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1 WORKING MEMORY CAPACITY AND EXTRANEOUS COGNITIVE LOAD DURING STRATEGY INSTRUCTION By JENNI L. SCHELBLE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENT S FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012
2 2012 Jenni L. Schelble
4 ACKNOWLEDGMENTS I thank my advisor, Dr. David Therriault, for his mentorin g and high standards which have taught me to strive for excellence as a researcher. I also thank Dr. M. David Miller, for hi s support and guidance throughout this process. I am grateful to my fellow graduate students, past and present, whose empathy and e ncouragement gave me many needed boosts along the way. Finally, I thank my family, including canines, for always being available t o listen and provide diversions.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ............................. 9 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 STATEMENT OF THE PROBLEM ................................ ................................ ......... 12 Introduction ................................ ................................ ................................ ............. 12 Working Memory: Cause or Effect of Strategies? ................................ ................... 12 The Effect of Strategies on Working Memory Performance .............................. 14 Other Factors Influencing Strategy Use ................................ ........................... 15 Working Memory and Strategy Use during Academic Tasks ................................ .. 16 Can Individuals with Low Working Memory Learn to Use Strategies Effectively? ... 19 Effects of Working Memory on Strategy Instruction Effectiveness .......................... 19 Working Memory and Cognitive Load During Instruction ................................ ........ 21 Theoretical Implications of Examining the Effect of Strategy Instruction on Performance ................................ ................................ ................................ ........ 22 Practice as a Determining Factor in Successful Strategy Use ................................ 25 The Present Study ................................ ................................ ................................ .. 27 General P redictions ................................ ................................ .......................... 27 Predicted Strategy Learning as a Function of Working Memory and Condition ................................ ................................ ................................ ....... 28 Predicted Problem Solving Differences as a Function of Working Memory and Strategy Learning ................................ ................................ ................... 29 Predicted Differences in Perceived Cognitive Load as a Function of Working Memory ................................ ................................ ........................... 29 2 METHOD ................................ ................................ ................................ ................ 31 Participants ................................ ................................ ................................ ............. 31 Materials ................................ ................................ ................................ ................. 31 Procedur e ................................ ................................ ................................ ............... 32 Low Load (Backwards Fading) Instruction Condition (Condition A) ................. 32 High Load (Example Problem Pairs) Instruction Condition (Condition B) ........ 33 Control Condition with Explanation (Condition C) ................................ ............. 33 Control Condition without Explanation (Condition D) ................................ ........ 34
6 3 RESULTS ................................ ................................ ................................ ............... 35 Descriptive Statistics ................................ ................................ ............................... 35 Differences in Problem Solvin g Performance and Cognitive Load as a Function of Learning Condition ................................ ................................ .......................... 35 Differences in Post Training Test Performance as a Function of Condition ............ 37 Differences in Strategy Use Success as a Function of Condition ........................... 38 Effects of Working Memory and Cognitive Load on Strategy Learning ................... 38 Effects of Working Memory, Strategy Instruction, Strategy Use, and Cognitive Load on Problem Solving During Learning ................................ .......................... 40 Effects of Working Memory, Strategy Instructi on, Strategy Use, and Cognitive Load on Post Training Problem Solving ................................ .............................. 41 Effects of Working Memory and Condition on Self Reported Cognitive Load ......... 44 4 DISCUSSION ................................ ................................ ................................ ......... 46 Learning Condition and Problem Solving Performance ................................ .......... 46 Strategy Use and Problem Solving Perfo rmance ................................ ................... 47 Effect of Perceived Cognitive Load on Problem Solving Performance ................... 49 Working Memory as a Predictor of Problem Solving Performance ......................... 50 Factors Influencing Successful Strategy Use ................................ .......................... 51 ................................ ... 52 Theoretical Implications ................................ ................................ .......................... 53 Practical Implications ................................ ................................ .............................. 55 Limitations ................................ ................................ ................................ ............... 56 Future Directions ................................ ................................ ................................ .... 56 Conclusion ................................ ................................ ................................ .............. 58 LIST OF REFERENCES ................................ ................................ ............................... 60 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 65
7 LIST OF TABLES Table P age 3 1 Descriptive statistics for probabilit y pro blem solving variables .......................... 35 3 2 Mean post training test scores, problem solving scores during learning, and self reported cogni tive load by condition ................................ ........................... 38 3 3 Analysis of variance for strat egy use during learning ................................ ........ 39 3 4 Correlation matrix of variables included in line ar regression analyses .............. 43 3 5 Linear regression of variables related to post training test performance ........... 44
8 LIST OF FIGURES Figure P age 1 1 Theories of the relationship between WM and strategy use. .............................. 30
9 LIST OF ABBREVIATION S HWM High working memory capacity LWM Low working memory capacity WM Working memory. Our limited capacity to simultaneously store and process information for a brief period of time. Also referred to as attentional capacity.
10 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the D egree of Doctor of Philosophy WORKING MEMORY CAPACITY AND EXTRANEOUS COGNITIVE LOAD DURING STRATEGY INSTRUCTION By Jenni L. Schelble May 2012 Chair: David J. Therriault Major: Educational Psychology Strategy use may play an important role in individual differences related to working memory (WM) capacity (Dunlosky & Kane, 2007; McNamara & Scott, 2001; Rosen & Engle, 1997). When individuals are engaged in a demanding task, subjecting them to additional cognitive load has different effects as a function of their working memory (WM) capacity. I examined the relationships between WM, cognitive load, and strategy learning condition. I hypothesized that individuals with low WM span would have more difficulty learning strategies, and that strategy use would be positively related to scores on the probability problem solving posttest. I also predicted that the level of cognitive load in the learning condition would interact with WM capacity to influence both strategy learning and pro blem solving performance. One hundred and eighty college students completed a mathematical problem solving task under one of four conditions, each with a different level of cognitive load. WM ability to learn a new strategy, supportin g the strategy as effect hypothesis of WM (Dunlosky & Thiede, 2 004a). H igher WM was associated with greater strategy learning success when the learning condition was novel and when overall performan ce in the condition was lower. P erceived cogn itive load wa s affected
11 preexisting knowledge about the topic, but no t by their WM capacity. Participants performed better in a more traditional learning format, and the relationship between WM and strategy learning disappeared in this format. Together th ese results indicate that reducing cognitive load during strategy learning is an effective way to teach strategies particularly to individuals with low WM capacity.
