This study examines the conceptual understanding of numbers and operations among 372 fifth-grade students, based on their responses to an online three-tier test designed to assess their number sense, declarative knowledge, explanatory knowledge, and confidence. The results showed that most students had low performance and low number sense, with…

Background/purpose: Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been conducted examining preschoolers' previous knowledge and misconceptions about…

The aim of this research is to determine the misconceptions among 6th, 7th and 8th grade students about the order of operations in line with arithmetic expressions and posing and solving problems related to arithmetic expressions. The research has a mixed-method research design with concurrent-triangulation design. The study group for the research…

Understanding the decimal system is challenging, requiring coordination of place-value concepts with features of whole-number and fraction knowledge (Moloney and Stacey 1997). Moreover, the learner must discern if and how previously learned concepts and procedures apply. The process is complex, and misconceptions will naturally arise. In a…

Many of us embrace the order and beauty in mathematics. The order of operations is an iconic mathematics topic that seems untouchable by time, reform, or mathematical discoveries. Yet, think for a moment about a commonly heard statement in teaching the order of operations: "You work from left to right." At another point in the…

Currently Australian pre-service teachers' levels of personal numeracy are under a great deal of scrutiny. There are calls for universities to raise entry standards into teaching degrees and counter-calls that the output of universities should be gauged rather than inputs. In 2015, doubts about the ability of graduate teachers to convey the…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

In this article, John West explores student misconceptions relating to division. A range of activities that promote the understanding of divisibility rules are provided.

How can a simple dot--the decimal point--be the source of such frustration for students and teachers? As the author worked through her own frustrations, she found that her students seemed to fall into groups in terms of misconceptions that they revealed when talking about and working with decimals. When asking students to illustrate their thinking…

Mathematics educators have had a long standing interest in students' understanding of decimal numbers. Most studies of students' understanding of decimals have been conducted within Western cultural settings. Similar research in other countries is important for a number of reasons, perhaps most importantly because it can provide insights that may…

This study sought to review literature pertinent to difficulties encountered by students in the learning and usage of mathematical terminology. The need to carry out this study arose from the concern by the Kenya National Examinations Council, and the general public, over the poor annual results in mathematics. Therefore, the objective of this…

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…

Through historical and contemporary research, educators have identified widespread misconceptions and difficulties faced by students in learning algebra. Many of these universal issues stem from content addressed long before students take their first algebra course. Yet elementary and middle school teachers may not understand how the subtleties of…

Going beyond measuring accuracy of teachers' judgments of students? achievements, this paper focuses on how prospective elementary teachers proceed in one-on-one diagnostic mathematics interviews. As part of the project diagnose:pro, prospective elementary teachers (PTs) conduct diagnostic interviews with children in grade one and reflect on…

This paper explores misconceptions of the number line which are revealed when pre-service primary teachers locate negative decimals on a number line. Written test responses from 94 pre-service primary teachers provide an initial data source which is supplemented by group responses to worksheets completed during a lesson and individual interviews.…