Prior Mathematical Knowledge Research Articles

Multistream-Based Marked Point Process With Decomposed Cumulative Hazard Functions.

When applying a point process to a real-world problem, an appropriate intensity function model should be designed based on physical and mathematical prior knowledge. Recently, a fully trainable deep learning-based approach has been developed for temporal point processes. In this approach, a cumulative hazard function (CHF) capable of systematic computation of adaptive intensity function is modeled in a data-driven manner. However, in this approach, although many applications of point processes generate various kinds of information such as location, magnitude, and depth, the mark information of events is not considered. To overcome this limitation, we propose a fully trainable marked point process method for modeling decomposed CHFs for time and mark prediction using multistream deep neural networks. We demonstrate the effectiveness of the proposed method through experiments with synthetic and real-world event data.

A Generalized Estimating Equations Approach to Investigate Predictors of Teacher Candidates’ Views of Coding

This paper reports the analysis of data from five different studies to identify predictors of preservice, early childhood teachers’ views of (a) the nature of coding, (b) integration of coding into preschool classrooms, and (c) relation of coding to fields other than computer science (CS). Significant changes in views of coding were predicted by time, prior robot programming experience, and perceptions of the value of coding. Notably, prior programming knowledge and positive perceptions of mathematics predicted decreases in views of coding from pre- to post-survey.

Examining preservice teachers’ noticing of equity-based teaching practices to empower students engaging in productive struggle

Our study examined ways preservice teachers (PSTs) make connections between teaching practices and use of student resources that support productive struggle and promote equity. Our research questions are: (1) How do PSTs notice and describe the equity-based mathematics teaching practice of leveraging student resources to support student struggles? and (2) In what ways do PSTs make connections to and interpret the role student resources play in the resolution of students’ mathematical struggles? The qualitative study examined 39 PSTs in a mathematics content course for PSTs. Data come from a video analysis assignment where PSTs described their mathematical interpretations of the student struggle(s) and teacher’s use of student resources to support the struggle resolution. Findings show that PSTs noticed teacher moves that leveraged student’s mathematical thinking and linguistic funds of knowledge and based the productive level of the struggle on actions built upon peers, linguistic knowledge and prior mathematical knowledge.

Assessment of domain-specific prior knowledge: A development and validation of mathematical problem-solving test

Science, technology, engineering, and mathematics (STEM) is a complex problem-solving that depends on the deep structures of domain-specific prior knowledge (DSPK) in mathematics. However, there is a lack of mathematics DSPK tests measuring several mathematics topics in every problem-solving phase in conceptual and procedural knowledge. This study aims to develop a mathematical problem-solving test as a mathematics DSPK test and investigate the content and construct validity. The product of test development is a 30-multiple-choice-item test in six mathematics topics. Every topic underlined all problem-solving phases in conceptual and procedural knowledge in a science or individual context. There were six experts performed the content validity sheets which analyzed using the content validity index (CVI) and intraclass correlation coefficient (ICC). The construct validity was examined using the Rasch model from 175 data of 7th grader students in Indonesia (Mage=12.66, SD=55). The result of content validity revealed overall items were valid (CVI≥83) and reliable (α=863; rxx=513). The construct of all items indicated fit (90≤weigheted MNSQ≤1.16) and were reliable (α=74) with various levels of difficulties and six low discrimination items. The recommendation for improvement is emphasized in language aspects. The absence of knowledge of facts could be an improvement for further study.

Enhancing topic-specific prior knowledge of students impacts their outcomes in mathematics

IntroductionThe aim of this study was to investigate how enhancing topic-specific prior mathematical knowledge of students before introducing new topics impacts their outcomes in mathematics achievements.MethodsA quasi-experimental design was applied to two groups: a control group [students who did not receive enhancement for their topic-specific prior mathematical knowledge (N = 37)] and an experimental group [students who received enhancement for their topic-specific prior mathematical knowledge (N = 36)].ResultsThe results revealed that there were no significant differences between the students’ average scores in ‘conceptual knowledge’ in the immediate post-test for groups; however, the difference was significant in the delayed post-test in favor of the experimental group. The results also showed that there were significant differences between the students’ average scores in ‘procedural knowledge’ in both the immediate and delayed post-tests in favor of the experimental group.DiscussionThe results showed the importance of this strategy in improving students’ outcomes.

