Use Of Mathematical Representations Research Articles

Teachers’ Teaching Practices and Students’ Self-Concept in Relation To Problem-Solving Performance

The teachers’ teaching practices and the students’ self-concept play a vital role in the performance of students in Mathematics. This study explored the extent of Mathematics teachers' teaching practices and the level of the students' self-concept toward mathematics in relation to problem-solving performance. It was conducted on a total of 111 Grade 10 students who participated in the limited face-to-face classes in all secondary schools in District 10 of the Division of Ozamiz City. This study employed a descriptive-correlational research design. Questionnaires and a problem-solving test were utilized in gathering the data that were analyzed and interpreted using Mean, Standard Deviation, Pearson Product-Moment Correlation Coefficient, and Stepwise Multiple Regression Analysis. Results showed that the Mathematics teachers' teaching practices were demonstrated to a great extent. The students have a fair level of learned self-concept, organized self-concept, and a good level of dynamic self-concept. However, the students' performance in problem-solving did not meet the expectations of the standards set by the DepEd. It was found that there was a significant relationship between the teachers' use of mathematical representations in teaching and the students' problem-solving performance in Mathematics. Furthermore, there was a significant relationship between students' dynamic self-concept and problem-solving performance. The use of mathematical representations of teachers and students' dynamic self-concepts were the predictors of students' problem-solving performance.

Inquiry and Discovery Learning Model in Student's Mathematic Representation Ability

Representational ability is a very important ability in learning mathematics, with representational ability students can solve mathematical problems. This study aims to compare the two Inquiry and Discovery learning models in overcoming students' representation abilities. This research was conducted at a school in NTB Province, Bima Regency with a total of 60 students with a sample of 30 participants from Science 1 and 30 participants from Science 2. Data collection techniques used observation and interviews. While the instrument uses a test. Data analysis techniques used Prerequisite test (Normality and Homogeneity) and Hypothesis Test (N_Gain, t test). In terms of this research, it shows that during representation learning, these two models really help students to understand the use of mathematical representations.

A critical exploration of student teacher’s choice and use of representations in a challenging environment

The teaching and learning of mathematics in economically challenged environments is demanding. Thus, the teachers who teach in these contexts should have a sound pedagogical content knowledge to make a success of their teaching thereof. International community in mathematics education agrees that multiple representations play a pivotal role in making mathematics accessible to learners. However, the challenge might be the feasibility of such a use in African contexts where a student teacher learns to teach mathematics in a crowded classroom of learners (n=80) with significantly varied age differences (ages 9-15). Against this background, therefore the purpose of the study was to explore the choice and use of mathematical representations in a grade 4 class in Lesotho. Data was collected through lesson observations and reflection sessions. Knowledge quartet typology was used as a data analysis approach. The findings of the study indicate that the use of fake money in the lesson improved participation and helped to scaffold learners’ strategies of addition and subtraction. It is therefore recommended that the prospective teachers be equipped with skills to choose and use multiple representations.

Mathematical modeling with digital technological tools for interpretation of contextual situations

This article has the goal of proposing physical contextual situations modeling as a way to interpret mathematical representations that are produced by digital technological tools. Thus, there is an experimental situation-problem about a physical phenomenon that is modeled through video analysis and dynamic geometry software; the methodological model Cuvima conducts the experimental activity. Pre-testing and post-testing measuring instruments were designed to obtain the information and previous conceptions of ten graduate students in Mathematical Education, which showed a conceptual change. Similarly, results prove that digital technology, from a didactical sequence, supports and strengthens experimental work simplifying modeling processes of a physical phenomenon, promoting the use of mathematical representations to solve a situation-problem.

Peran Representasi Matematis dalam Pembelajaran Perkalian Bentuk Aljabar melalui Pendekatan Matematika Realistik

Algebra is an abstract topic in mathematics that should initially be learned by students in junior high school level. In order that this topic is easier to understand by students meaningfully, relevant mathematical representations should be used in the learning process. This research aims to analyze the role of mathematical representations in the learning of multiplication of algebraic expressions through the use of realistic mathematics education approach. To do so, we used a qualitative research method, in the form of the learning and teaching process involving 23 grade VII students (12-13-year-old) from one of the schools in Bandung. We analyzed video data of the learning process and the student written work from a formative test. The results showed that visual representations are frequently used by students at the beginning of the learning process and symbolic representations are used after the students get used to using visual representations. The result of the formative test indicated that the use of mathematical representations meaningfully could help students in solving multiplication of algebraic expressions problems. We conclude that the use of mathematical representations—in particular of visual representations using geometry context in algebra learning—helps students to understand the topic of multiplication of algebraic expressions.

