Beyond numbers: The effect of prior mathematical knowledge on university progress of engineering students

Academic procrastination can be described as the delayed completion of academic tasks. This behavior is pervasive among students from different grade levels and cultures. A structural equation model was run to analyze the relationships between prior knowledge and procrastination in mathematics mediated by self-regulated learning and self-efficacy in mathematics. The model was analyzed using a sample of 1,000 Mozambican students from the 10th and 12th grades. Results indicated that both self-regulated learning and self-efficacy in mathematics were positively explained by prior knowledge in mathematics. Moreover, self-efficacy in mathematics was found to be positively related to self-regulated learning, and both were negatively related to mathematics procrastination. Finally, self-regulated learning and self-efficacy in mathematics mediated the effect of prior mathematics knowledge on mathematics procrastination. The study discusses these findings as well as their consequences, possible educational implications, and suggestions for educational practice.

This study attempted to determine the influence of prior knowledge in mathematics of students on learner-interface interactions in a learning-by-teaching intelligent tutoring system. One hundred thirty-nine high school students answered a pretest (i.e., the prior knowledge in mathematics) and a posttest. In between the pretest and posttest, they used the SimStudent, an intelligent tutoring system that follows a teaching-by-learning paradigm. The intervention period lasted for three consecutive days with 1 hour session each. SimStudent captured learner-interface interactions, such as time spent tutoring, number of quizzes conducted, and number of hints requested. It was disclosed that prior knowledge in term identification was the only skill that had a consistent, positive, and significant influence on learner-interface interaction with a SimStudent. Thus, the null hypothesis stating that prior knowledge in mathematics does not significantly influence interaction of students with a simulated student was partially rejected. It was concluded that the students may demonstrate or omit a skill, depending on their prior knowledge on identifying the terms of equations and the next step in solving equations. Recommendations and directions for future studies were presented.

The role of prior mathematical knowledge and interest in mathematics as internal factors that can influence the mathematical concept understanding ability in learning mathematics in schools is important to consider. The purpose of this study was to determine the effect of prior mathematical knowledge and interest in mathematics to mathematical concept understanding ability. This study uses a quantitative research approach with data analysis techniques using multiple linear regression analysis. The participants in this study totaled 91 students who were all students of class X MA As-syafiiyah 02 Kota Bekasi for academic year 2022/2023. The results of this study were obtained: 1) Students' prior mathematical knowledge had a significant effect on students' mathematical concept understanding partially 2) Students' interest in learning mathematics had a significant effect on student’s mathematical concept understanding partially 3) prior mathematical knowledge and interest in learning mathematics simultaneously had a significant influence to the mathematical concept understanding ability. This can be interpreted that the acquisition of students' mathematical concept understanding ability can be increased by considering the factors of prior mathematical knowledge and students' interest in learning mathematics.

This study examined how working memory (WM) and mathematics performance are related among students entering mathematics-intensive undergraduate STEM programs (N = 317). Among students of mechanical engineering and math-physics, we addressed two questions: (1) Do verbal and visuospatial WM differ in their relation with three measures of mathematics performance: numerical reasoning ability, prior knowledge in mathematics, and achievements in mathematics-intensive courses? (2) To what extent are the effects of WM on achievements in mathematics-intensive courses mediated by numerical reasoning ability and prior knowledge in mathematics? A latent correlational analysis revealed that verbal WM was at least as strongly associated with the three mathematics measures as visuospatial WM. A latent mediation model revealed that numerical reasoning fully mediated the effects of WM on achievements in math-intensive courses, both directly and in a doubly mediated effect via prior knowledge in mathematics. We conclude that WM across modalities contributes significantly to mathematics performance of mathematically competent students. The effect of verbal WM emerges as being more pronounced than has been assumed in prior literature.

This research was motivated by the importance of Computational Thinking (CT) ability for students to get a better thinking and problem solving abilities. The purpose of the study describes the students' CT ability in terms of their Prior Mathematical Knowledge (PMK). The subjects of this study were 6 junior high school students consisting of 2 students who had a high prior mathematical knowledge, 2 students who had a medium prior mathematical knowledge, and 2 students who had a low prior mathematical knowledge. The selection of subjects was not randomly selected. The method of research used was descriptive qualitative, where the data presented were deepened by interviews. Furthermore, the instruments used were test and non-test. In this case, the CT test was used to determine students' CT ability in terms of their prior mathematical knowledge, while the non-test in the form of interviews was used to find out the reasons for their test answers. The results of this study indicate that students who had a high prior mathematical knowledge were able to meet the CT mathematical indicators well. Furthermore, students who had a medium prior mathematical knowledge were able to meet several mathematical CT indicators, while students who had a low prior mathematical knowledge cannot fulfill mathematical CT indicators well.

