Learner Control of Context and Instructional Support in Learning Elementary School Mathematics

[ ] Gary R. Morrison Steven M. Ross Walter Baldwin

Gary R. Morrison and Walter Baldwin are with the Department of Curriculum and Instruction and Steven M. Ross is with Foundations of Education at Memphis State University

Learner-control strategies for selecting prob- lem context and the level of instructional support were examined separately and in combination on a computer-based mathemat- ics unit on the metric system. Subjects were 240 sixth-grade students assigned to 15 treatments formed by crossing five context conditions (animals, sports, clothing, no- context, and learner control) with three instructional support conditions (minimum, maximum, and learner control). As hypothe- sized, comparisons of instructional support conditions on posttest achievement showed performance to be lowest under learner con- trol. Subjects opted to view very few items and to decrease the amount they selected over the course of the instruction. No effects were associated with the context variable, although on one of the three lessons, learner-control subjects made significantly fewer on-task errors than did no-context subjects. Further analyses showed a strong tendency by learner- control context subjects to vary their selec- tion of contexts across lessons. Subjects in the context and instructional support learner- control strategies indicated positive attitudes toward the strategies.

[] An increasing focus in research on compu- ter-based instruction (CBI) is strategies for making lesson materials more adaptive for stu- dents (Hooper & Hannafin, 1991). From an instructional design perspective, the rationale is that, by accommodating the needs of indi- vidual learners, adaptive lessons have bene- tidal consequences for both motivation and cognition (Ross & Morrison, 1989). Two strat- egies that have shown potential for these purposes are adaptation of the amount of instructional support prescribed (Ross & Ra- kow, 1982; Tennyson & Rothen, 1977; see review by Whitener, 1989) and adaptation of the context or theme of text presentations (Anand & Ross, 1987; Bracken, 1982; Lopez & Sullivan, 1991; Murphy & Ross, 1990; Ross, McCormick, & Krisak, 1986). The former type of adaptation helps eliminate the problem that occurs in conventional instruction when high achievers receive "too much" support and become bored with the lesson, and low achievers receive too little support and become frustrated. The latter (contextual) adaptation helps ensure the material is relatable to stu- dents' backgrounds and interests and thus serves to promote attention and meaningful learning.

When considering ways to individualize instruction, a natural question is the degree to which students can make effective decisions on their own using learner control. Although results from the extensive research on learner

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control is inconsistent, an overall conclusion is that many students, especially low achiev- ers, lack the knowledge and motivation to make effective decisions regarding such con- ditions as pacing (Gay, 1986; Reiser, 1984), sequencing of context (Judd, Bunderson, & Bes- sent, 1970; Seidel, 1975; Seidel & Wagner, 1978), use of learning aids (Carrier & Sales, 1987), and amount of practice (Ross & Rakow, 1981; Tennyson, 1980; Tennyson & Buttrey, 1980).

On the other hand, it seems likely that stu- dents would be more knowledgeable than computers or their teachers about the types of contexts (e.g., application themes) that interest them most. For example, Ross et al. (1986) gave college students majoring in nurs- ing or education the option of selecting from several alternative themes (e.g., sports, med- icine, or education) to which examples and explanations in a statistics lesson would be related. Findings showed that these learner- control subjects tended to select themes that related to their major and performed better than control subjects who were prescribed standard themes. In another study, subjects using learner control to select the density of text (high or low contextual support) in CBI presentations performed better than subjects given standard-density presentations (Ross, Morrison, & O'Dell, 1988). Further, poorer readers in that study appeared to use learner control effectively by selecting high contextual support more frequently than low contextual support.

More recently, Ross, Morrison, and O'Dell (1989) found that college students significantly increased the number of supporting examples they elected to receive on a CBI statistics les- son when they were also permitted to choose the application theme (education, sports, business, or no-context) of those examples. However, neither learner control of number of examples nor of type of context affected achievement relative to control conditions. The authors inferred that, although interesting contexts appeared to increase subjects' inter- est in the task, the high difficulty of the par- ticular unit might have attenuated treatment effects.

The present study was designed to evalu- ate a comparable learner-control model devel- oped for use with elementary school children.

