best friend's name, and so on. The program operated by initially assigning the data values (through REAr) statements) to particular variables. These variables, along with the supporting text, formed a "template" from which the personalized context was constructed. The top section of Table 2 shows the actual template into which the personalized data values were inserted (compare with parallel contexts in Table 1), while the

154 ECTJ FALL1987

lower half shows the completed example for a fictitious student, "Joe."

TABLE 2 Sample Materials from the Personalized Context

Temp/ate J Student name had entered a contract with teacher name to finish his~her work on firne. He/she has earned 6 hours of free time from teacher name to favorite activity. He/she divides hislhe~ free time into sessions of 3/4 hour. How many sessions will student name have in all to favorite activity?

Completed Prototype = Joe had entered a contract with Mrs. Warren to finish his work on tirne. He has earned 6 hours of free time from Mrs. Warren to-watch TV He divides his flee time into sessions of u hour. How many sessions will Joe have in all to watch TV?

Data Joe, Mrs. Warren, his, he, watch T.V.

altaJicized items represe~nt categories that acquire specifx: referents in the completed prototype. Dltalicized items represent specific information acquired from the student that replace gera~al category (variable) names. (The present data are rmtit)ous.)

Depending on the example, when an appropriate personalized referent was not provided in the questionnaire response, either a standard referent was substituted (e.g., "watching TV" for favorite activity) or no specific referent was given. On the average, personalized examples used approx- imately 2.5 times more words than corre- sponding abstract context examples, and 2 times more words than concrete context examples. The additional words were needed to develop the applied themes, but were completely incidental to the problem solution.

Posttest. The achievement posttest consisted of 11 items, organized into a "context" section (n = 6), "transfer" section (n = 3), and "recognition" section (n = 2). A brief description of each follows.

Context problems (1-6) were patterned on lesson practice examples with regard to

structure and difficulty. Each involved dividing a whole number by a fraction. Two of the problems were presented in abstract contexts, two in concrete contexts, and two in personalized contexts. Three parallel lists were devised by rotating each of the six skeletal problems across each context type. For example, a given problem appeared on one list as a personalized item type, in another as a concrete item type, and in the third as an abstract problem type.

Transfer items (7-9) presented problems designed to differ in appearance or structure from lesson examples to test ability to apply learning to novel instances. Specifi- cally, Item 7 was identical in composition to the lesson examples, but presented only numerical values, without any verbal context. The two other transfer items featured verbal contexts, but varied the problem structures to division of a fraction by an integer (Item 8) and by another fraction (Item 9). (Recall that lesson examples all involved dividing integers by fractions.) Two parallel sets of transfer items were constructed by substituting different numerical values in the problem statements. The problems used on one of those sets were as foUows:

7 . 8 + u

8. V3 of a cake was divided equally among 4 boys. How much of the cake did each one of them get?

9. Ms. Perkins had W2 Ibs. of candy. She put candy into packages ofu lbs. In all, how many packages did Mrs. Perkins make?

Recognition i tems assessed memory of the rule def in i t ion and solut ion steps. The first i tem was a mult iple-choice question requiring identi f icat ion of the correct rule procedure. The second was an ordering task that involved rearranging a random listing of the four rule p rocedures in the p roper sequence. Only one set of these items was devised.

Six parallel forms of the problem-solving portion of the test (Items 1-9) resulted from combining the three context-item sets with the two transfer-item sets. The different forms were randomly distributed to subjects in roughly equal frequencies both

PERSONAUZING VERBAL Pr.'.'.'.'.'.'.'.'.~flLEMS 155

within and between treatments. Items were presented on index cards that were shuffled before each administration to create a different random ordering for each subject. Internal consistency reliability was determined to be .79 using the Kuder-Richard- son Formula 20 (KR-20).

Attitude Questionnaire Task attitudes were assessed by asking subjects to react to eight statements about the lesson using a five-point Likert scale (e.g., 5 = "s t rongly agree") . Abbreviated de- scriptors are: "Examples were easy to understand," "Examples were interesting," "Examples were more understandable than in other units," "Examples were easier to remember, .... Examples put me in the problem situations," "I enjoyed the lesson," "Amount of material was sufficient," and "'Lesson held my attention." Internal consistency reliability of these items, computed by the KR-20 formula, was determined to be .75. The questionnaire concluded with an open-ended item asking subjects to describe their feelings about "having math problems of this type."

