Personalizing context in teaching mathematical concepts: Teacher-managed and computer-assisted models

Personalizing Context in Teaching Mathematical Concepts: Teacher-Managed and Computer-Assisted Models Steven M. Ross Deborah McCormick Nancy Krisak Padma Anand

Steven M. Ross is Professor of Educational Psychol- ogy, Memphis State University, Memphis, TN38152; Deborah McCormick and Nancy Krisak are doctoral students in Educational Psychology, Memphis State University, Memphis, TN 38152; and Padma Anand is Psychology Instructor, Mount Carmel College, Bangalore University, Vasanthnager, Bangalore, 56 OOO3, India.

The present paper examines a strategy intended to facilitate mathematics learning by adapting the context of instructional material to students' backgrounds and interests. In four validation studies, the strategy was implemented through teacher management, using college students learning statistical probability rules as subjects. Achievement and attitude outcomes consistently favored treatment groups who received the adaptive contexts over control groups. The culmination of this research is the development of a computer-assisted model to increase the strategy's practicality and sensitivity to learner differences. The computer model uses stored information about each student to personalize explanations and story examples on a fractions unit.

ECTJ, VOL. 33, NO. 3, PAGES 169-178 ISSN 0148-5806

Compared to conventional teaching methods such as lecture and discussion, computer-assisted instruction (CAI) offers the important advantage of being able to adapt materials to the needs of each student. Further, such adaptations can be made and refined "on line" as learner needs change over the course of a lesson. Al- though considerable work has been done in developing CAI models that vary the amount or difficulty of instruction based on achievement outcomes (e.g., Carrier, Davidson, Higson, & Williams, 1984; Ross, 1984; Tennyson & Rothen, 1979), little atten- tion has been given to adaptations directly oriented to individual differences in background and interests. This article describes the development and evaluation of such a model as it is applied to the teaching of mathematical concepts expressed in story problems.

Solving verbally stated problems is one of the major weaknesses in childrens' mathematics achievement (National Assessment of Education Progress, 1979). The difficulty for many students appears to stem less from a lack of computational skills than from the inability to translate and comprehend what the problems are asking (Mayer, 1982; Muth, 1984; Zweng, 1979). Reading skill can thus become an influential factor (Marshall, 1984), as can experience with the specific problem structures (Mayer, 1982; Rosen, 1984). Another important variable may be the individual's familiarity with the types of verbal contexts presented. The story contexts that appear in conventional algebra

170 ECT3 FALL1985

and arithmetic textbooks frequently tend to be abstract or technically-oriented, involv- ing such topics as velocity, weights and measures, currency transactions, and work efficiency (see Mayer, 1981). To derive the numerical solutions, students may first have to translate unfamiliar vocabulary and determine the meaning of problem situations that have little relation to their real life experiences. A direct contrast is when children employ numerical concepts naturally and spontaneously to derive solutions to problems of personal interest, such as cal- culating percentages to determine batting averages or free throw accuracy in playing sports.

Effective mathemat ics teachers are usually very much aware of the value of using natural interests of students in teaching them basic skills. An exemplary approach integrates homework and class as- signments with interesting articles from the newspaper that contain mathematical information (Daruwalla, 1979). Another strategy is to use descriptions about unusual events, such as world records, as contexts for story problems (Jones, 1983). A third example is to use activities that students have collectively experienced (e.g., a field trip) for such contexts (Wright & Stevens, 1983). In each of these procedures, new concepts are related to experiences that are apparently meaningful to a class of students. A more powerful approach might be one that uses similar techniques to accommodate the unique needs and interests of individuals.

The specific purpose of the strategies discussed in this paper is to provide such individualized adaptation by matching the context of lessons to student background. This idea was first suggested in association with prior research by the first author on strategies for adapting level of instructional support to individuals' predicted performances in learning math rules (Ross & Rakow, 1981, 1982; Ross, Rakow, & Bush, 1980). Al- though achievement significantly improved under the adapt ive t reatments , rote memoriza t ion rather than meaningful learning appeared to be the predominant outcome for many students. Drawing from this research and from investigations of meaningful learning strategies in mathe-

matics instruction (e.g., Mayer, 1977, 1979, 1980), we became interested in the possible importance of individual differences in de- termining the meaningfulness of presentations. The rationale that influenced our subsequent research was essentially the same one expressed at the beginning of this article: If mathematical concepts are presented in familiar contexts, meaningful learning and more favorable attitudes toward the material should be engendered.

