High school teachers often encounter incorrect solutions from students, especially when teaching combinatorics. This study investigates the ability of prospective mathematics teachers to assess the correctness of solutions to combinatorial problems and to falsify incorrect ones. 39 second-year prospective teachers participated in the experiment,…

A newspaper article about the availability of guns in Chicago, presented at a mathematics education conference in that city in 1998, is linked to a tragic shooting near that city in 2022. The article was used in Australia for many years in research with teachers and students to assess statistical literacy in relation to sampling, until ethics…

Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we…

This study was designed to examine the use of mistakes to promote students' performance in undergraduate Algebra classes by developing a growth mindset. Participants were seventy-four students from three Algebra classes and received one of the three interventions along with regular instruction: (a) growth mindset feedback on mistakes…

Problem-solving is the essence of mathematics and is the main goal in learning mathematics. Many students did not have good problem-solving skills based on the field observations. The problems grew up because the students were not used to solving the problems and the problem-solving stages. They did not include issues with high complexity, such as…

Students' contributions that are not yet mathematically complete, precise, or correct are crucial for learning through classroom discussions. We aim to support teacher candidates (TCs) to see students' ideas as evidence of sensemaking and to respond in ways that keep student thinking central to the discussion. Although approximations of practice…

Errors in mathematics are common hurdles for teachers and students; therefore, it is important to learn what errors students make and how students treat them. This study initially identified the types of errors students made while working with algebraic expressions and documented and analyzed the process of students completing an error analysis…

Despite repeated discussions and practice, algebra students continue to make variable errors, in many ways, year after year. This same problem appeared thirty years ago in a list of common errors that math teachers today would immediately recognize, many involving exponents and distribution (Marquis 1988). Similar complaints even appeared in the…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

Learning Disabilities in Mathematics (LDM) or dyscalculia are a frequent and disruptive problem within schools. Nevertheless, this problem has received little attention from researchers and practitioners, if compared with the number of studies published on disabilities in reading. Therefore, teachers do not have enough guidance to help children…

Translation errors and conceptual misunderstandings made by students translating among graphical, tabular, and symbolic representations of linear functions were examined. The study situated student errors in the context of the "Translation-Verification Model" developed specifically for the purpose of explaining student behavior during the process…

The paper describes a study that examined the impact of two teaching approaches "focus on correctness" and "discuss errors" on secondary students' solutions to algebraic inequalities. Two groups of 10th graders were taught by two experienced teachers, Corry and Era, who followed their different didactical beliefs about the use of errors in…

This study compared errors made while solving equations using literals (letters) with errors made while solving the same equations using numerals. The subjects were 54 Navy students enrolled in a remedial mathematics course. Error data were analyzed by means of coding all errors into ten major categories, each containing subcategories. Students…

Discusses errors made by remedial intermediate algebra students in factoring polynomials in light of student definitions of factoring. Found certain beliefs about factoring to logically imply many of the errors made. Suggests that belief-based teaching can be successful in teaching factoring. (16 references) (Author/MKR)

This article describes pedagogic issues in setting objective tests in mechanics using Question Mark Perception, coupled with MathML mathematics mark-up and the Scalable Vector Graphics (SVG) syntax for producing diagrams. The content of the questions (for a range of question types such as multi-choice, numerical input and variants such as…