Overall purposes were (a) to examine how younger students (sixth-graders) would em- ploy the two types of learner-control strate- gies (instructional support and context), and 00) to determine strategy effects on learning and task interest. It was hypothesized that learner control of context would facilitate learning by enabling subjects to relate math- ematical concepts to applications they found more familiar or interesting. In contrast, sub- jects were expected to lack the maturity and knowledge to use learner control of instruc- tional support in accord with their learning needs. Specifically, it was expected that most individuals--low and high achievers alike--- would tend to select fairly low levels of sup- port throughout the lesson. The hypothesized result was poor performance in the learner- control treatment relative to a control treat- ment in which full ("maximum") support was provided.

M~HOD

Subjects and Design

Subjects were 240 sixth-graders from a uni- versity elementary school that serves a racially balanced population with a range of abilities. Subjects were randomly preassigned to 15 treat- ments formed by crossing five context condi- tions (animals, sports, clothing, no-context, and learner control) with three instructional support conditions (minimum, maximum, and learner control). Treatment n's varied from 13 to 19. These variations in treatments were due to two unanticipated problems. First, several subjects were absent the day they were scheduled to participate and could not attend at an alternative time. Second, in some sessions the number of subjects preassigned to a treatment was greater than the number of computer disks prepared for the treatment, in which case subjects were randomly assigned to other treatments.

Dependent variables were performance on an achievement posttest and reactions to the lesson as expressed on an attitude survey. In addition, analyses were made of learner-con- trol subjects' selections of instructional support

LEARNER CONTROL OF CONTEXr AND SUPPORT 7

and/or contextual options, and the relation- ships between those choices and selected indi- v idual difference variables. Al though the materials were directly related to topics in the math curriculum, no incentive was provided for part icipating in the study.

Mater ia l s

Instructional Unit

The learning material consisted of a three-part instructional unit on the metric system, cov- ering the topics of centimeters, decimeters, and meters. Accompanying the unit was a workbook that gave basic instructions and information relevant to some of the practice items (see discussion below). The unit was developed in collaboration with the two math- ematics teachers at the school and on the basis of a pretest adminis tered the year before to a pilot sample of 43 students. The pilot sample was also asked to rank order, on the basis of personal interest, ten themes to which the metric problems could be applied. The three themes receiving the highest mean rankings were "animals ," "spor ts , " and "clothing," respectively. These themes were then adopted as the contexts for the present unit.

Individual lessons on the three metric mea- sures were des igned ident ical ly in format. Specifically, each began with a s tandard intro- duction to the unit that identified the specific measure. This section was followed by a sec- ond, topic-specific section that def ined the measure and illustrated it using three exam- ples of context-related instances that would approximate the length concerned. For exam- ple, the topic-specific section for "centimeters" (animals-context version) read as follows:

A centimeter is smaller than a decimeter. It is 1/10 of a decimeter or 1/100 of a meter. A centi- meter is close to .4 (four-tenths) of an inch in length; about 2.5 (two and one-half) centimeters equal 1 inch. When we measure different kinds of animals, we frequently come across centime- ter lengths. Lees think of some examples that are about 1 centimeter. [A list of three examples followed.]

Following the introduction, from one to four support ing practice items were presented, the

exact quant i ty of which d e p e n d e d on the t reatment condition. The specific i tems ap- peared in the same sequence (positions 1-4) for all subjects. The first three i tems were multiple-choice word problems. Following an incorrect answer, verbal feedback presented on the computer screen indicated why the choice was incorrect. A subject could make a maximum of eight a t tempts to answer each of the first three questions.

Practice item I asked which of four context- related instances was closest to the length of the target metric measure. Item 2 involved converting a metric length to inches or feet. Item 3 involved indicating which of four lines shown on the monitor was closest to an iden- tified metric length. Item 4 required drawing a line of a specified metric length, which could then be compared for feedback purposes to a line of the correct length on a designated page of the workbook. For the lesson on meters, space limitations for representing meter lengths necessitated replacing the latter two graph- ics items with two verbal items parallel in form to items 1 and 2.

Contextual variations involved relating the practice items to different themes- -an imals , sports, clothing, or no-context. The latter con- text used general or abstract labels such as "object" or "thing" without reference to a spe- cific concept category. Parallel i tems compris- ing the four context sets were identical in structure and as closely matched as possible in the composit ion of the correct answer and distractors in relation to the metric measure assessed. To illustrate, Table 1 shows i tem 1 for decimeters as it was represented in each of the four contexts.