Computer-based multimedia testing: Effects of static and animated representational pictures and text modality

Static representational pictures (RPs) have been focused in research on the multimedia effect in testing and might be especially important in arithmetical word problems, which require a multi-stage mental processing to segment the task. To further highlight the task segments visually, dynamic visualizations could help. However, conventional animations might not apply to this context and the role of dynamic visualizations with temporal segmentations (i.e., animated RPs) is unexplored. This classroom experiment with 456 students investigated multimedia and modality effects in 24 mathematical word problems. Our 3 × 2 mixed design included three multimedia conditions (static RPs, animated RPs, and text-only) and two modality conditions (written text vs spoken text). We investigated effects on response correctness, metacognitive ratings, item-solving satisfaction and time on task. Both static and animated RPs increased response correctness, item-solving satisfaction, and metacognitive ratings compared to text-only. Time on task was affected in distinctive ways in both RP conditions and also varied depending on text modality. Spoken text barely increased response correctness in animated RP items but not at all in static RP items. Moderator analyses revealed that the effects of static and animated RPs on response correctness were dependent on the text modality but varied across school types and the level of mathematical prior knowledge. For students at non-academic-track schools or with low prior knowledge, static and animated RPs improved response correctness compared to text-only across both modalities. For students at academic-track schools or with high prior knowledge, mainly combinations of static or animated RPs with spoken text were effective.

The relationship between individual characteristics and practice behaviour within an adaptive arithmetic learning program

AbstractBackgroundAlthough research on mathematics learning programs has taken off in recent years, little is known about how different person characteristics are related to practice behaviour with such programs. When implementing a mathematics learning program in the classroom, it might be important to know whether students with specific characteristics need more encouragement to make use of this learning opportunity.ObjectivesUsing a supply‐use model, we analysed the predictive power of students' cognitive characteristics (prior mathematics knowledge), personality traits (conscientiousness), motivational‐affective characteristics (mathematics self‐concept and mathematics anxiety), and family background characteristics (socioeconomic status and migration background) for practising with an adaptive arithmetic learning program.MethodsWe used longitudinal data from 203 fifth graders from seven non‐academic‐track schools in Germany. Practice behaviour, measured by completed tasks in the learning program, was recorded weekly for every student over a period of 22 weeks.Results and ConclusionsThe results of our multilevel analyses showed that mathematics anxious students practised less with the program. We did not find any relationship with the other characteristics.TakeawaysOur results suggest that mathematics anxious students need more encouragement when practising with a mathematics learning program; otherwise, they do not get the chance to benefit from the use.

Трудни теми в учебното съдържание по химия от гледна точка на учителите

Teachers’ knowledge of students’ difficulties is a major component of pedagogical content knowledge (PCK) and a key element for effective instruction. The current research aims to identify teachers’ PCK for: difficult topics in the chemistry curriculum; reasons for student difficulty; students’ interest towards difficult topics and the skills needed to be successful in chemistry. For this purpose a questionnaire survey was conducted among 20 chemistry teachers from different schools in Bulgaria. Participating teachers consider Chemical equilibrium, Chemical calculations and Organic chemistry as being most difficult. Metals, nonmetals and their compounds, Redox reactions and Atomic structure on the other hand are viewed as easier and more interesting. Understanding scientific concepts, principles and laws, self-studying and logical thinking are the skills students need to be successful in chemistry. Teachers believe student difficulties are due to: the abstract nature of chemistry; the fact that learning chemistry requires effort, regular study and prior mathematical knowledge; insufficient instructional time and lack of interest towards the subject.

The Role of Prior Mathematical Knowledge and Interest in Mathematics on Mathematical Concept Understanding Ability in Senior High School Students

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.

Team-Assisted Individualization Type of the Cooperative Learning Model for Improving Mathematical Problem Solving, Communication, and Self-Proficiency: Evidence from Operations Research Teaching

The purpose of this study is to analyze the increase in the mathematical problem-solving (MPS), mathematical communication (MC), and self-proficiency (SPr) abilities of students by applying the team-assisted individualization type (TAI) of the cooperative and conventional learning models for the experimental and control classes. This is a quasi-experimental study comprising a sample of 50 and 42 students studying for an undergraduate degree in statistics for the experimental and control classes, respectively. Students’ mathematical prior knowledge (MPK) is grouped into three levels, namely high, medium, and low. The instruments used are the MPS test, the MC test, the self-proficiency scale, and observation sheets. Statistical analysis instruments used are parametric and non-parametric statistics, such as prerequisite tests for normality and homogeneity of variance, mean difference tests in two or more groups, the post hoc test, and description and interaction tests. The results showed an increase in MPS, MC, and SPr in the experimental class, which is higher than in the control class. Furthermore, there is no interaction between the experimental and control classes despite a significant correlation between MPS, MC, and MPS. These findings are relevant to mathematics and statistics teaching because it has been proven to improve students’ MPS, MC, and SPr; hence, learning outputs can be achieved objectively, specifically for operations research teaching.

