A review of research on formal reasoning and science teaching

A central purpose of education is to improve students' reasoning abilities. The present review examines research in developmental psychology and science education that has attempted to assess the validity of Piaget's theory of formal thought and its relation to educational practice. Should a central objective of schools be to help students become formal thinkers? To answer this question research has focused on the following subordinate questions: (1) What role does biological maturation play in the development of formal reasoning? (2) Are Piaget's formal tasks reliable and valid? (3) Does formal reasoning constitute a unified and general mode of intellectual functioning? (4) How does the presence or absence of formal reasoning affect school achievement? (5) Can formal reasoning be taught? (6) What is the structural or functional nature of advanced reasoning? The general conclusion drawn is that although Piaget's work and that which has sprung from it leaves a number of unresolved theoretical and methodological problems, it provides an important background from which to make substantial progress toward a most significant educational objective. All our dignity lies in thought. By thought we must elevate ourselves, not by space and time which we can not fill. Let us endeavor then to think well; therein lies the principle of morality. Blaise Pascal 1623-1662.     

A Piagetian-Based Programme for Learning “Elements and Symbols”

Piaget's learning theory on cognitive development has had considerable impact on science education (Piaget, 1964; Inhelder and Piaget, 1958; Craig, 1972). The theory classifies cognitive learning into four successive stages: (a) sensory-motor, (b) pre-operational, (c) operational, and (d) formal. Various programmes and instructional strategies have been developed based on the theory (Batt, 1980; Karplus, 1977; Renner and Stafford, 1979; Ryan, et al., 1980; Herron, 1978; Good et al; 1978). An application of this theory for teaching and learning scientific concepts is the Piagetian learning cycle (Karplus, 1977) which is of growing interest among science educators. This article intends to introduce briefly the learning cycle in general and suggest a learning cycle for teaching a topic in chemistry: “Elements and Symbols”.     

A comparison of concrete and formal science instruction upon science achievement and reasoning ability of sixth grade students

Several recent studies suggest concrete learners make greater gains in student achievement and in cognitive development when receiving concrete instruction than when receiving formal instruction. This study examined the effect of concrete and formal instruction upon reasoning and science achievement of sixth grade students. Four intact classes of sixth grade students were randomly selected into two treatment groups; concrete and formal. The treatments were patterned after the operational definitions published by Schneider and Renner (1980). Pretest and posttest measures were taken on the two dependent variables; reasoning, measured with Lawson's Classroom Test of Formal Reasoning, and science achievement, measured with seven teacher made tests covering the following units in a sixth grade general science curriculum: Chemistry, Physics, Earth Science, Cells, Plants, Animals, and Ecology. Analysis of covariance indicated significantly higher levels (better than 0.05 and in some cases 0.01) of performance in science achievement and cognitive development favoring the concrete instruction group and a significant gender effect favoring males.     

The four-card problem resolved? Formal operational reasoning and reasoning to a contradiction

To test the hypothesis that adolescents classified as formal operational, based upon use of proportional reasoning on the “Pouring Water Task” (Lawson, Karplus, & Adi, 1978) have acquired the mental structures necessary to comprehend hypothetico-deductive arguments of a pattern referred to as “reasoning to a contradiction,” while adolescents classified as concrete operational, based upon use of additive reasoning on the same task have not, a sample of 100 high school students were administered the task and three versions of a problem requiring use of reasoning to a contradiction before, immediately after, and one month after brief verbal instruction in use of that reasoning pattern. Results were generally supportive of the hypothesis as most of the concrete students failed the immediate and delayed posttest problems (62 and 80%, respectively) while most of the formal students succeeded (80 and 71%, respectively). Group differences were significant (p < .001) in both cases. These results suggest that, contrary to those who have argued that content plays a substantial role in logical performance, a general hypothetico-deductive reasoning competence exists in some adolescents and is applicable across a wide variety of task domains. Science instruction which aims to teach this competence is recommended.     