The remainder of this article will discuss the contextual adaptation strategy in more detail. An initial section will describe the design and validation of the teacher-managed model, which employed programmed- type learning materials for teaching college-level statistics. The second section will describe current work in developing and field-testing a computer-assisted model for teaching arithmetic concepts to elementary school children.

TEACHER-MANAGED MODEL

The target population for evaluating the teacher-managed model was college students taking a senior-level statistics course. The course employs a Personalized System of Instruction (PSI) orientation in which students learn the materials from self-study manuals and progress at their own rate by achieving criterion on mastery tests. For experimental purposes, three parallel forms of a self-instructional unit on probability were prepared. In one form, explanations and examples were embedded within an education context that related probability to test construction, grading, student selection, etc. In a second form, the same explanations and numerical problems were embedded within a medical context that described doc- tors, nurses, and patients concerned with probability in relation to recovery rates, accuracy of diagnosis, and so on. In a third form, the materials were presented in an abstract context that used general terms such as events, trials, items, etc. A unit posttest was developed to assess achievement on five types of learning outcomes: education-context problems, medical-context problems, abstract-context problems, transfer problems (novel applications), and memory of formulas. Using these basic ma-

PERSONALIZING CONTEXT 17~

terials, the four studies summarized below were performed.

Studies 1 and 2: Laboratory Validation Subjects in Study 1 consisted of education majors (preservice teachers). Study 2 served as a replication of Study 1 using nursing majors as subjects. Learning took place in both experiments in a laboratory setting designed to simulate the self-study orientation of the statistics course. Because this research is discussed in detail in other sources (Ross, 1983, 1984), its description here will be brief.

Subjects in each experiment were randomly assigned to receive one of the three contextual variations of the probability lesson (i.e., education, medical, or abstract contexts). After studying the materials, they completed an attitude survey and the unit posttest. Performance results in both experiments significantly favored the adaptive condition. Education majors learned best from the education context, whereas nursing students learned best from the medical context. Importantly, the strongest effects were found on context-related items (education and medical items in the respec- tive experiments) and on transfer items. Treatment outcomes varied least on memory of formulas. Findings on selected attitude items (e.g., "relevancy") also favored the adaptive context, although results were inconsistent across studies. These outcomes, overall, supported the major as- sumptions of the contextual adaptation strategy. It was inferred that probable benefits of the strategy were to increase interest in the task and to facilitate meaningful as- similation of the probability concepts with existing knowledge (Ausubel, 1968; Mayer, 1979).

Study 3: Applied Evaluation

As a test of its external validity, the context strategy was examined next under actual course conditions. In addition to the self- study component, other features of the statistics course included criterion- referenced testing and grading, retesting options, and unit mastery as a criterion for advancement. Relative to these procedures, major restrictive properties of Studies I and 2 were: (a) the unit had to be completed in a

single study session under fairly structured conditions; (b) the unit was significantly shorter in length than the regular course units; (c) although students were encour- aged to strive for a mastery score of 80% correct, they knew that the lesson was part of an experiment and would have no bearing on their actual course grades; and (d) not all subjects were actually enrolled in the course. Obviously, such factors could bias results compared to what would actually occur in a realistic context.

Subjects and Design. As in Studies 1 and 2, three context treatments were compared on five learning outcomes. Subjects were 42 nursing students enrolled in the statistics course to fulfill a baccalaureate degree requirement. The medical context was, there- fore, expected to comprise the adaptive lesson for this sample.

Materials and Procedures. The probability lesson used in Studies I and 2 was expanded into a full-sized course unit, identical in or- ganization, style, and requirements to all other course units. Briefly, its content was organized into four major sections, cover- ing: (a) probability statements, (b) addition rule for mutually exclusive events and for (c) nonmutually exclusive events, and (d) multiplication rule for independent and dependent trials. In conformity with normal course procedures, students could elect to complete the unit at any time following suc- cessful completion of all preceding units. The unit, in turn, constituted a prerequisite for all subsequent units. Students could study the material at any location and for as long a period as desired. If the posttest mastery criterion of 80% or higher was not at- tained, retesting was permitted. For research purposes, however, only the score obtained on the initial try was treated in the data analysis.