The procedures for administering items fol- lowed those used in the Ross et al. (1989) study. Subjects assigned to the four s tandard context condit ions received the same context on all items. Learner-control subjects selected the context they preferred at the beginning of each lesson. All lesson items were then pre- sented in that context.

Instructional suppor t variations consisted of present ing four practice items on each les- son in the "maximum" condition and one item on each lesson in the "min imum" condition. In the learner-control condition, subjects were asked after viewing the first item whether they

ETR&D, Vol. 40, No. 1

TABLE 1 [ ] Example of Parallel Items Represented in Each Treatment Context

Sports* John hits a fly ball to the outfield. The fielder jumps and misses it by I decimeter. About how close did he come to the ball?

a. I inch b. I foot c. 4 inches d. 2 feet

Clothing Gloria tries on her new tight-legged jeans. She can't fasten them because the waist is I decime- ter too short. About how much longer should the waist be?

Animals A cat tries to squeeze under a fence to catch a mouse. The opening in the fence is 1 decimeter too small. About how much larger should the opening be?

No-Context An object is 1 decimeter too short to fit correctly. About how much longer should the object be? *The exact set of multiple-choice alternative s was used on all context variations of a given example.

wanted to receive another. This selection option was repeated after the second and third items but not the fourth, thus allowing a range of from one to four items on each of the three lessons.

Instructions encouraged subjects to com- plete the lesson at their own pace and to ask the proctor any questions that arose. To in- crease experimental control over the learning activities, the lessons and items were admin- istered sequentially, with no opportuni ty to bypass any content or review old material.

Instrumentation

Attitude Survey

The attitude survey consisted of five core items that asked subjects to react, using a five-point Likert scale (1 = strongly disagree, 5 = strong- ly agree), to computer learning, the metric system, mathematics learning, the particular lesson, and the sufficiency of items. Internal- consistency reliability for this scale, computed using the KR-20 formula, was .75. Subjects in the instructional support and context learner- control groups received an addit ional item, one per learner-control treatment, concerning the desirability of being allowed to make the co r r e spond ing learner-control choices dur-

ing learning. All items were presented on the computer and responses were made via key- board input.

Achievement Posttest

The posttest consisted of 17 computer-pre- sented items designed to measure knowledge and performance. Performance items (n = 4) asked subjects to draw I centimeter and I deci- meter lines, respectively, using the comput- er 's right arrow key to lengthen the line and the left arrow key to shorten the line; later in the test, subjects used paper and pencil. The remaining 13 items were multiple-choice ques- tions testing knowledge of the lengths of the three metric measures (n = 5; e.g., "How many inches equal I centimeter?" and "Which of the following four lines is closest to I deci- meter in length?") and ability to identify com- mon objects approximating those lengths (n = 8; e.g., ' ~ hole in a pencil sharpener is dos- est to _ _ wide.") . The latter items were con- veyed in a variety of contexts and were parallel forms of practice items 1 and 2 from the les- sons. Two parallel versions of the test were developed and administered randomly to sub- jects. Internal-consistency reliabilit{es for Forms A and B, computed by the KR-20 formula, were .70 and .80 respectively. Preliminary data anal- yses failed to show main effects or interactions

LEARNER CONTROL OF CONTEXT AND SUPPORT 9

with treatment variables due to test form; thus, the two forms were combined for the final achievement analyses.

Procedure

Subjects were scheduled to complete the instruction in small, mixed treatment groups of three to five individuals. Each was seated at an Apple IIe computer with a monochrome monitor and given a workbook and an instruc- tional disk corresponding to his or her as- s igned t reatment . Instruct ions on the disk p resen ted an overview of the lesson and described how to respond on the computer. A proctor remained in the room throughout the session to answer any questions. At the completion of the instruction, the atti tude sur- vey and the posttest were administered on the computer.