The acquisition of formal operational schemata during adolescence: The role of the biconditional

To test the hypothesis that the basic “logic” utilized by individuals in scientific hypothesis testing is the biconditional (if and only if), and that the biconditional is a precondition for the development of formal operations, a sample of 387 students in grades eight, ten, twelve, and college were administered eight reasoning items. Five of the items involved the formal operational schemata of probability, proportions and correlations. Two of the items involved propositions and correlations. Two of the items involved propositional logic. One item involved the biconditional. Percentages of correct responses on most of the items increased with age. A principal-component analysis revealed three factors, two of which were identified as involving operational thought, one of which involved propositional logic. As predicted, the biconditional reasoning item loaded on one of the operational thought factors. A Guttman scale analysis of the items failed to reveal a unidimensional scale, yet the biconditional reasoning item ordered first supporting the hypothesis that it is a precondition for formal operational reasoning. Implications for teaching science students how to test hypotheses are discussed.     

The use of Lawson's test of formal reasoning in the Israeli science education context

Lawson's test of formal reasoning was used in the Israeli educational context in order to investigate the relationship between students' achievement in science and in mathematics, to compare the performance of boys and girls, and to compare the performance of Israeli and U.S. populations. It was found that, in general, boys outperform girls; there is only a small correlation between achievement in science and math and Lawson test; and that the Israeli population achieved significantly higher than the U.S. population on the Piagetian skills measured by the test: It was concluded that the future use of Lawson's test by the high school teacher is doubtful.     

Meaningful learning,reasoning ability,and students' understanding and problem solving of topics in genetics

The purpose of this study was to explore relationships among school students' (N = 189) meaningful learning orientation, reasoning ability and acquisition of meaningful understandings of genetics topics, and ability to solve genetics problems. This research first obtained measures of students' meaningful learning orientation (meaningful and rote) and reasoning ability (preformal and formal). Students were tested before and after laboratory-based learning cycle genetics instruction using a multiple choice assessment format and an open-ended assessment format (mental model). The assessment instruments were designed to measure students' interrelated understandings of genetics and their ability to solve and interpret problems using Punnett square diagrams. Regression analyses were conducted to examine the predictive influence of meaningful learning orientation, reasoning ability, and the interaction of these variables on students' performance on the different tests. Meaningful learning orientation best predicted students' understanding of genetics interrelationships, whereas reasoning ability best predicted their achievement in solving genetics problems. The interaction of meaningful learning orientation and reasoning ability did not significantly predict students' genetics understanding or problem solving. Meaningful learning orientation best predicted students' performance on all except one of the open-ended test questions. Examination of students' mental model explanations of meiosis, Punnett square diagrams, and relationships between meiosis and the use of Punnett square diagrams revealed unique patterns in students' understandings of these topics. This research provides information for educators on students' acquisition of meaningful understandings of genetics. © 1996 John Wiley & Sons, Inc.     

Relationships among informal learning environments,teaching procedures and scientific reasoning ability

Informal learning experiences have risen to the forefront of science education as being beneficial to students' learning. However, it is not clear in what ways such experiences may be beneficial to students; nor how informal learning experiences may interface with classroom science instruction. This study aims to acquire a better understanding of these issues by investigating one aspect of science learning, scientific reasoning ability, with respect to the students' informal learning experiences and classroom science instruction. Specifically, the purpose of this study was to investigate possible differences in students' scientific reasoning abilities relative to their informal learning environments (impoverished, enriched), classroom teaching experiences (non-inquiry, inquiry) and the interaction of these variables. The results of two-way ANOVAs indicated that informal learning environments and classroom science teaching procedures showed significant main effects on students' scientific reasoning abilities. Students with enriched informal learning environments had significantly higher scientific reasoning abilities compared to those with impoverished informal learning environments. Likewise, students in inquirybased science classrooms showed higher scientific reasoning abilities compared to those in non-inquiry science classrooms. There were no significant interaction effects. These results indicate the need for increased emphases on both informal learning opportunities and inquiry-based instruction in science.     