When students completed the im- mediately preceding course unit, a probability manual corresponding to one of the three context conditions was randomly selected and administered, thus determin- ing the assigned treatment. When students returned to the laboratory to take the unit mastery test, they were asked to complete an 8-item attitude survey pertaining to the

172 ECTJ FALL198,5

unit, followed by one of two randomly selected parallel posttest forms. The tests were the same ones used in the prior two studies and thus contained four abstract- context problems, four education-context problems, four medical-context problems, four transfer problems, and four formula items.

Results and Discussion. Treatment means on the five posttest item types are summarized in Table 1. One-way ANOVAs were con- ducted on each item type and total test score. No significant effects were obtained, although differences directionally favoring the adaptive (medical-context) group over other groups approached significance (p < .10) on education-context items, medical- context items, and total score. To provide a more sensitive test of treatment effects, it was decided to control for prior achievement differences by performing follow-up analysis of covariance (ANCOVA) on each dependent measure. The variable used as the covariate was cumulative points earned on initial course units. As expected, it was significant in all comparisons (all p's < .01). The ANCOVA results indicated significant treatment effects on education-context items, p < .01; medical-context items, p < .05; and total score, p < .05. Comparisons of adjusted means were made via Tukey HSD analyses. On education items, the adaptive (medical-context) group was superior to both the nonadaptive (education-context) group and the abstract group. On medical- context items and on total test score, the adaptive group surpassed the abstract group.

One-way ANOVAs on attitude responses yielded significant (p < .05) effects on two of the items. One effect was that the nonadaptive group evaluated the lesson as "faster" than did adaptive and abstract groups. No immediate explanation of this outcome comes to mind, as the three context variations were identical in length and were associated with comparable completion times. A more interpretable finding was the second effect showing higher ratings of "lesson relevancy" by the adaptive group compared to the abstract group.

Thus, similar to Studies I and 2, the adap- five treatment yielded positive performance outcomes. Its advantages over other treatments, however, were less pronounced than in the former studies. Another variation was the absence of transfer benefits due to adaptation. Interpretations of these effects must take into account that the applied conditions permitted much less control over subjects' learning activities. Second, in ex- panding the lesson into a full-sized course unit, more conceptual explanation and in- terrelationships of topics were provided relative to the fairly schematic presentations used in the laboratory studies. Third, completion of mastery tests on preceding units gave subjects prior exposure to transfer type problems. In view of these limiting factors, the supportive evidence obtained for contextual adaptation seems all the more encouraging.

Study 4: Learner Context Selection The main interest in Study 4 was whether individualized context selection would con- stitute a more powerful adaptive strategy than the group-based procedure used in

TABLE 1 Posttest Means by Treatment and Item Type in Study 3

Item Type

Context Treatment E d u c a t i o n Abstract Medical Formula Transfer

Adaptive 89.3 83.8 82.2 57.0 57.3 (Medical) Nonadaptive 67.8 82.1 78.5 64.3 64.3 (Education) Abstract 62.5 73.2 66.0 50.0 53.5

Note: Scores reflect the percentage correct on each item subset. All treatment n's = 14.

PERSONALIZING CONTEXT 173

previous studies. A second concern was whether unfamiliar (nonpreferred) thematic contexts might be detrimental to learning as a function of having low interest appeal and imposing increased processing de- mands (Marshall, 1984; Muth, 1984).

Subjects and Design. Subjects were 80 nursing students enrolled in the introductory statistics course described earlier. They were randomly assigned to the following four treatment groups (n = 20 each): (a) learner-adaptive, in which individuals received the context that they personally favored from a list of options; (b) standard- adaptive, in which all subjects received the medical context, regardless of individual preferences; (c) standard-nonadaptive, in which all subjects received the abstract context; and (d) learner-nonadaptive, in which individuals received the THEMATIC context that they least preferred from a list of options. These manipulations yielded a 2 x 2 factorial design consisting of two adaptive conditions (adaptive vs. nonadaptive) and two context selection conditions (learner vs. standard).

Materials and Procedure. The learning materials and tests were the same as those used in Studies I and 2. In addition to the existing education, medical, and abstract contexts, a fourth contextual variation, dealing with sports applications, was prepared. On the first day of class, subjects were administered an "interest inventory" in which they were asked to rate their past performances in and attitudes toward mathematics learning on a five-point scale. Forms administered to learner-adaptive and learner-nonadaptive subjects included an additional section asking them to rank-order the four different context options according to their

desirability as themes for learning math applications. Approximately one week later, subjects were administered the lessons appropriate to their treatment in simulated laboratory sessions. At the conclusion of the lesson they were administered a free recall measure on selected examples, an attitude survey, and the 20-item posttest.