Procedure

Subjects were individually administered the biographical questionnaire and pretest. Analysis of pretest scores, using a one-way A_NOVA, was not significant (F< 1.00), sug- gesting that treatment groups were com- parable in degree of prior knowledge.

From one to four subjects representing a random mixture of treatment groups were scheduled to attend a particular learning session. Prior to subjects' arrival, the experimenter prearranged the instructional materials according to treatment condition. In the case of the abstract- and concrete-context t reatments, s tandard manuals were used. For the personalized-context treatment, individualized manuals were pre- pared by entering the appropriate personalized data in the computer program and generating a print copy of the lesson. Subjects were seated at separate desks

and were administered materials individually. It was explicitly stated that the only requirement was to read the material, not to work out any example problems. After answering any questions about the proce-

dure, the experimenter gave a "ready" sig- nal and recorded the start time. Upon completion of the lesson, the experimenter recorded the finish time, and administered the attitude questionnaire followed by the posttest.

RESULTS

Multivariate Analysis of Variance Treatment means on the dependent variables of context items, transfer items, recognition items, and attitude score are sum- marized on Table 3. An initial multivariate analysis of variance (MANOVA) was performed to examine overall treatment effects on these measures. The rationale for using MANOVA instead of a within-subjects design involved consideration of (a) the widely uneven item n's in achievement subtests, (b) the relatively low correlations between posttest subtests and attitude scores (range = .11 to .34), and (c) the only moderately high intercorrelations between the subtests themselves. Specifically, although context and transfer subtests were correlated at .71, context and recognition subtests were correlated at only .43, while transfer and recognition subtests were correlated at only .34. The resultant MANOVA yielded a significant treatment effect, F (2,51) =- 7.08, p < .001, and a significant treatment by measure interaction, F (6, 98) = 4.03, p < .01. The follow-up ANOVA's described below were performed to determine where differences occurred. An alpha of .05 was used as the significance level in each.

Context Subtest A 3 (context treatment) x 3 (problem context) mixed ANOVA was performed on the context subtest. Problem context (abstract, concrete, and personalized) was the within- subjects variable. As shown in Table 4, the main effect for context treatments, F (2, 51) = 12.36, p<.001, was the only significant finding. Follow-up comparisons, using the Tukey HSD procedure, showed that the personalized-context group (M= 74% correct) performed significantly better than both the abstract-context (M = 27%) and concrete-context (M--24%) groups (see Ta- ble 3).

15X~ ECTJ FALL1987

TABLE 3 Treatment Means on Major Dependent Variables"

TREATMENT GROUP = Variable Abs~act Concrete Personalized Total

Context Subtest (6) M: 26.8 24.1 '74.1 41.7 SD: 34.8 30.8 35.6 40.5

Transfer Subtest (3) M: 11.1 13.0 38.7 21.0 SD: 16.1 25.9 28.6 26.9

Recognition Subtest (2) M: 61.0 38.9 69.4 56.1 SD: 40.4 40.4 30.4 38.9

Overall Posttest (11 ) M: 28.8 23.7 64.6 38.7 SD: 25.4 25.9 28.1 26.5

A~tude Tota~ (8) M; 3.97 3.75 4.11 3.9 SD: .58 .44 .63 55.7

Note: Numbers in parentheses indicate number of items on scales. ~ and overall posttest means are calculated as percentage correct. bn = 18 in each treatment. =based on a five-point scale on which 5 = "strongly agree"; 1 = "strongly disagree"

TABLE 4 Summary of Results from Context Treatment x Problem Context ANOVA

Source Mean Sq. df F

BETWEEN GROUPS Context Treatment (C) t 7.05 2 12.36" Error 1.38 51

WITHIN GROUPS Problem Context (P) 0.07 2 .31 C x P 0.41 4 1.72 Error 0.24 102

"p < .001

TABLE 5 Percentage of Subjects in Treatment Groups Correctly Answering Transfer Items

TREATMENT

Item Number Chi-Square and Description Absb'act C o n c r e t e Personalized Statistic

7. Number Context: Integer by Fraction 22.2 16.7 77.8 17.30"

8. Word Context: Fraction by Integer 11.1 16.7 11.1 .32

9, Word Context: Fraction by Fraction 0.0 5.6 27.8 7.87""

"p < .01 "'p < .05

PERSONALIZING VERBAL PROBLEMS 157

Transfer Subtest A one-way ANOVA on the transfer subtest yielded a significant treatment effect, F (2, 51) = 7.44, p < .01. Tukey analyses indi- cated that the personalized group (M = 39%) surpassed (p < .01) both the concrete (M -- 13%) and abstract (M = 11%) context groups.

