Conceptual Questions and Lack of Formal Reasoning: Are They

Article pubs.acs.org/jchemeduc

Conceptual Questions and Lack of Formal Reasoning: Are They Mutually Exclusive? Csaba Igaz* and Miroslav Prokša Department of Didactics, Psychology, and Pedagogy, Comenius University, Bratislava, 842 15, Slovakia S Supporting Information *

ABSTRACT: Using specially designed conceptual question pairs, 9th grade students were tested on tasks (presented as experimental situations in pictorial form) that involved controlling the variables’ scheme of formal reasoning. The question topics focused on these three chemical contexts: chemistry in everyday life, chemistry without formal concepts, and chemistry with formal concepts. The second task of each question pair contained three additional questions, designed according to the pillars of the cognitive acceleration through science education (CASE) intervention, which represents a set of activities using the schemata of formal operations aimed at improving children’s thinking by accelerating progress towards formal operations in Piaget’s terms. The first task did not have these questions. Results showed that some students could solve conceptual problems with specially designed additional questions even when the students could not solve the conceptual problems without such help. Statistical analysis revealed a correlation between the construction−metacognition additional question and the main cognitive conflict question in the second context of chemistry without formal concepts. The results indicate that conceptual questions designed using the CASE pillars have the potential of accelerating students’ formal reasoning abilities. KEYWORDS: High School/Introductory Chemistry, Chemical Education Research, Problem Solving/Decision Making, Constructivism FEATURE: Chemical Education Research • Concrete preparation to introduce the necessary vocabulary and clarify the terms in which a problem is set. • Cognitive conflict at a level to set the student’s minds a puzzle that is interesting and attackable. • Construction zone activity in which the conflict is at least partly resolved as students’ minds go beyond their previous thinking capability. • Metacognition in the sense of conscious reflection on the problem-solving process, and the naming of reasoning patterns developed for future use. • The bridging of these reasoning patterns to new contexts in order to both generalize them and consolidate their use. Implementing the CASE program involves teachers in using special lesson activities instead of some of their normal science curriculum lessons. The first problem with this is that the CASE activities do not appear specifically in the Slovakian national curriculum, which is highly content based. Therefore, school heads and teachers need to “give up” some of their normal curriculum activities if they want to apply the time requiring CASE activities; this may be a problem in countries such as Slovakia that have a

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he inability of some students to solve chemical conceptual questions has become evident over the past 25 years.1−5 Initially, researchers suggested that this was caused by an overemphasized focus on teaching algorithmic problem solving;2,6 however, recent studies have revealed another feature of this effect with a cognitive−psychological background. BouJaoude and Cracolice found that students with high formal operational reasoning ability or better higher-order thinking ability performed better on conceptual problems than those with low formal operational reasoning. 4,5 This finding was confirmed at high school and also at university levels. According to Cracolice, an excellent long-term model to foster intellectual development is the CASE intervention, developed by Adey and Shayer.5 Cognitive acceleration through science education (CASE) is an innovative teaching approach largely based on the work of Piaget and also incorporating fundamental tenets of Vygotsky’s theories of learning. The program aims to improve children’s thinking processes from age 11 by accelerating progress toward higher-order thinking skills or “formal operations” in Piaget’s terms.7 CASE intervention represents a set of activities, set in a scientific context and using the schemata of formal operations as a guiding framework.8 The five pillars that should maximize the chances of this program of inducing long-term effects on the general ability of learners are as follows:9 © 2012 American Chemical Society and Division of Chemical Education, Inc.

Published: July 13, 2012 1243

dx.doi.org/10.1021/ed100895c | J. Chem. Educ. 2012, 89, 1243−1248

Journal of Chemical Education

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well-defined national curriculum. Some educators sometimes use the curriculum as an excuse to block innovation: “we would like to try it, but we don’t have time to deviate from the curriculum”.7 The main problems we see in implementation of the program in Slovakia are the disjunction between the content of the CASE activities and the national curriculum, and the time demands of CASE activities relative to the curriculum in place. Our work concentrates on the creation of chemistry tasks that can assist as tools for accelerating students’ formal reasoning abilities. This is based on the CASE program,7−14 and types of test items used in the TOLT test (Test of Logical Thinking) developed by Tobin and Capie, which measures five formal reasoning modes: the controlling variables, proportional reasoning, combinatorial reasoning, probabilistic reasoning, and correlational reasoning.15 This test has been used in several studies4,16 to determine the level of formal reasoning of chemistry students.

