Bas Kollöffel
email: b.j.kolloffel@gw.utwente.nl

Tessa Eysink

Ton De Jong

The influence of representational format on learner-generated domain representations and mathematical achievement

The purpose of this study was (a) to assess the effects of learner-generated domain representations on understanding combinatorics and probability theory and (b) to investigate the effects of the format (graphical, arithmetical, or textual) in which learners create their domain representation. A pretest-posttest design was applied in which four conditions were compared: three experimental conditions in which learners constructed a personal representation of the domain in a graphical, arithmetical, or textual format, and a control condition in which learners did not have to construct a representation. It was found that the construction of a domain representation significantly increases learning outcomes. Furthermore, it was found that the format in which learners express their knowledge does not directly affect learning outcomes or the quality of the created domain representations. However, the arithmetical format prevents most learners from engaging and succeeding in externalizing their knowledge.

Introduction

The domain of combinatorics and probability theory is hard to grasp for many learners. Some of the reasons for this have to do with mathematics or science domains in general but others have to do with specific characteristics of the domain of combinatorics.

One of the more general reasons for students' problems with science and mathematics problems is that novices often have a tendency to focus on superficial details rather than on understanding the principles and rules underlying a science or mathematics domain [START_REF] Chi | Categorization and representation of physics problems by experts and novices[END_REF][START_REF] De Jong | Cognitive structures of good and poor novice problem solvers in physics[END_REF][START_REF] Reiser | Scaffolding complex learning: The mechanisms of structuring and problematizing student work[END_REF]. Science and mathematics problems require learners to go beyond the superficial details in order to recognize the concepts and structures that underlie the problem and to decide which operations need to be performed to solve it (e.g., [START_REF] Fuchs | Enhancing mathematical problem solving among third-grade students with schema-based instruction[END_REF]. In the case of probability instruction, the approach that needs to be taken to solve a problem is very dependent on the correct classification of the problem [START_REF] Lipson | Investigation of students' experiences with a web-based computer simulation[END_REF].

A second reason for students' difficulties is that the abstract and formal nature of often used arithmetical representations does not show the ______________ underlying principles or concepts as explicitly as pictorial and textual representations. Most learners tend to view mathematical symbols (e.g., multiplication signs) purely as indicators of which operations need to be performed on adjacent numbers, rather than reflections of principles and concepts underlying these procedures [START_REF] Atkinson | Aiding transfer in statistics: Examining the use of conceptually oriented equations and elaborations during subgoal learning[END_REF][START_REF] Cheng | Unlocking conceptual learning in mathematics and science with effective representational systems[END_REF][START_REF] Greenes | Mathematics learning and knowing: A cognitive process[END_REF][START_REF] Nathan | A theory of algebra-wordproblem comprehension and its implications for the design of learning environments[END_REF][START_REF] Niemi | Assessing conceptual understanding in mathematics: Representations, problem solutions, justifications, and explanations[END_REF][START_REF] Ohlsson | The function of conceptual understanding in the learning of arithmetic procedures[END_REF]. Therefore, they easily lose sight of the meaning of their actions. In this case, processing formal notations becomes an end in itself [START_REF] Cheng | Unlocking conceptual learning in mathematics and science with effective representational systems[END_REF]. Learning of arithmetical procedures without conceptual understanding tends to be error prone, easily forgotten, and not readily transferable [START_REF] Ohlsson | The function of conceptual understanding in the learning of arithmetic procedures[END_REF].

Third, the formal, abstract way in which subject matter is represented makes it hard for learners to relate the subject matter to everyday life experiences. [START_REF] Fuson | Mathematical understanding: An introduction[END_REF] argue that the knowledge learners bring into the classroom is often put aside in mathematics instruction and replaced by procedures that disconnect problem solving from meaning making. In the case of probability and combinatorics the integration of theory and everyday life experience is particularly important, because probability ideas often appear to conflict with students' experiences and how they view the world [START_REF] Garfield | Difficulties in learning basic concepts in probability and statistics: Implications for research[END_REF][START_REF] Kapadia | A brief survey of research on probabilistic notions[END_REF]. The conflicts arise because probabilities do not always fit learners' conceptions and intuitions (e.g., [START_REF] Batanero | What is the nature of high school students' conceptions and misconceptions about probability[END_REF][START_REF] Fischbein | The intuitive sources of probabilistic thinking in children[END_REF][START_REF] Greer | Understanding probabilistic thinking: The legacy of Efraim Fischbein[END_REF]. An example of a misconception is the gambler's fallacy, that is, the belief that the outcome of a random event can be affected by (and therefore predicted from) the outcomes of previous events.

These reasons are by no means exhaustive, but summarize some of the main problems encountered in the instruction of combinatorics and probability theory. Learners end up with a knowledge base that is biased towards procedural knowledge, which means that they know how to perform arithmetical operations but hardly understand the underlying principles, or the conditions under which the procedures are applicable. Moreover, they fail to relate their knowledge to everyday life situations. Instructional approaches therefore need to concentrate on ways to focus the learners' attention to the principles and rules underlying the domain rather than to superficial details and operations, while using representational formats that are most beneficial for understanding, preferably in a way that relates theoretical mathematical knowledge to everyday life experiences.

Using externalization activities to foster understanding

Gaining a full understanding of a domain requires learners to combine conceptual, procedural, and situational knowledge into meaningful schemata. These schemata can be acquired by performing cognitive activities such as selecting, organizing, and integrating information [START_REF] Mayer | The promise of multimedia learning: Using the same instructional design methods across different media[END_REF][START_REF] Mayer | Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction[END_REF][START_REF] Shuell | Cognitive conceptions of learning[END_REF][START_REF] Shuell | The role of the student in learning from instruction[END_REF][START_REF] Sternberg | A theory of knowledge acquisition in the development of verbal concepts[END_REF]. Selecting involves recognizing which information is relevant and which is not. Organizing involves combining pieces of information into a coherent and internally connected structure (e.g., a mental representation). Integrating refers to relating newly acquired knowledge to already existing knowledge structures (prior knowledge). Many learners do not engage in these cognitive activities, unless prompted to do so [START_REF] Pressley | Encouraging mindful use of prior knowledge: Attempting to construct explanatory answers facilitates learning[END_REF]. A promising way of prompting is to stimulate learners to externalize their domain knowledge. [START_REF] Cox | Representation construction, externalised cognition and individual differences[END_REF], for example, argues that the externalization of knowledge may elicit self-explanation effects and that the process of externalization consists of dynamic iterations and interactions between external models and mental models and therefore helps learners to refine and disambiguate their knowledge of the domain.

There are many ways to stimulate learners to externalize their domain knowledge. Frequently used instructions include asking the learners to write summaries [START_REF] Foos | The effect of variations in text summary opportunities on test-performance[END_REF][START_REF] Hidi | Producing written summaries: Task demands, cognitive operations, and implications for instruction[END_REF][START_REF] Spurlin | processing: Effects of summarization frequency on text recall[END_REF], or to create drawings [START_REF] Van Meter | Learnergenerated drawing as a strategy for learning from content area text[END_REF][START_REF] Van Meter | The promise and practice of learnergenerated drawing: Literature review and synthesis[END_REF] of the subject matter. A less well-known technique is letting learners build their own runnable computer model [START_REF] Löhner | The effect of external representation on constructing computer models of complex phenomena[END_REF][START_REF] Manlove | Regulative support for collaborative scientific inquiry learning[END_REF][START_REF] Van Joolingen | Co-Lab: Research and development of an online learning environment for collaborative scientific discovery learning[END_REF]. In this approach, learners construct a dynamic simulation of their own mental model. They can observe the model they created and draw conclusions based on the model output. Another example of externalization is asking the learners to construct a concept map during or after learning [START_REF] Gijlers | Confrontation and co-construction: Exploring and supporting collaborative scientific discovery learning with computer simulations[END_REF][START_REF] Nesbit | Learning with concept and knowledge maps: A meta-analysis[END_REF][START_REF] Novak | Concept maps and Vee diagrams -Two metacognitive tools to facilitate meaningful learning[END_REF][START_REF] Novak | Meaningful learning: The essential factor for conceptual change in limited or inappropriate propositional hierarchies leading to empowerment of learners[END_REF][START_REF] O'donnell | Knowledge maps as scaffolds for cognitive processing[END_REF]. A learner-generated concept map can give insight into which concepts are thought to be relevant or important and how the learner thinks the concepts are related to each other, and thus shows where gaps or misconceptions occur.

The type of externalization is related to the representational format in which learners are expected to express their knowledge. Representational format is known to play a critical role in learning and understanding [START_REF] Ainsworth | The effects of self-explaining when learning with text or diagrams[END_REF][START_REF] Cheng | Unlocking conceptual learning in mathematics and science with effective representational systems[END_REF][START_REF] Zhang | The nature of external representations in problem solving[END_REF]. The properties of representations are assumed to influence which information is attended to and how people tend to organize, interpret, and remember the information (e.g., [START_REF] Larkin | Why a diagram is (sometimes) worth ten thousand words[END_REF]. With regard to learner-generated externalizations of knowledge in the domain of combinatorics and probability theory, it has been found that learners avoid using conventional ways of representing the probability of events (i.e., using ratios or odds, or formal numerical probabilities) and prefer to use alternative forms of representation, ranging from textual statements to conventional numerical representations [START_REF] Tarr | How can teachers build notions of conditional probability and independence[END_REF]. This finding indicates that all formats may not equally suitable for learners trying to express their knowledge.

Research questions

The aim of the current study was to find out whether externalizing knowledge leads in general to better understanding in the domain of combinatorics and probability, and in particular, whether the representational format in which learners externalize their knowledge has a differential effect on understanding in this domain. Three formats in which learners could externalize their knowledge were compared: (a) a graphical format (i.e., concept maps), (b) an arithmetical format, and (c) a textual format. Externalization is assumed to focus the learners' attention more on conceptual and situational aspects of the domain, resulting in a knowledge base that contains conceptual knowledge, procedural knowledge, and situational knowledge instead of a one-sided focus on procedural knowledge. Externalization in the graphical format is hypothesized to stimulate conceptual knowledge in particular, because of the primary focus on the identification of concepts and their mutual relationships [START_REF] Nesbit | Learning with concept and knowledge maps: A meta-analysis[END_REF]. Although expressing knowledge in an arithmetical format is supposed to draw the learners' attention primarily to operational aspects, externalizing is still thought to improve conceptual and situational knowledge as compared to learners who do not externalize at all. Externalizations of a textual nature are assumed to direct the learners' attention to conceptual and situational aspects, although the conceptual issues might not be as strongly stressed as for learners who construct a concept map.