12 CHAPTER 1 STATEMENT OF THE PRO BLEM Introduction Research on connections between selectiv e attention and working memory (WM) has resulted in a greater understanding of the role individual differences play during demanding tasks (Conway, Cowan, & Bunting, 2001; Cowan et al., 2005; Engle & Kane, 2004; Gathercole et al., 2008). Strategy use may p lay an important role in individual differences related to WM capacity (Dunlosky & Kane, 2007; McNamara & Scott, 2001; Rosen & Engle, 1997). Some researchers have proposed that strategies are the cause of individual differences in WM (Cokely, Kelley, & Gil christ, 2006; Dunlosky & Kane, 2007; McNamara & Scott, 2001), and others argue that WM capacity constrains Turley Ames & Whitfield, 2003; Schelble, Therriault, & Miller 2012 ). Both strategy use and WM capacity influence performance on reading (Linderholm & van den Broek, 2002; Linderholm, Cong, & Zhao, 2008), mathematical (Keeler & Swanson, 2001; Geary, Frensch, & Wiley, 1993), and retrieval tasks (Rosen & Engle, 1997; Schelble, Therriault, & Miller, 2012 ). The purpose of this dissertation study was examine, via a laboratory experiment, how strategy use relates to WM, whether strategies can be successfully taught to individuals, and whether cognitive load affects strateg y instruction effectiveness. Working Memory: Cause or Effect of Strategies? Theories on the direction and magnitude of the relationship between WM and strategy use differ substantially. Providing evidence that informs our understanding of the relationshi p between WM and strategies is important for theoretical an d practical
13 purposes. Figure 1 1 summarizes the differences between the strategy as effect (Dunlosky & Thiede, 2004 a ) and strategy as cause (Dunlosky & Kane, 2008) views of the WM/strategy relations hip, as well as related theories that fall under each of these general views. According to the strategy as ef fect hypothesis, (Dunlosky & Th i e de, 2004 a ), WM items for recall, indi vidual s with hig h WM ( HWMs ) were more likely to use a strategy that made the task less difficult, even though all participants were instructed to use the str a teg y Dunlosky and Thiede interpreted this finding as evidence that HWMs were more capable of employing the strategy than individuals with low WM ( LWMs ) Evidence of lack of strategy use in young children (Guttmann, Levin, & Pressley, 1977) and span differences in performance following strategy instruction (Turley Ames & Whitfield, 2003) provide additional suppo rt for the strategy as effect hypothesis (Dunlosky & Thiede, 2004a) because they suggest that capacity is a determining factor in whether a strategy can be successfully employed. McNamara and Scott (2001) found that participants who demonstrated independe nt use of more effective memory strategies also demonstrated better verbal task performance, providing support for the strategy mediation hypothesis. McNamara and Scott described two ways in which strategy use and WM are related: natural strategy use is re lated to individual differences in WM task performance, and induced strategy use can improve task performance. The strategy affordance hypothesis takes the strategy mediation hypothesis a step further: It states that strategy use will mediate the relations hip between WM capacity and performance on cognitive tasks only if the
14 same strategies can be utilized on both types of tasks (Bailey, Dunlosky, & Kane, 2008). In a comparison of performance on WM, memory, reading, and general cognition tasks, WM correlate d with use of strategies previously classified as effective (Bailey et al., 2008). However, WM task strategy use was unrelated to reading comprehension performance. Even when both tasks afforded use of the same strategies, the relationship between WM and o ther measures was only partially mediated by strategy use. When both tasks did not afford use of the same strategies, strategy use failed to mediate the relationship between performance on those tasks. This finding is important when considering strategy in struction: Students must be both proficient in use of the strategy, and be engaged in a task to which the strategy is applicable (and to which they are aware that the strategy is applicable, see Atkinson, Renkl, & Merrill, 2003). For example, a student who is taught a multiplication strategy during regular, digit only mathematical problems might not independently apply the strategy during word problem solving, if the strategy was not explicitly taught with word problems. The Effect of Strategies on Working Memory Performance The relationship between WM capacity and attentional control may be partially explained by strategy use (Cokely, Kelley & Gilchrist, 2006). Many researchers conceive of WM capacity as attentional control (Engle & Kane, 2004). Cokely et a l. initially found a curvilinear relationship between WM span and interference. During free recall, HWMs outperformed LWMs. However, HWM participants exhibited greater interference effects during a recall task that required participants to learn multiple l ists when prompted with cues from the correct list. The highest HWM participants reported using interference prevention strategies when presented with cues (such as not looking at the cue words). When all participants were required to view cues, a positive linear
15 relationship between span and interference was o btained change as a result of cue presentation. Cokely et al. suggested that this finding was due process cues. When all participants were trained to use a recall strategy (linking the to be remembered words together in story format), no span differences in interference effects were found. Learned, as opposed to innate strategies, may account for diffe rences in span performance (Cokely et al., 2006; Ericsson & Kintsch, 1995; McNamara & Scott, 2001). Training LWMs to use effective strategies reduced span differences in recall performance. This suggests that performance differences may not result purely f rom capacity differences, because, following training, LWMs were able to effectively employ strategies they had not previously employed on their own. Other Factors Influencing Strategy Use Task characteristics may also affect strategy use. Fluency may par tially explain strategy selection beyond the role of WM. The term fluency refers to how difficult an individual perceives a task to be (Oppenheimer, 2008). From a dual process perspective, more fluent activities require less WM (Evans, 2007). In addition t o factors such as cognitive resources and motivation, an individual may choose to adopt a more demanding strategy based on their expectation that a simpler strategy will be unsuccessful (Oppenheimer, 2008). One important consideration is whether WM capacit participants with high WM capacity have different expectations for the success of more/less complex strategies than participants with low WM capacity?). The cognitive load of inst
16 HWMs and LWMs, because of their differing attentional capacities, may experience the same instructional condition differently (in terms of fluency). During recall tasks, particip ants often rely on previously learned strategies, even if semantic strategies (Atki ns & Baddeley, 1998). During strategy instruction, a high level of cognitive load may prevent individuals from effectively learning strategies, and consequently prevent them from employing strategies on future tasks. If the level of cognitive load during i nstruction does not prevent individuals from acquiring the Working Memory and Strategy Use during Academic Tasks Previous research on the relationship between WM and mathemat ical strategy use points to a central question in the relationship between WM and strategy use: Are individuals with high WM capacity capable of different strategies than individuals with low WM capacity, or are they simply better at executing the same str ategies? The variation in strategy use in accordance with age (Geary et al., 1993; Imbo & Vandierendonck, 2007), from task to task (Barrouillet et al., 2008), and as a function of cognitive load ( Schelble, Therriault, & Miller, 2012 ) makes a definitive ans wer to this question difficult. The definition of what constitutes a strategy has also deterred the synthesis of research on strategy use: Some strategy research focuses on problem solving (Barrouillet et al., 2008; Imbo & Vandierendonck, 2007) and compreh ension processes (Linderholm et al., 2008; Swets et al., 2007), while other researchers use the 1999).
17 A fundamental difference exists between WM span performance itself an d individual differences that arise in other situations as the (partial) result of WM span. In reading, strategies are examined by look use of text during comprehension tasks (Linderholm & van den Broek, 2002; L inderholm et al., 2008). Mathematical strategies can be broken down into retrieval and non retrieval categories (Andersson, 2008; Barrouillet et al., 2008; Wu et al., 2008). Retrieval itself can consist of multiple strategies (Barrouillet et al., 2008; Sch elble, Therriault, & Miller, 2012 ) and is alternately conceptualized as pattern activation in long term memory (Ericsson & Kintsch, 1995). Evidence of differences in retrieval (Andersson, 2008; Schelble, Therriault, & Miller, 2012 ), mathematical (Barrouil let et al., 2008), and reading strategy use (Linderholm & Zhao, 2008) across HWM and LWM individuals, combined with evidence of differences in their performance under load (Rosen & Engle, 1997; Schelble, Therriault, & Miller, 2012 ), suggest that HWMs and L WMs approach use of the same strategies differently. However, additional research is needed in order to determine whether the level of cognitive load during strategy instruction affects individuals differently in accordance with their WM capacity. This goa l is particularly relevant for educational research, which is frequently conducted with eventual classroom application in mind. For example, retrieval strategy research frequently involves category fluency tasks (Rosen & Engle, 1997; Schelble, Therriault, & Miller, 2012 ) which may not be representative of the types of retrieval typically required in academic settings. Consider the types of retrieval students typically encounter in a testing situation: A specific item from a category (e.g., the 26th Presiden t of the United States) must be recognized or
18 recalled. Frequently, time limits are in effect, which prevent students from using strategies such as retrieving every category exemplar until the right one is located. In this case, the student may have stored presidential information in a chronological list of Accessing either type of information could assist the student with retrieving the correct president. Other assessm ents require students to determine which category exemplar should be retrieved in order to effectively solve a problem (e.g., a statistical word problem that requires the student to determine which statistical test is appropriate). In such cases, the stude nt must retrieve information from a variety of categories: the category that contains information about the purpose of each type of test, the category that contains information about how to carry out the formula for each test, and the significance rules fo the types of connections they made during learning and studying, each type of statistical test information could be stored in completely separate, isolated categories, or it could all be co nnected in a meaningful way that allows the student to relate, for example, relevant formulaic information to the significance rules for each statistical test. situation may have significant effects on their success. If HWM students approach academic tasks (such as recall, reading comprehension, and mathematical problem solving) in a systematically different way than LWM students, differences in strategy use could explain some of the performance differences between WM groups. However, simply determining whether there are strategy use differences between HWM and LWM groups does not provide useful information for determining whether certain strategies
19 are more easily employed by HWMs (the strategy as effect and strategy affordance hypotheses) or if WM span itself is explained by strategy use (the strategy as cause hypothesis). Can Individuals with Low Working Memory Learn to Use Strategies Effectively? In addition to the numerous situational variables that affect instances of storage and retrieval, individual differences in WM capacity may systematically influence a uperior strategies ( Schelble, Therriault, & Miller, 2012 ), it may be the case that they were able to pick up these strategies without instruction, but that LWMs would be able to employ them effectively if they were able to learn them under less demanding c onditions. WM capacity does not account for all variance in strategy use (Dunlosky & Kane, 2007; Schelble et al., 2012 ), and although HWMs may have more experience successfully employing effective strategies, the possibility that LWMs can learn to use thes e strategies has not been ruled out (Burton & Daneman, 2007; Linderholm & van den Broek, 2002). LWMs seem to be capable of adapting to their limited WM capacity, provided they have other advantages (e.g., mature epistemic beliefs, Burton & Daneman, 2007). The present study examines whether effective strategy instruction can afford LWMs similar advantages. Effects of Working Memory on Strategy Instruction Effectiveness to imp benefit less from strategy instruction because they are more likely to already employ effective strategies during WM tasks (p. 311). Participants (older adults) did not need additi onal cognitive resources to employ the specific strategy they were trained to use
20 when high and low WM participants are given the same strategy instructions, HWMs retain t heir superior performance due to their unprompted, pre training strategy use for LWMs may be of benefit, particularly in the case of academic strategies for which factors ot her than WM are known to impact strategy success. The effectiveness of self explanation strategies is dependent upon individual expertise levels (Renkl, 1997). Self explanation strategies involve explaining the steps of a problem to oneself during problem solving or while studying examples (Renkl, 1997). Self her self (Atkinson, Renkl, & Merrill, p. 776). Principle based self explanations are most effective for individuals with low prior knowledge (Renkl, 1997). Principle based self explanations consist of specifying the goal structure and explaining the principle illustrated by the problem or example An example of a principle based self explanation for a subtraction explanation strategy while completing practice problems has been found to be more effective than practicing self explanation while studying examples (Aleven & Koedinger, 2002). Self explanation has the potential for wide application; prompting students to explain the steps of a process to themselves while compl eting the process may be useful for many academic tasks. However, the ability to learn the self explanation strategy has not been previously examined.