Box 1. Example of a Laboratory Challenge Question. Students use graphs, tables, and other data to predict or explain what happens in an experimental situation. Much of the analysis and interpretation of laboratory work could be used as a basis for assessing conceptual understanding if the laboratory is not constructed in a cookbook fashion. Adapted with permission from http://www.jce.divched.org/JCEDLib/ QBank/collection/CQandChP/CQs/LaboratoryCQs.html (accessed Jun 2012)

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AIMS Our overarching goal is to evolve conceptual tasks on mental schemes of formal reasoning that reflect CASE pillars while being responsive to curricular demands, yet the application of which is less time-consuming than more traditional CASE interventions. The first step and therefore the purpose of this particular study was to investigate whether conceptual tasks have the potential for accelerating the development of formal reasoning; in other words, if they could replace the activities of the CASE intervention. The aim of this study therefore is to address the preliminary steps rather than to achieve the ultimate goal of introducing the final form of the conceptual tasks.

The figure is a plot of temperature versus time for: (a) A pure liquid freezing. (b) A pure liquid boiling. (c) A solution freezing. (d) A solution boiling. (e) It is impossible to predict. Box 2. Example of a Tiered Conceptual Question. Tiered multiple-choice questions consist of a pair of questions asking what will happen in the first question and asking for a reason in the following question. One benefit of the two-tiered format is that it allows for the probing of two aspects of the same phenomenon. The first question asks about a predicted outcome of a physical or chemical change. The second question asks for an explanation. This allows the probing of the phenomenological domain with the first question and the conceptual domain with the second. Adapted with permission from http://www.jce.divched.org/JCEDLib/QBank/ collection/CQandChP/CQs/TieredCQs.html (accessed Jun 2012)

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CONCEPTUAL TASKS In the following description, we use the term “conceptual task” for a system of the stem and four additional questions, while the term “question” is applied to particular questions within the task. Conceptual tasks developed for this research involve combinations of the tiered multiple-choice question type and laboratory questions, as Nurrenbern and Robinson described them, and as shown in Boxes 1 and 2. The stem of the task contains an experimental situation that can be solved only by application of the controlling variables scheme (one of the mental schemes of formal reasoning). This situation is mainly expressed pictorially. The task also includes four additional questions. Three of these four are intended to help students solve the final fourth question, and all of the questions incorporate at least one of the pillars of the CASE activities. While activities of the CASE intervention with chemistry topics are devoted to developing the scheme of formal models, we believe that chemistry has the potential to develop other mental schemes of formal reasoning, such as the controlling variable scheme in this study. Description of such a task is summarized in Table 1.

A. Iron combines with oxygen and water from the air to form rust. If an iron nail were allowed to rust completely, one should find that the rust weighs: (a) Less than the nail it came from. (b) (b) The same as the nail it came from. (c) (c) More than the nail it came from. (d) (d) It is impossible to predict. B. What is the reason for your answer? (a) Rusting makes the nail lighter. (b) (b) Rust contains iron and oxygen. (c) (c) The nail flakes away. (d) (d) The iron from the nail is destroyed. (e) (e) The flaky rust weighs less than iron.

