Peter Gerjets
email: p.gerjets@iwm-kmrc.de.

Katharina Scheiter

Richard Catrambone

Designing Instructional Examples to Reduce Intrinsic Cognitive Load: Molar versus Modular Presentation of Solution Procedures

published or not. The documents may come

Designing Instructional Examples from a Cognitive Load Perspective

It has often been argued that probably the most important prerequisite for successful problem solving consists in the availability of abstract problem-type schemas [START_REF] Gick | Schema induction and analogical transfer[END_REF][START_REF] Reed | A schema-based theory of transfer[END_REF], that is, representations of problem categories together with category-specific solution procedures. "Schemas are defined as mental constructs that allow patterns or configurations to be recognized as belonging to a previously learned category and which specify what moves are appropriate for that category" (Sweller & Cooper, 1985, p. 60). Once a problem has been identified as belonging to a known problem category, the relevant schema is retrieved from memory, is instantiated with the information that is specific to the to-be-solved problem, and finally the category-specific solution procedure attached to the schema is executed in order to produce a solution to the problem (cf. [START_REF] Derry | Strategy and expertise in solving word problems[END_REF][START_REF] Vanlehn | Problem solving and cognitive skill acquisition[END_REF]. Mayer (1981, p. 153) reports that "several groups of researchers have shown that students try to find out what 'type' of problem is presented and then to use a solution strategy appropriate for that type". Schema-based problem solving is considered to be very efficient and therefore often seen as a marking feature of experts' problem solving [START_REF] Vanlehn | Cognitive skill acquisition[END_REF]. Accordingly, a substantial amount of research on skill acquisition has focused on the question of how such schemas can be acquired. An ubiquitous answer to this question is that studying concrete instances of problem categories (i.e., examples) is necessary for schema construction. In particular, worked examples (i.e., example problems together with step-by-step solutions) seem to play an important role in schema acquisition (cf. [START_REF] Atkinson | Learning from examples: Instructional principles from the worked examples research[END_REF][START_REF] Sweller | Cognitive architecture and instructional design[END_REF]. Studying worked examples is superior to directly teaching abstract principles as well as to actively solving training problems -at least with regard to initial skill acquisition. This 'worked-example effect' is usually explained by pointing to the fact that studying worked examples imposes lower levels of cognitive load on the learner than solving training problemsmainly because no extensive search processes with regard to the correct solution steps are involved. As a result, more cognitive resources might be left for the learner to engage in processes of schema construction. Moreover, it is assumed that studying worked examples (in contrast to attempting to solve training problems) focuses the learner's attention on information that is relevant to schema construction. For instance, studying worked examples might draw the learner's attention to structural task features that define to which problem category a particular problem belongs or it might draw the learner's attention to the solution rationale behind a category-specific solution procedure.

Conventional Example Design: Molar Presentation of Solution Procedures

Analyzing cognitive skill acquisition based on the notion of problem-type schemas quite naturally has specific implications for the design of instructional examples. [START_REF] Sweller | Cognitive architecture and instructional design[END_REF] propose that "learners' attention must be withdrawn from processes not relevant to learning and directed toward processes that are relevant to learning and, in particular, toward the construction and mindful abstraction of schemas" (p. 264). For instance, if worked examples are intended to foster schema construction their design should focus on the information that is related to the main components of problem-type schemas, namely on information related to problem-category membership, structural task features, and category-specific solution procedures. These considerations fit rather well to the way instructional examples are conventionally designed -at least in textbooks on knowledge-rich and well-structured domains like physics, mathematics, or programming. Examples that can be found in these textbooks often tend to present solution procedures in a molar way as 'recipes' that are appropriate for particular problem categories. In order to enable learners to apply these 'recipes' the examples demonstrate how to categorize problems by considering multiple (and often abstract) structural task features. For instance, with regard to algebra word problems Reed (1999, p. 92) notes that "the solution of algebra word problems typically begins with the categorization of the problem based on the situation described in the problems. " (p. 92). Mayer (1981) extensively elaborated the categorical structure of word problems by collecting 1100 story problems from 10 major algebra textbooks used in California secondary schools and developing a taxonomy consisting of families, categories, and templates that describe the category membership of problems at different levels of abstraction. Atkinson and Catrambone (in press) note that mathematical problem solving is often characterized by 'computationally-friendly' molar solution approaches in which multiple solution steps are collapsed into a single formula that represents the solution procedure. These 'recipe-like' formulas allow one to easily calculate solutions by simply inserting the correct variable values.

To sum up, math textbooks often present mathematical problem solutions in a molar way and use 'category-focusing' instructional examples that are designed to illustrate how these 'recipes' are applied. However, formulas are usually restricted to solving a narrow range of problems that fall into predefined problem categories corresponding to the solution formula.

Additionally, the strong focus on problem categories might cause learners to "memorize stereotypic solutions to problems based on their categorization" (Reed, 1999, p. 95). Thus, although schemas and problem categories are obviously very useful as a means for organizing knowledge representations and for guiding problem solving, they are not unequivocally advocated by math educators. For instance, [START_REF] Sowder | Cognitive psychology and mathematical problem solving: A discussion of Mayer's paper[END_REF] argues that students should also be enabled to solve problems without relying on problem categories.

To illustrate the notion of problem-type schemas in greater detail and to elaborate on how conventional molar (or category-focusing) examples are usually designed, we will refer to the domain of probability word problems that is illustrated in Table 1. The left column of Table 1 contains a conventionally designed molar solution for an example problem related to calculating complex event probabilities. The right column of Table 1 displays an alternative modular solution approach that we developed to improve example-based learning and that will be explained in greater detail below. Because we used problems like the one in Table 1 for experimentation in all studies reviewed in the second part of this paper, we will introduce the domain of calculating complex event probabilities in this section in some detail. Problems of calculating complex event probabilities are related to situations where the probability of selecting a particular configuration of elements randomly out of a set of elements has to be determined. A typical example includes calculating the probability of winning a lottery, for instance, calculating the probability of correctly guessing the six winning numbers out of a set of 49 numbers.

Four different problem categories are commonly distinguished in this area of probability theory (permutations and combinations, each with and without replacement) that differ with regard to two structural features. The first is whether the order in which elements are selected is important; the second is whether selected elements are replaced after being chosen. Depending on these two structural features different problems will require different formulas for their solution.

Accordingly -like in many other mathematical areas -the calculation of complex event probabilities can be taught by means of category-specific solution formulas. The rationale of this approach is to divide the number of acceptable complex events by the number of possible complex events; category-specific solution formulas are used to calculate the number of possible complex events. The solution procedure based on this approach comprises four steps that are illustrated in the conventional molar example format in the left column of Table 1, namely, (1) identify task features, (2) apply formula, (3) insert values, and (4) calculate probability.

----Insert Table 1 here ---This solution approach is a convenient and fast way of calculating complex event probabilities. The conventional molar example format illustrated in Table 1 might be well suited for conveying this approach by explaining how to categorize problems and how to apply category-specific solution formulas.

Profitable Example Processing and Patterns of Cognitive Load

When providing learners with conventional worked examples like the one presented in the left column of Table 1, instructors usually intend to trigger the construction of an appropriate problem-type schema that will allow learners to solve all problems that belong to the same problem category as the example problem. Research in the domain of learning from worked examples over the last 15 years has however demonstrated that the mere availability of conventional instructional examples does not seem to be sufficient to promote an adequate representation of problem categories, an understanding of category-specific solution procedures, and problem-solving transfer.

Rather, learners are often described as having difficulties identifying relevant information in worked examples (i.e., their structural task features) and as being distracted by the surface features of the examples [START_REF] Ross | Distinguishing types of superficial similarities: Different effects on the access and use of earlier problems[END_REF]. Furthermore, [START_REF] Renkl | Learning mathematics from worked-out examples: Analyzing and fostering self-explanations[END_REF] suggests that students often suffer from illusions of understanding when learning from worked examples. That is, they might have the false impression of having grasped the solution rationale of an example problem.

Similarly, Catrambone (1998, p. 355) notes that learners "tend to form solution procedures that consist of a long series of steps -which are frequently tied to incidental features of the problemsrather than more meaningful representations that would enable them to successfully tackle new problems". That is, learners have difficulties generalizing solutions from examples to novel problems [START_REF] Catrambone | Overcoming contextual limitations on problem-solving transfer[END_REF][START_REF] Reed | Usefulness of analogous solutions for solving algebra word problems[END_REF].