Given that the structure of each transfer problem was unique, it was decided to examine outcomes of each separately. Chi- square analyses of pass-fail f requencies were used for this purpose. A summary of the percent of each group passing the three items is shown in Table 5. On Item 7, which involved dividing an integer by a fraction (as in learning, but without a verbal context), a very strong effect was found, • (2) = 17.23, p < .001. The success rate for the personalized group was 78% compared to only 22% and 17% for the abstract-context and concrete-context groups, respectively. On Item 8, which involved dividing a fraction by an integer, no effect was found, X ~ (2) = .33, p > .05. The success rate was consistently low across groups (overall M = 13%). On Item 9, which involved dividing a fraction by a fraction, a significant effect was obtained, X ~ (2) = 7.88, p < .05. The success rate, which was also fairly low, was 20% for the personalized group compared to 0% and 6% for the abstract-context and concrete-context groups, respectively.

Recognition Subtest Treatment effects on the recognition subtest were found to be significant, F (2, 51) = 3.21, p < .05. Tukey analyses showed the personalized-context group (M = 69%) to surpass (p < .05) the concrete-context (M = 39%) group. The abstract-context group (M = 61%) did not differ from either group.

Attitude Results A one-way A_NOVA performed on total attitude scores failed to yield a significant treatment effect, F (2, 51) = 1.85, p > .05. Given that individual attitude items concerned different aspects of the learning experience, it was decided to perform separate analyses on each. Differences were significant (p < .01) on Item 3, "Examples were more understandable than in other

units"; and approached significance (p < .10), on Item 5, "Examples put me in the problem s i tuat ions ." Fol low-up tests on Item 3 means showed the abstract-context (M = 3.71) and personalized-context (M = 3.94) groups to surpass the concrete-context (M = 2.83) group. Inspection of the Item 5 means showed a similar ordering, with the personalized group (M = 4.12) h ighes t , the abs t rac t g r o u p next (M = 3.78), and the concrete group lowest (M = 3.50).

Lesson Completion Time Analyses were performed on three different time measures : (a) review time, dur ing which the prerequisite math material was reviewed; (b) lesson time, during which the fractions lesson was studied; and (c) posttest time. Analysis of review time and posttest time revealed no significant treatment effects (p > .05 in both cases). Differences were significant, however, for lesson time, F (2, 51) = 3.94, p < .05. The concrete- context group used less time than the abstract-context (p < .05) and personalized- context (2 < .06) groups.

Supplementary Analyses

Open-ended reactions. The last item of the attitude survey asked students to describe their "'feelings about having math problems of this type." Although this section was in- tended mainly as a qualitative measure, two quantitative analyses were suggested. First, it was noted that, out of 18 subjects in each group, 17 (95%) in the personalized-context treatment elected to write reactions, as contrasted with only 12 (67%) in the abstract-context g roup and 11 (61%) in the concrete-context g roup . Compar ing the personalized-context rate with the combined control group rates yielded, X" (1) = 4.35, p < .05.

The second analysis involved rating the response protocols on a favorable-unfavorable continuum. Responses were typed on index cards and evaluated by three inde- pendent raters us ing a five-point Likert scale (e.g., 1 = "very unfavorable"; 5 = "very favorable"). The ordering of the responses was varied for raters by shuffling

1,~ ECD FAU. 1987

the cards for each. Raters saw only the protocols and were thus unaware of the respondents ' identities or t reatment groups. In te r - ra te r cor re la t ions were qui te high, ranging from .81 to .90. The average rating for each protocol was then used in calculat- ing overall t rea tment means . The overall means were 4.26 for the personalized-context group and 3.4=3 for the control groups combined. Although this difference was in the predicted direction, it did not reach significance, t (38) = 2.02, p < .10. If it can be assumed, however, that subjects who failed to write a response were likely to be less positive (or less enthusiastic) about the material than those w h o did, this analys is would tend to underest imate differences, given the significantly lower response rate of the control groups.

In general, students in all treatments reacted positively toward the organized pres- en ta t ion and ru le -example format . Over half of the 17 respondents in the personalized-context group made specific reference to the helpful or interesting properties of the examples. Their responses were as follows:

I thought it was great to see the names of people I know . . . . I could relate to the problem. I really liked hearing the names of my friends and my dog!