Chinese and Australian Year 3 Children's Conceptual Understanding of Science: A multiple comparative case study

Children have formal science instruction from kindergarten in Australia and from Year 3 in China. The purpose of this research was to explore the impact that different approaches to primary science curricula in China and Australia have on children's conceptual understanding of science. Participants were Year 3 children from three schools of high, medium and low socio-economic status in Hunan Province, central south China (n?=?135) and three schools of similar socio-economic status in Western Australia (n?=?120). The students' understanding was assessed by a science quiz, developed from past Trends in Mathematics and Science Study science released items for primary children. In-depth interviews were carried out to further explore children's conceptual understanding of living things, the Earth and floating and sinking. The results revealed that Year 3 children from schools of similar socio-economic status in the two countries had similar conceptual understandings of life science, earth science and physical science. Further, in both countries, the higher the socio-economic status of the school, the better the students performed on the science quiz and in interviews. Some idiosyncratic strengths and weaknesses were observed, for example, Chinese Year 3 children showed relative strength in classification of living things, and Australian Year 3 children demonstrated better understanding of floating and sinking, but children in both countries were weak in applying and reasoning with complex concepts in the domain of earth science. The results raise questions about the value of providing a science curriculum in early childhood if it does not make any difference to students' conceptual understanding of science.     

Exploring high school students' use of theory and evidence in an everyday context: the role of scientific thinking in environmental science decision‐making

This study examined 10th‐grade students' use of theory and evidence in evaluating a socio‐scientific issue: the use of underground water, after students had received a Science, Technology and Society‐oriented instruction. Forty‐five male and 45 female students from two intact, single‐sex, classes participated in this study. A flow‐map method was used to assess the participants' conceptual knowledge. The reasoning mode was assessed using a questionnaire with open‐ended questions. Results showed that, although some weak to moderate associations were found between conceptual organization in memory and reasoning modes, the students' ability to incorporate theory and evidence was in general inadequate. It was also found that students' reasoning modes were consistent with their epistemological perspectives. Moreover, male and female students appear to have different reasoning approaches.     

Students' achievement in relation to reasoning ability,prior knowledge and gender

This study investigated students' achievement regarding photosynthesis and respiration in plants in relation to reasoning ability, prior knowledge and gender. A total of 117 eighth‐grade students participated in the study. Test of logical thinking and the two‐tier multiple choice tests were administered to determine students' reasoning ability and achievement, respectively. An analysis of covariance (ANCOVA) was conducted to assess the effect of reasoning ability on students' achievement. The independent variable was the reasoning ability (low, medium, high), the dependent variable was the scores on the two‐tier test. Students' grades in science in previous year were used as a covariate. Analysis revealed a statistically significant mean difference between students at high and low formal levels with respect to achievement. Stepwise multiple regression analysis revealed that reasoning ability, prior knowledge and gender were significant predictors of students' achievement in photosynthesis and respiration in plants, explaining 42% of the variance.     

Students' Understanding of the Objectives and Procedures of Experimentation in the Science Classroom

As part of a project to identify opportunities for reasoning that occur in good but typical science classrooms, this study focuses on how sixth graders reason about the goals and strategies of experimentation and laboratory activities in school. Collaborating with teachers, we explore whether reasoning can be deepened by developing instruction that capitalizes more effectively on the classroom opportunities that arise for fostering complex thinking and understanding. The design of the study includes (a) a baseline interview probing students' understanding of experimentation in the context of a standard, 40-min "hands-on" activity that is part of the standard sixth-grade curriculum; (b) a 3-week teaching study, in which five teachers, informed by the cognitive science research concerning the development of scientific reasoning, designed and taught a special experimentation unit in their classrooms; and (c) a series of follow-up interviews, in which students' understanding of experimentation was reexamined. The findings from the two learning contexts-one more supportive of student reasoning than the other-inform us about the kinds of reasoning that are developing in middle-school students and the forms of instruction best suited to exercising those developing skills.     