To sum up, numerous findings indicate that students experience serious difficulties in example-based learning resulting in the acquisition of rather shallow representations of problem categories and solution procedures.

Research on the role of example elaborations in learning has demonstrated that learners need to draw inferences concerning the structure of example solutions, the rationale behind solution procedures, and the goals that are accomplished by individual solution steps (e.g. by relating example-specific information to more abstract information; [START_REF] Chi | Self-explanations: How students study and use examples in learning to solve problems[END_REF][START_REF] Pirolli | Learning strategies and transfer in the domain of programming[END_REF][START_REF] Renkl | Learning from worked-out examples: A study on individual differences[END_REF] in order to overcome these difficulties. Example elaborations may in particular be helpful to foster learners' skills in solving novel problems that do not fall into known problem categories and that require an adaptation of procedures illustrated by worked examples.

Beyond example elaborations, learners have to engage in profitable processes of example comparison in order to notice structural features that differ among problem categories and that are shared by all problems within a category. If learners compare examples within and among problem categories with regard to their differences and similarities they might be more likely to identify the relevant features of worked examples and to avoid confusion due to the surface features of the examples [START_REF] Cummins | Role of analogical reasoning in the induction of problem categories[END_REF][START_REF] Quilici | Role of examples in how students learn to categorize statistics word problems[END_REF].

Unfortunately, it has often been observed that learners do not spontaneously engage in these profitable processes of example elaboration and example comparison when studying worked examples (e.g., [START_REF] Chi | Self-explanations: How students study and use examples in learning to solve problems[END_REF]Gerjets & Scheiter, 2003;[START_REF] Gerjets | Resource-adaptive selection of strategies in learning from worked-out examples[END_REF][START_REF] Schuh | Supporting learning from worked-out examples in computer-based learning environments[END_REF]. Rather, learners seem to need additional instructional support and carefully designed learning materials in order to make the most of instructional worked examples.

To address the issue of developing improved instructional settings that ensure profitable processing of worked examples, we refer to the instructional-design framework provided by cognitive load theory [START_REF] Sweller | Cognitive architecture and instructional design[END_REF]. According to this theory, constructing a problem-type schema might impose cognitive load on learners, that is, it demands working-memory resources because it requires learners to simultaneously process all information units that are to be integrated into that schema. These working-memory demands are particularly high for learners with low domain-specific prior knowledge. These learners lack complex knowledge structures that would otherwise help to increase the amount of information that can be held in working memory simultaneously by chunking individual knowledge elements into a single element.

Within cognitive load theory, three types of cognitive load are distinguished:

• Intrinsic cognitive load: The number of elements that are to be integrated into a to-belearned schema and therefore have to be processed in working memory simultaneously is referred to as intrinsic cognitive load. Intrinsic cognitive load depends on the relational complexity of the to-be-learned content (so-called element interactivity) and the learner's degree of prior knowledge (i.e., schema availability). It is usually assumed in cognitive load theory that intrinsic cognitive load cannot be altered by instructional design.

Beyond intrinsic cognitive load there might be additional cognitive load due to the instructional presentation of the material and the activities learners are engaged in. This load can be influenced by instructional design and can be categorized according to whether it is beneficial for schema construction (i.e., germane cognitive load) or not (i.e., extraneous cognitive load).

• Germane cognitive load: When intrinsic task demands (resulting in intrinsic cognitive load) leave sufficient cognitive resources available, learners might "invest extra effort in processes that are directly relevant to learning, such as schema construction. These processes also increase cognitive load, but it is germane cognitive load that contributes to, rather than interferes with, learning" (Sweller et al., 1998, p. 264). Germane cognitive load is imposed by adding higher-level cognitive processes to the mere simultaneous activation of elements in working memory; these processes integrate the elements into a schema. In the case of learning from worked examples, germane cognitive load might be imposed onto the learner by cognitively demanding activities like example comparisons and example elaborations.

• Extraneous cognitive load: Extraneous cognitive load is the result of implementing "instructional techniques that require students to engage in activities that are not directed at schema acquisition" (Sweller, 1994, p. 299). For instance, these activities might comprise processes of finding, relating, or integrating particular pieces of information within instructional materials (whereas with a redesign such processing might not be required to the same degree). Extraneous cognitive load might impede learning, as it requires cognitive resources that can no longer be devoted to mindful cognitive processes that are associated with germane cognitive load. Furthermore, cognitive resources required by extraneous cognitive load might result in an overall cognitive load that exceeds the limits of working-memory capacity.

From a cognitive load perspective, an important objective of instructional design in example-based learning is to reduce extraneous cognitive load and to encourage learners to invest unused resources in higher-level cognitive processes such as example comparisons and example elaborations that are associated with germane cognitive load. Accordingly, several suggestions have been made on how to design instructional materials in order to foster a profitable utilization of worked examples and thus to improve the resulting pattern of cognitive load during learning.

With regard to example comparisons it could be shown that the provision of multiple examples

can support schema induction [START_REF] Cummins | Role of analogical reasoning in the induction of problem categories[END_REF]. Additionally, providing multiple examples with different surface features might further improve example comparisons [START_REF] Quilici | Role of examples in how students learn to categorize statistics word problems[END_REF].

With regard to example elaborations it has been shown that training can be used to encourage learners to engage in self-explanations [START_REF] Chi | Eliciting self-explanations improves understanding[END_REF]. Additionally, it has been shown that grouping solution steps according to their subgoals [START_REF] Catrambone | The subgoal learning model: Creating better examples to improve transfer to novel problems[END_REF]) is effective because it provides affordances for learners to self-explain the meaning of individual solution steps [START_REF] Chi | Self-explanations: How students study and use examples in learning to solve problems[END_REF]). Finally, completion problems (van Merriënboer, 1990) and fading procedures [START_REF] Renkl | Structuring the transition from example study to problem solving in cognitive skills acquisition: A cognitive load perspective[END_REF] have been introduced to prevent learners from being overly passive in studying instructional examples.

Nearly all instructional interventions conceived to improve learning from (conventionally designed) worked examples are intended to either increase germane cognitive load (i.e., profitable example processing) and/or to decrease extraneous cognitive load (i.e., activities not directed at schema acquisition). In our own research we try to go beyond this general rationale and to find a way to reduce intrinsic cognitive load in example-based learning by abandoning the molar structure of conventionally designed worked examples.

Reducing Intrinsic Cognitive Load in Example-based Learning

As mentioned before, cognitive load theory usually assumes that intrinsic cognitive load cannot be manipulated by instructional design because it depends directly on the number of elements that are to be integrated into a to-be-learned schema and therefore have to be processed in working memory simultaneously. According to the theory, this element interactivity depends only on the relational complexity of the to-be-learned content and on the learner's degree of prior knowledge (i.e., on schemas already available). However, the assumption that intrinsic cognitive load cannot be manipulated is not uncontroversial (cf. [START_REF] Van Merriënboer | Taking the load of a learner's mind: Instructional design for complex learning[END_REF]. Different instructional approaches have been proposed that aim at reducing intrinsic cognitive load associated with learning materials.

• Part-whole sequencing: When the content of learning pertains to solving complex tasks, it is a well-known instructional approach to break down the complex task into simpler subtasks that can be conveyed separately. When learners have mastered the subtasks they may be instructed on how to solve the total complex task (cf. [START_REF] Gagné | The acquisition of knowledge[END_REF]. This partwhole sequencing strategy is suitable for reducing intrinsic cognitive load. First the load associated with acquiring the component tasks is lower than the one that would be imposed by starting with acquiring the total complex task right from the beginning.

Second, when learners are finally instructed on how to solve the total complex task later in the instructional sequence they will already possess a certain amount of domain-specific prior knowledge (in terms of schema availability) from their exposure to the component tasks. This prior knowledge will reduce the intrinsic cognitive load imposed by the need to finally acquire the skill of accomplishing the total complex task. However, it has to be noted that the part-whole sequencing strategy reduces the amount of intrinsic cognitive load during learning by changing the learning task in the early phases of the instructional sequence. So it might on the one hand be argued that this strategy does not predominantly change the cognitive load associated with a task but that it simply changes the task itself.

On the other hand, the total complex task that is acquired later in the instructional sequence is the same task that would have been used without the part-whole sequencing strategy. From the latter perspective this instructional strategy does not change the learning task but instead improves learners' knowledge and skills before being confronted with the learning task and thereby reduces intrinsic cognitive load during learning due to an increased availability of related schemas.