Mathematical representation analysis of students in solving mathematics problems

Representation of ideas in mathematics is fundamental to how students can understand and apply these ideas. This study aims to describe students’ mathematical representations in solving mathematics problems that include pictorial representations, symbol representations, and verbal-written representations. This study used descriptive qualitative which involved 20 respondents of seventh grade students of Aisyiyah junior high school Bengkulu. The instruments were sheet of problems and interview guides. Three respondents were selected based on the completeness of the answers then interviewed to clarify the answers. The completeness was based on the use of mathematical representations that include pictorial representations, symbol representations, and verbal-written representations. The results of the study showed that students can use various forms of mathematical representations in solving the given mathematics problems, and even students can use three forms of mathematical representations, and some student only used one or two forms of mathematical representations.

Teacher Goals and Dilemmas in the Use of Mathematical Representations

The purpose of this article is to describe the reported goals of teachers participating in professional development related to their efforts to consider multiple representations in their teaching. Through analysis of monthly written reflections and group discussion, we describe 3 teacher dilemmas that emerged related to their efforts to consider multiple representations in their teaching: (a) equitable practices when particular representations result in differential success, (b) a teacher's need to balance exposure and choice, and (c) a potential dilemma related to conflicts between competing goals. We provide suggestions of how mathematics educators might use these findings to support future professional development efforts.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

‘Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum’ (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students’ attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221–240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students’ coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling – utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

Is there a better way to predict death using heart rate recovery?

Heart rate recovery (HRR) during exercise testing is an independent predictor of prognosis. The relative predictive power of computational analysis of HRR as a function of resting and maximum heart rate (HR) compared with direct measurement of the drop in HR has not been determined. We aimed to improve on the prognostic value of HRR by the use of mathematical representations of HRR kinetics. In all, 2,193 patients who underwent exercise testing, coronary angiography, and clinical evaluation were followed up for 10.2 +/- 3.6 years. Mathematical functions were used to model HRR as a function of resting (HR(Rest)), maximum HR (HR(Peak)) and time (t): (a) HRR= HR(Rest) + (HR(peak) - HR(Rest)) X e(-kt) and (b) HRR= HR(Rest) + (HR(peak) - HR(Rest)) e(-kt2) Equation (b) provided the best fit of the recovery HR curve. An abnormal HRR at 2 min was a better predictor of mortality than HRR at 1, 3, or 5 min. At 2 min, HRR also predicted mortality better than computational models of HRR, relating HRR as a function of maximum and resting HRs. After adjusting for univariately significant predictors of mortality, HRR, age, exercise capacity, and maximum HR were chosen in order as the best predictors of mortality. Even though the computational models of HRR and the determination of HRR at different time intervals were significant predictors of mortality, the simple discrete measure of HRR at 2 min was the best predictor of mortality. At 2 min, HRR outperformed age, METs, and maximum exercise HR in predicting all-cause mortality.

Mathematization of experience in a grade 8 open‐inquiry environment: An introduction to the representational practices of science

AbstractThe purpose of this classroom study was to investigate the use of mathematical representations in three Grade 8 general science classes that engaged in a 10‐week open inquiry about the correlations between biological and physical variables in the environment. A constructivist perspective was used to design the study and to assemble the data sources. These data sources included videotapes of students in their work, audiotapes of teacher–student interactions and teacher interviews, the transcripts of these tapes, the students' field notebooks, field reports, special problem assignments, examinations, and the teachers' curriculum guides, field notes, and reflective journal. An interpretive method was used to construct assertions and the supporting data. In the setting provided, students increasingly used mathematical representations such as graphs and data tables to support their claims in a convincing manner; the use of abstract equations and percent calculations did not change over the course of the study. Representations such as graphs, maps, averages, and equations were not only useful as inscriptions (representations in some permanent medium, usually paper), but also as conscription devices in the construction of, and through which, students engaged each other to collaboratively construct meaning. This study demonstrates the use of representations as conscription devices, and illustrates how the use and understanding of inscriptions changes over time. Understanding representations as inscription and conscription devices focuses on the social aspects of knowing, which has important implications for teachers' conceptualization of learning and their organization of science classrooms.

Prediction of Critical Mixtures. Use of Mathematical Representations for Molar Free Energy of Mixing

Prediction of Critical Mixtures. Use of Mathematical Representations for Molar Free Energy of Mixing