I thought it was fun. Because my teacher gave me something ar~i I do have a pet Smokey . . . .

I was surprised. Usually questions are the same for everyone. It is helpful because a person needs to know when to do something too. It is helpful to know when and not just how.

1 was surprised to see my name in it and I thought it was very interesting. It was educational and fun.

Surprised they knew that much about me. Good, you would be in the situations.

I was interested in what was going to happen next. You would be more interested in reading about them.

I thought they [the examples] helped me understand better.

l think they [the examples] are better because they are easier to understand. The unit helped me a lot.

Good, because they [the examples] make it more understandable.

Gender Differences AdditionaJ analyses examined posttest performances as a function of subject gender. An initial 2 (gender) x 3 (treatment) x 3 (item type) mixed ANOVA was performed on content items. Results showed that nei- ther the main effect nor any interactions in- volving gender were significant. Separate one-way ANOVAs were performed to compare males and females on the transfer subtest, recognition subtest, and total attitude test. Only the transfer subtest yielded significant differences, F (1, 52) = 3.63, p < .05. Females (M = 29.6%) were superior to males (M = 12.3%) on that measure.

DISCUSSION

The purpose of this experiment was to in- vestigate the effectiveness of personal izing math examples using microcomputer-generated lessons. Consistent with findings from a CAI application of the same strategy (Anand & Ross, 1987), results were suppor- tive of the main research hypotheses. Spe- cifically, the personal ized-context group was superior to both the abstract-context and concrete-context groups in solving context problems and transfer problems, and to the concrete-context group in recogni- z ing rule formulas . At t i tude effects, although less striking, favored the personalized-context group over one or both control groups in several comparisons.

Closer examination of achievement outcomes reveals that the strongest advantages for the personalized-context treatment occurred in solving problems similar to those used as learning examples (i.e., context problems). Benefits on transfer and recognition items were not as large or consistent. In the case of recognition items, guessing error might have reduced the sensitivity of the treatment comparisons relative to other measures. Also, it seems reasonable that meaningful contexts would operate by dis- courag ing rote memor iza t ion , and thus have lower impact on verbatim retention of materials (i.e., r emember ing rule defini- tions) than on problem solving and transfer (Mayer, 1977; 1978).

Transfer results showed the identical pattern obtained by Anand and Ross (1987). On the two problems that maintained frac-

PERSONALIZING VERBAL PROBLEMS 159

tions as divisors, as in the learning examples, the personalized group was superior to both control groups. No differences occurred, however, on the problem containing a whole number divisor. The suggestion is that personalized contexts mainly served to strengthen encoding of the specific problem-solving algorithm taught. The result was superior "near transfer'' to new proto- types to which that algorithm could be directly applied. Specifically, both the transfer problem requiring "integer by fraction" division and the one requiring "fraction by fraction" division were directly manipulat- able through the specified scheme of "writ- ing the numerator as a fraction" and then "inverting the divisor . . . . " To use this scheme with the problem requiring "fraction by whole number' ' division, the integer divisor would first have to be converted to a fraction (an additional step). Few subjects in any treatment were successful in this "far transfer'' activity.

Without more sensitive measures of task performances and behaviors, it is only possible to speculate about how personalized contexts influenced learning. One likely function was to increase interest in the task. Judging from informal observations of subjects during the task as well as the open- ended survey responses, many reacted with genuine excitement and surprise to encountering the personalized materials. Analyses of attitude ratings, however, revealed only isolated treatment differences showing the concrete-context group to have the lowest mean on several items. Due to the greater length and semantic complexity of concrete contexts relative to abstract contexts, students may have found them more difficult to read (Muth, 1984). (The significantly shorter lesson completion times for the concrete-context group could be due in part to subjects hurrying through the materials for that reason.) It also seems important that the concrete contexts lacked the novelty and familiarity of the personalized contexts, qualities that could compensate for higher reading demands in making materials attractive to students.

A second possible function of personalized contexts was to strengthen what Mayer (1984) calls the "internal connections" (or logical consistency) of the material. Specif-

ically, personalized examples demonstrated rule applications within integrated themes featuring familiar people and events. Prob- lem descriptions and solutions thus became logically interrelated with the story themes conveyed (whether or not the underlying mathematical principles were understood). Semantic processing should have become easier as a result (De Corte, Verschaffel, & De Win, 1985).