• Simplified whole tasks: [START_REF] Van Merriënboer | Taking the load of a learner's mind: Instructional design for complex learning[END_REF] argue that the fragmented approach of part-whole sequencing might make it difficult to integrate and coordinate subtasks into total complex tasks. Therefore, they advocate a different approach to lowering intrinsic cognitive load during learning, namely, to start learning with a simplified whole task with lower element interactivity. That is, the number of subtasks out of which the to-be-taught complex task consists is kept constant during training. However, each of these subtasks is first taught in a simplified version and then the difficulty of the subtasks and thereby of the whole task is gradually increased. As with part-whole sequencing, this approach might be considered as changing the learning task at the beginning of the instructional sequence by confronting the learners with simpler problems initially. It is only at the end of the instructional sequence -when learners already posses sufficient prior knowledge -that they are presented with the task in its full complexity. Again, the increased prior knowledge at that point in time results in a lower level of intrinsic cognitive load when learning how to accomplish the complex task.

• Modular presentation of solution procedures: Inspired by the aforementioned approaches to reduce the intrinsic cognitive load associated with learning from worked examples, we tried to design instructional examples that allow learners to start with a total complex task right from the beginning but nevertheless reduce intrinsic cognitive load during learning.

Our approach was to develop a more modular solution procedure in examples that required a learner to keep only a limited number of elements active simultaneously in working memory. The basic idea behind this modular example format is to present solution procedures in a way that completely avoids references to conventional molar concepts like problem categories, clusters of structural task features, and category-specific solution procedures. It can be argued that these molar concepts -that refer to complex entitiesusually impose high levels of cognitive load onto the learner (for details see the next section). In contrast, modular examples focus on smaller meaningful solution elements and their relation to individual structural task features. This approach substantially decreases the number of elements that have to be considered at the same time. The modular examples that we constructed differ very much from a part-whole sequencing strategy because we convey right from the beginning how to solve total complex tasks rather than teaching how to solve smaller subtasks in isolation first. Furthermore, our approach is also different from using simplified whole tasks, because we do not alter the difficulty of learning tasks in the course of learning in order to reduce intrinsic cognitive load. Instead,

Designing Modular Worked Examples

In the construction of modular worked examples we started with a careful analysis of the pattern of cognitive load imposed by conventional molar examples. A main feature of conventional examples is that they are designed to explain how to categorize problems according to multiple structural task features and how to apply category-specific solution formulas. Thus, molar examples usually demonstrate a convenient and fast way of solving problems that is quite similar to the approach a domain expert would choose for problem solving. However, a strong focus on problem categories might be rather overwhelming for novice learners because they might not possess sufficient prior knowledge (in terms of schema availability) to cope with the cognitive load imposed by this approach. A category-based approach requires learners to keep in mind all category-defining structural features of a problem before they are able to accurately decide on its problem category and the appropriate formula needed for its solution. Accordingly, studying molar examples requires that learners consider multiple structural task features at the same time in order to understand the problem's category membership.

As problems are grouped together in a problem category because they share a common solution procedure at some level of abstraction, the solution procedure associated with a problem category (i.e., applying an appropriate solution formula) can usually be characterized as a molar entity. For instance, in mathematical problem categories, multiple solution steps are frequently collapsed into a single complex formula that represents the solution and can be used as a recipe that allows one to calculate solutions in a fast and computationally convenient way. However, one has to consider that during schema acquisition all information units that are to be integrated into that schema have to be simultaneously activated in working memory [START_REF] Sweller | Cognitive architecture and instructional design[END_REF].

Therefore, molar examples will result in a high level of intrinsic cognitive load -in particular for novice learners -depending on the number of structural task features that have to be kept in mind concurrently and depending on the complexity of the solution formula needed. As already mentioned before, a substantial amount of intrinsic cognitive load might prevent learners from engaging in profitable processes of elaborating or comparing examples that are necessary to overcome shallow representations of problems and their solution.

The modular example format that we developed in response to this analysis was intended to impose less intrinsic cognitive load on learners by avoiding the need for learners to consider multiple structural task features or multiple solution steps simultaneously. The rationale in the construction of this example format was to isolate task features and meaningful solution elements that can be conveyed and understood separately, thereby reducing intrinsic cognitive load.

Besides reducing cognitive load, a second advantage of this approach is that it might allow learners to understand relations below the category level, that is, relations holding irrespective of category membership such as relations between individual structural task features and individual solution steps. As a result, learners might acquire meaningful knowledge on modular solution elements that enables them to directly translate individual structural task features into characteristics of the problem solution. This knowledge might be much more helpful than conventional knowledge on problem categories and solution recipes for adapting solution procedures to novel problems beyond the known problem categories (cf. [START_REF] Catrambone | The subgoal learning model: Creating better examples to improve transfer to novel problems[END_REF].

When we considered how to 'rethink' the domain of calculating complex event probabilities in order to develop instructional examples that do not refer to problem categories, their defining structural features, and category-specific solution formulas, we relied on the fact that problems in probability theory can be solved by breaking down complex events into sets of individual events.

Accordingly, the calculation of a complex event probability by means of a formula can be decomposed into a sequence of simpler calculations, that is, calculations of individual event probabilities. In line with our approach, the calculation of individual event probabilities allows one to directly relate individual structural task features and individual characteristics of solution steps. This is not true for the molar approach of using a solution formula! The solution procedure based on the modular approach we developed comprises four steps that are illustrated in the worked example in the right column of Table 1 (the left column displays the conventional molar solution approach for solving the same task). In this example the probability of a complex event is calculated by determining the probabilities of all individual events that make up the complex event (steps 1 to 3) and then multiplying these individual event probabilities to calculate the overall probability (step 4).

When calculating a particular individual event probability one has to take into account how the number of possible and acceptable choices changes from the preceding to the current trial.

These changes depend on whether previously selected objects are replaced or not after having been selected (problem with or without replacement), and on whether there is more than one acceptable choice in a given trial (order of selection important or not). For problems without replacement the number of possible choices decreases from trial to trial (otherwise it remains the same). For problems in which the order of selection is important there is only one acceptable choice on each trial (otherwise there might be more than one acceptable choices).

The fact that the two structural features used to categorize problems in this domain correspond to particular characteristics of individual solution steps makes it easier to adapt the modular approach to novel problems. The solution procedure illustrated by the modular example format does not require one to categorize problems before solving them. Rather, decisions with regard to individual structural task features can be directly translated into modifications of individual solution steps (i.e., changes in the number of possible and acceptable choices from trial to trial). The reasoning exemplified in the modular example format thus should help learners to understand relations below the category level that hold irrespective of category membership.

What is even more important -in contrast to the category-based approach --is that this reasoning can be understood by holding only a rather limited amount of information in working memory simultaneously. Thus, this format should impose less intrinsic cognitive load than a molar example format and accordingly free cognitive resources that can then be used by learners to engage in profitable processes of elaborating and comparing example problems.

To sum up, compared to traditional molar examples, the alternative example format we constructed is modular because solution procedures are broken down into smaller meaningful solution elements that can be understood in isolation without holding large amounts of information active in working memory. These elements can be separately transferred when solving novel problems. In this respect, modular examples conform to the subgoal learning model that proposes to group sets of solutions steps according to the subgoals they aim to achieve in the solution procedure [START_REF] Catrambone | The subgoal learning model: Creating better examples to improve transfer to novel problems[END_REF].

In the second part of this paper we will review the available evidence that an example format characterized by a modular presentation of solution procedures can reduce cognitive load, improve learning from worked examples, and foster transfer to novel problems.

Review of Experimental Evidence

In order to evaluate the evidence for the claimed superiority of a modular example format we can refer to five studies that are reported in [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF], Gerjets, Scheiter, and Kleinbeck (in press), and Gerjets, Scheiter, and Catrambone (in press). An overview of these studies will be given in the following sections.

Study 1 [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF] In Experiment 1 of [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF], 66 learners studied a pair of worked examples in which both examples belonged to the same single problem category (permutation without replacement). Each worked example demonstrated how to calculate a complex event probability that was related to humans picking a particular configuration of objects by chance. Learners were asked to study carefully the booklet with the two examples at their own pace and they were told that they would be asked later to solve some problems without looking at the examples. After Study 2 [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF] In Experiment 2 of [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF] the findings of Study 1 where replicated under slightly different conditions. To further improve learning the participants (N = 78) received three worked examples of a single problem category (permutation without replacement) in the learning phase. Participants were not required to describe the solution procedure before solving the test problems as they were in Study 1. Finally, the wording of the test problems was slightly modified.