21 Working Memory and Cognitive Load During Instruction activities that help them acquire and automate schemas (Sweller, 1994). Schemas are cognitive collections of information organized in ac cordance with how the information will be used. During initial learning, schema acquisition is important. Activities such as studying worked examples assist with schema acquisition, while minimizing the amount of cognitive load associated with instruction (i.e., extraneous cognitive load; Sweller, 1994). Two other types of cognitive load also affect the learning process: intrinsic load, which is associated with the material itself, and germane load, which improves learning by focusing resources on the acqui sition and automation of schemas (Paas, Tuovinen, Tabbers, Van Gerven, & Pascal, 2003). Intrinsic cognitive load is high during initial learning, and cannot be adjusted by the instructor. Germane load and extraneous load can, and should, be varied dependin g on the expertise level of the learner (Paas et al., 2003). Because WM impacts various areas of functioning, it is highly desirable for instruction related to improving the use of this capacity to transfer to contexts beyond the laboratory. Kuhn (2007) i nsisted that practicing problem solving skills is essential if students are to become effective problem solvers. WM has been frequently described as a component of problem solving, a skill that is necessary in many contexts, within and beyond educational s solving skills transfers to strategy use during WM tasks, practice applying strategies should be effective at increasing effective strategy use. Kirschner, Sweller, and Clark (2006) advocated for the use of direct i nstruction until learners have a substantial amount of prior knowledge about a topic. According to
22 Kirschner et al., inquiry based instruction imposes more extraneous cognitive load than direct instruction. The demands of inquiry based instruction can be c ompared to those of the final problem solving stage described by Paas et al. (2003), although researchers who advocate a direct instruction approach to instruction suggest that inquiry based instruction is more demanding (Kirschner, Sweller, & Clark, 2006) Chandler and Sweller (1991) described strategy use as typically related to extraneous cognitive load, because strategies and the load associated with their use can be modified by the instructor. However, if strategies are learned simultaneously with mate rial during initial learning, it is possible that strategy use could be associated with intrinsic load. impact on strategy use (Rosen & Engle, 1997; Schelble, Therri ault, & Miller, 2012 ) and strategy instruction effectiveness (Linderholm & Zhao, 2008). Thus, by varying the amount of cognitive load associated with strategy instruction, I sought to examine the effect of WM and its interaction with cognitive load during learning on strategy learning. Theoretical Implications of Examining the Effect of Strategy Instruction on Performance The present study is central to the strategy as cause versus strategy as effect debate. It may also be relevant to the strategy affordanc e hypothesis and the concept of long term WM. In their description of retrieval structures, Ericcson and Kintsch (1995) emphasized the importance of retrieval cues in accessing information stored in long term memory. Retrieval structures are said to be dom ain specific, and individual differences result from differences in encoding strategies (Ericsson & Kintsch, 1995). More expertise in an area results in more elaborate retrieval structures, which are used to access relevant information in long term memory. The concept of long term WM,
23 then, is similar to the idea of retrieval strategies. Experts have more elaborate retrieval structures (Ericsson & Kintsch, 1995) and individuals with higher WM capacity have demonstrated more frequent use of advantageous stra tegies (Dunlosky & Thiede, 2004b). If strategy instruction and sufficient practice opportunities improve the performance of LWMs, such a finding could be interpreted as support for the long term WM hypothesis because Ericcson and Kintsch acknowledged the p ossibility of improving memory capacity by learning to resist interference. If the acquisition of new strategies improves encoding (and/or retrieval), long term WM theorists might interpret this as expansion of long term WM. Some researchers who have foun d that WM performance improves after strategy training claim that strategy use is the reason for individual differences in WM performance (McNamara & Scott, 2001). Our previous research partially supports this idea, as we found considerable overlap in the types of strategies employed by HWMs and LWMs during a category fluency task, in addition to WM related differences in the use of the most successful retrieval strategy ( Schelble, Therriault, & Miller, 2012 ). However, this discrepancy is as much the result of task differences as it is the result of Schelble et al., 2012 ) focused on retrieval strategies used during a category fluency task; McNamara and Scott examined performance during a WM task after m nemonic device training. Is the fact that we can improve performance on a task intended to be completed somewhat automatically relevant to the question of how WM capacity affects other types of strategy use? Other researchers who have obtained similar find ings caution against conditions that allow for variation in strategy use because the interpretability of the relationship between WM
24 influences WM span scores (Turley Ames & W hitfield, 2003). Even after strategy instruction, HWMs have been found to outperform LWMs (Dunlosky & Kane, 2007; Turley Ames & Whitfield, 2003). Strategy use, then, may be a contributor to individual differences in WM capacity, but it does not completely explain capacity differences. The design of the present study contributes to our knowledge of whether this is still the case when LWMs are taught using methods that may make different demands on their WM capacity. If, as Rosen and Engle (1997) suggested, increased cognitive load makes it more difficult for HWMs to perform at their usually superior level, an instruction al condition that is more demanding may decrease their ability to learn new strategies. Kirschner, Sweller, and Clark (2006) advocated for m inimally demanding learning conditions when prior knowledge about a subject is limited. Specifically, they proposed the use of direct instruction. Strategy use can be considered a form of knowledge, however, it remains to be seen whether knowledge of one e same task. Both WM capacity and knowledge about a topic affect performance on tasks requiring participants to learn new information about the topic (Hambrick & Engle, 2002 ). If strategies can be considered domain specific, previous knowledge about a strategy for the same domain could make learning a new strategy easier, but WM strateg y as cause view might suggest that learning a new (effective) strategy would as effect theorists would evaluate the likelihood of an individual effectively learning and employing a new strategy in terms of
25 th eir (pre existing) WM capacity. Strategy affordance theorists would take the task into account, and I suggest that this is the missing link among the various findings related to the relationship of strategy use and WM capacity. The strategy affordance hyp othesis states that strategy use is only related to WM capacity if the same strategies that can be employed during a WM task can also be employed during the task WM capacity is being compared to (Bailey et al., 2008). However, we know that allowing time fo r strategy use on a WM span task can alter performance (Turley Ames & Whitfield, 2003), and that the types of things classified as strategies vary from study to study. A fundamental similarity exists among the strategies used during mathematics, reading, a nd retrieval tasks found to correlate with WM performance. This similarity is also related to the ways individuals approach WM tasks. Just as expert readers retrieve words from long term memory, as opposed to sounding them out each time they encounter them expert mathematics problem solvers retrieve common math facts from long term memory (Geary et al., 1993; Tronsky, 2005). Expert strategists are experts because the strategies they employ are no longer effortful, and this is due to an advantage they acqui re over time: practice (Naumann et al., 2008). Practice as a Determining Factor in Successful Strategy Use LWM individuals may have fewer opportunities for practice if, initially, they find the use of strategies more demanding. Imagine that you are a seven year old learning mathematics. You have a worksheet full of problems in front of you. On the chalkboard, your teacher is demonstrating a strategy for two digit subtraction: To subtract 9 from a 2 digit number, take away 10, then add one. If you already fe el competent with single digit addition and subtraction, you may find this strategy useful. You may find it effortless to retrieve the subtraction facts you have memorized, and then perform some
