This qualitative case study aimed to investigate prospective middle school mathematics teachers' instructional responses based on the students' correct and incorrect functional thinking within the context of pattern generalization. The data were collected from thirty-two prospective teachers through a written task and semi-structured interviews…

To improve students' mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers' analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers'…

This article describes a carefully structured exploration of formative assessment, conducted in the form of a classroom research experiment. The authors are an instructor and a student in a graduate course that assigned teachers to research formative assessment strategies, implement one or more strategies for several weeks, collect data from…

This article endeavours to define how the application of incorrect or wrong solutions to mathematical equations or problems can be used to help stimulate students to perform a critical analysis of the mathematics being applied or the context of the equations used. The context of the application is discussed together with the specific learning…

Middle-grades teachers and students can have different perspectives on the value of discussing students' mathematical mistakes, despite various classroom evidence that such discussions can help foster strong conceptual understanding. Some teachers consider student mistakes to be an opportunity to correct errors in individual student thinking.…

This study extends past research on students' understanding of slope by analyzing college students' mistakes on routine tasks involving slope. We conduct quantitative and qualitative analysis of students' mistakes to extract information regarding slope conceptualizations described in prior research. Results delineate procedural proficiencies and…

To improve mathematics achievement, students' errors should be treated as a source to stimulate their understanding of the conceptual and procedural basis of their errors. The study investigated 20 Chinese and 20 U.S. high school teachers' interpretations and responses to a student's errors in solving a quadratic equation. The teachers' responses…

Although the use of simulation to teach the sampling distribution of the mean is meant to provide students with sound conceptual understanding, it may lead them astray. We discuss a misunderstanding that can be introduced or reinforced when students who intuitively understand that "bigger samples are better" conduct a simulation to…

The goal of this study was to determine the mathematics achievement level in basic numeracy and algebra concepts of students in a two-year program in a technical vocational school of higher education and determine the errors that they make in these topics. The researcher developed a diagnostic mathematics achievement test related to numeracy and…

Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students". The methods and examples included in…

Various studies suggest that French students (grades 7 to 10) may solve geometric problems within a paradigmatic framework that differs from that assumed by teachers, a situation prone to misunderstandings. In this paper, we study the extent to which secondary school teachers recognise the conflicting paradigms and how they handle the geometric…

The history of mathematics is full of rich examples that can help students to see the place of the discipline within our cultural heritage. Valuable as this can be, it also has the unfortunate side-effect of making students think that all the math has already been done and they do not get a sense that the subject is dynamic and growing.…

Presents an activity applicable at the beginning of the year to review necessary algebra concepts that are often misunderstood by students. Presents a true/false worksheet made up of examples illustrating common algebra and trigonometry errors made by students. (MDH)