RESULTS

A c h i e v e m e n t

On-task

To determine whether context variations pro- duced differential performance on the lesson items, a one-way analysis of variance (ANOVA) was performed on the number of trials taken on each lesson item (the more trials needed, the greater the difficulty experienced), with the five contextual variations as the indepen- dent variable. I tems 1-3 were included; i tem 4, which involved drawing, was not. Trials for each prototype were averaged across the three metric lessons. For item 1, all subjects were included; for items 2 and 3, only those sub- jects in the maximum instructional suppor t condi t ion the only group that always re- ceived i tems 2 and 3---were included.

ANOVA results showed no context effects on items 1 and 2. For item 3, however, the analysis yielded a significant difference F(4, 78) = 2.54, MSe = 3.74, p < .05. Follow-up comparisons of means were performed using the Tukey HSD test (alpha = .05). The only significant difference was between the no-con- text group, which averaged the highest num- ber of tries (M = 2.19), and the context learner-

control g roup , which averaged the lowest number (M = 1.74). Other means were sports, M = 2.05; clothing, M = 2.02; and animals, M = 1.91.

Posttest

Posttest achievement was analyzed via a 5 (con- text) x 3 (support) ANOVA. Treatment means and standard deviations are displayed in Table 2. Results showed a significant main effect for instructional support , F(2, 225) = 3.05, MSe = 9.98, p < .05. Neither the context main effectnor thecontext x support interaction was significant. Follow-up analysis of the suppor t effect using Tukey HSD tests showed that max- imurn suppor t (M = 7.30), which had the highest mean, significantly (p < .05) surpassed learner control (M = 6.02), which had the low- est mean. Minimum suppor t (M = 6.96) did not differ significantly from either of the other two conditions.

To analyze accuracy on the four drawing items, error scores were initially derived by computing the absolute value of the difference between the target measure (centimeters or decimeters) and the lines drawn by the sub- ject. These error scores were then d iv ided by the target line length to yield an error ratio. For the two computer drawings, the overall mean error ratios were 2.06 and .48 for centi- meters and decimeters, respectively. For the two paper-and-pencil measures, the respec- tive mean error ratios were 1.5 and .39. Thus, s tudents, in general, had difficulty construct- ing line estimates of the measures, especially in the case of centimeters, for which over 90% of the errors were overestimates. It is notewor- thy, however, that the direction of the results suggested that the lines drawn by hand tended to be more accurate than those constructed on the computer, even though instruction was primari ly computer-based.

Treatment effects on drawing accuracy were then assessed by conduct ing a 5 (context) x 3 (support) MANOVA on the error ratio scores for the two paper-and-pencil and two com- puter items. The main effect of suppor t was the only significant multivariate effect (p < .001). The univariate suppor t effect was sig- nificant for the decimeter pencil drawing, F(2,

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TABLE 2 [ ] Posttest Means and Standard Deviations for Context x Instructional Support Treatments

CONTEXT

INSTRUCTIONAL SUPPORT

Minimum Maximum Learner-Control MEAN (SD) MEAN (SD) MEAN (SD)

Sports 6.57 (3.37) 6.85 (3.18) 5.14 (3.39) Clothing 7.47 (3.20) 6.60 (3.04) 6.06 (3.38) Animals 7.31 (3.75) 7.47 (3.31) 7.38 (2.79) No-Context 7.05 (3.70) 6.07 (2.89) 5.88 (2.36) Learner-Control 6.47 (2.57) 9.17 (2.79) 5.78 (3.28) Total 6.96 (3.28) 7.30 (3.17) 6.02 (3.07) Note: Possible range of scores was 0-13. Posttest items involving drawings (n = 4) were excluded.

225) = 9.83, MS~ = 7.33, p < .001, but not for the centimeter pencil drawing or for either computer drawing. Tukey follow-up analyses indicated that error scores on the decimeter pencil drawing were lower (p < .01) for maxi- mum suppor t (M = .27) than for minimum support (M = .43) and learner control (M = .45). The direction of the suppor t t reatment error means on the other drawings were con- sistent with this pattern, but the univariate ANOVA results were not significant.

highest obtained on all at t i tude items. Thus, subjects appeared quite posit ive about the learner-control options.

Learner-Control Selections

A final set of analyses was conducted to exam- ine the nature of learner-control selections and their relation to different performance and affective outcomes.