Method

Participants

In total, 133 third-grade pre-university education students, 65 boys and 62 girls (six participants did not indicate their gender), participated. The average age of the participants was 14.63 years (SD =.62). The participants had no prior knowledge of combinatorics and probability theory. They attended the experiment during regular school time; therefore, participation was obligatory. Participants received a mark based on their post-test performance.

Design

The experiment employed a between-subjects design with the representational format (graphical, arithmetical, textual) in which learners had to express their knowledge as the independent variable. Participants in a control condition were provided with the same learning environment, assignments, and tests as participants in the experimental conditions. The only difference was that participants in the control condition were not required to externalize their knowledge. Participants were assigned randomly to conditions. Twelve participants were excluded from the analyses; seven of them did not attend one or more experimental sessions, and five were excluded because their post-test scores deviated more than 2 SDs from the mean scores within their condition. The distribution of the remaining 121 participants across conditions is displayed in Table 1. Domain The domain of instruction was combinatorics and probability theory. An example of a problem in this domain is: what is the probability that a thief will guess the 4-digit PIN-code of your credit card correctly in one go? The essence of combinatorics is determining how many different combinations can be made with a certain set or subset of elements. In order to determine the number of possible combinations, one also needs to know 1) whether elements may occur repeatedly in a combination (replacement) and 2) whether the order of elements in a combination is of interest (order). On basis of these two criteria, four so-called problem categories can be distinguished (for an overview, see Figure 1). The PIN-code example matches category 3 (replacement; order important). When the number of possible combinations is known, the probability that one or more combinations will occur in a random experiment can be determined.

Externalization tools

Participants in the experimental conditions were asked to construct a representation of the domain that would be meaningful to themselves and a fictitious fellow learner. This representation was to reflect the relevant principles underlying the domain, the variables playing a role in the domain, and their mutual relationships. Learners had to create their representations on an electronic on-screen externalization tool. There were three types of externalization tool, one for each experimental condition: (a) a graphical externalization tool (i.e., a concept mapping tool), (b) an arithmetical externalization tool, and (c) a textual externalization tool.

In the graphical externalization tool, learners were supposed to create concept maps of the domain. Learners could draw circles representing domain concepts and variables. Keywords could be entered in the circles. The circles could be connected to each other by arrows indicating relations between concepts and variables. The nature of these relations could be specified by attaching labels to the arrows. In the arithmetical externalization tool, learners could use variable names (N, K, and P), numerical data, and mathematical operators (division signs, equation signs, multiplication signs, and so on) in order to express their knowledge. Finally, the textual externalization tool resembled simple word processing software, allowing textual and numerical input. The contents of the externalization tools were stored automatically.

Learning environment

The instructional approach used in this study is based on inquiry learning (de Jong, 2005Jong, , 2006)). Computer-based simulation is a technology that is particularly suited for inquiry learning. Computer-based simulations contain a model of a system or a process. By manipulating the input variables and observing the resulting changes in output values the learner is enabled to induce the concepts and principles underlying the model [START_REF] De Jong | Scientific discovery learning with computer simulations of conceptual domains[END_REF].

The learning environment used in the current study, called Probe-XMT, was created with SIMQUEST authoring software [START_REF] Van Joolingen | SimQuest: Authoring educational simulations[END_REF]. Probe-XMT consisted of five sections. Four of these sections were devoted to each of the four problem categories within the domain of combinatorics. The fifth section aimed at integrating these four problem categories. Each section used a different cover story, that is, an everyday life example of a situation in which combinatorics and probability played a role. Each cover story exemplified the problem category treated in that section. In the fifth (integration) section, the cover story applied to all problem categories.

Each of the five sections contained a series of questions (both openended and multiple-choice items), all based on the cover story for that particular section. These questions involved determining which problem category matched the given cover story (situational knowledge), calculating the probability in a given situation (procedural knowledge), and selecting a description that matched the relation between variables most accurately (conceptual knowledge). In the case of the multiple-choice items, the learners received feedback from the system about the correctness of their answer. If the answer was wrong, the system offered hints about what was wrong with the answer. Learners then had the opportunity to select another answer. In the case of the open-ended questions, learners received the correct answer after completing and closing the question.

Most of the questions were accompanied by simulations that could be used to explore the relations between variables within the problem category. In the simulations, learners could manipulate variables and observe the effects of their manipulations on other variables. The simulations used a combination of textual and arithmetical representations.

The learning environment automatically registered user actions. User actions that were logged included measures like user path through the learning environment (which parts of the learning environment were opened, when, for how long, and in what sequence) and the number and nature of manipulations carried out in the simulations (how many experiments were carried out and the input values of each experiment).

Knowledge measures

Two knowledge tests were used in this experiment,: a pre-test and a posttest. These tests contained 12 and 26 items respectively. An overview of the test items and underlying knowledge types is presented in Table 2. In cases where learners had to calculate the outcome of an item, a calculator was provided on-screen. Both tests were administered via the internet. The questions were presented screen-by-screen without the possibility of skipping questions or turning back to previous questions.

Learner responses on both multiple-choice and open-ended items were collected and recorded electronically.

Procedure

The experiment was carried out in a real school setting in three sessions, each separated by a one-week interval. Learners worked individually and they were told that they could work at their own pace. The first session started with some background information with regard to the experiment (general purpose of the research, the domain of interest, learning goals, etcetera). This was followed by the pre-test. It was announced that the post-test would contain more items of greater difficulty than the pre-test, but that the pre-test items nonetheless would give an indication of what kind of items to expect on the post-test. At the end of the pre-test the learners received a printed introductory text in which the domain was introduced. The duration of the first session was limited to 50 minutes. During the last 15 minutes of the session, the experimenter demonstrated the use of the learning environment and the externalization tools.

During the second session, learners were working with the learning environment, whereby learners in the experimental conditions had to construct a domain representation while working with the learning environment. The duration of this session was set at 70 minutes. Despite the possibility of following a non-linear path through the learning environment, learners were advised to keep to the order of sections because they build upon each other.

The third session was set at 50 minutes. First, learners were allowed to use the learning environment for 10 minutes in order to refresh their memories with regard to the domain. Then all learners had to close their domain representations and learning environments, and had to complete the post-test. When learners finished the test they were allowed to leave the classroom.

Data preparation

The domain representations constructed by the learners were scored by means of a scoring protocol. This protocol revolved around the principle that scoring of the domain representation should not be biased by the representational format of the externalization tool, that is, all types of representations should be scored on the basis of exactly the same criteria. The protocol was used to assess the extent to which domain representations reflected the concepts of replacement and order, presented calculations, referred to the concept of probability, indicated the effect of size of (sub)sets on probability, and the effects of replacement and order on probability. The maximum number of points that could be assigned on the basis of the protocol was 8 points. The scoring protocol is displayed in Appendix I.

Results

Knowledge measures

Two measures of knowledge were obtained: prior knowledge (pre-test score), and post-test score. The reliability, Cronbach's α, was α = .56 for the pre-test and α = .79 for the post-test. The scores on the knowledge measures are displayed in Table 3. One-way analyses of variance (ANOVA) showed that there were no differences between conditions with regard to pre-test score, F(3,120) = 0.39, ns, and post-test score, F(3,120) = 0.85, ns. These results suggest that the externalization of knowledge and the representational format in which learners externalize do not affect learning outcomes. However, it turned out that not all participants in the experimental conditions externalized their knowledge. This issue will be addressed in the next section after, which a re-analysis of the data will be presented.

Externalizers vs non-externalizers Not all learners who were required to externalize their knowledge did so, and some only entered nonsense input (i.e., input that was not domain related and that could not be considered a serious attempt to create a domain representation; e.g., a drawing of a smiling face). Therefore, a distinction will be made between the group of learners who did externalize their knowledge (henceforth called "externalizers"), and the group of learners who did not externalize although required to (henceforth called "non-externalizers"). The numbers of externalizers and non-externalizers for each condition are displayed in Table 4. The numbers of externalizers and non-externalizers differed significantly between conditions, χ 2 (5, N = 89)= 11.25, p < .05. In the Arithmetical condition there were significantly fewer externalizers than in both the Graphical condition, χ 2 (1, N = 21)= 5.76, p < .05, and the Textual condition, χ 2 (1, N = 19)= 4.26, p < .05.

Knowledge measures revisited

The scores on the knowledge measures were reanalyzed, this time taking into account the distinction between externalizers and non-externalizers. Before reanalyzing, the comparability of the different groups with regard to prior knowledge (pre-test score) was established (see Table 5). A one-way ANOVA showed no difference between groups with regard to pre-test scores, F(2,120) = 0.72, ns.

The post-test scores, including the measures of the different knowledge types, were analyzed by applying one-way ANOVAs. The post-test measures for each group are displayed in Table 6. With regard to the post-test overall score, a significant difference was found between groups, F(2,118) = 7.01, p < .01. A post-hoc LSD analysis showed that the externalizers outperformed both the non-externalizers (p < .001) and the control group (p < .01). The post-test distinguished between three types of knowledge. One-way ANOVA's revealed significant differences between conditions with regard to conceptual knowledge, F(2,118) = 3.79, p < .05, procedural knowledge, F(2,118) = 3.19, p < .05, and situational knowledge, F(2,118) = 6.45, p < .01. Post-hoc LSD analyses showed that with regard to conceptual knowledge the externalizers outperformed the nonexternalizers (p < .05) and the control group (p < .01). With regard to procedural knowledge the externalizers outperformed the non-externalizers (p < .05) but not the control group. Finally, the average scores of externalizers on situational knowledge were also significantly higher compared to non-externalizers (p < .001) and the control group (p < .01).

In order to find the answer to our second research question (does the representational format in which learners externalize their knowledge have a differential effect on understanding?) we now focus on the externalization group. The post-test scores of externalizers using different representational formats are displayed in Table 7. No differences were found between representational formats with regard to post-test measures. The F(2,32) values for conceptual, procedural, situational, and post-test overall scores are 0.05, 1.30, 0.46, and 1.16 respectively. Therefore, the format in which learners expressed their knowledge did not influence post-test scores.