Approaches to learning have been identified as crucial factors that influence students’ mathematics performance. However, there have been mixed findings on which of the different approaches improve performance in undergraduate mathematics. Thus, this study aimed to unravel the specific effects of prior mathematics knowledge and approaches to learning on performance in mathematics among first-year engineering students. The design is cross-sectional, and the data are analysed with some structural equation modelling techniques. The findings show a positive effect of prior mathematics knowledge on performance. The effect of surface approaches to learning on performance is significant, negative, and surface approaches to learning mediate the effect of prior mathematics knowledge on performance. There are no substantial relations between prior mathematics knowledge, deep approaches to learning, and performance. Students who adopt surface approaches performed poorly but we found no evidence to claim that students who adopt deep approaches perform better in the course. By implication, our findings underscore the importance of discouraging engineering students from capitalizing on surface approaches to learning mathematics.

Planning is an instrument for effective teaching and learning of mathematics, which can address the dropping enrolments of year 12 students studying advanced mathematics. This study investigated teachers’ perceptions of how a planning framework on content sequencing from junior mathematical knowledge (years seven to 10) to senior mathematical knowledge (years 11 to 12) informs teaching and learning of mathematics in Queensland, Australia. This mixed methods study collected data through a survey and semi structured interviews with 16 high school mathematics teachers. The data reveals that the elements of the framework can enhance the process of content sequencing, promote an environment that enhances development of new knowledge from prior knowledge, and articulate the hierarchical nature of mathematics. The study found that the framework can enhance collaborative planning among teachers within and across year levels. The study argues that using the planning framework on content sequencing can be a significant tool that can play an important role in guiding teachers to plan and teach new mathematical knowledge building from prior mathematical knowledge.

The importance of students’ prior knowledge to their current learning outcomes cannot be overemphasised. Students with adequate prior knowledge are better prepared for the current learning materials than those without the knowledge. However, assessment of engineering students' prior mathematics knowledge has been beset with a lack of uniformity in measuring instruments and inadequate validity studies. This study attempts to provide evidence of validity and reliability of a Norwegian national test of prior mathematics knowledge using an explanatory sequential mixed-methods approach. This approach involves use of an item response theory model followed by cognitive interviews of some students among 201 first-year engineering students that constitute the sample of the study. The findings confirm an acceptable construct validity for the test with reliable items and a high-reliability coefficient of .92 on the whole test. Mixed results are found on discrimination and difficulty indices of questions on the test with some questions having unacceptable discriminations and require improvement, some are easy, and some appear too tricky questions for students. Results from the cognitive interviews reveal the likely reasons for students' difficulty on some questions to be lack of proper understanding of the questions, text misreading, improper grasping of word-problem tasks, and unavailability of calculators. The findings underscore the significance of validity and reliability checks of test instruments and their effect on scoring and computing aggregate scores. The methodological approaches to validity and reliability checks in the present study can be applied to other national contexts.

This study investigates the challenges faced by mathematics teachers during the critical transition from primary to upper-primary education in India, focusing on students’ prior knowledge, teaching strategies, and learning preferences. Employing a descriptive survey design, data were collected from 20 in-service TGT mathematics teachers across ten schools in Delhi/NCR using a structured questionnaire. The findings of the study reveal that teachers encounter moderate to high levels of difficulty in leveraging students’ prior mathematical knowledge, particularly in assessing individual understanding due to diverse learning backgrounds. A major challenge lies in facilitating students' shift from concrete to abstract thinking, compounded by time constraints and curriculum demands. Teaching strategies such as lecture-based methods, constructivist approaches, and engaging activities are used but often with limited success due to resource limitations and classroom management issues. Teachers also report moderate difficulty in accommodating varied learning preferences and designing engaging, differentiated lessons. Notably, connecting mathematical concepts to real-life situations was perceived as less challenging, offering a potential strength for instructional improvement. The study highlights considerable variability in teacher experiences, suggesting that context significantly influences the challenges encountered. The study suggests that teachers should receive specific training on diagnostic assessment, abstraction scaffolding, differentiation, and new teaching methods like flipped and blended learning. The study also advocates for curriculum refinement, time management, improved resource access, and collaborative support systems. Addressing these multifaceted challenges is crucial to strengthening foundational mathematics learning and sustaining student engagement during this pivotal educational transition. This research contributes to filling a significant gap in Indian mathematics education literature.

This study investigated the physical features, quality of printed modules, and prior knowledge in mathematics among public junior high school students in rural areas during the COVID-19 pandemic. The research was conducted within the Division of Butuan City, Caraga Region, Philippines specifically focusing on South Butuan District II. A descriptive-comparative research design was employed, and a survey questionnaire was administered to 607 Junior High School students selected through purposive sampling. Statistical tools, including the average mean, Kruskal-Wallis test, and Mann-Whitney U test, were employed for data analysis and interpretation. The findings indicated that the physical features, quality of printed modules, and prior knowledge in mathematics were assessed as high, suggesting that students, regardless of school location, received consistent features and module quality. Moreover, significant differences were observed among variables based on the type of school, while no significant differences were found regarding sex and distance from the school concerning the dependent variables.

