Evidence of Rote Learning of Science by Spanish University Students

The purpose of this investigation was to test for alternative conceptions of students enrolled in a second course of sciences at the Teacher Training School in Pamplona, Spain, regarding a geological topic (silicates) which had been studied in previous educational levels. The investigation also proposed to test the efficiency of Novak's concept mapping technique as a method of knowing the cognitive structure of the students. Students' concept maps showed the existence of a large number of alternative conceptions and the persistence and tenacity of these misconceptions after a period of instruction on the topic, even in the case of so-called “good” students.     

A false belief about fractions – What is its source?

This paper presents the results of interviews with 174 participants solving a problem of elementary mathematics, connected with the part–whole approach to fractions. The motive for the investigation was a specific kind of difficulty observed during a case study conducted to verify the elementary school student's understanding of the concept of fractions. The authors decided to examine the problem in a broader population of mathematics learners at different levels of education: from elementary school to university students and graduates of science majors. Approximately 65% of respondents reported the wrong answer immediately after reading the fraction problem taken from the fourth grade of elementary school. Detailed analysis of the respondents’ performance showed that the source of many wrong answers was a false belief about fractions: The only way to get 1/n of a given whole is to divide this whole into n equal parts, not yet described in educational literature.     

Analogies and Reconstruction of Probability Knowledge

The effectiveness of utilizing analogies to effect conceptual change in students' alternative probability concepts was investigated. Forty-one senior high school mathematics students were engaged in a knowledge reconstruction process regarding their beliefs about common everyday probability situations, such as sports events or lotteries. The students were given situations similar to those shown in previous research to reveal alternative mathematical conceptions. They were also given analogous researcher-generated anchoring situations that had been pretested and found to elicit mathematically acceptable responses. The cognitive dissonance produced by the conflicting responses motivated students to reconstruct their knowledge. The results of the investigation showed that analogies can be effective in producing a desired conceptual change in high school students' probability concepts.     

Investigating Elementary Teachers' Conceptions of Animal Classification

Numerous studies have been conducted regarding alternative conceptions about animal diversity and classification, many of which have used a cross‐age approach to investigate how students' conceptions change over time. None of these studies, however, have investigated teachers' conceptions of animal classification. This study was intended to augment the findings of past research by exploring the conceptions that elementary teachers possess about animal classification. Using interviews and written items, we documented teachers' conceptions about animal classification and compared them with student conceptions identified in previous research studies. Many of the teachers' conceptions observed in this study were similar to students' conceptions in that they were often too limited or too general compared with scientifically accepted conceptions. Also, the teachers in this study frequently used “non‐defining” characteristics, such as locomotion and habitat, to classify animals. As a result, several misclassifications were observed in the teachers' responses to the written items. Notably, the results of our study demonstrate that teachers often have the same alternative conceptions about animal classification as students. We explore some possible explanations for these alternative conceptions and discuss the instructional implications of the findings.     

What Children Bring to the Classroom: Learning Science From Experience

Extracurricular science-related experiences of young students were examined. The sample consisted of 539 elementary school students between the ages of 9 and 13. Students completed the Science Experiences Survey (SES) to identify the number of common scientific materials and activities they experienced outside of the classroom. The factor analysis isolated three underlying factors of extracurricular science-related experiences: life science-related experiences, physical science-related experiences, and general learning attributes related to science. Further analysis identified differences in reported experiences by gender. The data indicate that young girls tend to participate in nurturing life science-related activities, and young boys favor hands-on, action-oriented physical science-related experiences. The research suggests that the gender disparity in science follows a continuuum that begins with the experiences of elementary school students.     

Student Competence in Understanding the Matter Concept and Its Implications for Science Curriculum Standards

Using the US national sample from the 1995 Third International Mathematics and Science Study (TIMSS), this study examined students' competence levels in understanding the matter concept at grades 3, 4, 7, 8 and high school graduation, and compared them to the expectations in the US national science education standards. It was found that third‐grade students were developing understanding on mixtures, and fourth‐grade students were developing understanding on separating mixtures; seventh‐ and eighth‐grade students were only at the beginning level of differentiating chemical properties from physical properties; they were not ready for the particulate model of chemical change. High school physical science specialization students were still at the developing level of understanding kinetic and atomic models of chemical and physical changes; they may not be able to master those theories. The findings suggest that the Benchmarks for Science Literacy and Atlas for Science Literacy may have overestimated the competences of elementary, middle school, and high school students.     

Developing the roots of modelling conceptions: ‘mathematical modelling is the life of the world’

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a Modelling conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity, actions and conceptions of both modelling and mathematics that these beginners to modelling displayed. Understanding the conceptions of mathematics that students might hold or be developing and how these can be influenced in early schooling are essential ingredients in any plans for introducing modelling seriously into primary school classrooms. The majority of the students (22/25) were identified as displaying a developing conception of modelling as a way of problem handling. The three other students displayed the developmental roots of a way of understanding the world conception of modelling. These three students also displayed a Modelling conception of mathematics with one showing indications of developing towards a Life conception of mathematics.     