Identifying Science Understanding for Functional Scientific Literacy

Students' questions play an important role in meaningful learning and scientific inquiry. They are a potential resource for both teaching and learning science. Despite the capacity of students' questions for enhancing learning, much of this potential still remains untapped. The purpose of this paper, therefore, is to examine and review the existing research on students' questions and to explore ways of advancing future work into this area. The paper begins by highlighting the importance and role of students' questions from the perspectives of both the learner and the teacher. It then reviews the empirical research on students' questions, with a focus on four areas: (1) the nature and types of these questions; (2) the effects of teaching students questioning skills; (3) the relationship between students' questions and selected variables; and (4) teachers' responses to, and students' perceptions of, students' questions. Following this, some issues and implications of students' questions for classroom instruction are discussed. The paper concludes by suggesting several areas for future research that have significant value for student learning.     

Development and validation of a scientific (formal) reasoning test for college students

We present a multiple-choice test, the Montana State University Formal Reasoning Test (FORT), to assess college students' scientific reasoning ability. The test defines scientific reasoning to be equivalent to formal operational reasoning. It contains 20 questions divided evenly among five types of problems: control of variables, hypothesis testing, correlational reasoning, proportional reasoning, and probability. The test development process included the drafting and psychometric analysis of 23 instruments related to formal operational reasoning. These instruments were administered to almost 10,000 students enrolled in introductory science courses at American universities. Questions with high discrimination were identified and assembled into an instrument that was intended to measure the reasoning ability of students across the entire spectrum of abilities in college science courses. We present four types of validity evidence for the FORT. (a) The test has a one-dimensional psychometric structure consistent with its design. (b) Test scores in an introductory biology course had an empirical reliability of 0.82. (c) Student interviews confirmed responses to the FORT were accurate indications of student thinking. (d) A regression analysis of student learning in an introductory biology course showed that scores on the FORT predicted how well students learned one of the most challenging concepts in biology, natural selection.     

Should physicists preach what they practice?

Does one need to think like a scientist to learn science? To what extent can examining the cognitive activities of scientists provide insights for developing effective pedagogical practices? The cognition and instruction literature has focused on providing a model of expert knowledge structures. To answer these questions, what is needed is a model of expert reasoning practices. This analysis is a step in that direction. It focuses on a tacit dimension of the thinking practices of expert physicists, “constructive modeling”. Drawing on studies of historical cases and protocol accounts of expert reasoning in scientific problem solving, it is argued that having expertise in physics requires facility with the practice of “constructive modeling” that includes the ability to reason with models viewed generically. Issues pertaining to why and how this practice of experts might be incorporated into teaching are explored.     

Epistemological resources for thought experimentation in science learning

Thought Experiments (TEs) are reasoning processes that are based on 'results' of an experiment carried out in thought. What is the validity of an experiment- that has not been actually executed- for knowledge about the physical world? What are the features that make it distinctive and how do we integrate it into learning environments to support such thought processes? This study suggests that a thought experiment draws on three epistemological resources: conceptual-logical inferences, visual imagery and bodily-motor experience. We start by stating how students' TEs are related to recent research on learning science and then proceed to describe the nature of TEs. The central part of the paper deals with cognitive theories and empirical examples of visual imagery and bodily imagery. It also deals with how these enable implicit knowledge about the world to be retrieved. Students may have, but are not aware of, such knowledge for it is hidden when learning is only based on formal representations. We show that imagination is structured, goal-oriented, based on prior experiential imagery and internally coherent. Students can, for example, mentally rotate objects at constant velocity. Students can 'zoom in and out' to inspect imaginary situations, transfer objects, predict paths of imaginary moving objects and imagine the impact of forces on mechanical systems. We show that the TEs are powerful because of these capabilities. We further claim that these are not exploited by school learning environments and offer a first step towards understanding imagery in science learning.     

Comments on “the uses of Lawson's test of formal reasoning in the israeli science education context”

In a recent article that appeared in this journal, Hofstein and Mandler (1985) reported a study which employed the Lawson's (1978) classroom test of formal reasoning to determine, among other things, the relationship between achievement in science and mathematics in a sample of Israeli students. Based on their findings, the authors raised objections to the classroom utility of the test for diagnosing students' developmental levels. The present author, however, argued that the case has not been properly established in view of one major methodological problem which seemed to characterize the study. Accordingly, the plea to abandon Lawson's test of formal reasoning was questioned.     