The quality of domain externalizations

The domain representations created by the externalizers show large differences. The quality of the domain representations is determined by the extent to which the externalization properly represents the domain and contains all relevant concepts and relations. The quality of the created domain representations was determined on the basis of the coding scheme presented earlier in this paper (see also Appendix I). The resulting quality scores are displayed in Table 8. A one-way ANOVA showed that there were no differences between representational formats with regard to quality scores, F(2,34) = 1.10, ns.

Discussion and Conclusion

The aim of the current study was to find out whether externalizing knowledge leads to better understanding of the domain and in particular whether representational format has a differential effect on this. The results show that the externalization of knowledge significantly enhances conceptual knowledge, procedural knowledge, situational knowledge and overall post-test performance. Therefore, externalization leads to better understanding of the principles that govern the domain and of the interrelations between units of knowledge in the domain (conceptual knowledge), enhanced ability to execute action sequences to solve problems (procedural knowledge), and to analyze, identify, and classify problems, to recognize the concepts that underlie the problem, and to decide which operations need to be performed to solve the problem (situational knowledge). Moreover, earners who externalized their knowledge did not differ from other learners with regard to time-on-task. Therefore, the effects cannot be attributed to the time the learners spent on their learning process. Externalization appears to be an effective method to enhance learning results, without requiring the investment of much time.

The second research question concerned the different representational formats in which learners could externalize their knowledge. It was hypothesized that externalization in the graphical format would lead to more conceptual knowledge, that externalization in the arithmetical format was supposed to draw the learners' attention primarily to operational aspects, although externalizing still was thought to improve conceptual and situational knowledge as compared to learners who do not externalize at all. Externalization in the textual format was assumed to lead to more conceptual and situational knowledge, although the focus on conceptual aspects would not be as marked as in the case of the graphical format.

Results show that the hypotheses were not confirmed. No differential effects on post-test scores were found between representational formats. Furthermore, it turned out that the representational format in which learners created a domain representation did not affect the quality of these domain representations.

Although representational format did not have a direct effect on knowledge measures and quality of domain representations, it turned out that format did play an important, although indirect role. The format determined to a large extent the likelihood that learners engaged (and succeeded) in externalizing their knowledge. The graphical and textual formats appear to equally foster the externalization of knowledge. Having learners express their knowledge in an arithmetical format is not recommended, because this format prevented most learners from engaging and succeeding in externalizing their knowledge. The low number of learners who succeeded in constructing a domain representation by using the arithmetical format suggests that this format is not very helpful for externalizing knowledge. This finding corroborates the observation that learners apparently experience difficulties with using standard mathematical representations.

If learners have the choice, they prefer to use other types of representations [START_REF] Tarr | How can teachers build notions of conditional probability and independence[END_REF]. Still, the finding that learners apparently consider the arithmetical format too difficult for externalizing their knowledge is interesting. In an earlier study, [START_REF] Kolloffel | The effects of representational format in simulation-based inquiry learning[END_REF] found that in learning from (pre-constructed) representations, the best results were obtained with arithmetical representations. This suggests that arithmetical representations are very well suited for learning, but not for expressing knowledge. -"fewer options = higher chance" (Abstract) -"If fewer runners attend the race, the chance your prediction is correct will increase" (Concrete)

A formula or a series of calculations showing the effect (in the latter case, k needs to be constant) Examples:

Examples: -"(1/n) x (1/n) x (1/n)=1/n 3 " -"1/5 x 1/4 x 1/3 = 1/60 1/
-"(1/n) x (1/n) = 1/n 2 (1/n) x (1/n) x (1/n) = 1/n 3 " -"1/5 x 1/4 = 1/20 1/5 x 1/4 x 1/3 = 1/60" Examples:

-"When your prediction is less elaborate, the probability that your prediction will be correct increases" (Abstract) -"If you only predict who will win the race and not the top 3, then the chance is greater that your prediction will be correct" (Concrete) G Effect of replacement on probability -Descriptive or on basis of calculations showing the effect (in the latter case, n and k need to be constant)

Examples:

-"If it is a matter of replacement, your chances will decrease" (Abstract) -"...if you have 10 different cell phones and you need to select one, your chance will be 1 out of 10, if you put the phone back your chance will be 1 out of 10 again, but if you leave it out your chance will increase that you will select the next phone as predicted" (Concrete)

A series of formulas or calculations showing the effect, but the outcome (p) needs to be represented as well and n and k need to be constant

Examples:

-"(1/n) x (1/n) = 1/n 2 (1/n) x (1/(n-1)) = 1/(n 2 -n)" -"1/5 x 1/4 x 1/3 = 1/60 1/5 x 1/5 x 1/5 = 1/125" -Descriptive or on basis of calculations showing the effect (in the latter case, n and k need to be constant)

Examples:

-"If it is a matter of replacement, your chances will decrease" (Abstract) -"...if you have 10 different cell phones and you need to select one, your chance will be 1 out of 10, if you put the phone back your chance will be 1 out of 10 again, but if you leave it out your chance will increase that you will select the next phone as predicted" (Concrete)

1 H Effect of order on probability -Descriptive or on basis of calculations showing the effect (in the latter case, n and k need to be constant)

Examples:

-" If order is important, the chance your prediction will be right will decrease" (Abstract) -"...If there are 7 runners and you predict the top 3, then A series of formulas or calculations showing the effect, but the outcome (p) needs to be represented as well and n and k need to be constant

Examples:

-"(1/n) x (1/n) = 1/n 2 (k/n) x ((k-1)/n) = (k 2 -k)/n 2 " -"1/5 x 1/4 x 1/3 = 1/60 3/5 x 2/4 x 1/3 = 6/60" -Descriptive or on basis of calculations showing the effect (in the latter case, n and k need to be constant)

Examples:

-" If order is important, the chance your prediction will be right will decrease" (Abstract) -"...If there are 7 runners and you predict the top 3, then 1 15 the probability is 1/7 x 1/6 x 1/5 = 1/210, but without specifying the positions of specific runners in the top 3 the probability is 3/7 x 2/6 x 1/5 = 6/210..." (Concrete) the probability is 1/7 x 1/6 x 1/5 = 1/210, but without specifying the positions of specific runners in the top 3 the probability is 3/7 x 2/6 x 1/5 = 6/210..." (Concrete)

MAXIMUM NUMBER OF POINTS 8

Table 1

 1 Number of participants per condition

			Condition
		Graphical	Arithmetical	Textual	Control
	Number of participants	31	28	30	32

  Problem categories within the domain of combinatorics

		ORDER IMPORTANT?
		Yes	No
		Category 1:	Category 2:
	No	No replacement;	No replacement;
	REPLACEMENT?	Order important Category 3:	Order not important Category 4:
	Yes	Replacement;	Replacement;
		Order important	Order not important
	Figure 1.

Table 2

 2 Overview of test items

	Knowledge type	Description	Number and type of items
	Pretest
	Conceptual	Items about relations between variables	4 mc
	Procedural	Solving combinatorial problems	4 open and 4 mc
	Post-test
	Conceptual	Items about relations between variables	13 mc
	Procedural	Solving combinatorial problems	9 open
	Situational	Analyzing, identifying, and classifying problems	4 mc

-

x (1/(n-2))= P" -"1/5 x 1/4 x 1/3 1/5 x 1/5 x 1/5" -"p = 1/10 x 1/10 x 1/10 p = 1/5 x 1/4 x 1/3"

or descriptive

Examples:

-"Order" (Abstract) -"Category 1: without replacement; order important" (Abstract) -"...At a game of Bingo, order is not important" (Concrete)

or a concrete calculation

Examples:

-p = acceptable outcomes/ possible outcomes (Abstract) -1/5 x 1/4 x 1/3 (Procedural) -... when you also bet ont he order in which the marbles will be selected, your chance

Formal (formula) or a concrete calculation

Examples:

-"(1/n) x (1/n) x (1/n)" -"1/5 x 1/4 x 1/3" -Formal, literally, descriptive, or a concrete calculation

Examples:

-p = acceptable outcomes/ possible outcomes (Abstract) -1/5 x 1/4 x 1/3 (Procedural) -... when you also bet ont he order in which the marbles will be selected, your chance 1


Ton de Jong Wouter R Van Joolingen
email: w.r.vanjoolingen@utwente.nl

Sarah Manlove

CIEL: setting the stage for integrated inquiry learning

We present an integrated framework for the design, authoring, and evaluation of innovative learning scenarios for Collaborative Inquiry and Experiential Learning (CIEL). This framework has been designed to promote interoperability in environments for productive, open-ended learning, such as inquiry learning, but also learning by design and experiential learning. The CIEL framework centers around a repository of learner generated learning objects that can be saved, and retrieved in standardized format and of which the collection can be queried for objects relevant for a given task. Issues are the ontology of learning objects needed for the support of inquiry learning, the generation of metadata and the semantic interoperability of tools.

Introduction

There are several environments that are designed to support different forms of inquiry learning, such as SimQuest for designing computer simulations [START_REF] Van Joolingen | SimQuest: Authoring educational simulations[END_REF], environments for structuring inquiry processes, such as WISE [START_REF] Slotta | The web-based inquiry science environment (WISE): Scaffolding knowledge integration in the science classroom[END_REF] and ThinkerTools [START_REF] White | ThinkerTools: Causal models, conceptual change, and science education[END_REF], modelling tools such as STELLA [START_REF] Steed | Stella, A Simulation Construction Kit: Cognitive Process and Educational Implications[END_REF] and Cool Modes [START_REF] Pinkwart | Group-oriented modelling tools with heterogeneous semantics[END_REF], and tools trying to integrate collaboration, modelling and discovery learning, such as Co-Lab (van Joolingen, de Jong, Lazonder, Savelsbergh, & Manlove, 2005). CIEL scenarios aim to combine the strong points of different environments maintaining conceptual consistency. For instance, learners may gather data in one environment, process the data in another, and create a model describing the data in a third. A number of these encompassive learning environments that include one or more of the above mentioned design guidelines on different domains have been created in various places. Examples are: CoolModes/FreeStyler [START_REF] Hoppe | Collaborative Learning in Open Distributed Environments -Pedagogical Principles and Computational Methods[END_REF] providing generic worksheets for a variety of symbolic languages, SimQuest [START_REF] Van Joolingen | SimQuest: Authoring educational simulations[END_REF] for authoring simulation-based learning environments, Co-Lab for collaborative inquiry learning, FLE [START_REF] Leinonen | Fle3: Future Learning Environment[END_REF][START_REF] Mørch | Integrating agents with an open source learning environment[END_REF] for progressive, collaborative inquiry, JEMUE [START_REF] Baggetun | Pedagogical agents for collaborative telelearning scenarios[END_REF], providing pedagogical agents in collaborative knowledge building, and more domain specific environments such as ARI-LAB [START_REF] Bottino | Technological Advances and Learning Environments[END_REF] for mathematics learning and Tangibles [START_REF] Cerulli | Exploring randomness via studying, building and sharing models[END_REF] for learning basic concepts on statistics and randomness.