Results At the time of this writing, only preliminary statistical analyses of posttest and attitudi- nal data have been completed. Free recall protocols are still being scored and tabu- lated. Initial examination was made of rankings of context preferences by subjects in the learner-adaptive and learner-nonadaptive treatments. Findings revealed that the medical context was ranked first by 36 out of the 40 subjects. The abstract context was ranked first by two subjects, and the education and sports contexts by one subject each. Clearly, the medical context com- prised the dominant preferential theme for the sample. The abstract context was the least popular choice, being ranked last by 21 subjects. Education received somewhat higher rankings than did sports. As previously indicated, subjects in the learner- nonadaptive condition were administered their least preferred thematic context during learning. That selection was education for 7 subjects, medical for 1 subject, and sports for the remaining 12.

Posttest means are summarized by treatment and item type in Table 2. Scores on each item type and on the total test were analyzed using a 2 (adaptation) x 2 (selection) ANOVA. Results indicated a significant adaptation main effect on transfer items, F(1,76) = 5.89, p < .05. As predicted, adapt ive contexts (X = 59% correct) were superior to nonadaptive contexts

TABLE 2 Posttest Means by Treatment and Item Type in Study 4

Context Treatment Education Abstract Medical Formula Transfer

Learner-Adaptive 82.3 85.0 88.8 61.3 60.0 Standard-Adaptive 81.3 77.5 81.3 63.8 58.0 Learner-Nonadaptive 71.3 77.5 68.8 63.8 45.0 Standard-Nonadaptive 75.0 88.8 75.0 73.8 40.0

Note: Scores reflect the percentage correct on each item subset. All treatment n's = 20.

174 ECTJ FALL198,5

(X = 42.5% correct). No main effects or interactions were significant on the other item types. To provide a more powerful test of treatment effects, parallel analyses were performed using the math attitude and performance self-ratings as a covariate. Results showed significant adaptation main effects on transfer items, F(1,75) = 8.88, p < .01; medical items, F(1,75) = 5.50, p < .05; and total test, F(1,75) = 4.57, p < .05. On each of these measures, the adaptive group surpassed the nonadaptive group. No selection main effects or adaptation by selection interactions were obtained.

Two-way ANOVAs performed on attitude scores yielded significant adaptation main effects on two items and on attitude total score (all p's < .05). The adaptive g roup , c o m p a r e d to the nonadap t ive group, rated the material as more "interesting" (X's = 3.25, and 2.85, respectively) and more "relevant" (X's = 3.40 and 2.25). Total scores again favored the adaptive group (X's = 19.59 and 17.01).

These results provided further substanti- ation for the hypothesized benefits of adapting context to student background. As in Studies 1 and 2, results were most pronounced on transfer items and on context- related items (i.e., medical items, in this study). The hypothesis that learner selection would be more advantageous than group adaptation was not supported. It seems important to note, however, that nearly all learner-adaptive subjects selected the medical theme as the preferred context. Consequently, the contexts received were virtually identical in the two adapt ive treatments. More heterogeneous samples would be necessary to make a conclusive test of the learner selection hypothesis. The relatively poor performance of the learner- nonadapt ive group is also noteworthy. Such outcomes could possibly mirror learn- ers' experiences in applied settings when story example themes are perceived as unfamiliar or uninteresting.

COMPUTER-ASSISTED MODEL

Although the context strategy consistently enhanced learning in the previous studies, it was also found to contain several limiting properties. From an adaptation standpoint,

the availability of only three context options greatly limits the sensitivity with which learner preferences can be accommodated. In the experiments, it was quite reasonable to assume that subjects would prefer contexts relating to their academic majors over the other choices. Such contexts may not be preferred, however, relative to ones based on personal hobbies, experiences, and interests that take place outside educational settings. Further, in most teaching situations (such as those found in the lower grades), classes having such homogeneous academic backgrounds (e.g., all students are nursing or education majors) would be exceedingly rare. Many different contexts would be needed to accommodate each individual's prior learning history. From a practical standpoint, preparing the alternative context lessons and matching them to students is a t ime-consuming task that teachers might not be very willing to per- form on their own.

