This paper reports on students' conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as well as erroneous "mis-out examples" that mistakenly regard examples as non-examples and "mis-in examples" that mistakenly grant non-examples the status of examples. We used Tall and…

This paper reports on a two-part investigation into how students think about and use summation (sigma) notation. During an instructional design experiment, two participating students struggled with this notation, but also reasoned about it in creative ways. This motivated a follow-up study in which we administered a free-response three-item survey…

Students' difficulties in differentiating the direct proportion and inverse proportion problems cause interference. Proactive interference is the error that occurs when old information (concept of direct proportion) interferes with new information (concept of inverse proportion). In solving the problem of inverse proportion, students often use the…

The understanding mathematical concept is an error that often occurs in classroom learning among students when solving mathematical problems. The most difficult part for students is solving problems, because it requires numeracy skills, high concept mastery, as well as the ability to use good language, and so on so that students don't make any…

We conducted a descriptive study among first-year engineering students at the Anton de Kom University of Suriname. We analyzed students' errors regarding necessary prior knowledge in a calculus A exam. We found that the stage of the solution in which prior knowledge is required impacts the importance of prior knowledge. We also found that many…

The present study falls into the efforts to improve practices for addressing errors produced by learners in various situations involving the calculation of integrals. We attempt to clarify as precisely as possible the types of errors that secondary school students produce when using integrals in algebraic and graphical frames. Based on the…

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

The authors developed an instructional nudges as part of a larger research project. These instructional nudges are designed to be small but powerful changes to teachers' existing practices. Some instructional nudges focus on modifying tasks used in classrooms. In this article, the authors share Rate and Review. The goal of Rate and Review is to…

When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…

Get a deeper understanding of teaching functions, 9-12 with our concise and comprehensive Go-To Guide. Based on "Developing Essential Understanding of Functions 9-12" and "Putting Essential Understanding of Functions into Practice 9-12," this summary distills the key concepts and ideas into a quick-reference guide that's…

The study aimed to establish an assessment model for mathematics teachers' knowledge of students' misconceptions in the "Space and Shape" domain, develop the testing tool, investigate and analyse the overall and differences in performance, and propose suggestions for improvement. The assessment model included content knowledge and…

Many countries do not include the normal distribution concept in their middle school mathematics curriculum, but on the grounds that middle school mathematics teachers need to know more than just mathematics, researchers argue that preservice teachers (PTs) ought to have knowledge and skills in this area. This study was aimed to investigate PTs'…

Previous research examining comparison relations in word problems primarily focused on students' achievements in word problems with one operation. In this paper, we extend previous research to examine the achievement of students of different ages on word problems that integrate compare and combine word problems, hereafter referred to as…

This study offers a comprehensive investigation of 14-15-year-old students' comprehension of non-Euclidean geometries, with a specific focus on the assessment of their understanding through a 15-itemed test. The primary objective of this research is to assess the current state of students' knowledge and proficiency in non-Euclidean geometries and…

Teaching at the Right Level (TaRL) is an emerging and widely implemented remedial educational approach that is currently being piloted in many countries. Morocco has been experimenting with this approach since the 2022-2023 school year. This study aims to assess the effectiveness of using the TARL approach as a remedial model in addressing…