Supporting advanced pedagogical scenarios

Each of the learning environments mentioned in the previous section offers specific kinds of support, usually for one or a limited amount of pedagogical scenarios. A pedagogical scenario is defined as an orchestrated set of activities that learners undertake to learn. Scenarios can represent episodes of scientific inquiry, technological design, engineering or others. The basic idea of these scenarios is to engage learners in a constructive, realistic context in which knowledge is created and used at the same time.

Paper presented at the AERA annual meeting. Chicago, April 9-13, 2007

In the example learning environments presented above the scenarios are supported by offering specific (cognitive) tools [START_REF] Lajoie | Computers as Cognitive Tools[END_REF][START_REF] Van Joolingen | Cognitive tools for discovery learning[END_REF] to learners. These tools have a role within the environment they were created for, but also may have broader application. The CIEL project aims at integrating such tools into a framework that supports a multitude of advanced pedagogical scenarios that support the building of scientific knowledge by learners. The main reasons for starting this undertaking are:

•

Combining specializations. Each tool has its merits of supporting specific parts of advanced pedagogical scenarios such as a collaborative inquiry learning process, including support for collecting data, modeling and specific means of collaboration. Instead of trying to create a single tool that can do it all CIEL strives to enable semantic interoperability [START_REF] Koedinger | Component-based construction of a science learning space[END_REF], between tools.

• Support of longer term learning scenarios. Most learning environments support a specific type of activity, such as doing research on the greenhouse effect, or create a model of volcanic activity. This means that the typical duration of use will be limited. CIEL strives to design scenarios that extend over longer time periods, involving multiple activities and tools.

In a typical pedagogical scenario that takes more than a few lesson periods, learners will perform diverse activities.

Each of these activities will represent steps in the process of scientific knowledge building, and the whole scenario may therefore be supported by a variety of tools. CIEL aims to create an architecture in which many tools can interoperate to construct many different inquiry learning scenarios.

Figure 1 Two examples of tools to support transformative learning processes.

In several empirical studies, data has been collected to inform the design of an architecture of interoperating tools that support the scenarios we aim at within CIEL. Most of these studies compare different versions of cognitive scaffolds or tools for the processes of inquiry learning (van Joolingen, de Jong, & Dimitracopoulou, 2007). Scaffolds can support both the transformative processes of learning, such as the generation of hypotheses [START_REF] Njoo | Exploratory learning with a computer simulation for control theory: Learning processes and instructional support[END_REF][START_REF] Van Joolingen | Supporting hypothesis generation by learners exploring an interactive computer simulation[END_REF] or the creation of models [START_REF] Löhner | The effect of external representation on constructing computer models of complex phenomena[END_REF] as well as regulative processes of inquiry learning. For the latter we conducted an empirical study with a cognitive tool which assisted students to plan, monitor, and evaluate their inquiry activity. 86 students participated from three international high schools in the Netherlands. We compared a full support version of the process coordinator (PC+) with a lean support version (PC-).The full support version (See Figure 2 ) included an inquiry cycle [START_REF] White | Inquiry, modelling, and metacognition: Making science accessible to all students[END_REF] goal list, hints, note cueing, and prompts within note templates. In addition the PC+ condition received a lab report template to support student evaluation work The PC-enabled students only to make their own goals and take notes. Learner generated objects, such as models, lab reports, and notes were utilized to determine the extent to which the PC assisted students in achieving higher quality models and lab reports. Log file analysis of student actions with the PC was also conducted. Findings indicate that, while use of the PC was significantly higher by PC+ groups, and they had significantly higher lab report scores then their PCcounterparts, it was the PC-group who achieved significantly higher model quality scores. Further analysis revealed that PC-groups consulted help files more often then PC+ groups which may explain this unexpected finding. The help files contained more domain specific information related to modeling. So while regulative support did effect evaluation type work, further research is needed to see how it can better support domain constructing type activities.

Figure 2 Process Coordinator used by the PC+ groups, as an example of regulative support

The resulting insights from this and other studies are that (1) supportive tools can have an effect on the process of inquiry learning and (2) that the process as well as the scaffolds that support this can be modelled in terms of objects created by learners using the scaffolds and tools within the environment. The latter insight is important because it allows us to define what we mean by interoperability of tools and scaffolds, viz. that tools are interoperable when they can consume and produce objects that can be interpreted within a shared ontology of learning objects. In other words, tools are interoperable when the objects they can operate upon can be exchanged on both a technical and conceptual level. The meaning an object has for a learner should not change when it is transferred from one tool to another.

An example pedagogical scenario

Figure 3 presents an example of an advanced pedagogical scenario for scientific inquiry learning. Learners working within this scenario mix solo work with collaborative work possibly in different groups. For instance, as depicted in Figure 3, learners may first collect data in a laboratory, using a mobile device. During data collection they probably work alone or in a small group (pairs or triads). These data can then be used to construct a model of the domain they are investigating using a modeling tool. In the modeling process they may use the data they collected themselves, but the scenario may also allow using other students' data. For instance comparing two data sets may help them to obtain a deeper understanding of the influence of experimental conditions on the results obtained. Comparing data and -at a later stage -models requires a collaboration at the level of larger groups. Part of this collaboration can be a debate, supported by the construction of an argument, using a dedicated argumentation builder such as Belvedere [START_REF] Suthers | Belvedere: Engaging students in critical discussion of science and public policy issues[END_REF]. Finally (not visible in Figure 3) individual learners may complete the activity by writing a report and submitting this to their teacher. Figure 3 depicts how this whole scenario is integrated around a common repository through which the different tools exchange information (e.g., data or models). On the one hand such a scenario should be semantically integrated, meaning that the learning process as a whole, including the transitions from tool to tool take place in a smooth and meaningful way. On the other hand integration should also take place at a technical level, ensuring smooth data exchange between tools.

On the semantic level, it is important to support the flow of information and activity in the task context. This can be facilitated and implemented in different ways. One possibility is to map data onto specific objects that can be physically transferred (e.g., data can be captured on a PDA and thus be transferred). Another possibility is to transfer information between places and different environments by real time synchronization. Milrad et al. [START_REF] Milrad | Exploring the use of mobile devices to facilitate educational interoperability around around digitally enhanced experiments[END_REF] discuss several of such interoperability patterns from both an engineering and an educational design view.

Here the environments can possibly be heterogeneous. This second option requires a tight coupling in terms of processing and time constraints. A loose coupling which implies much less restrictions is often facilitated through a common repository, although a real time synchronization is not supported in a loose coupling model. It needs a common data format which can be 'understood' and generated by the different tools. In CIEL, we have first adopted the loosely coupled model for our technical approach.

The CIEL ontology

CIEL aims to support both levels of integration by bringing together several systems that support collaborative inquiry learning and make them interoperate at the two indicated levels. At the semantic level CIEL works on integration of concepts such as learning processes, learning objects and learning tools. The basic assumption behind CIELs conceptualization is that all activities of learners leave traces in the learning environment in the form of products created or, for instance, as communication with other students or with a teacher. In the example presented in Figure 3 , the products that are created are the data sets collected, the hypotheses and models made and the arguments exchanged between learners. In order to appreciate this role of products generated by learners we extended the concept of learning objects [START_REF] Friesen | Three Objections to Learning Objects. Online Education Using Learning Objects[END_REF], to include objects created by learners during the activity in the pedagogical scenario. Learning tools can then be defined in terms of the learning objects they consume and produce. Learning processes are the mental activities that are reflected in working with the tool. So, in defining tools and processes learning objects take a pivotal role.

For each of the types of learning objects, shared definitions are created that provide meaning to data that are stored. Examples of these definitions include "data set", "experimental setup", "phenomenon", "experiment", and "model". Such definitions allow consistent support of learning processes across learning environment. If two systems treat the same object, for instance an "experiment" in a semantically consistent way, continuity of the learning scenario can be reached. The shared definitions in CIEL are created within the CIEL ontology. The main functions of the CIEL ontology are:

• To create a shared framework of understanding for learning processes and objects that are supported by existing open learning environments. That is to support the semantic level of integration, in such a way that learner activities have a meaning with respect to the status of other tools and environments that have a place within the same scenario.

•

To provide a context for a technical level of integration between various platforms. The definitions provided in the ontology form the starting point for formalization in terms of data formats. In order to exchange data between tools, XML definitions are given of the terms in the ontology. This leads to a common data format shared by a set of tools that each can play a part in scenarios for collaborative inquiry and experiential learning. This approach is depicted in Figure 4. Currently the CIEL ontology contains about 50 definitions of learning objects and about the same number of definitions of processes and tools.

CIEL architecture and implementation

The CIEL architecture is created to provide technical support for the advanced pedagogical scenarios. As will be clear from Figure 3, the central service is a repository, called the CIEL broker. The CIEL broker offers functionality and interfaces for storing and retrieving learning objects, as well for searching and notification of changes in the repository.

The basis of the architecture is an XML database, with XML schemata based on CIEL glossary definitions. Searching learning objects is facilitated by tagging with metadata, using the IMS-LOM metadata model (IMS global consortium, 2006). Searches are specified as LOM templates, and tools can register to receive notification when changes in search results appear.

The repository is independent of the tools that connect to it. This opens up the road for scenarios that combine tools from different origins, and even scenarios in which learners diverge in the tools they use. For instance, it is possible in one scenario to combine data from different data sources, collected with different tools, or to compare models created using different modeling tools. This is enabled by the combined semantic and technical integration implemented in the CIEL architecture.

