Procedural Fluency from the View of Students of Mathematical Disposition Level through Google Classroom Assisted Learning

This study aims to describe procedural fluency in solving problems for students of the Mathematics Education Department at the STKIP Pamane Talino who obtain high and low mathematical dispositions through learning assisted by Google Classroom. This research is a qualitative research. The research subjects were two students in the third semester. Subjects were selected by purposive sampling. The research data was obtained by tests and interviews, and the validity of the data was obtained by using the triangulation method. The techniques of data analysis were trough: 1) classifying data into three indicators of the smoothness of the procedure; namely: a) implementing procedures appropriately, b) selecting and utilizing procedures, c) modifying procedures, then reducing data that are not included in the 3 indicators; 2) presenting data in a narrative; 3) concluding the procedural fluency obtained from the indicators of procedural fluency in problem-solving steps. The results of the high mathematical disposition analysis showed that students had excellent procedural skills because they could apply procedures appropriately. They were able to select and utilize procedures accurately, and were able to apply procedures properly and flexibly. In the other side, the students with low mathematical disposition, they had poor procedural skills because even though they were able to apply the procedure, choose, and use the procedure appropriately, they still could not comply with the procedure appropriately and accurately for they answered all the questions incorrectly.

Brain-based learning model to explore students’ procedural fluency ability in learning quadrilateral 2D shapes

This study aims to determine the completion of student learning in procedural fluency through the Brain Based Learning model, along with their procedural fluency in flexibility, efficiency and accuracy in quadrilateral 2D shapes. It employed sequential explanatory research design. The research subjects were 7th graders (VII B) at SMP Negeri 2 Sokaraja, academic year 2019/2020. The data collection technique was procedural fluency test for students on quadrilateral 2D shapes; and the data analysis technique was the z-test. Results showed that students’ procedural fluency through BBL achieved learning mastery. In terms of flexibility, students were able to solve procedural fluency test questions in two ways. Students could perform each step of the method in terms of efficiency; and in terms of accuracy, it was shown that results were repeated consistently. These findings implied that procedural fluency through BBL along with students’ flexibility, efficiency, and accuracy belong to the fairly fluent category.

Building Preservice Teachers’ Diagnostic Competence: An Exploratory Study in the Domain of Fractions

In this study, we explored elementary preservice teachers’ (PSTs’) competence to make diagnostic inferences about students’ levels of understanding of fractions and their approaches to developing appropriate tiered assessment items. Although recent studies have investigated beginning teachers’ diagnostic competency, teachers’ ability to design and evaluate diagnostic assessment items has remained largely underexplored. Fifty-seven PSTs, who enrolled in a mathematics methods course at a midwestern university in the U.S., participated in developing and attempting to differentiate diagnostic assessment items considering individual students’ varied levels of understanding. An inductive content analysis approach was used in identifying general patterns of PSTs’ approaches and strategies in designing and revising tiered assessment items. Our findings revealed the following: (a) the PSTs were well versed in students’ cognitive difficulties; (b) when modifying the core questions to be more or less difficult, the PSTs predominantly used strategies related to procedural fluency of the questions; and (c) some strategies PSTs used to modify questions did not necessarily yield the intended level of difficulty. Further, we discussed the challenges and opportunities teacher education programs face in teaching PSTs how to effectively design tiered assessment items.

The Impact of Rhetorical Argumentation on Achieving the Mastery of Fluency and Accuracy in Communicative Competence: A Case Study of 2 nd Year Students at the University Des Frères Mentouri, Constantine

The present study is a comparison between the impact of rhetorical argumentation and narrating stories on students’ fluency and accuracy in communicative competence. We aimed at evaluating the usefulness and suitability of these tasks, and their efficiency when it comes to teaching fluency and accuracy by analysing the direct effects of the tasks on the indices of fluency and accuracy. The problematic issue in this research investigates the effects of the task rhetorical argumentation, and whether it is an important task that teachers should rely on it in teaching speaking in academic contexts. The sample is composed of 65 students which are divided in between 30 students in the control group and 35 students in experimental group. The data was collected by a test which was used to evaluate three main areas which are: classroom interaction, topic knowledge and language knowledge. The results of the experiment show that there are two types of fluency which are procedural and automatic. Rhetorical argumentation can be used to develop procedural fluency, and not automatic since the task is considered as difficult and students were not familiar with it.

Measuring Conceptual Understanding, Procedural Fluency and Integrating Procedural and Conceptual Knowledge in Mathematical Problem Solving

The main aim of this paper is to meassure students’ mathematical proficiency on conceptual understanding and procedural fluency, and their ability of integrating procedural and conceptual knowledge in problem solving. Based on the PCK taxonomy (Ho 2018), we design a questionnaire consisting of 12 questions with 22 tasks whose content is focus on linear functions and equations. The collected data is analysed by the statistical software IBM SPSS Statistics 22. Moreover, we use the structural equation modeling (SEM) to study the correlation between these two components of mathematical proficiency and the ability of integrating procedural and conceptual knowledge in problem solving, implemented in IBM SPSS AMOS 24. The findings show that students’ mathematical proficiency on procedural fluency on linear functions and equations is higher than that of conceptual understanding, and their ability of integrating procedural and conceptual knowledge is very low. Moreover, these categories have a bi-directional relationship, in which the affection of mathematical proficiency on conceptual understanding to the ability of integrating procedural and conceptual knowledge in problem solving is stronger than on procedural fluency.

Students’ Algebraic Proficiency from the Perspective of Symbol Sense

Algebraic proficiency, including procedural fluency and conceptual understanding, is widely discussed worldwide. Algebraic proficiency refers largely to proficiency in symbolic representations which can be investigated through a framework of symbol sense. This research, therefore, aims to analyze students’ algebraic proficiency in terms of symbol sense. We set up a pilot study, involving 22 Indonesian mathematics education students (18-19 year old), in the form of two weeks teaching that combine a conventional approach and the use of a camera calculator in the learning and teaching of quadratic and related equations. The results showed that more than half number of students lacks of symbol sense in the sense that they tend to use procedural strategies rather than symbol sense strategies in solving equations. From the perspective of symbol sense, we concluded that the students acquired more on procedural fluency than on conceptual understanding.