The results of Study 2 were similar to those from Study 1 in that learners who received modular examples clearly outperformed the molar group in transfer performance.

However, both of the initial studies of [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF] demonstrating the superiority of a modular example format were characterized by two limitations with regard to the claims elaborated in the current paper. First, no measurement of learning time and no measurement of cognitive load was administered; thus we do not know whether the molar and modular example formats differ in their processing demands as can be expected from the theoretical considerations outlined in this paper. Second, the experiments did not address the ecologically more natural situation of learners studying multiple problem categories in a domain. The latter concern may easily result in an artificial bias in favor of the modular example format: When students are confronted with multiple problem categories during learning and problem solving they might strongly profit from being able to distinguish among these categories with regard to their structural task features, an ability that might be better supported by molar examples. Thus, the initial results of [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF] might be valid only in the rather restricted situation in which learning only one problem category is required.

Study 3 (Gerjets, Scheiter, & Kleinbeck, in press) The first experiment reported in Gerjets, Scheiter, and Kleinbeck (in press) changed the design of Study 1 and 2 used in [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF] in that learners had to acquire multiple problem categories by using a nonlinear hypertext learning environment that allowed the experimenters to measure the time for learning and later problem solving by means of logfiles. Time parameters were used to measure the processing demands of the two different example formats. In this experiment 52 learners could study two example problems for each of six different problem categories related to calculating complex event probabilities. These examples contained instructional explanations as illustrated in Table 1. The examples could be retrieved by means of hyperlinks in the learning environment used for self-paced study. In the introductory instructions of the experiments, participants were informed that they would have to solve six probability test problems on their own after having studied the worked examples. To avoid memory artifacts -in particular in the molar group that had to remember six different solution formulas -a re-examination of the instructional examples during the test phase was possible. In the test phase every participant had to solve three isomorphic and three novel test problems.

Isomorphic test problems differed from the instructional examples only with regard to their surface features, whereas novel test problems were constructed in a way that two complex event probabilities had to be found and then multiplied in order to calculate the required probability.

Logfiles were used to measure example-study time, time for retrieving instructional examples during problem solving (re-examination time), and time for solving the test problems.

As a performance measure the percentage of correctly solved test problems was registered. A declarative pretest was used to distinguish between high and low prior-knowledge learners within the two groups learning with molar or modular examples. Prior knowledge was used as an additional independent variable because it is strongly related to intrinsic cognitive load according to the cognitive load theory (cf. [START_REF] Sweller | Cognitive architecture and instructional design[END_REF].

The results of Study 3 showed that learning with modular examples led to better problemsolving performance for isomorphic as well as novel problems irrespective of learners' level of prior knowledge (cf. Figure 1). Additionally, learning with modular examples required significantly less example-study time as well as re-examination time during problem solving. No differences with regard to problem-solving time were obtained.

---Insert Figure 1 here -----In sum, Study 3 demonstrated that a modular example format is not only superior when a single problem category has to be acquired but also in case of multiple problem categories. This finding rules out the concern from Study 1 and 2 [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF] that the superiority of a modular example format might be an artifact due to the restricted learning situation used. It seems that students' ability to distinguish among different problem categories with regard to their structural task features will not be better supported by molar examples than by modular examplesalthough molar examples are explicitly designed to convey knowledge on problem categories and their structural task features. To explore this issue in greater detail we conducted a replication of Study 3 that used a slightly different instruction and that contained two additional dependent measures.

Study 4 (Gerjets, Scheiter, & Kleinbeck, in press) The second experiment reported in Gerjets, Scheiter, & Kleinbeck (in press) Classification task: To accomplish this task, participants had to identify one out of six word problems that was most similar to a given test problem with regard to its structural features. Four of the instructional examples that were already known from the learning phase were used as test problems. For each of the four test problems six word problems were presented as multiple-choice items that differed with regard to the problem category they belonged to. For each test problem participants had to identify the structurally most similar word problem, that is, the word problem that belonged to the same problem category as the test problem.

Comparison task: In this task, participants had to compare pairs of word problems with regard to their structural similarities and differences. Six problems from different problem categories were used as test problems. These problems were already known from the learning phase. From the 15 possible problem pairs that could have been made up from these six problems, we selected six problem pairs that were presented to participants for the comparison task. For each pair participants had to fill in a form that asked for structural similarities and differences of the two word problems.

Following the learning phase participants had to accomplish three different tasks. First they had to solve the same test problems as in Study 3 without having been informed about this task in advance. Subsequently, they had to work on the two tasks that had been announced and explained to them at the beginning of the experiment. The same time data as in Study 3 were obtained by means of logfiles.

The results of Study 4 were similar to those of Study 3 and again supported the claim that learning with modular examples led to better problem-solving performance for isomorphic as well as novel problems irrespective of learners' level of prior knowledge (cf. Figure 2). Again, learning with modular examples required significantly less example-study time as well as less reexamination time during problem solving. No differences with regard to problem-solving time were obtained.

---Insert Figure 2 -----With regard to the comparison task and the classification task that were used to investigate the influence of example formats and prior knowledge on the acquisition of structural features of problem categories, we found that performance in the classification task was affected only by participants' prior knowledge. Both example formats were equally effective in conveying knowledge on structural features of problem categories necessary to solve the classification task.

The same pattern of results were obtained for the comparison task.

These findings can be seen as indicating that learners might experience substantial difficulties in extracting and understanding information on abstract structural task features and problem categories molar worded examples although these examples are explicitly designed to convey that information. In line with our initial cognitive load analysis, learners studying molar worked examples might have few cognitive resources left to engage in profitable processes of example elaboration and example comparison which are, however, often shown to be necessary to construct more abstract knowledge from specific example problems.

An explanation might be that the understanding of molar example solutions requires learners to hold a substantial amount of information simultaneously in working memory. In contrast, understanding modular example solutions might be less demanding for students so that they are able to develop an understanding of structural problem features and to infer the categorical structure of the domain by themselves without being explicitly provided with this information. Accordingly, they accomplished the same level of performance in the classification task and the comparison task that were used to measure this particular aspect of students' knowledge. In our view, this can be seen as evidence that students learning from modular worked examples may possess unused cognitive resources that might be invested in (germane) processes that are directly relevant to learning and understanding (e.g., self-explanations).

Study 5 (Gerjets, Scheiter, & Catrambone, in press) To provide more direct evidence for the line of reasoning outlined above, we conducted another experiment (described as Experiment 2 in Gerjets, Scheiter, and Catrambone, in press) that involved a cognitive load measurement in order to test whether the cognitive load is indeed lower for studying modular example solutions than for studying molar example solutions. Beyond including measures of cognitive load we manipulated the availability of instructional explanations in Study 5. Two competing hypotheses can be formulated with regard to the impact of instructional explanations: On the on hand, learners using the modular example format might have sufficient cognitive resources available to engage in self-explanations, whereas learners using the molar example formats might suffer from cognitive overload when trying to understand molar solution procedures. Accordingly, students learning with modular examples might not need highly elaborated examples compared to students learning with molar examples. On the other hand, the substantial amount of instructional explanation provided in Study 3 and 4 (cf., Table 1) might have imposed cognitive load on learners that is especially harmful for those studying molar worked examples. According to this line of reasoning, learners with molar examples might benefit from a more condensed and therefore less overwhelming presentation of solution procedures, whereas learning from modular examples might be less vulnerable to cognitive overload due to the provision of instructional examples. This ambiguity with regard to the expected effectiveness of instructional explanations is consistent with the existing literature on this instructional manipulation (cf. [START_REF] Renkl | Learning from worked-out examples: Instructional explanations supplement self-explanations[END_REF].

In this experiment 68 students from the Georgia Institute of Technology learned with a shortened and linearized version of the learning environment used in Study 3 and 4 (in order to reduce navigational demands). Learners were provided with two worked examples for each of four problem categories taught. After studying the examples participants solved three isomorphic and six transfer problems. Novel problems were constructed similarly to the ones used in Study 3 and 4 (Gerjets, Scheiter, & Kleinbeck, in press). In contrast to these experiments, however, participants were given no opportunity to re-examine instructional examples in the test phase.