Survey Results

Responses to the five core survey items (max- imum item score = 5.0) were analyzed via a 5 (context) x 3 (support) MANOVA. The mul- tivariate effect was significant for the instruc- tional suppor t variable. Significant univariate effects of suppor t (p < .05) were indicated on item 3, "I like learning the lesson on the com- puter," and item 5, "The metric system was easy to learn." Tukey follow-up tests indicated that, in both cases, the only significant differ- ence was that the minimum-suppor t group reacted more positively than the maximum- suppor t group (M = 4.48 vs. M = 3.90 on item 3; M = 4.36 vs. M = 3.96 on item 5).

Additional analyses examined the reactions of suppor t learner-control subjects and con- text learner-control subjects to their respective control t rea tments (items 6 and 7). Those means (4.72 and 4.70, respectively) were the

Context Selection Patterns

Examination of context learner-control group's selections showed the highest total frequency for sports (f = 51), followed by animals (f = 48), clothing (f = 35), and no-context ~f = 29). This ordering was similar to that obtained in our pilot survey of context preferences, except that the ordering of the two most popular contexts---animals and spor ts - -was reversed. A repeated-measures ANOVA performed on total context selections yielded F(3,159) = 3.04, MS~ = .69, p < .05. None of the Tukey follow-up comparisons was significant.

Also examined was the number of different contexts context learner-control subjects opted to view across the three lessons (one for each lesson). Relative percentages revealed that 63.0% of the sample selected three different contexts, 20.4% selected two different con- texts, and only 16.6% selected one context throughout. The number of contexts selected

LEARNER CONTROL OF CONTEXT AND SUPPORT 11

was correlated with posttest scores and atti- tude item scores. Only one correlation was significant ( r = - .33, p < .05), indicating a ten- dency for subjects who found the lesson easy to learn to show less variation in their con- text selections.

Instructional Support Selections

Frequency data for support learner-control subjects (n = 73) indicated that the highest percentage (42.3%) selected a total of only three items across the three lessons, with approximately 40% selecting a total of four or five items (minimum = 3). Only one individ- ual selected the maximum level of 12 items. Correlations of the quantity of support se- lected with attitude item scores and posttest scores showed no significant relationships. In fact, correlations of posttest scores and atti- tudes toward math with the quantity of sup- port selections were almost zero ( - . 0 6 and. 05, respectively).

In a final analysis, the relationship of con- text received to the quantity of support se- lected was examined via a one-way ANOVA comparing the five context groups. The anal- ysis yielded F(4,73) = 8.61, MSe = 3.26, p < .05. Follow-up analyses indicated that the animals-context group (M = 5.71) selected sig- nificantly more items than did the clothing- context group (M --- 3.64). Other means were learner control, M --- 4.33; no-context, M = 4.25; and sports, M = 4.06.

DISCUSSION

It was hypothesized that giving learners the opportunity to exercise control over instruc- tional content would be beneficial to achieve- ment in the case of context (theme of items) but detrimental in the case of quantity of sup- port (number of items received). This hypoth- esis received partial support from the research results. Specifically, whereas the predicted instructional support effects were evidenced on several dependent measures, context ef- fects were found in only one comparison: that showing the learner-control group to surpass the no-context group on on-task responses

to item 3. Interpretations of these findings are provided below.

Our theoretical rationale regarding the con- text learner-control strategy was that it would facilitate learning by increasing both learner motivation and ability to relate the lesson material to existing knowledge, as was sup- ported in previous studies (Ross et al., 1986; Ross & Anand, 1987). On the one hand, results of the attitude survey suggest that sub- jects reacted extremely favorably to the con- text learner-control options, with close to 90% indicating strong agreement with the state- ment "I liked being able to pick the different topics for items." It was also the case that about two-thirds of the sample, especially those who experienced difficulty with the unit, opted to vary the material to the maxi- mum extent possible by selecting a different context on each lesson. By comparison, Ross et al.'s (1989) college-level subjects were much less inclined to vary contexts, with as many as 39% selecting the same context on eight successive lessons.