Preservice Elementary Teachers' Conceptions of What Causes Night and Day

Two different procedures were utilized to study 50 preservice elementary teachers' conceptions of what causes night and day on earth. The numbers of responses representing alternative conceptions for the models with written and verbal explanation procedures were 27 and 14, respectively. The alternative conception most frequently expressed for both procedures was that night and day are caused by the earth revolving around the sun. The frequency with which alternative conceptions were expressed by future teachers is a problem which should be addressed with instruction using models.     

Academic achievement with cooperative learning using homogeneous and heterogeneous groups

Cooperative learning is a proven teaching strategy that teachers have been using for over 40 years. Teachers often group students heterogeneously so that students who are lower achieving are learning with and from higher achieving students. The purpose of this study was to test homogeneous and heterogeneous grouping while using cooperative learning teaching structure. This study aimed to answer the question of whether students be grouped homogeneously or heterogeneously while participating in cooperative learning. The primary research design for this study was a quasi-experimental nonequivalent control-group design. A convenience sample of fifth-grade students was drawn from a Georgia elementary school in the 2017–2018 school year. The data were analyzed using analysis of covariance (ANCOVA) and paired samples t tests. The ANCOVA was run to compare the scores from the FOSS Survey/Posttest, and the analysis showed no significant difference between the homogeneous and heterogeneous group posttest scores. Both groups made significant gains (as shown by the results of the paired samples t-tests).     

Fifth-grade students�� approaches to and beliefs of mathematics word problem solving: a large sample Hungarian study

Mathematical word problems used in Verschaffel et al.??s (Learning and Instruction 7:339?C359, 1994) study were applied in several follow-up studies. The goal of the present study was to replicate and extend the results of this line of research in a large sample of Hungarian students using an alternative set of data-gathering and data-analysis techniques. 4,037 students forming a nationwide representative sample of the Hungarian fifth-grade student population (aged 10?C11) completed the test. The test contained five word problems from the list of 10 P(??problematic)-items from Verschaffel et al.??s test. In contrast to all previous research in this domain, we used a multiple-choice format, where three options were given for each task: (a) routine-based, non-realistic answer, (b) numerical response that does take into account realistic considerations, (c) a realistic solution stating that the task cannot be solved. The hypotheses of this study were: (1) Students?? responses will confirm previous results, i.e. upper elementary school students prefer to respond to P-items by means of the routine-based answer; (2) Most students will demonstrate a more or less consistent preference for a given answer type (a, b or c) over problems; (3) Students?? school math marks will have low correlation indices with students?? achievement on these word problems. Our results confirm student??s overall tendency to follow non-realistic approaches when doing school word problem solving. The tendency even holds when confronting students with various kinds of realistic answers. Our results show that students demonstrate response patterns over problems, and that the correlation with math school performance is significant but small.     

Lakatos’Proofs and Refutations Comes Alive in an Elementary Classroom

This paper presents an alternative pedagogy implicit in Imre Lakatos’ Proofs and Refutations: The Logic of Mathematical Discovery. Through the voices of his characters, Lakatos reveals that learning mathematics is a discourse laden activity. In this approach it is acceptable, if not preferable, to refute a conjecture. Examples of the use of a Lakatosian approach in an elementary classroom are given. In this classroom setting students are able to propose more mature solutions, through posing and refuting conjectures.     

Exploring the Responses of Underrepresented Students in Science to an Elementary Classroom Outreach Program

This paper describes a subset of results from a large‐scale two‐year independent evaluation study conducted with the Scientists in School (SiS) outreach program and two large school boards in Ontario, Canada. Specifically, it explores the responses of elementary students (n= 811) from typically underrepresented groups in science (English language learners [ELL], girls, and students at low‐achieving schools) to the SiS outreach program. It explores responses related to enjoyment, interest, perceptions of role modeling, and future career choice in science. Compared to other students, findings suggest that girls and students from low‐achieving schools found the program more enjoyable and reported that it provided positive science role models. Students at schools with high ELL populations also reported higher levels of enjoyment and reported that the program helped get them excited about science.     

Asking mathematical questions mathematically

It is proposed that the style and format of the questions used by lecturers and tutors profoundly influence students' conceptions of what mathematics is about and how it is conducted. By looking at reasons for asking questions, and becoming aware of different types of questions which mathematicians typically ask themselves, we can enrich students' experience of mathematics. Drawing on recent work by Watson and Mason stimulated by the ideas of Zygfryd Dyrszlag, the paper proposes that mathematical themes, powers, heuristics and activities generate a mathematical discourse which is not always represented in the questions students are asked, and that the real purpose of questions is to provoke students into construal, into constructing their own stories which constitute meaning and understanding, and which equip them for the future. The use of questions of whatever type depends on both scaffolding and fading their use with and in front of students, so that students internalize the questions into their own learning and doing of mathematics. The framework directed—prompted—spontaneous is proposed as an alternative to scaffolding—fading for informing interactions with students.     