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METHODS Three conceptual task pairs were administered (this material is provided in the Supporting Information). Each pair consists of a conceptual task without any additional questions (only the stem and a cognitive conflict or CC1 question, analogical to the CC2 question; see Table 1) and a similar task with additional questions, as described in Table 1 (Figure 1). The aim of this research design was to identify students who could not solve conceptual tasks without the further questions, but who could solve the conceptual tasks when additional questions were supplied. The purpose of such a design was to ensure that the

final statistical analysis involved only the students who need further instruction to fully master their higher-order thinking potential. Three chemical contexts were chosen to test which one was the best for further application of such conceptual tasks: (i) chemistry in everyday life, (ii) chemistry without formal concepts, and (iii) chemistry with formal concepts. The reason 1244



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Table 1. Description of Conceptual Tasks Aimed at Accelerating Formal Reasoning Task Structure Stem 1st question 2nd question 3rd question 4th question

CASE Pillar Involved

Question Symbola

Question Summaries

Concrete preparation, cognitive conflict Concrete preparation

A list of experiments with a set of appropriately controlled variables



Which variables are the same and which are different in each experiment

CP1

Concrete preparation

Which variable is different in two particular experiments

CP2

Construction−metacognition

What is the outcome of the comparison of two particular experiments and why it is so

C−M

Cognitive conflict

Select two experiments with appropriately controlled and independent variables to find their relationship to the required dependent variable

CC2

a

The most important additional question is the C−M question, as its appropriate formulation can direct students’ thinking to a higher-order level. The bridging pillar is incorporated into a set of tasks having different physical−chemical contexts. CP indicates “concrete preparation”; C−M indicates “construction−metacognition”; CC indicates “cognitive conflict”.

Figure 1. Example of a conceptual task pair for the context chemistry without formal concepts, with CC1-type question in Task 3 and questions characterized in Table 1 for Task 4. This figure illustrates the third and fourth question from Table 2. Note that the stem of the two tasks is the same. The only difference between the CC1 and CC2 question is the independent variable. 1245



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Table 2. Description of Task Pairs in the Test Concept Tested

Question Number

Chemistry in everyday life

1 2

Chemistry without formal concepts

3 4

Chemistry with formal concept

5 6

Question Type

Question Summaries

Conceptual Conceptual, with additional questions Conceptual Conceptual, with additional questions Conceptual Conceptual, with additional questions

for this is that formal operations are not applied uniformly across all knowledge domains, only across those in which the person has some expertise, familiarity, or training.17 We have also used Herron’s classification of concepts into a group of concrete and formal concepts according to perceptibility of their examples and attributes.18 These three contexts were incorporated into the theme of reaction rate, which is part of the chemistry curriculum for Slovakian middle school students.19 The topics and description of these question pairs are summarized in Table 2. Our sample consisted of 220 9th grade students who were, on average age, 14.9 years old. The research took place in Slovakia, in May 2009, with 5 schools and 10 classes being involved. The tasks were presented all at once yet each on a separate sheet. Students could not go back and change their answers to CC1 after looking at the next task. Two series of tasks were created, to ensure students’ individual work. The only differences between these two sets were in changed CC1 and CC2 questions. Classroom discussion, which is a very important component of CASE activities, is missing in this research. Because this component ensures social constructivism within CASE activities, it may seem that the construction pillar is missing from the task. In our research, the construction phase is initialized by the construction−metacognition, or C−M question. Although this question does not represent a fullvalued substitution for classroom discussion, it is expected to initiate construction for some students. Therefore, it is likely that if there were students who could solve the CC2 question with the help of the C−M question even if they could not solve the CC1, then conceptual tasks and real classroom discussion, which fully ensures the construction phase, would have a similar effect on a larger group. The classroom discussion had to be eliminated in this first phase of the study because we wanted to see the performance of particular students. If the students solved the tasks within groups, we would be unable to determine whether the right answer was due to a shift in the mind of the student to higher-level thinking, and therefore confirm the functionality of the conceptual task, or if the answer emanated from the most gifted student in the group.

Rate of ice melting dependent on amount of added salt

Reaction rate dependent on the temperature and the size of solid particles

Reaction rate dependent on the temperature and concentration of liquid reagent

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training, then the correlation between C−M and CC2 questions would be strongest in the first concept, chemistry in everyday life.

RESULTS Supporting the first hypothesis, we found students who could not solve the CC1 question, but who could cope successfully with the CC2 question. Some of these students also managed to solve the C−M question. Figure 2 illustrates the number of these students.

Figure 2. The proportion of students who could do the CC2 and those who could do the CC2 and C−M from all those unable to solve the CC1.