Instead, solution formulas were provided during problem solving for those participants who had to apply these formulas (i.e., those learning with molar examples). The formula list was provided during problem solving in order to allow direct access to the solution formulas and to rule out the possibility that a potential inferiority of the molar example format may be traced back to 1).

As dependent variables, problem-solving performance for isomorphic and novel problems as well as example-study times and problem-solving times were recorded. In order to test the assumption that using modular examples would lead to a reduction of intrinsic cognitive load during learning, we additionally assessed different aspects of cognitive load after the learning phase by administering a modified version of the NASA-TLX questionnaire [START_REF] Hart | Development of NASA-TLX (Task Load Index): Results of experimental and theoretical research[END_REF]. We preferred the NASA-TLX to the usual cognitive load questionnaire introduced by Paas and van [START_REF] Paas | Variability of worked examples and transfer of geometrical problem solving skills: A cognitive load approach[END_REF] because it allows for a more detailed analysis. Each of the three cognitive load items was rated on a scale ranging from 0 (low cognitive load) to 100 (high cognitive load). The following subscales were used: 'Effort' (How hard did you have to work in your attempt to understand the contents of the learning environment?), 'Stress' (How insecure, discouraged, irritated, stressed, and annoyed did you feel during the learning task?), and 'Task demands' (How much mental and physical activity was required (e.g., thinking, deciding, calculating, remembering, looking, searching etc.)? Was the learning task easy or demanding, simple or complex, exacting or forgiving?).

Analyzing the cognitive load data revealed that the example formats influenced learners' subjective experience of cognitive load whereas the degree of instructional explanations had no reliable impact (see Figure 3). First, with regard to the effort participants believed they had to invest in the task, they indicated that they had to work less hard in order to understand the instructional contents when learning with modular examples. Second, participants experienced far less stress during learning with modular examples. However, there was no effect of example format on the task demands associated with the learning task, but there was a significant interaction between example format and instructional explanations. The interaction indicated that participants judged the learning task as being less demanding with modular examples than with molar examples -but only when instructional explanations were provided -whereas there was no difference between the two examples formats when no explanations were given.

---Insert Figure 3 here ---As expected, participants who had learned with modular examples clearly outperformed participants learning with molar examples with regard to problem-solving performance for isomorphic as well as for novel problems (see Figure 4). There was, however, no effect of instructional explanations nor did any of the factors interact. Finally, analyzing the time data revealed that not only were participants learning with a modular example format more successful with regard to problem-solving performance, but they also needed far less time studying the examples than participants learning with molar examples. Rather naturally, the examples that included explanations took longer to process. There was no interaction between the two factors.

As in the previous studies there were no effects with regard to problem-solving time.

---Insert Figure 4 here ---

Discussion

Much of the existing research on learning from worked examples has been based on the notion of problem-type schemas as a central prerequisite for proficient problem solving. In this paper, we have argued that this conventional approach of designing examples in a way that focuses on teaching schemas might result in molar examples that impose high levels of cognitive load on learners. The cause for this problem might be that all the information that has to be integrated into the schema (e.g., multiple task features, formulas) has to be kept active in mind simultaneously. This high degree of cognitive load associated with molar, schema-based examples might prevent learners from implementing higher-level example processes like elaborations and comparisons. Instructional designers have addressed this problem by inventing a variety of techniques to either foster profitable processing of molar examples (and thereby increasing germane cognitive load) and/or to reduce unnecessary demands imposed on the learner (and thereby decreasing extraneous cognitive load).

In our work we took another approach by trying to design examples in a way that reduces the task-related, intrinsic load. Similar approaches of reducing intrinsic load have already yielded promising results recently [START_REF] Van Merriënboer | Taking the load of a learner's mind: Instructional design for complex learning[END_REF]. The basic idea of our modular approach was to break down solution procedures into smaller. more meaningful, pieces that can be conveyed and understood separately. In five studies we provided evidence that indeed these modular examples are superior to molar examples with regard to problem-solving performance for isomorphic and novel problems, different measures of learning time, and cognitive load.

The positive effects of modular examples were found to be superior regardless of the number of problem categories taught, the learning task announced, and the amount of instructional explanations given. Furthermore, modular examples proved to be superior for learners with low as well as with high prior knowledge. Therefore, the advantages of modular examples for teaching problem-solving skills seem to be very stable over a variety of instructional conditions.

One possible critique that we are aware of is that the design of modular versus molar examples might be restricted to this specific area of probability theory, that is, calculating complex event probabilities. We do not believe that this is the case; rather we are convinced that this approach might be extended to other well-structured domains where problems fall into categories. In fact, [START_REF] Catrambone | Improving examples to improve transfer to novel problems[END_REF] has already successfully attempted to extend this approach to the domain of algebra word problems -a line of research that we would like to follow in our future work. Another possible critique might be that modular examples might be helpful only for calculating complex event probabilities when rather small numbers are involved, whereas the strength of using formulas comes into play for problems dealing with larger numbers. However, we are convinced that in order to be able to apply a formula to novel cases, a learner must have already achieved an understanding of the domain. Therefore, we recommend using modular examples for initial skill acquisition in order to foster this kind of understanding and to switch to a molar approach in later stages of skill development. Learners would have at that point sufficient prior knowledge available to cope with the complexity of the formulas, that is, for them even a molar approach might be characterized by a low level of element interactivity. That is, we do not propose that the solution procedures conveyed by means of modular and molar examples are mutually exclusive; rather it is the instructional designer's important and difficult task to decide when to quit a modular approach in favor of using formulas and to rely on learners' ability to categorize problems according to their structural features. This decision should be based on empirical evidence with regard to finding the most suitable transition point between these two approaches. However, this empirical evidence is not yet available and has to be obtained by future research.

MOLAR EXAMPLE FORMAT M ODULAR EXAMPLE FORMAT

IDENTIFY TASK FEATURES This problem is a permutation-without-replacement problem. Problems of this type have two important features: First, the order of selection is important, and second, there is no replacement of selected elements. We are not interested only in finding out just which 3 of the 7 sprinters win medals, rather we want to know specifically which sprinter wins which medal. Therefore, the order of selection matters. A sprinter can win at most only one medal. Thus, this problem is a problem without replacement. That is, after a sprinter wins a medal he is not eligible for being selected again.

APPLY FORMULA

For this type of problem the following formula should be applied: A = n!/(n-k)! with n being the number of all sprinters and k being the number of sprinters that have to be correctly guessed.

INSERT VALUES

In the given example there are 7 sprinters to choose from. This is the set of elements for selection (n = 7). As we want to find out the probability of correctly guessing the winner of the gold, the silver, and the bronze medals, 3 sprinters out of these 7 sprinters have to be selected. Therefore, the number of selected sprinters equals k = 3. Inserting these values into the formula for permutation without replacement yields 7! / (7-3)! = 210 possible permutations.

CALCULATE PROBABILITY

In order to calculate the probability of correctly guessing the winner of each of the three medals, divide 1 (the particular permutation we are interested in) by the number of possible permutations. Thus, the probability of getting this permutation (the winner of each of the three medals) equals 1/210.

FIND 1ST EVENT PROBABILITY

In order to find the first event probability you have to consider the number of acceptable choices and the pool of possible choices. The number of acceptable choices is 1 because only 1 sprinter can win the gold medal. The pool of possible choices is 7 because 7 sprinters participate in the 100m-sprint. Thus, the probability of correctly guessing the winner of the gold medal is 1/7.

FIND 2ND EVENT PROBABILITY

In order to find the second event probability you again have to consider the number of acceptable choices. The number of acceptable choices is still 1 because only 1 sprinter can win the silver medal. The pool of possible choices is reduced to 6 because only the remaining 6 sprinters participating in the 100m-sprint are eligible to receive the silver medal. Thus, the probability of correctly guessing the winner of the silver medal is 1/6.

FIND 3RD EVENT PROBABILITY

In order to find the third event probability you again have to consider the number of acceptable choices. The number of acceptable choices is still 1 because only 1 sprinter can win the bronze medal. The pool of possible choices is reduced to 5 because only the remaining 5 sprinters participating in the 100m-sprint are eligible to receive the bronze medal. Thus, the probability of correctly guessing the winner of the bronze medal is 1/5.