The computer-assisted model to be described in this section was designed to provide a more powerful and practical means of adapting context to student interests. Its main objectives were to: (a) personalize context so that each student would receive a unique presentation; (b) orient the adaptive contexts to many different types of background and interest variables (e.g., hobbies, interactions with friends, one's birthday) rather than to educational variables only; and (c) automate the tasks of lesson preparation and administration. The model is now being field-tested for the first time. A summary of its procedural compo- nents and preliminary outcomes follows.

Learning Materials and Target Population Present application of the model is directed toward mathematics instruction at the fifth- and sixth-grade levels. This age group seemed especially appropriate for the field test, given the instructional focus on word problems and the procedural requirement for students to interact with the computer without the need for close teacher supervi- sion. Following consultation with teachers at the site school, the content area selected for the lesson was division of fractions. There was strong teacher agreement that this part of the math curriculum was rela-


tively difficult, and that the availability of a CAI unit as an additional resource could be especially helpful.

The CAI lesson was adapted from the textbook, workbook, and teacher-made materials currently in use. It begins with a review of terminology and special symbols. The next section introduces the rule for di- viding fractions and illustrates its application to an example problem using the following four-step solution: (a) identify dividend and divisor, (b) write the divisor as a frac- tion, (c) invert the divisor to obtain its reciprocal, and (d) multiply the dividend by the reciprocal to obtain the answer. This format (example and explanation) is then repeated for four additional division problems. The lesson is written in BASIC for presentation by an Apple IIe or compatible microcomputer (Apple II, II+, etc.). Stu- dents proceed through the lesson at their own pace by pressing the "Return" key to advance frames. Support material consisting of special instructions and a hard copy of selected CAI frames is provided in an accompanying handout.

Personalized Model The above section described the CAI lesson in general. In the personalized version, the individual student is "made part" of the material by incorporating aspects of his or her background and interests into examples and explanations. The appropriate information is obtained by having students complete a biographical questionnaire a week or so prior to beginning the fractions unit. The types of responses requested include the individual 's birthdate, friends' names, hobbies, vacation trips, and "favorites" in categories such as TV stars, candy, super- markets, books, magazines, and school subjects.

Once the information is collected, it is entered on DATA statements in the BASIC program. The program is then saved on disk for use with that particular student. DATA items are always entered in a pre- scribed order, so that, for example, Item #1 will always be birthdate, Item #2 best friend's name, etc. Since the questionnaire responses are similarly sequenced, data entry can be completed fairly rapidly, requiring only about 10 minutes per student. The

program operates by assigning the data to particular variables. The variables, along with supporting text, form a "template" from which the personalized context is con- structed. A simplified example is repre- sented in the following BASIC statements:

10 READ BD$, F15, FV$ 20 PRINT "ON YOUR BIRTHDAY,";

BD$;"," 30 PRINT "YOUR FRIEND, ";F15;

"BROUGHT YOU "; FV$ 40 PRINT "TO DIVIDE 4 WAYS."

2000 DATA "JULY 10, 1974", "BILLY", "A PIZZA"

Thus, by changing the three data values, a unique context can be created in which the focus is the student's favorite food brought by a friend on the student's birthday. In the actual lesson, such personalized examples are structurally and thematically similar to conventional word problems that would normally be presented via textbooks and classwork. The only difference is the sub- stitution of personalized information as concrete referents. One of the lesson examples is presented for illustrative purposes in Table 3. The top section of the table shows the template into which the personalized data are inserted, while the lower half shows the completed example. In a few in- stances, due to incomplete or inappropriate questionnaire responses, it is not possible to identify a personalized referent in a particular category. When this occurs, either a standard referent is substi tuted (e.g., "cake" for food) or no specific referent is given (e.g., birthdate is left out), whichever seems more appropriate for expression concerned.

Try-Out and Evaluation

Field-testing of the model is being con- ducted using a three-treatment design consisting of personalized contexts, concrete contexts, and abstract contexts. In all treatments, students initially complete the biographical questionnaire and a lesson pretest. Approximately one week later they are scheduled individually, or in small groups, to receive the lesson. Each student is seated at a separate microcomputer and completes the lesson independently. Fol- lowing the lesson, a posttest and follow-up attitude survey are administered. The post-

t76 ECTJ FALL I985

TABLE 3 Sample Materials From the Personalized Context

Template:a

Student name's teacher, teacher name, surprised him~her on birthday when he~she presented student name with 3 favorite candy. Student name cut each one of them in one-half so that he~she could share the birthday gift with his~her friends. In all, how many pieces of favorite candy did student name have for his~her friends?