The problem of adverse effects of prior knowledge in mathematics learning has been amply documented and theorized by mathematics educators as well as cognitive/developmental psychologists. This problem emerges when students’ prior knowledge about a mathematical notion comes in contrast with new information coming from instruction, giving rise to systematic errors. Conceptual change perspectives on mathematics learning suggest that in such cases reorganization of students’ prior knowledge is necessary. Analogical reasoning, in particular cross-domain mapping, is considered an important mechanism for conceptual restructuring. However, the use of analogies in instruction is often found ineffective, mainly because the structural similarity between two domains is obscure for students. To deal with this problem, John Clement and his colleagues developed the bridging strategy that uses multiple analogies to bring students to pay attention to the structural similarity that often goes unnoticed. This paper focuses on the cross-domain mapping between number and the (geometrical) line that has been instrumental in the development of the number concept. I summarize findings of a series of studies that investigated students’ understandings of density in arithmetical and geometrical contexts from a conceptual change perspective; and I discuss how this research-based evidence was used to design an intervention study that used the analogy “numbers are points on the number line”, and a bridging analogy (“the number line is like an imaginary rubber band that never breaks, no matter how much it is stressed”) with the aim of bringing the notion of density within the grasp of secondary students.

This study investigated the effects of 1) proximal grouping of numbers, 2) problem-solving goals to make 100, and 3) prior knowledge on students’ initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state. We recorded students’ solution strategies and focused on the productivity of their first steps—whether their initial action led them closer to the goal. We analyzed log data within the game from 227 middle-school students solving four addition problems and four multiplication problems consisting of a total of 1,816 problem-level data points. Logistic regression modeling showed that students were more likely to use productive initial solution strategies to solve addition and multiplication problems when 1) proximity supported number grouping, 2) 100 was the problem-solving goal, and 3) students had higher prior knowledge in mathematics. Furthermore, when problem-solving goals were non-100s, students with lower prior knowledge were less likely to use productive initial solution strategies than students with higher prior knowledge. The findings of the study demonstrated that perceptual and number features influenced students’ initial solution strategies, and the effect of number features on initial solution strategies varied by students’ prior knowledge. Results yield important implications for designing instructional activities that support mathematics learning and problem-solving.

This study aimed to determine the effect of the NHT (Numbered Head Together) cooperative learning model on mathematical problem-solving abilities in terms of students' mathematical prior knowledge. The researchers employed quasi-experimental research and collected the mathematical problem-solving data using a description test. At the same time, the researchers investigated students’ mathematical prior knowledge using the mid-semester examination (UTS) scores. The hypothesis was tested using the two-way ANOVA with unequal cells. The results showed that the NHT learning model provided better problem-solving skills than the direct learning model. The category of students' prior knowledge also affected their mathematical problem-solving abilities. Therefore, teachers should pay attention to the prior knowledge possessed by students so that an appropriate learning model can be selected.

The transition from school to tertiary mathematics courses, which involve advanced mathematics, is a challenge for many students. Prior research has established the central role of prior mathematical knowledge for successfully dealing with challenges in learning processes during the study entrance phase. However, beyond knowing that more prior knowledge is beneficial for study success, especially passing courses, it is not yet known how a level of prior knowledge can be characterized that is sufficient for a successful start into a mathematics program. The aim of this contribution is to specify the appropriate level of mathematical knowledge that predicts study success in the first semester. Based on theoretical analysis of the demands in tertiary mathematics courses, we develop a mathematical test with 17 items in the domain of Analysis. Thereby, we focus on different levels of conceptual understanding by linking between different (in)formal representation formats and different levels of mathematical argumentations. The empirical results are based on a re-analysis of five studies in which in sum 1553 students of bachelor mathematics and mathematics teacher education programs deal with some of these items in each case. By identifying four levels of knowledge, we indicate that linking multiple representations is an important skill at the study entrance phase. With these levels of knowledge, it might be possible to identify students at risk of failing. So, the findings could contribute to more precise study advice and support before and while studying advanced mathematics at university.

This study aims to determine whether there are differences in mathematical communication skills between students who are taught by the Search, Solve, Create, and Share (SSCS) learning model and students who are taught using conventional learning; find out whether or not there is a difference in the mathematical communication skills of students who have high, medium, and low prior knowledge of mathematics; and see whether or not there is an interaction between students' prior knowledge in mathematics and the SSCS learning model on students' mathematical communication skills. This research is a quasi-experimental study with a posttest-only control group design. The population in this study were all seventh grade students of SMP Negeri 3 Tambang for the 2019/2020 academic year. The sample in this study was class VII.1 as the experimental class and class VII.3 as the control class which was selected by simple random sampling. The data was collected by using a test technique in the form of a mathematical communication ability test instrument and PAM test questions. Analysis of the data used for hypotheses 1, 2 and 3 using a two-way ANOVA test. The results of data analysis show that there are differences in mathematical communication skills between students who follow the SSCS learning model and students who follow conventional learning. there are differences in mathematical communication skills between students who have high, medium and low PAM, and there is no interaction of PAM factors on mathematical communication skills. students at SMP Negeri 3 Tambang.