To determine whether a correlation exists between the achievement on C−M and CC2 questions, two-by-two tables were constructed with a consecutive χ2 and ϕ coefficient analysis. In this analysis, we reduced the sample sizes because we had to eliminate students who solved the CC1 question, as this ability indicated that these students were fully able to use their formal reasoning potential. Results are summarized in Table 3.

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Table 3. Correlation Analysis of the Relationships between C-M and CC2 Questions

HYPOTHESES The two initial hypotheses follow: 1. If the ability of students to go beyond their actual level of formal reasoning were related to conceptual tasks that include CASE pillars, then there would be students who could solve the CC2 question, even if they could not solve the CC1. 2. If formal operations were best applied across domains in which the person has some expertise, familiarity, or

a

Pairs

Sample Size

χ2 Values

P Values

ϕ Values

First pair Second pair Third pair

130 133 136

0.03 7.80 3.18

0.8657 0.0052a 0.0745

 0.2422 

Statistically significant relationship at the .001 level.

The data in Table 3 show a weak relationship between the C−M and CC2 questions, but only in the case of the 1246



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tion strength is weak. We expect a stronger effect after applying Vygotsky’s tenets in the form of classroom discussion. This discussion must be applied in further studies also because some students could solve the cognitive conflict question (CC1) without additional questions, but they could not solve a similar one (CC2) with this help. We believe this confusing effect can be eliminated by applying Vygotsky’s social constructivism. This means that after solving the questions, there should be classroom discussion among the students in which the teacher acts as a mediator. Such an approach could support weakening of naive conceptions and at the same time enable the strengthening of correct conceptualizations. In other words, the construction of knowledge and understanding becomes a social process, exactly as Vygotsky established it. An excellent model of this that could be implemented is described by Sprod.20 The teacher’s role is to direct students’ thinking with carefully structured help so that the students can solve the problem, or at least gain sufficient understanding so that a solution is more likely to become available later.

second pair of tasks, which does not accord with our second hypothesis. Finally, another group of students is worthy of mention. This involves a considerable proportion of students who could not solve the CC2 question although they could do the CC1. Figure 3 illustrates the number of these students in comparison

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ASSOCIATED CONTENT

S Supporting Information *

Text of tasks 1−6. This material is available via the Internet at http://pubs.acs.org.

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Figure 3. Proportion of students who could do the CC1 and CC2 together, and those who could not do the CC2, from all those able to solve the CC1.

AUTHOR INFORMATION

Corresponding Author

to the total number able to solve CC1, and also to those who solved both the CC2 and CC1, which denoted students with higher reasoning abilities.

*E-mail: [email protected]. Notes

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The authors declare no competing financial interest.

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CONCLUSION We can conclude from our results that our first hypothesis was correct. Some students can solve conceptual questions with the aid of additional questions even when these students cannot solve the conceptual questions without that aid. In contrast to the second hypothesis, we found a correlation between the C−M question and the CC2 question, but only in the case of the second concept, chemistry without formal concepts. We expected correlation in the case of the first context, chemistry in everyday life because we assumed that this context is the most familiar for students. The unexpected correlation may be the result of at least two factors: (i) the context chemistry without formal concepts is more familiar to students than the context chemistry in everyday life, because chemistry teachers in Slovakia focus mainly on this context; and (ii) students were not experienced with the question format while solving tasks 1 and 2 (context of chemistry in everyday life), but they learned to use it while solving tasks 3 and 4, which led to better performance in the chemistry without formal concepts context. As these contexts were tested by only one question pair, further testing is required for an unequivocally clear conclusion. Despite this, these results indicate that lack of formal reasoning does not necessarily exclude the ability to solve conceptual questions. When conceptual questions include CASE pillars, then they are available both for students who can fully use their formal reasoning potential, and also for students who have the potential but are not yet able to solve these questions without further help. We had to eliminate the classroom discussion in our study, and this therefore weakened the effect of Vygotsky’s social constructivism. In our opinion, this is the reason the correla-

ACKNOWLEDGMENTS This research was supported by the grant of MS SR, VEGA 1/ 0417/12. REFERENCES

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Conceptual Questions and Lack of Formal Reasoning: Are They

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