A th i rd possible funct ion was to strengthen "external connections" (Mayer, 1984) between the rule information and existing knowledge schema. The underlying assumption is that as students read about familiar people and events, they can relate the applications described to actual experiences. For example, in considering the problem of how to divide a favorite soft drink equally among friends (Example 5), the student may think of a similar experience that actually occurred (or could take place) and embellish it with the details of the problem. At the time of recall, that schema can be invoked and the component problem-solving information (algorithm steps) more easily reconstructed. If such processes occurred, the transfer results (as noted above) suggest that their primary impact was to improve learning of the specific algorithm taught. Personalized contexts, perhaps, provide highly memorable illus- trations of rule applications, but may not necessarily function to increase conceptual understanding of the mathematical principles involved.

When technology plays a central role in the design or delivery of instruction, one may question its influences on the learning outcomes obtained. Accordingly, although personalized materials were presented in alternate modes (CAI and print) in the An- and and Ross (1987) study and in the present study, the effects on learning were al- most identical. This outcome adds credence to Clark's (1983) contention that learning gains come from effective instructional strategies, not from the medium used to deliver the instruction (also see Clark, 1984; 1985; Salomon & Gardner, 1986). For example, Clark (1983) states that "media are mere vehicles that deliver instruction but do not influence s tudent achievement any more than the truck that delivers our gro-

t60 ECTJ FALL I9B7

ceries causes changes in our nutrition" (p. 45). Continuing with this analogy, however, our nutritional health could well be at risk if a delivery truck lacked certain attributes (e.g., a refrigeration unit) needed to deliver products in good condition. In the same sense, special media attributes of the computer could allow certain "educational products" to be delivered that would be un- feasible or impossible to provide by other means (Petkovich & Tennyson, 1984). The personalized lessons administered in this experiment are examples. Using a computer, such lessons could be generated for an individual student within 10-15 minutes time. Without a computer, the time and work involved would be prohibitive for applied classroom use.

Our experiences in evaluating CAI (An- and & Ross, 1987) and print applications of the personalized strategy suggest some differences in how the two approaches might affect the preparation and administration of experimental tasks. These impressions are based only on informal observations, and should be treated as speculative. Further research is suggested to test their general- izability to other contexts. They are as follows.

1. The CAI lessons were easier to administer than the print lessons by eliminating the need to prepare and distribute individualized study manuals for each student.

2. The CAI model, however, had the dis- advantage of being dependent on the avail- ability of individual computers in determin- ing group size and classroom location.

3. Students seemed more serious and task-oriented in reviewing the CAI materials. Enthusiasm and interest also seemed higher under CAl. Possible factors include the greater novelty, formality, and "profes- sional" appearance of the CAI presentations.

4. In the CAI study, proctors were asked for fewer directions, even though the print materials provided identical information. In general, students seemed more oriented to work independently at the computer.

5. The print mode offered less control over task presentations as a result of students sometimes glancing ahead to see what material remained or back to review.

6. The print materials created awareness

of total lesson length, which may have influenced student pacing.

7. Subjects receiving print materials tended to spend less time studying the lesson (overall M = 13.9 min.) than those receiving CAI (overall M = 18.6 min.). We recently discovered the same pattern in comparing college students' pacing on a math lesson presented in CAI and print modes (Ross & Morrison, in press). Two interpretations are that students experience greater difficulty in reading information from monitor displays, and that they may regard the experimental tasks more seri- ously under the less familiar and more structured CAI format. Further research is needed to substantiate these impressions. Perhaps it will be found that with increased classroom exposure to CAI, any tendencies by students to react to it differently from traditional methods will decrease. For re- searchers who use computers to deliver experimental materials and keep records, this will mean increased control over methods (high internal validity) without sacrificing the external validity of findings.

REFERENCES

Anand, R, & Ross, S. M. (1987). Using computer- assisted instruction to personalize math learning materials for elementary school children. Journal of Educational Psychology, 79, 245-252.

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In Forthcoming Issues

Characteristics of Cognitive Engineering: The Next Generation of Instructional Systems Francis J. Di Vesta and Lloyd P. Rieber

Using "Sesame Street" to Facilitate Children's Recognition of Letters and Numbers Robert A. Reiser, Naja Wil/iamson, and Katsuaki Suzuki

The Effects of Age of Viewer and Gender of the Narrator on Children's Visual Attention and Recall of Story Ideas James D. K/ein, Dalene R. Voss, and Robert A. Reiser

Documents

A computer-based strategy for personalizing verbal problems in teaching mathematics