Math misconceptions: Mistakes, misunderstanding, and confusion

Gulf journal of mathematics, 2024

This paper is a report of a qualitative case study conducted in South Africa that sought to identify students' misconceptions and how those misconceptions hinder students' conceptual understanding of mathematical concepts, with a focus on algebraic expressions. The Structure of the Observed Learning Outcomes (SOLO) theory was adopted as the theoretical framework. The media for data collection were: classroom observations, activities, unstructured interviews and standardized tests. Participants were required to explain their solutions to the standardized test via unstructured interviews. This guided the researchers to identify students' misconceptions and how they hindered their conceptual understanding of mathematical concepts. Content analysis was carried out on participants' written and oral responses by applying the SOLO theory. From this study, the researchers established that conceptual misunderstandings are the main students' misconception in algebraic expressions. This misconception serves as barriers to students developing conceptual understanding as it does not invoke students' rational reasoning.

2004

Middle school is a significant period in students' mathematical development, a period in which they crystallize their understanding of mathematical concepts and procedures and make the unconscious decision as to whether they will be successful in math. The project is intended to be an instructional resource providing teachers of middle school mathematics with information about common mathematical misconceptions held by students. The data for this research is taken from actual student work on the applied skills sections of the 2002 6 th and 8 th grade ISTEP+ Mathematics Assessments. The misconceptions are categorized according to specific standards as defined by NCTM, and corresponding Indiana Academic Standards are identified. lowe a great thanks also to Donna Biggs and Marilyn De Weese for your willingness to allow me to use the test data and your copy machine and also for making room for me to come in to the school frequently to work on my research.

Networks: An Online Journal for Teacher Research, 2013

2004

Middle school is a significant period in students' mathematical development, a period in which they crystallize their understanding of mathematical concepts and procedures and make the unconscious decision as to whether they will be successful in math. The project is intended to be an instructional resource providing teachers of middle school mathematics with information about common mathematical misconceptions held by students. The data for this research is taken from actual student work on the applied skills sections of the 2002 6 th and 8 th grade ISTEP+ Mathematics Assessments. The misconceptions are categorized according to specific standards as defined by NCTM, and corresponding Indiana Academic Standards are identified. lowe a great thanks also to Donna Biggs and Marilyn De Weese for your willingness to allow me to use the test data and your copy machine and also for making room for me to come in to the school frequently to work on my research.

Proceedings: First International Conference on Teaching & Learning, 2015

Students' errors and misconceptions are intelligent generalizations of their experiences and incomplete knowledge acquired. In order to help students unlearn the misconceptions and relearn the correct conceptions, it is important that teachers are aware of these errors and misconceptions, and their formation. The purpose of this paper is to bring awareness of some of the errors students make and the misconceptions they have with regard to mathematical concepts, and suggest how the formation of these errors and misconceptions can be prevented and remedied. This paper reports the findings based on analysis of 2,411 examination papers of students enrolled in pre-University mathematics courses between January 2012 and April 2015. The literature discussed in this paper makes a case for K-12 school teachers to have an in-depth and more flexible understanding of the mathematics they teach, so they can recognize how the structure of mathematical concepts should be presented while teaching mathematics.

Mathematics Education Trends and Research, 2014

Students' errors are causally determined, and very often systematic. Systematic errors are usually a consequence of student misconceptions. These can include failure to make connections with what they already know. There are beliefs held by students that inhibit learning from errors, such as they cannot learn from the mistakes and that mathematics consists of disconnected rules and procedures. Student errors are unique and they reflect their understanding of a concept, problem or a procedure. This study investigated how much mathematics have been understood and remembered by Year 11 repeating students, how their confidence level affects their responses to test items, and the causes for errors and misconceptions. A total of 74 Year 11 repeating students participated in this study and nine Year 11 mathematics teachers were surveyed. The sets of data were collected from the student test performance, student confidence level scale, and student and teacher questionnaires. The quantitative analyses of the students' results suggested that their test performance was not notably affected by their confidence. However, students' misconceptions seemed to have a significant impact on their progress and achievement in the test. The findings also suggested that students' errors and misconceptions were not only varied but there exist different causes as well.

Journal of Education and Learning (EduLearn), 2023

Early mathematicians viewed mathematics as a beautiful and ethereal art form. However, the pupils in school appear to have no idea of this beauty. Misconceptions about mathematics among students, parents, and instructors are thought to be one of the root causes of the problem. Mathematical misconceptions and myths among instructors, parents, and students were examined in this study. These findings were obtained using a descriptive qualitative method of investigation. Research participants included elementary school pupils and their parents from East Java, Indonesia as well as 10 instructors, 10 students, and 10 parents. Random selection was used to pick the respondents. The results of this study showed that teachers, parents, and students have a wide range of misconceptions about mathematics. Among the misconceptions that occur among students, teachers and parents are: i) The conception of mathematics; ii) The aim of learning mathematics is only to train students to count and memorize formulas; iii) Mathematical ability is a genetic talent and only people who have talent will be proficient in mathematics; and iv) Mathematics is a non-applicable. The consequences of widespread misconceptions about mathematics among teachers, parents, and students are detrimental to the learning process and hinder the development of strong mathematical skills.

The Mathematics Educator, 2013

In an age when reform is based on standards and instruction is based on research, this article gives practical advice for how mathematics teachers can analyze errors in student problems to create interventions that aid not only the individual’s development, but the entire class’s as well. By learning how to correct mathematics students’ misconceptions, rather than their mistakes, teachers have the potential to both target more students and increase those students’ conceptual understanding of the topic at hand. From the post-test scores on the Common / Habitual Algebra Student Misconceptions – Function Families (CHASM) , a tool used to assess teachers’ function family content knowledge and pedagogical content knowledge that was given after a three-day, overnight professional development workshop, , teachers averaged a 43% improvement in their ability to identify the common misconceptions present in students’ scenario test example problems and in creating suitable interventions for th...

This study investigated secondary school students' errors and misconceptions in algebra with a view to expose the nature and origin of those errors and to make suggestions for classroom teaching. The study used a mixed method research design. An algebra test which was pilot-tested for its validity and reliability was given to a sample of grade 11 students in an urban secondary school in Ontario. The test contained questions from four main areas of algebra: variables, algebraic expressions, equations, and word problems. A rubric containing the observed errors was prepared for each conceptual area. Two weeks after the test, six students were interviewed to identify their misconceptions and their reasoning. In the interview process, students were asked to explain their thinking while they were doing the same problems again.