Completed Prototype: b

Joseph's teacher, Mrs. Williams, surprised him on December 15 when she presented Joseph with 3 Hershey Bars. Joseph cut each one of them in one-half so that he could share the birthday gift with his friends. In all, how many pieces of Hershey Bars did Joseph have for his friends?

Data:

Joseph, Mrs. Williams, him, she, Hershey Bars, his

altalicized items represent categories that acquire specific referents in the completed prototype. bltalicized items represent specific information acquired from the student that replace general category (vari-

able) names. (The present data are fictitious.)

test consists of: (a) word problems presented in abstract, concrete, and personalized contexts; (b) number problems; and (c) transfer problems.

For the personalized treatment, the lessons are prepared in the manner previously described. For the concrete treatment, however, referents used in the problems consist of thematically appropriate but tic- titious names and events (e.g., teacher = "Mrs. Jones"; food = "ice cream"; etc.) and are the same for all students. For the abstract context, referents consist of abstract terms unrelated to any meaningful theme, such as quantity, unit, arid item.

Although the number of subjects tested thus far is too limited to permit a valid assessment of treatments, some initial results have been obtained. The available data, which represent approximately half (about 10 subjects per treatment) of the total to be collected, were subjected to preliminary de- scriptive and inferential analyses. The latter mainly consisted of one-way ANOVAs comparing means from the personalized, concrete, and abstract treatments. Results reflected the following: (a) higher scores for the personalized context than the abstract context on conventional word problems (p < .05) and (b) higher scores for the personalized context than both abstract and concrete contexts on number problems (p < .01), attitude scores (p < .05), and memory of rule procedures (p < .01).

Preliminary impressions of the personalized model's effectiveness have also

been formed through our experiences and observations. First, the procedural requirements for preparing and administering the personalized materials appear both feasible and practical. The personalized information can be extracted from the questionnaire answer sheets and entered in the computer quite easily and rapidly. When the student is ready to receive the lesson, all that is required is to locate and boot the disk containing his or her name. From that point on, the lesson is completely self-adminis- trable. Second, consistent with the above attitude findings, observations suggest that students react very favorably to the personalized materials. They seem both amazed and genuinely pleased by the ap- pearance of familiar names and events in the math examples. In contrast to the usual difficulties the authors experience in solicit- ing volunteers to serve as research subjects, the present task actually seems a popular activity in which students are very willing to participate. That the subject is mathematics makes this observation all the more meaningful. It should be noted that generally favorable reactions also seem to prevail in the control treatments. Based on student and teacher comments, the critical factor is un- questionably the computer-assisted presentation. Although most students have had previous exposure to CAI from commercial software, the present task represents their first experience with materials made by teachers and specifically adapted to their curriculum. These impressions, of course,


are subjective and must be viewed cau= tiously for that reason. More valid judgments regarding both attitudes and performance can be made when the complete evaluation data become available later this year.

SUMMARY

Historically, arithmetic story problems have presented special difficulties for students at all grade levels. One reason, it would seem, is lack of familiarity with the language used and applications described in typical problem prototypes. The main assumption of the present research is that meaningfulness of materials can be increased and learning improved by adapting the context of explanations and examples to student background and interests.

This idea was explored in preliminary studies by administering statistical materials embedded in different contexts to college undergraduates. In the adaptive treatments, context was related to subjects' academic backgrounds in either nursing (health and medical treatment) or education (teaching, testing, etc.). Preparation and administration of contexts were controlled via management by the teacher. Findings from four independent studies showed the adaptive treatment to be superior to control treatments on achievement and attitude measures. Achievement advantages in three studies tended to be strongest on transfer items and context-related items. These outcomes imply the ability to apply what was learned to new problem-solving situations as well as to problems relating specifically to the student's present career specialization. Despite the apparent educational importance of such results, the re- liance on management by the teacher appeared limited from a practical standpoint. In most applied contexts, student background will be much more heterogeneous than was the case for the present subjects. Also, few teachers will be willing to spend the time needed to prepare, administer, and evaluate performance on adaptive materials.