An actual first implementation of an integrated scenario along the lines described above has been created. For the topic of "sampling" in the domain of statistics, a scenario has been designed and implemented that involves multiple activities and tools. The learner is placed in the role of an employee of a forest agency that is involved in the production of wood. For a certain forest area it must be determined whether the trees are tall and wide enough to harvest the wood. In doing so a sample of trees has to be taken. The task for the learner is to determine the best sampling strategy, so that a reliable decision can be made based upon the sample.

The scenario is supported by two simulations, one in Flash TM and one made in Co-Lab [6]. Both allow creating samples and computing parameters such as the average and standard deviations of each of the samples. The data from the samples are stored as learning objects in the CIEL XML format can be imported in Freestyler, which are modeling tools that allow for modeling a variety of domains, including statistics. The sampling strategy can be modeled in FreeStyler.

Discussion

The sampling scenario is a proof of concept of the CIEL ideas. It demonstrates the interoperability between previously unconnected tools in a single, realistic scenario. It is the beginning of a process of deeper integration. Interesting problems that are identified and currently addressed are:

•

Adding content intelligence to the broker. In order to allow better facilities for supporting the learning processes, it is necessary that search in the database becomes dependent on the content of the learning objects: what is the domain, subdomain and topic for which the learning object was created, and in what context did a learner construct the object. The idea is that such metadata will be added automatically to the learning objects. A challenge is to combine the CIEL ontology with an appropriate domain ontology to realize such content intelligence.

• Structuring the repository. Instead of just being a searchable collection, the repository is able to show a trace of learning activity. For instance it is of interest to extract the developing objects created by a single learner and to that objects of one type (e.g. datasets) relate in some way to other type (e.g. models) created by the same learner (e.g. the dataset contradicts the model). This would enable the CIEL architecture to be used not only for the design of scenarios that combine tools of different origins, but also become more than the sum of the parts, and use the inter-tool and inter-object relations as the basis for generating new kinds of instructional support.

Figure 3

 3 Figure 3 A multi-tool scenario supported by CIEL.

Figure 4

 4 Figure 4 Structure of the CIEL work, depicted as two layers: theoretical and technical. The contents of the four cells are examples of a wider range of possible content.

Acknowledgement

CIEL is funded as part of the Kaleidoscope Network of Excellence supported by the European Community under the Information Society Technologies priority of the 6th Framework Programme. Apart from the authors of this paper the following people have contributed to the work in CIEL: Jakob Sikken, Andre Berloth, Hannie Gijlers (University of Twente), Lars Bollen, Björn Hassing, Ulrich Hoppe (University of Duisburg-Essen), Muriel Ney, Cedric d'Ham (MeTAH), Barbara Wasson, Aleksander Krzywinski (University of Bergen), Augusto Chioccariello (CNR), Sten Ludvigsen and Jeremy Toussaint (University of Oslo).


Turadg Aleahmad

Jim Slotta

Wouter Van Joolingen
email: w.r.vanjoolingen@utwente.nl

New authoring frameworks for integrating collaborative learning technologies

This workshopis intended for CSCL researchers and/or their technologists who are interested in designing and then actually creating rich, interactive learning materials in a technology-enhanced environment. The workshop will present the work of two complementary approaches to the design of environments for collaborative, productive and open ended learning, such as collaborative inquiry learning and learning by design. Participants bring in their own issues and work on the design of learning environments in a hands-on experience.

Theme and goals

This workshop offers participants the chance for hands-on experience with two recent authoring frameworks for technology-enhanced CSCL activities. We will describe how to adopt these environments as sustainable research platforms, and discuss the vision of a community of developers. We address the issues of interoperability, re-use, open source and open content, as well as recent trends toward standardization (e.g., SCORM or IMS/LD). We invite participants to bring with them: A description of a CSCL activity that they would like to develop; a specific CSCL tool or technology that they would like to integrate within a larger framework; an idea for a new tool or feature that they would like to create; research questions they would like to address. We will discuss key issues and present demonstrations in the morning, followed by direct hands-on work by individual participants, in consultation with workshop leaders. The leaders of this workshop have a wealth of experience in the development of technology frameworks for CSCL activities. Jim Slotta (2000Slotta ( , 2004) ) led the design of the WISE learning environment (http://wise.berkeley.edu ) -a Web-based system that allows researchers to develop interactive inquiry projects, delivers the content to students, collects all data, and supports teachers as they implement the materials in their classrooms. Numerous research labs now use WISE as a research platform for the development and delivery of experimental materials. Wouter Van Joolingen and his colleagues [START_REF] Van Joolingen | SimQuest: Authoring educational simulations[END_REF][START_REF] Van Joolingen | Co-Lab: research and development of an online learning environment for collaborative scientific discovery learning[END_REF] have developed Simquest (http://www.simquest.nl ), which guides learners through a structured inquiry process, and more recently, Co-Lab (Collaborative Laboratories -http://www.co-lab.nl ), which allows learners to collaboratively set up a study of the climate in a greenhouse, design experiments, process the data from these experiments, develop models and theories, and report about their work. Turadg Aleahmad (Slotta & Aleahmad, in press) has led the design of the new Scalable Architecture for Interactive Learning (SAIL, http://sail.sourceforge.net ), a framework for developing pedagogical software, and Pas, an application suite for collaborative inquiry learning. We will demonstrate our latest innovations, discuss the most pressing topics related to technology frameworks, and consult with participants to help them take forward strides in developing their own materials or make decisions about research platforms. This new generation of open software allows a greater degree of innovation and enables a wider range of pedagogical scenarios (Slotta & Aleahmad, in press). SAIL is Java component framework that enabled the rapid development of Pas, which like WISE includes everything required for researchers to adopt as a stand alone research platform. All SAIL-based objects can be shared amongst any SAIL-based platform, allowing the development of an exchange community. The hope is that this will encourage a community of open source development, enabling rapid evolution and exchange amongst researchers. Another framework is CIEL: Collaborative Inquiry and Experiential Learning (http://www.cielproject.eu ), which enables collaborative real time environments to interoperate with other learning technologies. These resources are available to CSCL researchers right now. Indeed, most labs that were using the WISE system are now adopting their own SAIL-based platforms, and will go forward with separate but interoperable systems.

Workshop held at the Computer Supported Collaborative Learning Conference. New Brunswick, NJ CIEL has enabled the integration of the Co-Lab software with a suite of tools called Cool Modes developed by researchers in Duisburg-EssenUniversity [START_REF] Pinkwart | A plug-in architecture for graph based collaborative modeling systems[END_REF][START_REF] Pinkwart | Group-oriented modelling tools with heterogeneous semantics[END_REF]. The goal of this workshop is to offer such resources to the wider community, discuss a range of issues including interoperability, scalability and sustainability, and engage participants in hands on design and authoring activities.

Outcomes and contributions

• In advance of the workshop, each participant will complete a wiki template concerning: their topic of research; specific scenarios concerning the kinds of learning materials or tools they would like to develop; their questions with regard to interoperability; their personal goals for the workshop. • In advance of the workshop, these participant submissions will by synthesis by the leaders into a small number of discussion categories for the workshop. This and the discussion at the workshop will remain in the wiki for future reference and discussion. • We will offer each participant open access to all the technology, including them in a community (ENCORE, http://www.encorewiki.org ) that will provide ongoing support. We hope for participants who have the intention of adopting these systems, and will work with them to develop a clear understanding of their next steps, as well as a sense of active membership in a community of peers. • For each participant, the workshop will contribute distinct, individuated progress in their thinking about the design, development and implementation of CSCL activities using these new frameworks.

Format

• Designed for 5-20 participants.

• In the morning, we will have introductions, demos and discussion. One goal of discussion is to address common issues relating to technology frameworks (e.g., standards, re-use, learning content management, etc). Another is to develop shared views on the architectures for collaborative inquiry learning, expressed in a shared collection/classification of learning objects and tools. We would also review the ideas from the pre-workshop wiki, examining the scenarios of inquiry learning, etc. • In the afternoon there will be hands-on authoring, design, and question and answer consultation, giving each participant a direct experience of progress, including "next steps" for their participation. • The workshop will conclude with a synthesis discussion and presentation of ENCORE.


A Lakshmi-Narayana

M Dhananjaya

N Guru-Prakash

O M Hussain

A Mauger

C M Julien

Li2TiO3/graphene and Li2TiO3/CNT composites as anodes for high power Li-ion batteries

Keywords: solid state reaction, Li2TiO3/graphene, Li2TiO3/CNT, composite anodes, electrochemical performance

Three-dimensional composites Li2TiO3/graphene (LTO/Gr) and Li2TiO3/carbon nanotube (LTO/CNTs) were synthesized by solid-state reaction for application as anode materials for lithium-ion batteries. These composites are structurally characterized by X-ray diffraction, Raman spectroscopy and high-resolution transmission electron microscopy, while electrochemically tests are performed by cyclic voltammetry and chronopotentiometry. The synergetic effect of graphene and CNTs with LTO facilitate the network conduction leading to faster electron and Li + ion transfer and improve cycling stability and rate capability of the anode.

The LTO/Gr and LTO/CNTs composites exhibited an initial discharge capacity as high as 154 and 149 mAh g -1 at 1C rate, respectively and retained excellent cycling stability of 98% and 96% after 30 charge-discharge cycles.