26 very simple addition in order to obtain the correct answer. I n other words, if you have successfully performed subtraction in the past, and were able to store the subsequent answers in long term memory, the strategy you are currently being taught may not be difficult to apply. Without relevant subtraction facts stor ed in long term memory, this strategy requires double the mathematical problem solving: instead of just retrieving the 10 subtraction fact, you must go through the necessary steps to figure out what X 10 is, and then add one to that number. Because you d o not have access to a previously memorized correct answer, you may perform further steps to ensure that your answer is correct. At first glance, it may appear that you are less able to perform the strategy of subtracting 10, then adding one. In this case, we do not know whether you are capable of performing the strategy or not, because you do not have the facts stored in long term memory that are necessary to carry out the strategy. Consequently, you are unable to practice the strategy, because your WM is busy carrying out the mathematical function of subtracting 10, then adding one. LWMs are at greater risk for mathematical difficulty (Keeler & Swanson, 2001); determining the most effective method of strategy instruction may be an effective way to allow th em the opportunity for successful practice, resulting in improved the mathematical performance. Much previous research on strategy instruction does not include any variation in teaching methods (Linderholm & Zhao, 2008; Naumann et al., 2008; Turley Ames & Whitfield, 2003), however, Atkinson, Renkl, & Merrill (2003) varied instructional methods and found that backwards fading (i.e.., having students first solve part of a problem, then gradually moving towards solving an entire problem) was more effective t han having students view an example, then solve a problem. It may be the case that
27 backwards fading and example problem pairs affect HWMs and LWMs differently. Specifically, if LWMs are given the opportunity to learn to use strategies in low cognitive load (backwards fading) conditions, later attempts to employ those strategies may be more successful because of their previous successful practice opportunities during the learning process. Although this type of instruction may not be possible in every learnin g situation, it may be possible to teach LWMs a strategy for learning strategies, i.e., to determine how HWMs are approaching tasks differently and give LWMs the opportunity to practice those strategies (Naumann et al., 2008). The Present Study I examine d whether cognitive load during strategy instruction affected individuals differently as a function of their WM capacity. The effect of the independent variables WM and learning condition on the dependent variables strategy learning, performance during lea rning, self reported cognitive load during learning, and post training test performance was measured. The effect of strategy learning as an independent variable on performance during learning and post training test performance was also measured, as were th e effects of self reported cognitive load on strategy learning, performance during learning, and post training test performance. General Predictions learned to apply effective str ategies, due to previous findings regarding the relationships between strategy use, WM, capacity, and performance on cognitive tasks (Bailey et al., 2008; Lehmann & Hasselhorn, 2007; Linderholm & Zhao, 2008; McNamara & Scott,
28 2001; Touzani et al., 2007). L WMs may be helped by strategy instruction and low demand practice time; their performance may improve, and they may become more comfortable with employing strategies. However, I expected the general capacity theory of WM (Engle, Cantor, & Carullo, 1992) to hold: LWMs have less WM capacity than HWMs, so their ability to perform WM demanding tasks and use strategies is constrained. Although low demand practice opportunities will decrease the WM load of learning to use strategies, strategy deployment is still likely to be somewhat demandin g during task performance. P articipants assigned to Condition A were expected to perform better on problem solving tasks than participants assigned to Conditions B, C, and D Participants were expected to perform better in th e two strategy instruction conditions ( Conditions A and B ) than in either of the control conditions (Conditions C and D) because strategy instruction was expected to improve performance (Atkinson, Renkl, and Merrill, 2003). Predicted Strategy Learning as a Function of Working Memory and Condition Both HWMs and LWMs were expected to learn strategies more successfully in Condition A than in Condition B (Atkinson, Renkl, & Merrill, 2003). The difference between high and low WM participants was expected to be s maller in Condition A due to previous research on the effect of load on HWMs (Rosen & Engle, 1997; Schelble, Therriault, & Miller, 2012 ). Condition A was designed to allow LWM individuals to practice using new strategies under conditions that do not sap al l of their WM resources.
29 Predicted Problem Solving Differences as a Function of Working Memory and Strategy Learning HWM participants were expected to learn strategies more effectively due to their higher cognitive capacity, resulting in better problem sol ving performance during learning. Individuals who learned strategies better during learning were expected to perform better on problems solved during learning and on the post training test regardless of WM capacity, however, because higher WM capacity was expected to positively influence strategy learning, HWMs were expected to bring two advantages to the post training test: Higher WM capacity for problem solving, and more successful previous use of the self explanation strategy (which should help performa nce on the post training test). Among participants who received strate gy instruction (i.e., assignment to Condition A or Condition B ) training test performance was expected to b because cognitive load in the post training tes t was equal for both conditions. Predicted Differences in Perceived Cognitive Load as a Function of Working Memory I expected LWMs to report higher perceived cognitive load than HWMs due to ical difficulties (Keeler & Swanson, 2001; Geary, Frensch, & Wiley, 1993). I also predicted that the interaction of WM and self reported cognitive load would affect problem solving performan ce during learning (i.e., LWMs with higher p erceived cognitive load were expected to perform worse on problems solved during learning than HWMs who reported high perceived cognitive load).
30 Strategy as effect view (Dunlosky & Thiede, 2004 a ) WM causes differences in strategy use and effectiveness. Strategy affordance hypothesis (Bailey, Dunlosky & Kane, 2008) Mediation occurs only if same strategies can be used for WM and other tasks. Strategy as cause view (Dunlosky & Kane, 2007) Strategies are the cause of differences in WM capacity. Strategy mediation hypothesis (McNamara & Scott, 2001) WM explains some of the variance in strategy use. Figure 1 1. Theories of the relationship between WM and strategy use.
31 CHAPT ER 2 METHOD Participants The study participants consisted of 23 1 undergraduate students enrolled in introductory educational psychology courses at a large southeastern university participated in the study. Participants were given course credit in exchange for participation in the study. The experiment took approximate ly 90 minutes for each participant. Five participants were excluded because they did not follow instructions during one or more of the tasks. Two participants were excluded due to a high number of accurac y errors on the SymSpan task. Twenty eight participa nts were excluded due to missing data on one or more measures. Outlier removal procedures were used on the remaining 196 participants, resulting in a final sample of 180 participants for all analyses. Materials WM capacity was measured using the Symmetry S pan task (SymSpan) and a backwards digit span task. During the SymSpan, participants assess the symmetry of shapes on the screen while simultaneously trying to remember the position of boxes. Participants view a shape followed by a prompt to indicate wheth er the shape is shape/box combinations, participants view a screen of boxes, and must recall the correct red box positions (in order). During the backwards digit span task, participants are presented with sets of series of numbers, then asked to recall each set in reverse order.