Pre-service elementary teachers’ strategies for tiling and relating area units

It has been established that preservice elementary school teachers (PSTs) often employ procedural methods when solving measurement problems without conceptual understanding or flexibility, but a significant gap exists in the literature identifying why. Through the lens of discrete and continuous interpretations of area, this study extends the research base by describing strategies PSTs use to tile a two-dimensional space with varying size tiles and what these strategies imply about PSTs’ conceptions of area measurement. These strategies and implied conceptions enable further discussion on the multiple purposes of the area model as an illustrative measure for mathematics throughout the elementary school curriculum.     

Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts

Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called Number Worlds that was designed to support the exploration of elementary number theory concepts by making the essential relationships and patterns more accessible to learners. Based on our research with pre-service elementary school teachers, we show how both the visual representations embedded in the microworld, and the possibilities afforded for experimentation affect learners' understanding and appreciation of basic concepts in elementary number theory. We also discuss the aesthetic and affective dimensions of the research participants' engagement with the learning environment. This revised version was published online in July 2006 with corrections to the Cover Date.     

Zimbabwean in-service mathematics teachers’ understanding of matrix operations

In Zimbabwe, school pupils study matrix operations, a topic that is usually covered as part of linear algebra courses taken by most mathematics undergraduate students at university. In this study we focused on Zimbabwean teachers who were studying the topic at university while also teaching the topic to their high school pupils. The purpose of the study was to explore the mental conceptions of matrix operations concepts of a sample of 116 in-service mathematics teachers. The Action Process Object Schema (APOS) theoretical framework describes the development in understanding of mathematics concepts through the hierarchical growth of mental constructions called action, process, object and schema. The results showed that many of the participants had interiorized actions on matrix operations of addition, scalar multiplication and matrix multiplication into processes. However, more than 50% of the participants struggled with scalar multiplication of a row matrix by a column matrix. In terms of notational errors, some participants could not distinguish between brackets that denote a matrix and that of a determinant, while some used the equal sign as an operator symbol and not as one denoting equivalence between two objects. It is recommended that future in-service teacher programs should try to create more structured opportunities to allow participants to engage more deeply with these concepts.     

Functional thinking ways in relation to linear function tables of elementary school students

One of the basic components of algebraic thinking is functional thinking. Functional thinking involves focusing on the relationship between two (or more) varying quantities and such thinking facilitates the studies on both algebra and the notion of function. The development of functional thinking of students should start in the early grades and it should be improved gradually and extended over a long period of time. Also, patterns represented by function tables are the tools which support the early development of functional thinking. In this regard, the aim of this study was to investigate the functional thinking ways in the early grades, particularly those of elementary school fifth grade students through linear function tables. The study data were collected via task-based interviews conducted with a total of four elementary school fifth graders. Consequently, it was found that the four fifth grade students thought on covariation while working with the linear function tables. It was further obtained that the students were able to discover the correspondence relationship and generalize this relationship. The results of the study also revealed information about the reasoning abilities of the students, in other words about their alternative ways of thinking in generalizing the correspondence relationship.     

Perceived Helpfulness and Amount of Use of Technology in Science and Mathematics Classes at Different Grade Levels

Use of technology in science and mathematics classes has been increasing, but there are differences in the amount of use of and students' perceptions of its helpfulness across grade levels and subject areas. Technology was reported as used only occasionally. Technology was used most often to understand or explore in more depth concepts taught in class. The second most frequent use was as a tool of investigation or assessment. The lowest reported use of technology was as tool of communication. Students in middle school classes perceived technology as less helpful than did students in elementary or high school classes. Students in mathematics classes perceived technology as more helpful than did students in science classes. Girls perceived technology as more helpful than did boys. Additionally, teacher and student perceptions of amount of use varied with teachers reporting more use than students.     

Scientific Methodology and Elementary School Mathematics

Investigations provide an exciting and relevant background for the study of mathematics. In this article children's conceptions of the laws of motion, introduced by Eckstein and Shemesh (1993), are extended with an emphasis placed upon the benefits to mathematics education. The focus is on the principle that the faster an object is moving when it is dropped, the greater the distance it will travel away from the drop point. The problems faced by a class of elementary school children who focus upon this experiment are described, and the impact of these problems upon the decisions made by the class are discussed. The use of mathematics in support of this experiment, particularly concepts of probability and statistics, are discussed, as well as suggestions for alternative methods of evaluating children's performance.     

Conceptions of mathematics and student identity: implications for engineering education

Lecturers of first-year mathematics often have reason to believe that students enter university studies with naïve conceptions of mathematics and that more mature conceptions need to be developed in the classroom. Students’ conceptions of the nature and role of mathematics in current and future studies as well as future career are pedagogically important as they can impact on student learning and have the potential to influence how and what we teach. As part of ongoing longitudinal research into the experience of a cohort of students registered at the author's institution, students’ conceptions of mathematics were determined using a coding scheme developed elsewhere. In this article, I discuss how the cohort of students choosing to study engineering exhibits a view of mathematics as conceptual skill and as problem-solving, coherent with an accurate understanding of the role of mathematics in engineering. Parallel investigation shows, however, that the students do not embody designated identities as engineers.