CALCULATE THE OVERALL PROBABILITY

The overall probability is calculated by multiplying all individual event probabilities. Thus, the overall probability of correctly guessing the winner of each of the three medals is 1/7 * 1/6 * 1/5 = 1/210. Note: In experimental conditions with instructional explanations the example solutions contained all information stated in the relevant table column. Conditions without instructional explanations contained only the information printed in bold.

  we use exactly the same example problems for designing modular examples as we used for designing molar examples. The next section illustrates in greater detail how examples with a modular presentation of solution procedures might differ from examples with a conventional molar presentation of solutions.

  studying, learners wrote a description of how to solve problems in the domain. Finally, they solved four test problems that either belonged to the same problem category as the learning examples (isomorphic problems: permutations without replacement) or to a different problem category (novel problems: combinations without replacement). The experimental manipulation was whether the two worked examples for learning were designed to be molar or modular. The molar examples explained the appropriate solution formula for solving the problems and demonstrated how to insert the correct variable values into the formula. The modular examples explained how to consider the complex event in question as a sequence of individual events and how to integrate individual event probabilities into an overall complex event probability. The modular-example group outperformed the molar-example group on transfer performance. These results provided initial evidence that modular examples might help to foster learning from worked examples.

  used exactly the same procedure as in Study 3 (including the same set of worked examples and test problems). However, a different task was announced to learners at the beginning of the experiment. Instead of telling participants that they would have to solve test problems later on, they were instructed to study the instructional examples with the goal of acquiring structural features of problem categories. Participants were informed that they would have to work on a classification task and on a comparison task after having studied the instructional materials. They were made aware of the importance of knowing about structural features of different problem categories by familiarizing them with these two tasks they later would have to accomplish in the test phase.

  participants merely forgetting formula details (or having difficulties in finding the appropriate formula when re-examining instructional examples). As in the previous studies, the worked examples were either presented in the molar or the modular example format. Additionally, we varied the degree of instructional explanations between subjects. Half of the participants learned from the highly elaborated examples used in Study 3 and 4 while the other half studied a rather condensed version of the examples. Whereas the highly elaborated examples provided detailed justifications for solution steps, the condensed examples focused on the mathematical structure of example solutions without providing instructional explanations (see Table

FigureFigure 1 :

 1 Figure Caption(s)

Figure 2 :

 2 Figure 2: Problem-Solving Performance (% Correct) for Isomorphic and Novel Problems,

Figure 3 :Figure 4 :

 34 Figure 3: Cognitive Load (Scale Values) as a Function of Example Format and Degree of

Table 1

 1 Molar and Modular Example Formats Used for Experimentation

100M-SPRINT EXAMPLE At the Olympics 7 sprinters participate in the 100m-sprint. What is the probability of correctly guessing the winner of the gold, the silver, and the bronze medals?

The work reported in this paper was supported by the German Research Foundation DFG (Collaborative Research Center 378: Resource-adaptive Cognitive Processes) and by the Alexander von Humboldt-Foundation (TransCoop-Program). We thank Julia Schuh for helpful comments on an earlier version of this paper.


Daniele Allard
email: allard@ei.sanken.osaka-u.ac.jp

Riichiro Mizoguchi

Jacqueline Bourdeau

Danièle Allard

Can Language and Culture Go Hand in Hand? Cross-Linguistic Influence in the L2 Acquisition Process

come

Cross-linguistic Influence:

Cross-linguistic influence, which is also referred to as transfer, is the process by which L1 can impact L2 in its process of acquisition. That is to say: "the influence resulting from similarities and differences between the target language and any other language that has been previously (and perhaps imperfectly) acquired" (Odlin, 1989, p.27). This influence can have two facets: "Transfer is both a facilitating and limiting factor which provides one basis for the learner to form and test hypotheses about the second language he or she is learning" (Ringbom, 1985, abstract). In other words, transfer can be viewed as positive or negative. Positive transfer is the transfer of a skill inspired from L1 (or any other previously acquired language) that facilitates the learning of a skill in L2, given similarities between the two skills at hand. Negative transfer is the transfer of a skill that is different from that used in L2, and as such may actually impede learning [START_REF] Noor | Some Implications of the Role of the Mother Tongue in Second Language Acquisition[END_REF]. Interferences, which are related to negative transfer, are "errors in the learner's use of the foreign language that can be traced back to the mother tongue" (Lott 1983, p. 256). 2 Learner errors can of course be traced to various different sources, as second language learning involves more than a process of making use of L2 words to be placed in L1 sentence structures. Yet, interferences do account for many errors learners make (Ellis, 1997, Lightbown and[START_REF] Lightbown | How Languages are Learned. 2 nd Edition[END_REF]. Concepts of interference and transfer are related to research in contrastive analysis, which has roots in behaviorism, and was especially popular in the last half of the previous century. Given eventual shifts of paradigms in language acquisition research, namely away from behaviorist views, this type of research came to meet with resistance. In the words of Gregg: "contrastive analysis, error analysis, etc. are not simply unrelated to linguistic theory in particular, they are dead meat in general." (qtd. in [START_REF] Swan | The Influence of the Mother Tongue on Second Language Vocabulary Acquisition and Use[END_REF]. And yet, recent research has shown that overall patterns of error do tend to be language specific, which explains why English might sometimes be called "Thai English" or "Greek English." "There is less disagreement than there used to be about how far interlanguages are influenced by learners' native languages, and most linguists would probably now agree that the mother tongue can affect learners' English in several ways." (Swan and Smith, 2001, p. xi) Learners actually bring a tremendous amount of knowledge to the task of tackling L2 acquisition, among which is knowledge of L1. In the early stages of the acquisition process, especially, it is expected they draw on L1 knowledge [START_REF] Ellis | Second Language Acquisition[END_REF]. In fact, "the learner tends to assume that the system of L2 is more or less the same as in his L1 until he has discovered that it is not" (Ringbom, 1987, p. 135). Concurrently, if L1 and L2 are related, it will be easier for the student to acquire proficiency, but if they are unrelated, the process, especially in the earlier stages of acquisition, will prove more difficult and time-consuming [START_REF] Ringbom | The Role of the First Language in Foreign Language Learning[END_REF].

Our study focuses on "Japanese English." Based on observation and teaching experience in Japan, we, like others before us, have noticed that Japanese students tend to make certain types/patterns of errors on a regular basis, and several among these can be traced to influence from L1. We have found that identifying the source of an error, then providing explanations along with practice drills that are based on a comparison of the L2 problem area with corresponding L1 patterns seems to be of benefit in such cases. This is not to say that we always compare English to Japanese in explanations given to students, nor that such explanations need to be made in Japanese. Rather, we are proposing that an analysis of the cause of interference may reveal aspects explaining L2 usage that are otherwise left implicit in generic explanations. Making these aspects explicit, and using them to target usage explanations in such a way that the student might more readily understand, seems to bear fruit. In the process, we thus try, when possible, to promote positive transfer, encouraging students to make use of knowledge they already have, albeit with some necessary adjustments.

We will provide two examples to this effect: usage of come and go, and usage of had better. Our examples will not be expanded into extensive comparisons between both languages, which are beyond the scope of this paper, but rather aim at highlighting some illustrative key points in terms of L1 transfer and its potential impact. We will assume the position of an English teacher who has little knowledge of Japanese and little experience in teaching to Japanese students. The reason for these assumptions is to illustrate how explanations of a language point may potentially gain from adding elements linked to knowledge of corresponding L1 patterns.

Appropriate Usage of Come and Go:

In a conversation between a native English speaker and a native Japanese speaker, it is not uncommon, in response for example to (1) "Will you come to my home on Saturday?" to get a response from the Japanese speaker such as "Yes, I'll go" or "Yes, I'll go in the afternoon" (inappropriate usage) as opposed to "Yes, I will" (come is implied) or "Yes, I'll come in the afternoon."

In explaining generic rules of usage for come and go, a language teacher might consider the following: come is used for movements to the place where the speaker or hearer is, and go for movement to other places (Swan, Practical English Usage, 2005). In example (1) above, movement flows in the direction of the speaker, and the answer thus follows accordingly. The teacher might provide the following examples to further illustrate [START_REF] Swan | Practical English Usage[END_REF]:

(2) When did you come to live here? (3) Can I come see you? (4) I want to go and live in Greece.

(5) In 1577, he went to study in Rome. (6) Let's go and see Peter and Diane.