Introduction

Lithium-ion batteries (LIBs) have been considered as one of the promising technologies for next generation plug-in hybrid electric vehicles (HEV), electric vehicles (EV) and stationary power storage due to the merits of high-energy density, high voltage, small self-discharge and light weight. [START_REF] Julien | Lithium Batteries: Science and Technology[END_REF][START_REF] Lu | A review on the key issues for lithium-ion battery management in electric vehicles[END_REF] In commercial LIBs, lithiated metal oxides and carbonaceous materials are commonly employed as positive and negative electrode materials, which are active elements determining the energy and power densities. However, carbon-based anodes suffer from formation of solidelectrolyte interface (SEI). Since the SEI is resistive, it may generate heat during operation and cause fire with the presence of carbonates in electrolyte. [START_REF] Mauger | Critical review on lithium-ion batteries: are they safe? Sustainable?[END_REF] Among alternative anode materials, lithium titanate Li4Ti5O12 has attracted much attention, because of its reversible lithium-ion insertion and extraction reaction due to its zero-strain properties during charge/discharge process. [START_REF] Li | Preparation of Li4Ti5O12 nanorods as anode materials for lithium-ion batteries[END_REF] Another titanate Li2TiO3 (denoted LTO hereafter) is also a possible zero-strain anode material in LIBs but is hampered by unsatisfactory rate capability due to kinetic issues associated with poor electrical conductivity (σe=10 -11 S cm -1 ) and initial capacity loss. [START_REF] Laumann | Metastable formation of low temperature cubic Li2TiO3 under hydrothermal conditions -Its stability and structural properties[END_REF][START_REF] Dash | Electrical properties of bulk and nano Li2TiO3 ceramics: a comparative study[END_REF][START_REF] Kim | Electrochemical and structural properties of xLi2M'O3۰(1-x)LiMn0.5Ni0.5O2 electrodes for lithium batteries (M'=Ti[END_REF] Thus far, several effective approaches have shown to improve σe of titanate materials such as doping with metallic or non-metallic ions, [START_REF] Park | Effects of a dopant on the electrochemical properties of Li4Ti5O12 as a lithium-ion battery anode material[END_REF] reduction of particle size to nanoscale, deposition of a thin layer (coating) on the particle surface, [START_REF] Li | Preparation of Li4Ti5O12 nanorods as anode materials for lithium-ion batteries[END_REF] and/or fabrication of composite material. [START_REF] Zhang | Preparation of Li4Ti5O12 nanosheets/carbon nanotubes composites and application of anode materials for lithium-ion batteries[END_REF] The drawback of doping atoms is a decrease of the amount of active Ti 4+ ions, and thus a decrease of the capacity of the titanate anode. [START_REF] Zhang | Hydrothermal synthesis of Zndoped Li4Ti5O12 with improved high rate properties for lithium ion batteries[END_REF] Reduction of the size of the particles to the nano-range is expected to enhance the capacity and rate capability owing to the reduction of the length of the path that ions and electrons have to travel to reach the surface of the particles. [START_REF] Guo | Superior electrode performance of nanostructured mesoporous TiO2 (anatase) through efficient hierarchical mixed conducting networks[END_REF] However, the inherent disadvantage is the agglomeration of primary particles limiting their uniform dispersion in the electrode. In addition, nanocomposites made of metal oxides with carbonaceous materials have enhanced electrochemical properties owing to improved electric conductivity and morphological stability. [START_REF] Ren | In-situ synthesis of nano-Li4Ti5O12/C composite as an anode material for Li-ion batteries[END_REF][START_REF] Ko | Characteristics of Li2TiO3-LiCrO2 composite cathode powders prepared by ultrasonic spray pyrolysis[END_REF] Furthermore, the dispersion of metal oxides with the carbon material hinders the agglomeration of particles providing efficient and stable framework during charge/discharge cycling. Noteworthy, the rate capability of Li4Ti5O12 and Li2TiO3 has been significantly improved by forming nanocomposites by various synthesis methods. Carbon based materials such as carbon nanotubes (CNTs), reduced graphene oxide (rGO) and graphene were used in the preparation of such nanocomposites with Li4Ti5O12. [START_REF] Chen | Electrochemical performance of Li4Ti5O12/carbon nanotubes/graphene composite as an anode material in lithium-ion batteries[END_REF][START_REF] Shu | In situ fabrication of Li4Ti5O12@CNT composites and their superior lithium storage properties[END_REF] Graphene (Gr) and rGO are the most conductive forms of carbon and thus a usual additive to increase the C-rate of any lithium-based battery. To our knowledge, however, Li2TiO3 mixed with acetylene black has been tested recently as an anode, but not Li2TiO3/CNTs, Li2TiO3/Gr composites, which is the purpose of the present work.

Many research reports are available on electrochemical properties of Li2TiO3. In prior work, Chauvaut et Cassir reported the Li + insertion as a diffusive process with the Ti non-

stoichiometry in Li2+xTi IV 1-xTi III xO3
. [START_REF] Chauvaut | Electrochemical intercalation of Li + in Li2TiO3 at 600 and 650 °C[END_REF] Wang et al. [START_REF] Wang | Solid-state synthesis of submicron-sized Li4Ti5O12/Li2TiO3 composites with rich grain boundaries for lithium ion batteries[END_REF] studied the galvanostatic discharge-charge of an electrode Li2TiO3: acetylene black: PVDF binder (80:10:10) cycled at current rate of 0.5C, which showed a specific discharge capacity of 30 mAh g -1 . This value is comparable with 10 mAh g -1 reported by Tabuchi et al. [START_REF] Tabuchi | Fine Li(4-x)/3Ti(2-2x)/3FexO2 (0.18≤x≤0.67) powder with cubic rock-salt structure as a positive electrode material for rechargeable lithium batteries[END_REF] and 47 mAh g -1 reported by Morales et al. [START_REF] Morales | Electrochemical activity of rock-saltstructured LiFeO2-Li4/3Ti2/3O2 nanocomposites in lithium cells[END_REF] for materials employed as anodes in non-aqueous rechargeable coin-type Li + -ion cells. Close examination of these works shows that the electrochemical performance of Li2TiO3 is very sensitive to the morphology and size of particles induced by different synthesis process. In this context, β-Li2TiO3 has been considered as an element of composite electrodes, owing to its excellent structural stability and its good ionic conductivity with three-dimensional path for Li + ion migration. This phase was then used to enhance the electrochemical performance of various electrodes taking advantage of the strong Ti-O bond in Li2TiO3. [START_REF] Ko | Characteristics of Li2TiO3-LiCrO2 composite cathode powders prepared by ultrasonic spray pyrolysis[END_REF][START_REF] Shigemura | Lithium extraction and insertion behavior of nanocrystalline Li2TiO3-LiFeO2 solid solution with cubic rock salt structure[END_REF][START_REF] Zhang | Electrochemical and ex situ XRD investigations on (1-x)LiNiO2•xLi2TiO3 (0.05≤x≤0.5)[END_REF][START_REF] Yang | Facile synthesis and performances of nanosized Li2TiO3-based shell encapsulated LiMn1/3Ni1/3Co1/3O2 microspheres[END_REF][START_REF] Shi | Evaluation of the electrochemical characteristics of silicon/lithium titanate composite as anode material for lithium ion batteries[END_REF][START_REF] Bhatti | Electrochemical characteristics and Li ion intercalation kinetics of dual-phase Li4Ti5O12/Li2TiO3 composite in voltage range of 0-3 V[END_REF] For example, in Si/Li2TiO3 nanocomposite synthesized by sol-gel method, Li2TiO3 acts as excellent buffer to the Si powders and partly compensate the capacity loss of the anode exhibiting a specific capacity of 471 mAh g -1 after 50 cycles. [START_REF] Bhatti | Electrochemical characteristics and Li ion intercalation kinetics of dual-phase Li4Ti5O12/Li2TiO3 composite in voltage range of 0-3 V[END_REF] The specific reversible capacity of Li2TiO3 was estimated to 100 mAh g -1 . The best results to our knowledge, were obtained with β-Li2TiO3, acetylene black as conductive agent and polyvinylidine fluoride (PVDF) binder at a weight ratio of 80:10:10, which delivered a capacity of 120 mAh g -1 at C/50 rate. [START_REF] Narayana | Nanocrystalline Li2TiO3 electrodes for supercapattery application[END_REF] In the present study, nanocrystalline Li2TiO3 and its composites Li2TiO3/graphene (denoted as LTO/Gr) and Li2TiO3/carbon nanotubes (denoted as LTO/CNTs) were synthesized by a simple solid-state reaction using commercially available carbon nanotubes and graphene sheets prepared via a thermal exfoliation route of oxidized graphite. The composites are investigated as anode materials for lithium-ion batteries using cyclic voltammetry, galvanostatic dischargecharge and cycling tests. These novel composites compared with Li2TiO3 show lower impedance, high capacity and good structural stability with better cycleability than that of the pristine.

Experimental Section

Synthesis procedure

Li2TiO3 was synthesized by a solid-state reaction method using TiO2 (anatase) and Li2CO3 taken as starting materials in stoichiometric ratio and then mixed in acetone and ball-milled for 24 h.

The obtained precursor slurry was treated at 80 °C to obtain powders further calcinated at 800 °C for 12 h in Ar atmosphere. The Li2TiO3/graphene composite (denoted LTO/Gr) was prepared by the same method using 6 wt.% home-made graphene nanosheets. Li2TiO3/CNTs composite was synthesized using commercial TiO2, Li2CO3 and CNTs provided by the University of Hyderabad as follows. The CNTs are multiwalled nanotubes with a diameter and length of about 20-30 nm and 1-2 μm, respectively. Firstly, TiO2 and Li2CO3 were mixed in acetone and ball-milled for 24

h to obtain a homogeneous mixed slurry. In the second step, 6 wt.% CNTs were dispersed in acetone with sufficient ultrasonication to form a uniform slurry. Finally, the slurries were mixed together and treated at 80 °C. To obtain the Li2TiO3/CNTs nanocomposite, it was further calcinated at 800 o C for 12 h.

The two-dimensional graphene sheets have been prepared via a thermal exfoliation route, including graphite oxidation as an important step under modified Hummer method, followed by subsequent rapid thermal expansion of graphene oxide at 1050 °C in nitrogen atmosphere. 27 TiO2 (anatase) and glucose were taken as starting materials with a weight ratio of 4:1 then mixed in ethanol-water compounds (10:1 in volume) and stirred for 2 h, further drying for 10 h under aircirculating oven at 100 °C. The obtained mixture was heated at 600 °C for 5 h under N2

atmosphere to obtain carbon-coated TiO2. The carbon content was 6 wt.%. Li2CO3, TiO2 and graphene were dispersed in hexamethylene, and ball-milled under atmosphere at rotational speed of 200 rpm for 4 h. Finally, the LTO/Gr composite was obtained by drying the slurries at 80 °C and further calcination at 800 °C for 12 h in N2 atmosphere.

Characterization

The sample structure was characterized by X-ray diffractometry (apparatus Siefert, model 3003 TT) using a CuKα radiation (λ =0.15406 nm). Data were collected in the 2θ range 10°-70°. The morphology and phase identification of the composites were observed using high resolution transition electron microscope (HRTEM) and selected-area electron diffraction using a HRTEM-

Results and discussion

Structural properties

The X-ray diffraction patterns of pristine Li2TiO3, LTO/CNTs and Li2TiO3/Gr composite synthesized by solid-state reaction at 800 °C for 5 h are shown in Fig. 1. All XRD spectra exhibit the predominant (002) reflection line along with (110), (-131), (-133), (-204), ( 006 literature. [START_REF] Dorrian | Refinement of the structure of Li2TiO3[END_REF][START_REF] Kataoka | Crystal growth and structure refinement of monoclinic Li2TiO3[END_REF] The elementary unit volume (V=abc sinβ ) is 429.1 Å 3 .