Despite subjects' apparent receptivity to the context strategy, benefits for posttest achieve- ment did not occur. Two factors that might have limited contextual influences are sug- gested. First, the posttest means (see Table 1) indicate that the material was relatively diffi- cult for subjects. Although the selected con- texts may have made particular items more interesting and memorable, they did not change either the basic instructional methods or the lesson content. Second, as in Ross et al. (1989), the contextual variations, which simply involved substituting theme-related referents in brief items, may not have been suf- ficiently powerful to increase the meaningful- ness of the mathematical concepts conveyed. In contrast, the personalized items (Anand & Ross, 1987; Davis-Dorsey, Ross, & Morrison, 1991; Lopez & Sullivan, 1991; Ross & Anand, 1987) and integrated themes (Ross, 1983; Ross et al., 1986) used in previous studies appear to have provided more salient and substan- tive contextual adaptations.

A second research focus was the effective- ness of learner control of instructional support. As hypothesized, the instructional support learner-control group had the lowest scores on

1 2 ~ , vow. 40, No. 1

the posttest measures (on both problems and drawings). Examination of the support selec- tions on the unit suggests one explanation. Similar to the high school and college students tested in previous studies (e.g., Carrier & Sales, 1987; Ross & Rakow, 1981; Tennyson & Buttrey, 1980), the present elementary-school subjects tended to select minimal instructional support (less than 1.5 items per lesson). This behavior occurred despite their generally favor- able reactions toward the lesson. Further, cor- relations of the quantity of support selected with attitude and performance measures were close to zero. The implication is that there was no tendency for lower-ability sub- jects to seek more instructional support rela- tive to their peers.

It may seem unusual that learner-control subjects failed to outperform minimum-sup- port subjects, who received the fewest items of all treatments. One consideration, however, is that the support differential between the learner-control and minimum-support groups was actually quite small, approximating only .5 items per lesson. Another may be the pos- sibility that subjects in the minimum-support group took relatively greater advantage of the items they did receive, recognizing that no opportunities to receive additional support would follow.

Considering the context and support strat- egies in combination, an underlying assump- tion of this research was that when students could select application themes that interested them, they would be more likely to select addi- tional supporting items. Although this as- sumption was directly supported by Ross et al. (1989) using college students, it was not supported in the present study using elemen- tary-school students. The group that received the animal context--the second most fre- quently selected theme by learner-control subjects (after sports)--selected the greatest number of items; the group receiving the clothing context selected the least. Contrary to expectations, context learner-control sub- jects did not differ in their support selections from any of the other groups.

Taken as a whole, these results provide additional insights into the effects and prac- tical uses of contextual adaptation and learner

control in computer-based learning. Major conclusions are summarized as follows. First, elementary-school students appear receptive to learner control of context and try to use it adaptively. Specific examples are selecting themes that interest them and changing selec- tions across lessons to increase the variety of the presentation.

Second, contextual variations that are re- stricted to simple word substitutions in brief examples (as done here) may not be suffi- ciently substantive to increase the meaning- fulness of the material. Consequently, the impact on learning may be limited. More pow- erful approaches appear to lie in designs that personalize materials for individuals (Anand & Ross, 1987; Davis-Dorsey et al., 1991; Lopez & Sullivan, 1991) or present sets of problems relating to an integrated theme (see Murphy & Ross, 1990; Ross et al., 1986).

Third, similar to older subjects (Carrier, Davidson, & Williams, 1985; Ross et al., 1989; l~ss & Rakow, 1982; Tennyson, 1980), elemen- tary-school children appear to use learner con- trol of instructional support ineffectively by selecting only a minimum number of exam- ples. Another factor affecting the poor perfor- mance of the learner-control group might have been the lack of extrinsic incentive to perform well in an artificial learning setting. The amount of instructional support (i.e., the number of items selected) might be greater in realistic contexts where performance actu- ally counts toward grades. It seems unreason- able to assume that young students would possess sufficient metacognitive skills, subject matter knowledge, and self-discipline to be able to diagnose personal needs and follow through accordingly in their selections of prac- tice materials. A preferable CBI design, it would seem, would be to use program (com- puter) control of support adapted to on-task performance (e.g., Tennyson & Rothen, 1977) or computer advisement ("coaching") on how much support to select (e.g., Tennyson & Buttrey, 1980). []

The authors would like to acknowledge the cooperation of the Memphis State University Campus School with this study.

LEARNER CONTROL OF CONTEXTAND SUPPORT 13

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