32 Participants received instruction and testing on probability calculation. Modified versions of materials developed by Renkl (1997) and Atkinson, Renkl, and Merrill (2003) were used for the probability knowledge test, post training test, practice problems, and instructional text. Perceived cognitive load was measure d using Paas and van Procedure Participants were randomly assigned to one of four conditions: the low load strategy instruction condition (backwards fading Condition A), the high load strategy instruction c ondition (example problem pairs Condition B), a control condition with explanation (Condition C), and a control condition without explanation (Condition D). All participants completed a probability knowledge test in order to account for previous probabilit y knowledge (Atkinson, Renkl, & Merrill, 2003). Low L oad (B ackwards F ading) Instruction C ondition (Condition A) Participants in Condition A received written probability calculation instructions (Atkinson, Renkl, & Merrill, 2003). Next, participants receive d additional instruction in the form of faded examples: participants viewed a worked example presented in steps, followed by a problem in which the third (final) step was left blank for the participant to solve, then a problem with the second and third ste ps left blank, and finally, a problem that the participant solved completely independently, with no worked steps provided. A sheet containing a list of the probability rules/principles that were explained in the written strategy instructions was provided ( probability of an event, principle of complementarity, multiplication principle, and addition principle). Participants were prompted to indicate which rule/principle was used in each step of the problem, as they solved each problem (this is the self explan ation prompt). After each problem,
33 participants rated their level of perceived cognitive load (Paas & van Merrienboer, 1994). Finally, participants completed a probability calculation post training test (Atkinson, Renkl, & Merrill, 2003) and two WM measure s (the SymSpan and the backwards digit span). Hig h Load (Example Problem P airs) I nstruction C ondition (Condition B) Participants in Condition B received written probability calculation instructions identical to those in Condition A Next, they received add itional instruction in the form of worked examples paired with practice problems to complete (Atkinson, Renkl, & Merrill, 2003). The sheet of probability rules/principles described above was provided. As in Condition A, participants were prompted to indica te which rule/principle was used in each step of the problem they were solving. After each problem, participants rated their level of perceived cognitive load. Finally, participants completed the post training test and WM measures described above. Control Condition with E xplanation (Condition C) The purpose of Condition C was to demonstrate that open ended self explanation is not sufficient to benefit probability problem solving performance; instead, self explanation must direct the problem on to specific information that will assist with the current problem solving task. Participants in Condition C received written probability calculation instructions identical to those in Conditions A and B Next, participants solved the same probability pr actice problems that were provided in Condition B except that the participants were not required to solve each step of the problem in a separate box. After each problem, participants described how they solved the problem and rated their level of perceived cognitive load. Finally, participants completed the post training test and WM measures.
34 Control Condition without E xplanation (Condition D) The purpose of Condition D was to demonstrate that practice alone would not benefit probability problem solving per formance as much or more than self explanation strategy instruction. Participants in Condition D received the written probability calculation instructions, followed by the same probability practice problems provided in Condition C After each problem, part icipants rated their level of perceived cognitive load. Next, participants completed the post training test, followed by the same WM measures used in Conditions A, B, and C
35 CHAPTER 3 RESULTS Descriptive Statistics from 6 to 42, with a mean score of 28.64 (SD = 7.51). Backwards digit span scores ranged from 1 to 10, with a mean score of 6.13 (SD = 1.44). Freshmen, sophomores, juniors, and seniors were included in the sample (mean year in college = 2.41, SD = 1.11), as were a wide range of mathematical ability levels, ranging from no college mathematics courses to high grades in several advanced courses (mean mathematics course score = 2.42, SD = 1.53). 58% of the sample had taken a college level statistics course. Th e mean GPA of participants in the sample was 3.15 (SD = 0.97). There were 41 participants in Condition A, 40 participants in Condition B, 51 participants in Condition C, and 47 participants in Condition D. Table 3 1 contains descriptive statistics for the probability problem solving variables. Table 3 1. Descriptive statistics for probability problem solving variables (N = 180). Variable Range Mean SD Probability knowledge test score 0 7 5.66 1.50 Percent of problems solved correctly during learning 0 100 41.62 40.24 Strategy use score (Conditions A & B only, N = 81) 1 12 8.99 3.23 Self reported cognitive load during learning 1 4.7 1.97 0.75 Post training probability problem solving test score 0 10 4.84 3.49 Differences in Problem Solving Performance and Cognitive Load as a Function of Learning C ondition One way between subjects analysis of variance (ANOVA) was used to examine
36 during learning varied significantly as a function of learning condition, F(3, 175) = 28.57, p < .001. Thus, the hypothesis that the condition participants were assigned to would affect their problem solving performance was supported. A priori hypotheses regarding differences between learnin g conditions were tested using Bonferroni adjusted alpha levels of .0125 per test (.05/4). The Bonferroni test was used in order to examine differences between specific groups (i.e., to compare the performance of participants in each learning condition to the performance of participants in every other learning condition). Participants in Condition A performed significantly better during learning, M = 57.32, SD = 35.75, than participants in Condition C M = 22.55, SD = 34.01, p < .001, and Condition D, M = 2 0.21, SD = 31.55, p < .001. Participants in Condition B M = 75.0, SD = 31.52, also significantly outperformed participants in the control conditions. These results supported the hypothesis that participants in the strategy instruction conditions (Conditio ns A and B) would perform better than participants in the control conditions (Conditions C and D) The pairwise comparison of problem solving performance during learning in Condition A to performance in Condition B was not significant, p = .107. On the su rface, this result indicates that the hypothesis regarding the relationship between learning condition cognitive load and problem solving performance during learning was not reports of cognitive load indicate that the re were no significant differences in cognitive load as a function of condition, F(3, 176) = .825, p = .482, despite Condition A being (Atkinson, Renkl, & Merrill, 2003). Table 3 2 contains mean values for st rategy use scores, post training test scores, problem solving performance during learning, and self
37 reported cognitive load during learning. Surprisingly, participants performed better (in terms of problem solving) in Condition B than in Condition A Diffe rences in Post Training Test Perfor mance as a Function of Condition Differences in post training test performance as a function of learning condition, measured using a one way between subjects ANOVA, revealed significant differences, F(3, 176) = 6.42, p < .001. Bonferroni tests of a priori hypotheses indicated that post training test performance was significantly higher in Condition B M = 6.76, SD = 3.08, than in Condition C M = 3.96, SD = 3.32, p < .001 and Condition D M = 4.11, SD = 3.21, p = .002. The posttest performance of participants in Condition A M = 4.88, SD = 3.75, was not significantly different from the posttest performance of any other group, suggesting th at Condition A did not provide participants with the most effective learning format. T his result contradicted the hypothesis that backwards fading would lead to more successful problem solving.
38 Table 3 2 Mean post training test scores, problem solving scores during learning, and self reported cognitive load by condition (N = 180). Condit ion Strategy use score Problem solving score (percent) Post training test performance score Self reported cognitive load A (Backwards faded instruction) 7.98 57.32 4.88 1.14 B (Example problem pairs instruction) 10.00 75.00 6.76 1.12 C (Practice with se lf explanation) -22.55 3.96 1.13 D (Practice problems only) -20.21 4.11 1.14 Differences in Strategy Use Su ccess as a Function of Condition Participants in Condition B correctly used the self explanation strategy correctly significantly more often t han participants in Condition A F(1, 80) = 8.83, p = .004. The mean number o f correct strategy usages in Condition B was 10.0, SD = 3.21. The mean number of correct strategy usages in Condition A was 7.98, SD = 2.95. These results are surprising becau se C ondition A was expected to be the most successful strategy instruction condition based on previous research (Atkinson, Renkl & Merrill, 2003) Effects of Working Memory and Cognitive Load on Strategy Learning The SPSS 19 General Linear Model (GLM) was used to examine all relationships discussed in the remainder of this section. The GLM provides both one way between subjects ANOVA results and linear regression results for each model, so the reminder of this section includes descriptions of both types of anal yses as appropriate. Table 3 contains all variables included in the GLM analysis for strategy use during learning. Because the dependent variable was strategy use, on ly data from C ondition A (n = 41) and Condition B (n = 40) was used in this analysis.
