The level of arithmetic knowledge of a high school student was explored when solving additive word problems considering the semantic structure and syntactic component. The methodology was qualitative and developed in four stages: the first is the selection of the participant, the second is the design of a questionnaire with twenty additive…

Math problem solving frequently involves choices among alternative strategies. Strategy choices, and effects of problem features on strategy choices, both vary among individuals. We propose that individual differences in strategy choices can be well characterized in terms of parametric variation in three types of influence: global bias, relevant…

This study explores student flexibility in mathematics by examining the relationship between accuracy and strategy use for solving arithmetic and algebra problems. Core to procedural flexibility is the ability to select and accurately execute the most appropriate strategy for a given problem. Yet the relationship between strategy selection and…

In this paper, we describe an experiment in using history to work on problem-solving and the relationship between arithmetic and algebra. The students involved attended the first year of the Italian upper secondary school (grade 9). The original sources we used are problems from Italian treatises on arithmetic and algebra that appeared in the…

The aim of the exploratory method research centered on the presence of mathematical tools in STEM through three main questions: Is mathematics an essential tool in the field of STEM? Can mathematics complete projects solely with mathematical and digital tools? Does understanding mathematical modeling affect STEM teaching? A better understanding of…

Students' previous knowledge at a superficial level is reviewed when they solve mathematical problems. This action is imperative to strengthen their knowledge and provide the right information needed to solve the problems. Furthermore, Pirie and Kieren's theory stated that the act of returning to a previous level of understanding is called folding…

Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

In this study, the author examined student attempts to translate a verbal problem into an algebraic statement relating two variables, after they had solved an arithmetic question from the same problem. A total of 645 students from New England (U.S.A.) answered the problem on a mathematics assessment administered at the beginning of the school…

The student's criterion for being diagnosed with MLD (Mathematics Learning Disabilities) can be classified as low arithmetic skills and poor working memory. The goal of this research is to understand students' process of thinking through the Polya stages when tackling arithmetic problems, as it has been expounded by Dr. Polya For students who have…

This study aims to look at tenth-grade a mental retardation student in solving the problem of a division operation. The method used is Single Subject Research (SSR) with learning outcomes as variables that are measured and describe student learning activities in solving problems using Math GASING. The data collection technique is done by video…

The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…

The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…

The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly…

This study assessed the relation between long-term memory retrieval and mathematics calculation and mathematics problem solving achievement among elementary, middle, and high school students in nationally representative sample of US students, when controlling for fluid and crystallized intelligence, short-term memory, and processing speed. As…

Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed…