Prospective Mathematics Teachers’ Algebraic Proficiency From a Symbol Sense Perspective: The Case of Solving Inequalities

Procedural fluency and conceptual understanding are two aspects of mathematical proficiency discussed worldwide, including in Indonesia. In the algebra domain, algebraic proficiency concerns an ability to deal with symbolic representations that can be viewed from a symbol sense perspective. This algebraic proficiency is considered indispensable for prospective mathematics teachers for their future careers. This research aims to analyze prospective mathematics teachers’ algebraic proficiency from the perspective of symbol sense. To achieve this aim, we set up a qualitative case study, involving 19 Indonesian mathematics education students (21-23 years old) as prospective mathematics teachers, in the form of a two-week online teaching and learning process (4 x 50 minutes) and its corresponding formative assessment for solving quadratic, cubic, and rational inequalities. The results revealed that the majority of the participants lack algebraic proficiency as they use procedural strategies more than symbol sense strategies to solve inequalities

An Investigation of Master Student Understanding on Mathematical Literacy Problems

Indonesian government has been promoting the National Literacy Movement since 2016 to response disappointing results of the Program for International Student Assessment on literacy and mathematical literacy skills of students. This movement involves many parties, including educational universities, to prepare mathematics education students of master level, as prospective teachers or lecturers, to understand mathematical literacy. To investigate this condition, this study aims to analyze master student understanding on mathematical literacy problems. To do so, we conducted an online survey via Google Form involving 32 master students from several universities in Bandung. In this survey, each master student was called for sending two mathematics problems and solutions that considered to be literacy problems. The results revealed that 17 (53%) involved master students understand mathematical literacy problems. The most frequent category of literacy problems to appear was Change and Relationship followed by categories of Space and Shape, Uncertainty and Data, and Quantity, respectively. Another result showed that word problems seemed to be regarded as the same as mathematical literacy problems by some students. We conclude that master student understanding of mathematical literacy needs to be improved for facing future educational careers

Problem-solving Approach and Its Impact on Creative Thinking Ability of Prospective Mathematics Teachers

This study aims to investigate the implementation of a problem-solving approach and its corresponding impact on the creative thinking ability of prospective mathematics teachers. A qualitative case study approach was used in this study in the form of observations of learning and teaching processes for geometry topics through the use of a problem-solving approach and of a written test involving 20 prospective mathematics teachers, in one of the state universities in Bandung, Indonesia. The results showed that the implemented problem-solving approach influenced prospective mathematics teachers’ creative thinking in solving problems. The use of different strategies showed prospective teachers’ creative thinking ability in problem-solving processes. The effect of the problem-solving approach on prospective mathematics teachers can be investigated further to obtain a more comprehensive understanding of creative thinking ability

Mathematical Representation of Students in Solving Linear Program Problems

The purpose of this study is to describe mathematics representation of vocational high school students insolving linear program problem. The representation that will be seen is pictorial representation, symbolicrepresentation and verbal representation of students with varying abilities. The research subjects were 3students of class XII from one of the Vocational High Schools in Jambi with a variety of high, mediumand low ability levels. The data was collected by giving two linear program problems that the studentswould work on, then conducting interviews based on each student's answer sheet to strengthen the testresult data. Answer sheet data and interview results were analyzed and presented in narrative text.Students with high abilities implement the three forms of representation accurately and are able to changethe form of one representation to another representation. Students with moderate abilities do notimplement pictorial representation and symbolic representation accurately. Low ability students do notimplement pictorial representation in problem solving

Realistic Mathematics Education Principles for Designing a Learning Sequence on Number Patterns