The impact of a classroom intervention on grade 10 students' argumentation skills,informal reasoning,and conceptual understanding of science

The literature provides confounding information with regard to questions about whether students in high school can engage in meaningful argumentation about socio‐scientific issues and whether this process improves their conceptual understanding of science. The purpose of this research was to explore the impact of classroom‐based argumentation on high school students' argumentation skills, informal reasoning, and conceptual understanding of genetics. The research was conducted as a case study in one school with an embedded quasi‐experimental design with two Grade 10 classes (n = 46) forming the argumentation group and two Grade 10 classes (n = 46) forming the comparison group. The teacher of the argumentation group participated in professional learning and explicitly taught argumentation skills to the students in his classes during one, 50‐minute lesson and involved them in whole‐class argumentation about socio‐scientific issues in a further two lessons. Data were generated through a detailed, written pre‐ and post‐instruction student survey. The findings showed that the argumentation group, but not the comparison group, improved significantly in the complexity and quality of their arguments and gave more explanations showing rational informal reasoning. Both groups improved significantly in their genetics understanding, but the improvement of the argumentation group was significantly better than the comparison group. The importance of the findings are that after only a short intervention of three lessons, improvements in the structure and complexity of students' arguments, the degree of rational informal reasoning, and students' conceptual understanding of science can occur. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 47: 952–977, 2010     

Testing one premise of scientific inquiry in science classrooms: Examining students' scientific explanations and student learning

In this study, we analyzed the quality of students' written scientific explanations found in notebooks and explored the link between the quality of the explanations and students' learning. We propose an approach to systematically analyzing and scoring the quality of students' explanations based on three components: claim, evidence to support it, and a reasoning that justifies the link between the claim and the evidence. We collected students' science notebooks from eight science inquiry‐based middle‐school classrooms in five states. All classrooms implemented the same scientific‐inquiry based curriculum. The study focuses on one of the implemented investigations and the students' explanations that resulted from it. Nine students' notebooks were selected within each classroom. Therefore, a total of 72 students' notebooks were analyzed and scored using the proposed approach. Quality of students' explanations was linked with students' performance in different types of assessments administered as the end‐of‐unit test: multiple‐choice test, predict‐observe‐explain, performance assessment, and a short open‐ended question. Results indicated that: (a) Students' written explanations can be reliably scored with the proposed approach. (b) Constructing explanations were not widely implemented in the classrooms studied despite its significance in the context of inquiry‐based science instruction. (c) Overall, a low percentage of students (18%) provided explanations with the three expected components. The majority of the sample (40%) provided only claims without any supporting data or reasoning. And (d) the magnitude of the correlations between students' quality of explanations and their performance, were all positive but varied in magnitude according to the type of assessment. We concluded that engaging students in the construction of high quality explanations may be related to higher levels of student performance. The opportunities to construct explanations in science‐inquiry based classrooms, however, seem to be limited. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 47: 583–608, 2010     

Rethinking Intensive Quantities via Guided Mediated Abduction

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses a/b analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students' sensation of an intensive quantity could serve as a powerful resource for grounding its formal expression, accepting the mathematical form requires students to align the sensation with a new way of reasoning about the phenomenon. I offer a case analysis of a middle school student who successfully came to understand the intensive quantity of likelihood. The analysis highlights a form of reasoning called abduction and suggests that sociocognitive processes can guide and mediate students' abductive reasoning. Interpreting the child's and tutor's multimodal action through the lens of abductive inference, I demonstrate the emergence of a proportional concept as guided mediated objectification of tacit perception. This “gestalt first” process is contrasted with traditional “elements first” approaches to building proportional concepts, and I speculate on epistemic and cognitive implications of this contrast for the design and instruction of these important concepts. In particular, my approach highlights an important source of epistemic difficulty for students as they learn intensive quantities: the difficulty in shifting from intuitive perceptual conviction to mediated disciplinary analysis. My proposed conceptualization of learning can serve as an effective synthesis of traditional and reform-based mathematics instruction.