39 Tabl e 3 3 Analysis of variance for strategy use during learning (N = 81) Variable df F p Condition 1 5.70 .020 College statistics class (0 = no, 1 = yes) 1 .175 .677 SymSpan score 1 1.28 .262 Backwards digit span score 1 3.78 .056 College math course av erage 1 .164 .687 GPA 1 2.69 .106 Probability knowledge test score 1 .686 .410 Time spent studying information sheet 1 .051 .823 Problem solving during learning score 1 1.67 .200 Self reported cognitive load 1 .510 .478 SymSpan x Condition interacti on 1 4.30 .042 SymSpan x Condition score interaction 1 1.66 .202 Error 68 (2.98) Values enclosed in parentheses represent mean square errors. Condition was significantly related to strategy use, as was the interaction of condition and SymSpan score. P reported cognitive load was not significantly related to strategy use. Table 3 4 contains the correlation matrix of all variables included in the linear regression analyses of variables predicting strategy use and post training test perfo rmance. The purpose of reporting regression results for the dependent variable strategy use was to further explain the significant interaction of WM and condition in the ANOVA (please see Table 3 3 ) with an examination of the specific interactions of each
40 condition with WM. Linear regression analysis revealed that the interaction of being assigned to Condition A and WM significantly predicted strategy use, b = .500, t(68) = 2.07, p < .05, suggesting that higher WM was associated with better strategy use in Condition A, but not in Condition B Although this result is the opposite of the hypothesized relationship, the hypothesized relationship was dependent upon the assumption th at Condition A resulted in lower c ognitive load than Condition B lf reported cognitive load scores indicate that this was not the case, as there were no significant differences in self reported cognitive load as a function of condition. Ef fects of Working M emory Strategy Instruction, Strategy Use, and Cognitive Load o n Problem Solving During L earning Linear regression analysis of performance during learning revealed that the interaction of being assigned to Condition C and SymSpan score was significantly related to performance during learning, b = .522, t(162) = 2.18, p < .001. Thus, higher WM wa s an advantage in Condition C Pre training probability knowledge test performance was positively related to problem solving during learning, b = .314, t(162) = 5.10, p < .001. Self reported cognitive load had a negative effect during learning, b = .218, t(162) = 3.73, p < .001. The worse performance of part icipants assigned to Condition C (compared to particip ants in Conditions A and B ) demonstrates that self explanation alone does not help with problem solving; it must occur on line (i.e., during the problem solving process) in order to benefit the problem solving process. A between subjects one way ANOVA was used to examine the effect of strategy use on problem solving performance during learning. Because strategy use was i ncluded in the analysis, only data from Conditions A and B (n = 81) was used. Results
41 indicated that correct use of the self explanation strategy significantly predicted problem solving performance during learning, F(1,71) = 49.14, p < .001. Having taken a college statistics course, F(1, 71) = 3.98, p = .05, and a lower level of self reported cognitive load, F(1, 71) = 8.10, p = .006, also had significant positive effects on performance. The cognitive load finding is consistent with the regression ana lysis results for Conditions A, B, C, and D reported above, however, it is interesting to note that having taken a college statistics course was only significantly related to problem solving during learning in the analysis of Conditions A and B (without Conditio ns C and D) Effects of Working Memory, Strategy Instruction, Strategy Use, and Cognitive L oad on Post Training Problem Solving Table 3 5 contains the results of the linear regression analysis of independent variables regressed on post training test perf ormance. Strategy use was not included in this analysis because Conditions C and D did not use the self explanation strategy, and the purpose of this analysis was to compare the post test performance of participants in Conditions A, B, C, and D Linear reg ression revealed a significant relationship between post training test performanc e and the SymSpan/Condition C interaction. The interactions of SymSpan with Conditions A and B were not significant predictors of post training test performance. Higher WM cap acity was an advantage during the p ost training test in Condition C but not in Conditions A and B (the strategy instruction conditions) Assignment to Condition B helped performance on the post training tes t, but assignment to Condition C hurt performan ce. Perfo rmance in Conditions C and D was substantially worse than in Conditions A and B (i.e., participants answered less than
42 25% of post training test problems correctly in Conditions C and D, and over half of problems correctly in Conditions A and B, p lease see Table 3 2). The interaction of SymSpan score and cognitive load had the largest effect on the post training test; low WM combined with high self reported load resulted in poor post training test performance (please see Table 3 5). Interestingly, self reported load did not independently predict post training test performance. This result, combined with the direction of the relationship between the SymSpan/load interaction and post training test performance, suggests that HWM individuals were not af fected by experiencing high cognitive load as neg atively as LWM individuals were Results of a between subjects one way ANOVA (including only Conditions A and B n = 81) indicated that correct use of the self explanation strategy during learning was not s ignificantly related to post training test performance, F(1, 69) = 2.00, p = .162. Thus, the hypothesis that more successful use of the self explanation strategy during learning would result in better post training test performance was not supported. Ho wev er, because assignment to Condition B was associated with better post training test performanc e, and assignment to the Condition C was associated with worse post training test performance, it appears that strategy instruction in a specific format (example problem pairs) did help post training test performance, even though the overall success using strategies during instruction did not predict post training test performance.
43 Table 3 4. Correlation matrix of variables included in linear regression analyses (N = 180) Variable 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1. Condition 1 2. Statistics course .079 1 3. SymSpan .077 .115 1 4. Back. Dig. Span .028 .049 .322** 1 5. Math average .003 .281** .070 .103 1 6. GPA .001 .106 .073 .040 .402** 1 7. Knowledge score .130 .170* .251** .236 ** .163* .113 1 8. Info. sheet time .031 .072 .004 .090 .196** .157* .142 1 9. Learning score .456** .079 .280** .132 .077 .007 .3 99** .151* 1 10. Self report load .006 .102 .197** .137 .063 .028 .415** .077 .376** 1 11. Strategy score .315** .340 ** .321** .243* .146 .073 .536 ** .080 .833** .613 ** 1 12. Post train. score .167* .143 .315** .236** .1 20 .078 .654** .188* .724** .452** .707** 1 1 3. SSpan x load .072 .092 .961** .285** .099 .065 .146 .019 .173* .073 .135 .189* 1 14. SSpan x cond. .795** .108 .504** .191* .050 .035 .206** .026 .251** .080 .391** .002 .495** 1 p < .05, ** p < .001 N = 81 for correlations between strategy score and all other variables.
44 Table 3 5. Linear regression of variables related to post training test performance (N = 180) Variable B SE B Condition A .195 1.79 .024 Condition B 3.23 1.63 .389 Condition C 4.01 1.49 .518 College statistics .015 .313 .002 SymSpan score .686 .287 .086 BD Span score .148 .110 .061 College math course average .002 .028 .001 GPA .001 .001 .082 Probability knowledge test score .820 .122 .353 ** Time spent studying information sheet .073 .088 .035 Problem solving score during learning .049 .005 .564 ** Self reported cognitive load 13.06 7.25 .107 SymSpan x Cognitive load interaction .558 .249 1.35 Condition A x SymSpan i nteraction .026 .059 .094 Condition B x SymSpan interaction .093 .054 .343 Condition C x SymSpan interaction .149 .051 .566 Effects of Working Memory and Condition on Self Reported Cognitive Load Data from Conditions A, B, C, and D (n = 180) was used to examine the relationships between WM, self reported cognitive load, and condition. Neither WM, F(1,170) = 2.26, p = .135, instructional condition, F(1,170) = 1.34, p = .262, nor the interaction of WM and instructional condition, F(1,170) = 1.40 p = .246, significantly
45 predicted self reported cognitive load during learning. Only average math course grade, F(1,170) = 3.93, p = .049, and pre training test score F(1,170) = 21.9, p < .001, reported cognitive load. Thus, the hypothesis that HWMs would experience less cognitive load than LWMs in the high load conditions was not supported.