The number pattern is one of mathematics topics taught for junior high school students that relate between arithmetic and algebra domain. This topic bridges arithmetical and algebraic thinking. Therefore, the learning for this topic should be designed meaningfully. This research aims to design a learning sequence on the number patterns using principles of Realistic Mathematics Education (RME). To do this, we used design research method, particularly the preliminary design phase, with the following three steps. First, literature study was conducted to collect student difficulties in the learning of number patterns, relevant studies, and the theory of RME. Second, we observed Indonesian mathematics textbooks addressing the number patterns to see a learning sequence for this topic. Finally, we designed a learning sequence for the number patterns using the RME principles, particularly the reality principle, level principle, and intertwinement principle. The result of this research includes the learning sequence for the number patterns according to the RME principles, which consists of three activities: relationship between patterns and numbers; exploration of numbers; and generalization of number patterns. We conclude that the three principles of RME are fruitful for designing a meaningful learning sequence for the topic of number patterns

Inquiry Co-Operation Model: An Effort to Enhance Students’ Mathematical Literacy Proficiency

The urgency and proficiency of students’ mathematical literacy in Bandung that have not been optimal are the basis of this study. The aim of this study is to explain the enhancement of students' mathematical literacy proficiency due to the implementation of the inquiry co-operation model (experimental class) and conventional learning (control class) in terms of basic mathematical proficiency. This study is a quasi-experimental study with a non-equivalent control group design, and the research subjects were seventy students of class VIII of Bandung that were selected through a purposive sampling technique. The research data was obtained through mathematical literacy tests of material in a polyhedron. The results of the data analysis showed that: (1) the enhancement in mathematical literacy proficiency of the experimental students class was better than the control studentsclass in terms of the basic mathematical proficiency (high and medium); (2) there is no significant difference in the increase of mathematical literacy proficiency in experimental students class in terms of the basic mathematical proficiency. It can be concluded that inquiry co-operation model espouses the enhancement of students' mathematical literacy proficiency

An investigation of students algebraic proficiency from a structure sense perspective

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for advanced study or professional work. This study, therefore, aims to investigate students algebraic proficiency in terms of structure sense. To reach this aim, we set up a qualitative case study with the following three steps. First, after conducting a literature study, we designed structure sense tasks according to structure sense characteristics for the topic of equations. Second, we administered an individual written test involving 28 grade XI students (16-17 year-old). Third, we analyzed students written work using a structure sense perspective. The results showed that about two-Thirds of the participated students lack of structure sense in which they tend to use more procedural strategies than structure sense strategies in solving equations. We conclude that the perspective of structure sense provides a fruitful lens for assessing students algebraic proficiency

USING GRAPHIC CALCULATOR IN TRIGONOMETRIC LEARNING: A DIDACTICAL DESIGN FOR TEACHER

This study explored the activitiesusing a graphing calculator of 10th-grade high school students on the trigonometry topic. A total of 65 students were divided into two classes, the first class consisted of 32 students, and the second class consisted of 33 students. The main objective of this study is to present classroom activities enriched with graphing calculators and observe responses about teaching with this approach. This study is research on developing learning designs within the Didactical Design Research (DDR) framework presented in an exploratory narrative. Data were collected by using two trigonometry worksheets and lesson observations. The worksheets were constructed based on the following focus areas: behaviour of graphs, constructing related-angle formula, and overall performance of the learner. The result of this research is a learning design that has been tested on 65 high school students. The research results on how to analyze the results of the implementation of structured learning designs provide information that educators can use, including the use of graphing calculators to help and make it easier for students to identify graphs more quickly and make students accustomed to using trigonometric function symbols. Another finding from structured instructional designs is that working in groups allows students to share experiences more effectively

AN INVESTIGATION OF STUDENTS’ ALGEBRAIC PROFICIENCY FROM A STRUCTURE SENSE PERSPECTIVE

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for advanced study or professional work. This study, therefore, aims to investigate students’ algebraic proficiency in terms of structure sense. To reach this aim, we set up a qualitative case study with the following three steps. First, after conducting a literature study, we designed structure sense tasks according to structure sense characteristics for the topic of equations. Second, we administered an individual written test involving 28 grade XI students (16-17 year-old). Third, we analyzed students’ written work using a structure sense perspective. The results showed that about two-thirds of the participated students lack of structure sense in which they tend to use more procedural strategies than structure sense strategies in solving equations. We conclude that the perspective of structure sense provides a fruitful lens for assessing students’ algebraic proficiency