These considerations stimulated efforts to develop a computer-assisted model to automate the adaptat ion process. The

model operates by incorporating background information about the student into a CAI lesson on fractions. The result is that students read explanations and solve problems that relate the math concepts to actual events and people in their lives. This personalized strategy is now being field-tested with fifth- and sixth-grade students. Pre- liminary statistical results and subjective impressions are that the model is effective for learning, practical to use, and very favorably regarded by students and teachers alike. More valid judgments will be made on the basis of evaluation data to be collected in the coming school year.

If found to be effective, the context strategy could provide a valuable means for helping students out of the math story problem bind. During acquisition learning, personalized examples could be employed to introduce new concepts. As the individual gains proficiency and confidence, abstract or general contexts (e.g., conventional problems dealing with motion, time, currency, etc.) could be gradually substituted. From a meaningful learning standpoint (Ausubel, 1968; Mayer, 1984), such a sequence appears much more logical than the often used opposite pattern in which abstract problems become the focus of acquisition learning and subsequent foundation for transfer.

REFERENCES

Ausubel, D. P. (1968). Educational Psychology: A cognitive approach. New York: Holt, Rinehart & Winston.

Carrier, C., Davidson, G., Higson, V., & Williams, M. (1984). Selection of options by field independent and dependent children in a computer-based concept lesson. Journal of Computer-Based Instruction, 11, 49-54.

Daruwalla, A. (1979). A study of the effectiveness of the use of the newspaper in the classroom on student achievement in 7th grade mathematics classes. Un- published doctoral dissertation, Memphis State University.

Jones, B. M. (1983). Put your students in the pic- ture for better problem solving. Arithmetic Teacher, 30, 30-32.

Marshall, S. P. (1984). Sex differences in children's mathematics achievement: Solving computations and story problems. Journal of Educational Psychology, 76, 194-204.

178 ECTJ FALL1985

Mayer, R. E. (1977). Different rule systems for counting behavior acquired in meaningful and rote contexts of learning. Journal of Educational Psychology, 69, 537-546.

Mayer, R. E. (1979). Can advance organizers in- fluence meaninfgul learning? Review of Educa- tional Research, 49, 371-383.

Mayer, R. E. (1980). Elaboration techniques that increase the meaningfulness of technical text: An experimental test of the learning strategy hypotheses. Journal of Educational Psychology, 72, 770-784.

Mayer, R. E. (1981). Frequency norms and struc- tural analysis of algebra story problems into families, categories, and templates. Instruc- tional Science, 10, 135-175.

Mayer, R. E. (1982). Memory for algebra story problems. Journal of Educational Psychology, 74, 199-216.

Mayer, R. E. (1984). Aids to text comprehension. Educational Psychologist, 19, 30-42.

Muth, K. D. (1984). Solving arithmetic word problems: Role of reading and computational skills. Journal of Educational Psychology, 76, 206-210.

National Assessment of Educational Progress. (1979). Second assessment of mathematics: Mathe- matical applications (Report No. 09-MA-03). Denver, CO: Educational Commission of the States.

Rosen, D. R. (1984). Students' schemata for algebra word problems. Paper presented at the annual

meeting of the American Educational Research Association, New Orleans.

Ross, S. M. (1983). Increasing the meaningfulness of quantitative material by adapting context to student background. Journal of Educa- tional Psychology, 75, 519-529.

Ross, S. M. (1984). Matching the lesson to the student: Alternative adaptive designs for individualized learning systems. Journal of Computer-Based Instruction, 11, 42-47.

Ross, S. M., & Rakow, E. A. (1981). Learner control versus program control as adaptive strategies for selection of instructional support on math rules. Journal of Educational Psychology, 73, 745-753.

Ross, S. M., & Rakow, E. A. (1982). Adaptive instructional strategies for teaching rules in mathematics. Educational Communication and Technology Journal, 30, 67-74.

Ross, S. M., Rakow, E. A., & Bush, A. J. (1980). Instructional adaptation for self-managed learning systems. Journal of Educational Psychol- ogy, 72, 312-320.

Tennyson, R. D., & Rothen, W. (1979). Manage- ment of computer-based instruction: Design of an adaptive control strategy. Journal of Computer-Based Instruction, 5, 129-134.

Wright, J. P,, & Stevens, N. K. (1983). Improving verbal problem-solving performance. Arithme- tic Teacher, 31, 40-42.

Zweng, M. J. (1979). The problem of teaching story problems. Arithmetic Teacher, 27, 3-4.

Documents

Personalizing context in teaching mathematical concepts: Teacher-managed and computer-assisted models