46 CHAPTER 4 DISCUSSION Learning Condition and Problem Solving Performance Participants in Conditions A and B (the strategy instruct ion conditions) outperformed participants in Conditions C and D (the control conditions) during learning (i.e., while learning to use the self explanation strategy/com pleting practice problems ). These results supported the hypothesis that strategy instruct ion would benefit problem solving. Surprisingly, partici pants in Condition A which was designed to reduce cognitive load, did not perform significantly better than participants in Condition B on either measure. On the post training test, participants assi gned to Condition B performed better than partic ipants in Conditions C and D The scores of participants assigned to Condition A were not significantly differe nt from those of Conditions C, or D on the post training test. During learning, assignment to eit her strategy instruction condition ( Conditions A or Condition B ) appeared beneficial. Following training, however, only assignment to Condition B was helpful. Conditions A and B may be the result of mo re complex in struction in Condition A due to the novelty and inconsistency of the problem solving format. Factors such as expertise and procedural errors during problems (Ayres, 200 6). Alth ough Condition A probability problem, participants may have found the fading format confusing. During the study se veral participants who were assigned to Condition A started to solve the faded problems from the beginning, before realizing that they were only required to
47 solve the last step of the problem. Realizing that they had erroneously written solutions to an ear lier step of the problem on the part of the answer sheet meant for a later step may have resulted in confusion. This experience, along with possible errors during their initial problem solving (made clear by reviewing the steps that had already been comple ted for them) could have resulted in increased cognitive load. For each problem, participants had to gauge how much of the problem they were required to solve (i.e., the same number of steps had not been completed for them on each problem). Participants ma y have faced additional load if the fading format was not something they had seen before, because their cognitive resources were taxed by figuring out the problem design in addition to performing the problem solving and self explanation tasks. A ssignment to Condition A benefitted participants during learning (compared to Conditions C and D). Conditions A and B were designed to teach participants to use the self explanation strategy, which should have been helpful during problem solving. Although Conditions A and B required additional work of participants (i.e, reporting encouraged them to attend more carefully to their problem solving process, resulting in better performanc e due to use of a beneficial strategy (self explanation) (Chi, Bassok, Lewis, Reimann, & Glaser, 1989). Strategy Use and Problem Solving Performance Taking together the superior performance of participants in Conditions A and B during learning (compared to Conditions C and D ), the positive effect of being assigned to Condition B on post training test performance regardless of WM capacity, and the effect of the interaction of WM and condition for Condition C on post training test performance, it appears that teaching individuals to use a self explanation strategy
48 benefits problem solving more than solving prac tice problems alone When strategy instruction was not provided, participants were more heavily reliant on their WM capacity to solve problems, so those with higher WM capacity performed better. However, when strategy instruction was provided, WM capacity did not appear to have a significant effect on performance. Research on other types of strategies has demonstrated that use of a successful strategy can compensate for low WM capacity ( Schelble, Therriault, & Miller, 2012 ). This pattern appears to hold for use of the self explanation strategy during probability problem solving. However, it is important to note that successful strategy use (as measured by learning) did not benefit problem solving when participants were not explicitly told to use the self explanation strategy (i.e., during the post training test). Through the strategy affordance hypothesis lens (Baile y, Dunlosky, & Kane, 2008), this suggests that participants were not aware that using self explanation during the post training test would benefit their performance. Additi onally, only participants in Condition B demonstrated superior performance on the po st training test, even though participants Conditions A and B were taught to use the self explanation strategy. Problem solving scores during learning were higher in the Condition B than in any other condition. Although the problems participants solved in Condition B were identical (content wise) to the problems in Conditions A, C, and D the traditional example, then p roblem, format of Condition B may have facilitated learning more than th e format of Conditions A, C, and D If example problem pairs are mor e familiar to students, learning to use the self explanation strategy in this format
49 may free up cognitive resources for other tasks (e.g., learning to apply probability principles, which is also useful on the post training test). Participants who correct ly used the self explanation strategy solved more probability problems correctly during learning. However, this effect did not persist into the post training test; strategy scores during learning were unrelated to post training test performance. Participan ts were not explicitly instructed to use the self explanation strategy on the post training test; the hope was that they would elect to use the strategy because it benefitted them during learning. Expecting students to self explain spontaneously may be unr ealistic, even if such behavior has benefitted them in the recent past. Possible explanations for this phenomenon include too little practice self explaining in order to engage in it without prompting, not thinking to use the strategy due to the level of c ognitive load during the post training test, or simply viewing use of the strategy as unnecessary (and un required) extra work. Effect of Perceived Cognitive Load on Problem Solving Performance reported cognitive load was related to their performance during learning the more load participants reported experiencing, the worse they did on the task. On the surface, this indicates that cognitive load hindered e: Participants who did poorly may have been aware of their poor performance, which may have influenced the level of cognitive load they reported. However, previous research indicates that poor performers are more likely than successful performers to over estimate their performance (Dunning, Johnson, Ehrlinger, Kruger, 2003), so the former explanation may be more likely.
50 Self reported cognitive load during learning was not related to performance on the post training test. Thus, participants whose problem s olving performance during learning was negatively affected by cognitive load during learning were not automatically worse performers on the post training test. Although we did not measure cognitive load during the post training test, if some participants w ere more likely to report a high level of cognitive load simply due to the type of problems they were solving (i.e., probability problems), a relationship between self reported load during learning and post training test performance should have emerged. Th e interaction of WM and cognitive load was a strong predictor of post training test performance; this relationship will be discussed in the next section. Working Memory as a Predictor of Problem Solving Performance Despite the inclusion of other variables related to post training test performance in the analysis (e.g., previous probability knowledge and problem solving score during learning), higher WM capacity was associated with a higher score on the post training revious probability knowledge or success during learning, solving problems on the post training test taxed WM. The interaction of WM and b eing assigned to Condition C was also significantly related to post training test performance. Par ticipants who were a ssigned to Condition C did better on the post training test if they had higher WM capacity. For the strategy instruction conditions (i.e., Conditions A and B ), WM capacity did not interact with condition to predict post training test performance; in Condit ions A and B ability to benefit from strategy instruction for the purposes of performing on the post training test.