Analysis of usage in Japanese, on the other hand, shows that come and go varies essentially according to speaker (not speaker and hearer), which explains the mistake Japanese students might make in example (1), in fact a direct translation from Japanese. In Japanese, come indicates a movement in the direction towards the speaker or the speaker's viewpoint, and go expresses movement away from the speaker or the speaker's viewpoint (Makino and Tsutsui, 1986). Consequently examples (2), ( 4), ( 5), and (6) would essentially call for the same verbs as in the English examples, but (1) would imply a different answer, and (3) would require go instead of come. 3 Given both similarities and differences in usage, English usage of come and go is often quite confusing for Japanese students.

In view of this situation, can anything be supplemented to generic explanations to help facilitate student understanding and awareness of appropriate usage? In addition to English usage explanations, raising awareness of what one does in L1 as a comparison appears to be useful in this particular case. To begin with, the following graphic illustration can be considered: whereas Japanese is speaker-oriented, English is both hearer and speaker oriented.

Japanese

来る (come)

行 く ( go)

English

Come Go

This difference in perspective leads to usage differences, especially with respect to come. More specifically, we have observed that Japanese students often make L1-related mistakes when answering questions, in reply to a prompt, or when making statements using the first person ("I"). Other situations calling for come and go show that inappropriate usage does not usually occur, though there may be underlying nuances in intended meaning. 4 The above diagram can therefore be shown to students, followed by an explanation of how usage differs in English, firstly when answering questions or replying to prompts. Simply put, in English, if the direction of the movement is the same in both question and answer, the same verb will be used. For example, if someone asks: "What time are you coming on Friday?" the answer could be "I'm coming at noon." (not, as in Japanese, I'm going at noon). We extrapolate to third person situations: "When will your brother come see me? He will come after lunch (not: he will go after lunch). 5 "When are you going to Italy? I am going in July." (here, usage is the same in both languages). Inappropriate usage can also be seen in reply to a prompt: if A and B who live together have decided to go shopping, but A, tired of waiting for B, states "I'm going!"on the doorstep, then B, who wants to accompany A, would reply "I'm coming!" (not: I'm going!).

Using the diagram once again, explanations of the above paragraph can be summarized using the following approximation: go is used in statements or questions when the goal of the movement is not towards either the hearer and/or speaker. If it is, the statement or question calls for come. 6 Besides answers to questions or reply to prompts, Japanese students must also pay attention to usage of come in terms of "I." For example, in English, appropriate usage would call for: "May I come see you this afternoon?" (not: May I go see you?). Wrapping up, an example of a situation in which movement is different between the question and the answer can be provided. This implies that the choice of the verbs will vary: Did you come to the university on Tuesday after all? No, I didn't. I went to City Hall. Usage is similar to Japanese, but this example is used to reinforce understanding of the above approximation. 7

Carefully going over such an explanation, which in some respects parallels and contrasts usage in Japanese, along with targeting examples and practice so that students become more keenly aware of the mechanics of English usage in relation to what they know, in our experience, facilitates the acquisition process. Though generic explanations of rules of usage and generic exercises may certainly bring students to the same end result, if targeted explanations and practice takes them there faster, we believe the latter will then have been of benefit.

"Linguistic differences between L1 and L2 may not automatically mean learning problems, but if the learner is able to perceive structural lexical similarities between L1 and L2 there will be an absolutely essential absence of some important learning problems at the early stages, especially as far as comprehension and vocabulary learning are concerned" (Ringbom, 1987, p.60). That is to say, if the learner is able to root his (her) understanding of L2 in the understanding he has of L1, learning can be facilitated. Though this will be easier to do in cases of obvious similarities between L1 and L2, it can also apply to cases of dissimilarities provided the student develops a sense of what is similar to L1 and what is not.

Appropriate Usage of Had better:

Our second example centers on the English modal had better. Consider the following statements: (1) "You had better take your umbrella." (2) "You had better go to Osaka Castle to see the beautiful cherry blossoms." (3) "You had better read this book." Though these are not uncommon in English used by Japanese native speakers, they have sometimes struck English native hearers to whom they were addressed as somewhat odd, if not inappropriate. The Japanese speaker who reported example (1) was eventually told by his foreign visitor that this type of advice was not completely appropriate: the visitor was able to decide for himself whether or not he needed to bring an umbrella -to the surprise of the Japanese speaker. Similarly, though comments were not voiced, (2) and

(3) elicited reactions from native English speakers to the effect of: "What if I don't go to the castle -or read this book? Do I need to worry about something?" Of course, depending on the context, usage of had better may not necessarily bring about such reactions, but the fact that it can, we believe, needs to be addressed.

In questioning Japanese speakers/students, it appears that had better is essentially seen as an equivalent for the Japanese expression ほうがいい. It is offered as a possible translation in various Japanese-English dictionaries, and is translated as such by Makino and Tsutsui (1986) in their dictionary of Japanese grammar. These linguists explain ほう がいい it in the following way: "it is strongly suggested that someone do something." In Practical English Usage, [START_REF] Swan | Practical English Usage[END_REF] explains had better in terms of strong advice, or

telling people what to do (including ourselves) [START_REF] Swan | Practical English Usage[END_REF]. ほうがいい and had better therefore appear, at first glance, to be equivalent expressions.

Other English grammar books add to Swan's explanation that usage of had better can also imply that if the advice given is not followed, there is the possibility of a problem or a danger [START_REF] Murphy | English Grammar in Use[END_REF][START_REF] Azar | Understanding and Using English Grammar[END_REF]. Bearing this in mind, it might then be explained to students that in example (2) for instance, usage of "had better" is not the best choice since there is not any particular problem or danger in view of not seeing cherry blossoms at Osaka Castle. Barker (2003) stresses this point using a similar example in 英語と仲直り できる本 (Coming to Terms with English: A Reference Book). 8

When examining the issue more closely, however, it seems that there are deeper issues at stake, which stem from cultural differences. Informal discussions with Japanese speakers have revealed that ほうがい also carries the implication of negative consequences. This is actually the reason for giving the advice, and demonstrates concern for the hearer's welfare, or at least for the possibility of missed opportunities. Should the severity of the consequence then be considered in terms of usage of had better? Makino, Tsutsui, and Swan all refer to the idea of "strong" advice in their respective explanations of the Japanese and the English expression. How strong, then, is strong? Cultural perspectives, it appears, vary in this respect.

The relative strength of ほうがいい and had better appears to gravitate at opposite ends of a spectrum when compared to other advice expressions in each respective language. In English, had better is stronger than might/could, but weaker than have to/have got to/need to; the negative form had better not is ranked as the strongest possible modal of negative advice (Celce-Murcia and Larsen-Freeman,1999). In comparison, ほうがいい is ranked as the weakest Japanese expression of advice (Makino and Tsutsui,1986). 9 This seems to confirm that "strong advice" is indeed culturally dependent.

The English hearer who reacted to the suggestions of bringing an umbrella highlights another important issue: sensitivity to advice. Japanese people are generally receptive to advice, even viewing it as normal, if not desirable. This is probably linked to the Japanese proclivity towards maintaining group harmony which rests upon a series of socially accepted rules. These serve as guidance towards maintaining harmony, and as such, are necessary and useful. They in turn contribute to generating a strong sense of duty, as well as, generally speaking, a sense of ease with respecting and following rules, as well as an openness towards various forms of advice from other group members with a similar concern for harmony. Westerners, on the other hand, tend to value individualism and the capacity to decide for oneself, and as such, may react negatively to advice, especially if it is perceived as unsolicited. In other words, whereas "strong" advice using ほうがいい would likely not ruffle a Japanese hearer, "strong" advice using had better may not always be well received by an English-speaking hearer. We acknowledge that the preceding explanation is a series of generalizations. We further acknowledge that "cultural generalizations are necessarily statements of likelihood and potential, not of certainty" (Storti,3). Yet, it is not possible to talk about culture, about groups of people, without making generalizations. As these do contain a kernel of truth, used wisely, along with discrimination, generalizations can at least set a way towards clearer mutual understanding. [START_REF] Storti | Figuring Foreigners Out[END_REF] The context, tone of voice and relationship of speaker and hearer when expressing / receiving advice need of course to be taken into consideration. Depending on these, had better can take on different connotations. To this effect, a Japanese speaker may consciously articulate had + better when uttering a statement, rather than use the (pronoun)'d better abbreviation more common to everyday English. Furthermore, the rhythm of the sentence may end up making the advice sound stronger/more threatening than it is actually intended to be because it is stated by a non-native speaker not used to English rhythm / inflection / pronunciation.

How does an English teacher then deal with explaining had better to Japanese students?