The addition of either graphene sheets or CNTs to the precursor does not influence the formation of the phase pure monoclinic Li2TiO3 during the heat treatment excepted a weak peak at 2θ = 26° marked by a star in the pattern of Li2TiO3/graphene composite (Fig. 1), which is due to re-stacking of graphene sheets in the disordered composite. [START_REF] Yu | Facile access to graphene oxide from ferro-induced oxidation[END_REF] Note however that the intensity of this peak is very small, which means that the re-stacking is only marginal. The low intensity of the XRD peaks of the LTO/Gr composite is due to the screening of the LTO reflection by the presence of graphene. These results reveal that graphene and CNTs as carbonaceous additives do not have significant impact on the crystal structure of monoclinic Li2TiO3 prepared by solid-state reaction. Note that similar results were observed in the XRD patterns of LiMO/C composites (M = transition metal, C=carbonaceous material). [START_REF] Rosas | Interfacial electrochemical analysis on LiCoO2/carbon nanotubes layers as cathode composite in aqueous electrolytes[END_REF][START_REF] Dettlaff-Weglikowska | Effect of single-walled carbon nanotubes as conductive additives on the performance of LiCoO2-based electrodes[END_REF] The crystallite size Lc of composites was calculated using the Scherrer's formula by considering the (002) reflection line:

   sin K L c  , ( 1
)
where K is the Scherrer constant (0.89 for spherical crystallites), λ is the wavelength of X-ray radiation (0.15406 nm),  the full-width at half maximum (FWHM) expressed in radians and  the Bragg angle. Values of the average crystallite size and lattice strain are listed in Table 1. The effect of carbon addition on LTO is the reduction of the crystallite size and the minimization of the lattice strain. The slowing-down of the crystallite growth rate of inorganic substances in presence of carbon in the synthesis process is well known. [START_REF] Davis | The effects of crystallite growth and dopant migration on the carbon monoxide sensing characteristics of nanocrystalline tin oxide based sensor materials[END_REF][START_REF] Li | Effects of active carbon carrier on phase transform and crystallite growth of titanium dioxide in TiO2/AC[END_REF] The difference between the crystallite size of composites and that of pristine LTO can be attributed to the fact that the great adsorbability and amorphous-like layer of active carbon retard the crystallite growth of Li2TiO3.

Table 1. Crystallite size and lattice train of LTO-based compounds. Li2TiO3, [START_REF] Ramaraghavulu | Analysis of structural and thermal properties of Li2TiO3 ceramic powders[END_REF] the vibrational mode observed at 411 cm -1 is attributed to Li-O stretching vibration in LiO4 tetrahedra, while the weak band at 283 cm -1 is associated to Li-O bending vibration of LiO6 octahedra. [START_REF] Bian | Sintering behavior, microstructure and microwave dielectric properties of Li2+xTiO3 (0≤x≤0.2)[END_REF] The main feature of LTO/Gr and LTO/CNTs is the broadening of the Raman bands with respect to the LTO spectrum. Since the penetration depth of the laser beam in Raman experiments is small, Raman spectroscopy is a probe of the vibrations of molecular units in the vicinity of the surface of LTO in contact with the carbon. This is at contrast with XRD spectra that probe the core region of the LTO particles, because for particle size the order of 50 nm, the proportion of atoms in the surface layer is small. Therefore, the fact that the XRD spectra is not sensitive to the Gr and CNT means that the bulk of the particles is unaffected by the carbon, while the broadening of the Raman bands gives evidence that the bonds between the Li, O and Ti are affected at the surface in presence of the carbon. Therefore, these Raman spectra give evidence of a strong anchoring of the LTO particles on the carbon nanotubes or the graphene sheets. Such an effect has been observed with TiO2 particles that disperse homogeneously on graphene sheets in presence of surface hydroxyl centers, due to the anchoring of the particles on the graphene sheets via esterification between hydroxyl groups of TiO2 and carboxylic groups of graphene. [START_REF] Wu | Markedly enhanced surface hydroxyl groups of TiO2 nanoparticles with superior water-dispersibility for phtocatalysis[END_REF][START_REF] Zhang | Homogeneous anchoring of TiO2 nanoparticles on graphene sheets for waste water treatment[END_REF] In the same way, this anchoring of the LTO particles on graphene evidenced by the band broadening in Fig. 2 explains why the LTO particles did not agglomerate, despite the propensity of titanate oxide particles to aggregate. This is a marked difference with the case when only acetylene black is simply added to the LTO particles, in which case the particles form agglomerates and the Raman bands are narrow, [START_REF] Narayana | Nanocrystalline Li2TiO3 electrodes for supercapattery application[END_REF] meaning that there is no interaction between LTO and the acetylene black. Three main Raman active modes of carbon ascribed to D-band, graphitic G-band and G'band are observed at ~1347, ~1584, ~2690 cm -1 , respectively. The D band is the so-called "disordered induced band" attributed to the vibration of carbon lattice disturbed by edges/defects (K-point phonons with A1g symmetry), the graphitic G-band is the primary in-plane breathing mode of hexagonal sp 2 -carbon rings of graphite (E2g phonons) and the G' band is a second-order overtone of a different in-plane vibration of D-band. These spectral features can be applied to both graphene and CNTs materials. [START_REF] Malard | Raman spectroscopy in graphene[END_REF] The Raman intensity of the D band increases with increasing the amount of disorder in graphene. Thus, the ratio of the absolute peak intensities ID/IG indicates the degree of graphitization of composites. [START_REF] Julien | Characterization of the carbon coating onto LiFePO4 particles used in lithium batteries[END_REF][START_REF] Sadezky | Raman microspectroscopy of soot and related carbonaceous materials: spectral analysis and structural information[END_REF] The value of ID/IG for both LTO/Gr and LTO/CNTs is ~0.5 and ~1.0, respectively, suggesting that the degree of graphitization of carbon in graphene is higher than that in CNTs sample; this implies a higher electrical conductivity and an increase of the rate capability of the LTO/Gr electrode. [START_REF] Zhang | Preparation of Li4Ti5O12 nanosheets/carbon nanotubes composites and application of anode materials for lithium-ion batteries[END_REF] Figure 3. SEM images of (a) Li2TiO3, (b) Li2TiO3/CNT and (c) Li2TiO3/graphene samples.

The morphology and microstructure of pristine LTO and its composites were studied from FE-SEM and TEM experiments. Figure 3 presents the SEM images of the three samples, which obviously show smaller particles (~50-70 nm) for LTO/Gr and LTO/CNTs composites than for pristine Li2TiO3 (~100-150 nm). This observation matches well with the crystallite data from XRD. As particle sizes are comparable to those of crystallite sizes deduced from Eq. 1, we conclude that LTO particles are mainly single crystals. They are homogeneously distributed and have a monoclinic-like shape with well-defined facets (Fig. 3a). Figure 3b-c Figures 4a-c show the detailed microstructure of LTO observed by TEM and SAED micrographs. The low-magnification TEM bright field image (Fig. 4a) shows well-dispersed particles with relatively uniform nanostructured shape. Figure 4b displays the SAED pattern of LTO, which clearly presents bright spots; the observation of (002), (-131) and (-133) diffraction spots indicates a high crystallinity of the material. The HRTEM image (Fig. 4c) confirms the well-resolved lattice of pristine LTO with fringes at interplanar distance ~0.47 nm corresponding to the (002) plane. Figure 4d presents the SAED pattern of the LTO/CNTs composite, which displays blurred diffraction rings indicating the nanosized carbon particles that are wrapped on LTO grains. Similar pattern with blurred rings is observed for the LTO/Gr composite. The TEM image of the LTO/Gr composite is shown in Fig. 4e, in which well-dispersed graphene nanosheets connect the LTO particles and form a conducting network with a robust inner connected architecture. Figure 4f depicts the HRTEM image of LTO/Gr composite; it gives clear evidence that graphene sheets stick on LTO particles as a 3-5-nm thick pseudo-coating deposited on the surface (graphene layer). The LTO/Gr composite obtained by an annealing step of the LTO precursor at 800 °C reveals a unique morphology of submicron-sized particles. This temperature is commonly used for the carbonization process of electrode materials, for examples LiFePO4, [START_REF] Julien | Characterization of the carbon coating onto LiFePO4 particles used in lithium batteries[END_REF] and Li4Ti5O12, [START_REF] Guo | Carbon coating of Li4Ti5O12 using amphiphilic carbonaceous material for improvement of lithium-ion battery performance[END_REF] for which a ~5-nm thick carbon layer favors their high electrochemical performance.