51 The interaction of WM and cognitive load was the strongest predictor of post training test per formance, demonstrating that LWMs who reported high load during learning were at a distinct disadvantage. Because WM did not predict self reported load, the possibility that all LWMs experienced high load during learning cannot explain this relationship. I nstead, it appears that a combination of factors related to previous mathematical success predicted cognitive load, and LWMs were particularly susceptible to the negative effects of these variables during the post training test. WM did not independently pr edict performance during the learning portion of the experiment. However, the interaction of WM with Condition C was significantly related to performance during learning. Condition C required self explanation, but because it did not occur on line (i.e., as part of the problem solving process), it may not have had the participants approached self expl anation in Condition C may have been different because it was a separate task, in a ddition to the primary task of probability problems solving, participants may have used additional resources shifting their attention to self explaining (as opposed to viewing self explanation as part of the problem solving proces s, which was more likely i n Conditions A and B, where self explanation occurred in the midst of problem attention between tasks (Kane, Bleckley, Conway, & Engle, 2001), which may explain why WM aff ected performance i n the Condition C Factors Influencing Successful Strategy Use Although strategy use was not related to performance on the post training test, it was related to performance during learning. Both WM and assigned learning condition had significant effects on success of strategy use, however, the relationships between
52 these variables were unexpected: Significant relationships between WM and strategy use were expected in Conditions A and B (i.e., individuals with higher WM capacity were expected to use the self explanation strategy more successfully than participants with low WM capacity). WM was expected to have a strong er effect on strategy use in Condition B because Condition B was expected to produce higher cogniti ve load than Condition A However, the relat ionship between WM and strategy success was si gnificant in Condition A, but not in Condition B in Condition A (which was supposed to produce less cognitive load), higher WM was associated with better performance on the strategy use portion of the task, but in Condition B the relationship between strategy success and WM was not significant. In Condition A explanation strategy, but in Condition B (the condition in which participants performed better), WM success of strategy use is not inevitably tied to WM capacity. Under certain circumstances (e.g., under learning conditions that result in better performance), in dividuals with low WM are just as capable of using a successful strategy as individuals with high WM. Research on retrieval strategies has provided evidence that LWMs are sometimes capable of using effective unprompted strategies ( Schelble, Therriault, & M iller, 2012 ). Despite the findings that WM was related to performance in the Condition C and to st rategy use in Condition A load in any cond ition. In fact, the only factors that predicted self reported cognitive load
53 courses and score on the pre training probability knowledge test). There are several possible expl anations for these unexpected findin gs: in Conditions A and B WM was not related to performance, so it is not surprising that WM did not predict how difficult participants found the task, if the task was not particularly taxing of their cognitive resource s. Overall, participants did not rate the task as particularly difficult (the mean difficulty rating was 1.97 on a 5 point scale). Thus, another possible explanation for the lack of a significant relationship between WM and self reported load is that HWMs and LWMs rated the task similarly difficult for different reasons (e.g., perhaps LWMs rated the task less difficult because they were less aware of their own poor performance, while HWMs found the task less difficult due to their previous success on mathem atical tasks). These speculative explanations illustrate the possibility that perceived cognitive load could originate differently as a function of WM. Whether participants found the task difficult seems to be most closely related to their domain specific experience with mathematical and probability problem solving, strategy for improving probability problem solving performance. Finding ways to reduce cognitive load in ins tructional settings with similar tasks presents challenges because the factors that predicted cognitive load were previous mathematical success and probability knowledge (as opposed to easily manipulated factors such as learning condition load). Theoretica l Implications The present research has several implications for theories of WM and its relationship to strategy use. The interaction of WM and learning condition in predicting strategy success indicates that, under some circumstances, WM affects participa
54 abilities to learn and use the self explanation strategy. These results provide support for the strategy as effect hypothesis, i.e., that strategy use is a result, rather than a cause, of WM capacity (Dunlosky & Thiede, 2004a). The finding that strate gy acquisition differences between HWMs and LWMs disappear under some circumstances (i.e., during strategy instruction provided in an example problem pairs format) indicates that hich they use to learn strategies. It may be the case that teaching participants to use a strategy during problem solving without taking steps to reduce cognitive load represents a distinct type of load (perhaps similar to a dual task situation) that taxes WM differently than simply being given a task in a more difficult format (which still consists of a single task). condition that partici pants performed the best in (Condition B ), my results provide support for the theory of long term WM (Ericcson & Kintsch, 1995). According to Ericcson and Kintsch, learning to resist interference may improve memory capacity. Although I would not suggest that strategy use improves WM capacity itself, learning to use of WM, perhaps by increasing resistance to interference during a particular task through use of an effective strategy. Thus, low load learning conditi ons provide a vessel through which LWM individuals can gain access to some of the benefits that HWM individuals experience, resulting in improved performance on tasks that are traditionally more difficult for LWMs.
55 Practical Implications The ability of WM to predict str ategy use in Condition A, but not in Condition B supports the findings of Kirschner, Sweller, and Clark (2006) regarding differences appear to behave as advance d learners, demonstrating a superior ability (when compared to LWMs) to learn from the novel backwards faded format of Condition A This finding may benefit those teaching introductory probability and statistics courses, who are likely to encounter student s with a range of WM capacities. Presenting new information about probability may be initially more effective in a traditional format, particularly for individuals with low WM capacity. The strong effect of the WM/self reported cognitive load interaction o n post training test performance indicates that LWMs who experienced high cognitive load during learning were at a distinct disadvantage during the post training test, further illustrating the importance of providing low load instruction for LWMs. Explicit instruction to use a self explanation strategy also appears to benefit learners, as demonstrated by the finding that t he average scores in Conditions A and B were higher than the average score s in Conditions C and D Encouraging students to use a self exp lanation strategy when teaching them to apply probability principles may enhance their understanding of probability theory. If presented in a traditional format, improve th eir application of probability theory when they are not explicitly told to use the self explanation strategy (as demonstrated by the higher post test performance of particip ants in Condition B ).
56 Limitations Because participants completed all of the study tasks in the same day, I was unable to determine whether the benefits of strategy instruction persisted. Future researchers may consider providing a break of several days or weeks between learning and post training testing. Similarly, providing additional practice beyond the single learning task is likely to benefit problem solving and strategy use; future research should examine whether practice related benefits differ as a function of WM. The instructional format was primarily self paced (i.e., particip ants received some verbal instructions and were time limited to 90 minutes for all tasks) and involved reading instructions and completing problems independently. Therefore, it was not ance in other instructional formats (e.g., individual or group format led by an instructor). Discovering whether findings regarding the interaction of WM, condition, and strategy learning persist following different instructional formats would be beneficia l to our understanding of the impact of WM on learning and strategy use. An unanticipated finding of the study was that participants did not perform best in the condition that was designed to produce the least cognitive loa d (Condition A ). I attribute this to the novelty of the backwards faded format of Condition A however, future researchers may wish to consider alternate explanations for this finding. Future Directions The present study demonstrated that use of a self explanation strategy during probab ility problem solving, when paired with specific instructions, can be useful to participants even following the task where they are explicitly instructed to use the strategy. A related question is whether students believe that self explanation is helpful,
57 and consequently use self explanation unprompted in future learning situations. One way to answer this question would be to show students that the strategy helped them (i.e., make it clear that their strategy use scores were related to their performance d uring learning), and then determine whether providing this information increased their later independent use of the strategy. Finding ways to motivate students to use effective learning techniques can provide valuable information for educators. A surpris ing finding of the study was that students did not report significantly different levels of cognitive load as a function of learning condition, even though the conditions were designed to produce different levels of load, and there were distinct difference s in student performance as a function of assigned condition. Examining to their own cognitive load (thus increasing load) may be valuable. We also found that cognitive knowledge of probability, but was unrelated to WM. Future researchers may wish to explore ways to reduce cognitive load specifically associated with mathematical skill level. Finally, the relationship between WM and cognitive load, and its effect on performance, should be explored in more detail. In some cases, individuals with high Schelble, Therriault, & Miller, 2012 ), but i n the present study, high WM was an asset under high load conditions. This may be due to the nature of the cognitive load: does artificial load affect participants differently than task related load? Alternately, how much load can a learning situation enco mpass before additional WM capacity (or a successful strategy)
58 is necessary for superior performance? Is there a specific level of load at which WM is no longer an asset? Discovering the answers to such questions may have practical and theoretical benefits Conclusion variety of tasks (Geary, Frensch, & Wiley, 1993; Keeler & Swanson, 2001; Linderholm, Cong, & Zhao, 2008; Linderholm & van den Broek, 2002; Rosen & Engle, 1997; Schelble, Therriault, & Miller, 2012 ). In the present study, I found that WM was also as effect hypothesis of WM (Dunlosky & Thiede, 2004a). Specifically, individuals with h igher WM were more successful at learning a new strategy when the learning condition was novel and when overall performance in the condition was lower. This suggests that HWM individuals behave more like advanced learners than novices (Kirschner, Sweller, & affected by their preexisting knowledge about the topic, but not by their WM capacity. In a more traditional learning format, participants performed better, and the relationship between WM and strategy learning disappeared, indicating that reducing cognitive load during strategy learning is an effective way to teach strategies to individuals with low WM capacity. Although previous research indicates that high WM indi viduals perform poorly when under increased cognitive load (Rosen & Engle, 1997; Schelble, Therriault, & Miller, 2012 ), the present study found that high WM was an advantage under conditions in which overall performance was lower. This discrepancy may be d ue to the type of load experienced in this study (i.e., load related to actual performance of the task) being
59 different from the type of load induced in previous studies (i.e., load produced by requiring participants to engage in an unrelated additional ta sk). Future research should examine the effect of WM on strategy learning in a variety of high load conditions. Such information would be beneficial to scholars of cognitive control mechanisms and to educators, whose students encounter various forms of cog nitive load in their learning environments.
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65 BIOGRAPHICAL SKETCH Jenni L. Schelble earned a Bachelor of Arts in sociology from Mesa Stat e College in 2002, and a Bachelor of Arts in psychology from Mes a State College in 2003. She received her Master of Arts in Education in Educational Psychology from the Univers ity of Florida in 2009. Jenni completed her Doctor of Philosophy in Educational Psychology at the University of Florida in May 2012.