To begin with, one might emphasize that the English modal is not a translation for ほう がいい, while explaining issues of sensitivity to advice in view of comparative cultural considerations --at least in terms of impact on a Western hearer. In the process, the teacher can provide relevant examples of use, and situate had better in relation to other advice modals in terms of relative strength --the point might also be made that had better and ほうがいい tend to be at opposite ends of a strength spectrum in each respective language. The teacher might also show how the examples given at the beginning of this section can be toned down, for instance by expressing them using might, could or should.

In fact, a good review of modals and advice expressions, along with targeted exercises and drills in view of potential L1 interference, accompanied by discussion of impact on a potential hearer should prove useful.

The study of modals can further lead to practice in the usage of imperatives, which Japanese students find difficult to apply in English. "Bring your umbrella!" said in a casual tone is not a forceful statement, but in Japanese, it is comparatively much stronger, regardless of the tone of voice, which likely explains reluctance on the part of Japanese speakers to use English imperatives. We shall not enter here into a comparative discussion of imperatives, but we raise the issue to show how attention to cross-linguistic influence and the difficulties they may cause can suggest instructional sequences that may facilitate acquisition and understanding while following an order that might not otherwise be taken in generic teaching methodologies. That is to say, linking the study of imperatives to that of modals may facilitate understanding of their usage for Japanese students.

.

Towards Tackling L1 Interference in L2:

One of the first steps in dealing with L1 interferences is to begin identifying them. Personal experience in the classroom and with students can certainly be a valuable source of information, as are exchanges with seasoned teachers on the subject. Published literature on the topic may also be helpful. To this effect, we recommend two works of reference. The first is Learner English -A teacher's guide to interference and other problems, edited by Michael Swan and Bernard Smith. This is a collection of essays, each covering relevant features of a given language in relation to English, including Japanese. It lists various typical mistakes that learners are apt to make, while providing cultural notes. It does not provide teaching strategies or targeted exercises.

The second work is David Barker's 英語と仲直りできる本 (Coming to Terms with English: A Reference Book). The book is written in Japanese but it features indexes both in Japanese and English. The work is an extensive collection of problem areas that Barker has encountered in the course of over ten years teaching English to Japanese students. Though it may not be accessible to teachers of English unfamiliar with Japanese, it nevertheless remains a valuable tool: Japanese students may consult the work as they see fit, or be advised to read about specific problem areas. Not only does Barker explain appropriate English usage, he also makes several comparisons with Japanese, which help clarify some of the points he makes. A few useful practice exercises are interspersed within the book.

In a different article, Barker (2003) stresses the importance for English teachers who are in Japan for an extended period of time to learn Japanese. Among various points, he emphasizes that "a teacher with a detailed knowledge of the differences between the L1 and the target language will be better equipped to anticipate and overcome problems […] the students are likely to face." In this sense, a working knowledge of Japanese on the part of the English teacher can indeed be useful. This is however not always possible.

Japanese teachers of English familiar with Japanese, for their part, have not necessarily examined the phenomena of cross-linguistic influence closely, and may not have ready access to concise information concerning the sources of difficulties they create, in addition to possible strategies to overcome them. Our research is therefore concerned not only with highlighting cross-linguistic difficulties, but with making such information available to both teachers and students. More specifically, we are working towards the design of a CALL system that helps identify difficulties related to cross-linguistic influence, while providing relevant instructional strategies and activities to overcome them. That is to say, a teacher working with such a system could access information on such difficulties, for example when preparing a course or a given lesson, in addition to teaching suggestions, targeted exercises and drills. The student working on an activity might be prompted by the system concerning an area of difficulty, and directed to specific explanations and activities for further practice.

We have been especially concerned with drawing out categories that have roots in cultural differences. For instance, we have shown that the use of come and go is guided by speaker/hearer perspective. We can therefore begin to deal with a concept called "speaker/hearer perspective," and examine whether other interferences might follow a similar pattern and establish significant links. Usage of had better, as we have seen, can also be linked to "speaker/hearer perspective," as can the use of the imperative.

The mapping of cross-linguistic difficulties in our CALL system then does not follow grammatical or linguistic categories, but considerations related to culture. Languages, as we mentioned in our introduction, are imbued with culture. Cultural understandings, as our examples have shown, are embedded within language use, and differences to this effect can not only lead to errors in L2, but to potential misunderstandings, as the example of had better has demonstrated. We therefore seek to not only reduce the impact of cross-linguistic influence, but also to raise awareness in view of cultural similarities and differences in the course of an L2 acquisition process. Furthermore, we hope the concepts we identify will enable eventual comparison of different sets of L1 and L2 in terms of cross-linguistic difficulties using similar parameters. We hope to elaborate on the progress of our research in the near future.

Concluding remarks:

There is a Japanese pub on the outskirts of Kyoto with a most interesting name -at least to an English speaker. It is called: Bar --Sushi and Men. Is that to say -with a touch of humour -that the Japanese like their men raw? As most foreigners living in Japan are well-aware, roman characters and English words are commonly used in advertising, store signs, stationary, fashion items, etc. In this particular case, the owner(s) of the bar linked two Japanese words with an English conjunction, words which were written in roman characters instead of characters used in Japanese. The result? L1 interference with an interesting twist. To begin with, a bar generally does not serve meals, so to call the place a "bar" was not completely appropriate. And for those not familiar with Japanese, "men" in Japanese stands for "noodles." Thus, what we had seen was a place to eat sushi and noodles, while having a drink.

The process of acquiring L2, especially in the early stages, is not without challenges, many of these stemming from L1 influence. In this presentation, we have given examples of cross-linguistic influence and interference, illustrating potential difficulties in bridging Japanese and English. We have also made some suggestions towards tackling L1 interference in L2, while briefly examining the possibility of using CALL applications to overcome some of the problems they create, with a focus on cultural considerations.

We hope to further elaborate on the results of our research in future presentations.

Acknowledgements:

This paper was one of three presentations within the Teacher Education SIG Forum: Can Language and Culture Go Hand in Hand? It is dedicated to co-presenters, Anthony Robins Brian Cullen. We are also indebted to Nicolas Gromik, Tohoku University for valuable comments, Michael Swan, for kindly answering linguistic questions, especially in terms of usage of come and go, and to students at Osaka University and Doshisha Women's College of Liberal Arts for relevant feedback when approaching the topics of come and go and that of expressing advice.

English and L1 is Japanese, as Japanese native students acquiring English as L2 are the focus of our study. This is also a population which, especially at the high school level, has generally not yet been exposed to another L2. 3 We indicate "essentially," because in Japanese, some of these examples would not need to be expressed using come or go. For example (4) might be expressed as ギリシャへ移住したい (I want to emigrate/settle in Greece), in order to convey the English idea of "go and live." Otherwise, the movement of going to Greece would be expressed using go in Japanese as well. Similarly, (5) might be translated as 1577 年にローマーへ留学しました(In 1577 he went to study in Rome); in Japanese there is a specific expression for the idea of "go to study," and as such go is not required. 4 Let us consider an example: B and C are discussing A's upcoming party (A is not present). In English, if B asks C: "Are you coming to the party?" it generally implies that B is attending the party, without necessarily being a comment on the relationship between B and A. In Japanese, if B uses the verb come in the same question, it not only implies that B is going to the party, it also shows some kind of a positive feeling towards A, more so than it would in English. If B felt little connection to A, then B would likely say in Japanese: "Are you going to the party?" This being said, both come and go can be used in either English or Japanese in this situation. There are some nuances in underlying meaning, but as they do not lead to usage mistakes, we do not usually bring these issues up with students. 5 Objects that are related to speaker and / or hearer (in this case the hearer's brother) can be considered, both in English and in Japanese, to be an extension of either of them, so to speak. In other words, though the brother is not physically present in this exchange, he is considered as if he were. 6 We are grateful to Michael Swan for corroborating that this is a valid approximation. 7 The same explanations also help in explaining usage of bring and take, another problematic area for Japanese students. 8 The example of misuse that Barker gives is: If you go to London, you had better go to the British Museum. He explains that if this is friendly advice, usage of had better is not appropriate. Had better should be thought not only in relation to した方がいい, but also した方がいい、そうしないと嫌なことがある (had better otherwise something undesirable might/will happen). (p. 111) There are many possible English translations for the title of Barker's book. The one suggested is one among several possibilities. 9 ほうがいい is ranked below すべきだ which is weaker than しなければならない.