Electrochemical properties

Figure 5 shows the cyclic voltammograms (CV) of aqueous cells with LTO, LTO/CNTs and LTO/Gr composites carried out in the voltage range 0.0 -1.0 V at 1 mV s -1 sweep rate using 1 mol L -1 saturated Li2SO4 electrolyte. These CV curves are similar for all electrodes indicating that the addition of ~6 wt.% of graphene and CNTs does not affect the electrochemical redox response of the LTO active material. One set of well-defined oxidation/reduction peaks is observed at 0.64/0.29 V for LTO/graphene, 0.75/0.22 V for LTO/CNT, 0.8/0.2 V vs. Li + /Li 0 for pristine LTO. which are attributed to the redox reaction of Ti 4+ /Ti 3+ related to the reduction of Ti IV upon the insertion of a fraction x of Li + ions. The CV current peaks for composites are stronger than those of pristine Li2TiO3 electrodes, which gives evidence of an improvement of electron transport and enhancement of the lithium-ion diffusion in composite frameworks. The potential separation between the oxidation and reduction peaks (ΔEp) appearing in the order ΔEp(LTO/Gr) < ΔEp(LTO/CNTs < ΔEp(LTO) indicates the decreasing degree of polarization of the LTO/Gr electrode due to the higher electronic conductivity of the unique integrated architecture with graphene. The graphene nanosheets facilitate the 3D network that well electrically connects the LTO particles to the current collector. As a consequence, Li4Ti5O12/graphene composite as anode material delivered 96% of its initial capacity after 50 cycles at 10C rate. [START_REF] Zhang | Synthesis and characterization of Li4Ti5O12/graphene composite as anode material with enhanced electrochemical performance[END_REF] Figure 5. Cyclic voltammograms carried out at 1 mV s -1 sweep rate for lithium cells including Li2TiO3, Li2TiO3/CNT, Li2TiO3/graphene as anode materials. material and the contact phase angle element (CPE) including double layer capacitance, [START_REF] Shaju | EIS and GITT studies on oxide cathodes, O2-Li2/3+x(Co0.15Mn0.85)O2 (x=0 and[END_REF] and

(3) further, at the low-frequency region, a straight line is ascribed to the Warburg impedance corresponding to the diffusion regime of Li + ions through the LTO electrode. As shown in Fig. 7, the depressed semicircle of LTO/Gr composite is smaller than those of other samples that implies higher electronic and ionic conductivity. The impedance spectra were fitted using the Randles equivalent circuit shown in the inset of Fig. ions into the LTO-based electrode is strongly controlled by a diffusion process. In this regime, the impedance varies with the angular frequency ω according to the law: [START_REF] Zhang | Synthesis and characterization of LiNi1/3Mn1/3Co1/3O2 by wet-chemical method[END_REF] Z'

= Rs + Rct + σw ω -1/2 , (2)
The Warburg impedance σw is obtained from the slope of Z' vs. ω -1/2 in the low-frequency range (Fig. 8). Typical values of σw are listed in Table 2. EIS can be used to evaluate the apparent Liion diffusion coefficient DLi+ from the low-frequency Warburg impedance according the equation: [START_REF] Zhang | Synthesis and characterization of LiNi1/3Mn1/3Co1/3O2 by wet-chemical method[END_REF] (3)

where R, T and F are the usual constants, A the surface area of the electrode-electrolyte interface, CLi is the lithium-ion concentration in the electrode. Values of DLi+ are reported in Table 2. We observed an increase of DLi+ by a factor 2 for the LTO/Gr sample. The high values of the diffusion coefficient of Li+ ions (DLi+ > 10 -9 cm 2 s -1 ) reflect the ionic character of Li2TiO3 materials. Therefore, the composite LTO/Gr has the lower Warburg factor σw, which results in its higher DLi+ = 1.1×10 -8 cm 2 s -1 . 1.1×10 -8

6.1×10 -9 Figure 9 shows the cycleability of the LTO-based electrodes for lithium cells cycled at discharging and charging constant current of 1C rate. All the electrodes have good electrochemical stability. The initial discharge capacity of LTO/Gr, LTO/CNTs and LTO still remained at 150, 143 and 113 mAh g -1 respectively, even after 30 discharge cycles. The LTO/Gr composite exhibits the best cycling performance with capacity retention of 98% compared to 93% for LTO. In summary, among the LTO-based electrode, the results reveal that the LTO/Gr composite exhibits the best cycling stability and rate capability.

This capacity of 150 mAh g -1 at high current density (1C rate) is due to different synergetic effects. First, the high electrical conductivity of the graphene improves the rate capability. Second, the anchoring of the LTO particles on the graphene sheets, prevents the restacking of the graphene sheets despite the high sintering temperature in the synthesis process.

Third, this anchoring also insures a homogeneous distribution of LTO particles on the graphene sheets. As a consequence, LTO/Gr is thus composite that allows LTO to deliver the best capacity that has been reported for this material so far in the literature, to our knowledge.

Conflicts of interest

There are no conflicts to declare

FEI microscope (TECHNAI G 2 -

 2 30 S-twin D905) at an accelerating voltage of 200 kV. Field emission scanning electron microscopy (FE-SEM) was used to analyze the size and surface morphology of the particles with a SIRION 200 microscope. Raman scattering (RS) spectra were recorded at room temperature in the range of 200-3000 cm -1 using a Jobin-Yvon LAB RAM HR spectrometer with a spectral resolution of 1 cm -1 . The laser excitation source of 532 nm was produced by a air-cooled Nd:YAG laser doubled frequency at an excitation power of 50 mW. A 100× objective lens was used to focus the laser light on sample surface and the Raman spectra consisted of 20 acquisitions averaged together, with the duration of each acquisition set at 60 s.Electrochemical testsElectrochemical properties of the synthesized composites were investigated at room temperature using a three-electrode Pt//Li2TiO3 aqueous cell using the Li2TiO3 composite, an Ag/AgCl and a platinum metal strip as the working, reference and counter electrodes, respectively. The working electrode consisted of a mixture of 90 wt.% Li2TiO3/graphene, Li2TiO3/CNTs composite and 10 wt.% polyvinylidene fluoride (PVDF) dissolved in NMP (N-methyl-pyrrolidinone) to form a slurry spread on Ni metal substrate. This electrode of area of 0.25 cm 2 containing 3-4 μg of slurry was dried at 100 °C for 3 h to reduce impurity traces. The electrolyte was composed of 1 mol L-1 Li2SO4 in aqueous solution. The electrochemical performances were tested with an electrochemical workstation model CHI 608C (CH Instruments Inc., USA) in the potential range 0.0-1.0 V. Electrochemical impedance spectroscopy (EIS) was carried using a phase sensitive multimeter (model PSM 1700, UK) in the frequency range 1 Hz-1 MHz using a voltage bias of 5 mV.

Figure 1 .

 1 Figure 1. X-ray diffraction patterns of Li2TiO3, Li2TiO3/CNT and Li2TiO3/graphene samples. The reflection noted (*) is due to carbon.

Figure 2 .

 2 Figure 2. Raman scattering spectra of Li2TiO3, Li2TiO3/CNT and Li2TiO3/graphene samples. RS spectra were recorded using the 532 nm laser line as excitation source.

  depicts the SEM images of LTO/CNT and LTO/Gr composites, respectively. These images confirm the smaller grain sizes for LTO particles grown in the presence of carbon. The CNTs are wrapped into all the Li2TiO3 particles, indicating that well-connected CNTs adhere closely on the surface of the Li2TiO3 particles and form a conductive network. This network provides strong anchoring between Li2TiO3 nanoparticles, facilitating fast electronic transport that results in a significant improvement in rate capability of the electrode material. The LTO/CNTs composite particles are also well distributed with a tendency to agglomerate. In the SEM image of LTO/Gr composite (Fig.3c), the LTO particles are well-dispersed among the graphene sheets, which extend in all directions like a stretched network.

Figure 4 .

 4 Figure 4. TEM, HRTEM images and SAED patterns of Li2TiO3, Li2TiO3/CNT, and Li2TiO3/graphene samples. (a-c) low magnification TEM images, (d-f) SAED patterns and (g-i) HRTEM images.

Figure 6 .

 6 Figure 6. Charge-discharge curves performed at 1C rate of lithium cells including Li2TiO3, Li2TiO3/CNT, Li2TiO3/graphene as anode materials.

Figure 6

 6 Figure6shows the discharge-charge curves of the aqueous lithium cells with LTO-based electrodes. Galvanostatic measurements were carried out in the cutoff voltage 0.0 -1.0 V at 1C rate. The S-shape of the charge-discharge profiles of the Li//Li2TiO3 cell with a mid-voltage of ~0.5 V corresponds to the formation of a non-stoichiometric single phase Li2+xTiO3 without formation of distinct plateaus. Similar electrochemical behavior is noticed for Li//Li2TiO3/Gr and Li//Li2TiO3/CNTs cells. Initial specific discharge capacities of 149 and 154 mAh g -1 are respectively delivered in the first cycle by LTO/CNTs and LTO/Gr composite electrodes against 122 mAh g -1 for the pristine electrode (the theoretical capacity of LTO being 229 mAh g -1 ). Note that electrodes using composite materials do not have additive carbon such carbon Super-P or acetylene black, so that the use of only 6 wt.% of graphene or CNTs is a gain of gravimetric capacity of the whole cell. Both CV and galvanostatic results match well, showing the best electrochemical performance of the LTO/Gr composite because of the high efficiency of the conductive network among the LTO nanoparticles. Note that the electrochemical features of Li2TiO3 are different from the behaviors of Li4Ti5O12 spinel, which displays a wide voltage plateau at 1.5 V upon insertion of 3Li per formula unit.[START_REF] Aldon | Chemical and electrochemical Li-insertion into the Li4Ti5O12 spinel[END_REF] Electrochemical impedance spectroscopy (EIS) was carried out over the frequency range from 1 Hz to 1 MHz for electrodes in the fully charged state. Figure7depicts the Nyquist diagrams (EIS curves) of Li2TiO3/graphene, Li2TiO3/CNT composite and pristine Li2TiO3. Nyquist plots are composed of three contribution: (1) the interception of x-axis at high frequency indicates the solution resistance or ohmic resistance (Rs) contributed by electrolyte, (2) the depressed semicircle in the high-and intermediate-frequency range originates from the charge transfer resistance Rct corresponding to solid-state diffusion of Li + in the bulk of the active

Figure 7 .

 7 Figure 7. Electrochemical impedance spectra of Li2TiO3, Li2TiO3/ CNT, Li2TiO3/graphene anode materials.

Figure 8 .

 8 Figure 8. Z' vs.  -1/2 plots in the Warburg region of the impedance spectra for Li2TiO3, Li2TiO3/ CNT, Li2TiO3/graphene samples.

Figure 9 .

 9 Figure 9. Cycling performance for Li2TiO3, Li2TiO3/ CNT and Li2TiO3/ graphene anode materials discharged at 1C rate.

  7. Calculated values of ohmic resistance RS, charge transfer resistance Rct are listed in Table 2. The smaller charge transfer resistance of LTO/Gr, i.e. 93 Ω vs. 180 Ω for LTO/CNTs is consistent with the previous electrochemical data. The Warburg regime observed at low frequencies gives evidence that the insertion mechanism of Li +

Table 2 .

 2 Results of the EIS measurements. Fitting was performed using the Randles equivalent circuit shown in the insert of Fig.7.

	Electrode	Rs (Ω)	Rct (Ω)	Zw (Ω s -1/2 )	DLi+ (cm 2 s -1 )
	LTO	12	244	561	5.2×10 -9
	LTO/Gr	19	93	384
	LTO/CNT	19	180	477