MATHEMATICAL SELF-ESTEEM ABILITY OF JUNIOR HIGH SCHOOL STUDENTS IN PROJECT-BASED LEARNING

The main objective of this research is to study the achievement of their mathematical self-esteem, as a result of Project-based Learning (PBL) and Conventional Learning (CL). This research is conducted mathematical self-esteem to be possessed by students, but in reality shows their self-esteem are still low. This research used quasi experimental methods. The population of this study is students of State Junior High Schools in Bandung City, West Java Province. The sample comprises the students of grade VIII. One class as an experimental group that received PBL learning and another class as a control group that received CL learning. The instruments used in this study are Prior Mathematical Knowledge (PMK) worksheet and mathematical self-esteem scale. The results indicate that: (1) the achievement of mathematical self-esteem of the students who received PBL learning is better than the students who received CL learning; (2) there is no interaction effect between learning model and PMK on the achievement of students' mathematical self-esteem.

The relation between working memory and mathematics performance among students in math-intensive STEM programs

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.

Psychometrics for physicians: everything a clinician needs to know about assessments in medical education.

Assessments in medical education, with consequent decisions about performance and competence, have both a profound and far-reaching impact on students and their future careers. Physicians who make decisions about students must be confident that these decisions are based on objective, valid and reliable evidence and are thus fair. An increasing use of psychometrics has aimed to minimise measurement bias as a major threat to fairness in testing. Currently, there is substantial literature on psychometric methods and their applications, ranging from basic to advanced, outlining how assessment providers can improve their exams to make them fairer and minimise the errors attached to assessments. Understanding the mathematical models of some of these methods may be difficult for some assessment providers, and in particular clinicians. This guide requires no prior knowledge of mathematics and describes some of the key methods used to improve and develop assessments; essential for those involved in interpreting assessment results. This article aligns each method to the Standards for educational and psychological testing framework, recognised as the gold standard for testing guidance since the 1960s. This helps the reader develop a deeper understanding of how assessors provide evidence for reliability and validity with consideration to test construction, evaluation, fairness, application, and consequences, and provides a platform to better understand the literature in regards other more complex psychometric concepts that are not specifically covered in this article.

Improving Learning Efficiency for Wireless Resource Allocation with Symmetric Prior

Improving learning efficiency is paramount for learning resource allocation with deep neural networks (DNNs) in wireless communications over highly dynamic environments. Incorporating domain knowledge into learning is a promising approach to dealing with this issue. It is also an emerging topic in the wireless community. In this article, we briefly summarize two approaches for using domain knowledge: introducing a mathematical model and prior knowledge to deep learning. Then, we consider a type of symmetric prior permutation equivariance, which widely exists in wireless tasks. To explain how such a generic prior is harnessed to improve learning efficiency, we resort to ranking, which jointly sorts the input and output of a DNN. We use power allocation among subcarriers, probabilistic content caching, and interference coordination to illustrate the improvement of learning efficiency by exploiting the property. From the case study, we find that the required training samples to achieve given system performance decreases with the number of subcarriers or contents, owing to an interesting phenomenon called “sample hardening.” Simulation results show that the training samples, the free parameters in DNNs, and the training time can be reduced dramatically by harnessing the prior knowledge. The samples required to train a DNN after ranking can be reduced by 15 ∼ 2,400 folds to achieve the same system performance as the counterpart without using prior.

Perceptual and number effects on students’ initial solution strategies in an interactive online mathematics game

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.

Emphasizing visual tools: using R to understand dynamic models of biology and epidemiology

ABSTRACT Epidemiological models have enhanced relevance because of the COVID-19 pandemic. In this note, we emphasize visual tools that can be part of a learning module geared to teaching the SIR epidemiological model, suitable for advanced undergraduates or beginning graduate students in disciplines where the level of prior mathematical knowledge of students may not be very strong. Visual tools – phase portrait, flow field and trajectory and line plots – available in the R software are presented in a step by step manner, moving from the exponential growth model to the logistic growth model and then to the SIR model. Code for numerical simulation of differential equations and estimation of parameters is presented for the SIR model. Suggestions for students to connect the learning from these examples with research papers on COVID-19 are provided.

Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

The preservice primary school mathematics teacher needs training that focuses on school mathematics and its didactics. Research has shown the importance of developing mathematical content knowledge as well as adequate didactic knowledge. Teacher education programs must address both to provide an effective teaching-learning process. The present research aims to assess the mathematical content knowledge of 194 prospective teachers about fraction word problems faced by students at the Primary Education stage, based on the Mathematics Teachers′ Specialized Knowledge (MTSK) model. By means of the preservice teachers’ written answers, we explored their knowledge and identified the associated error to fraction word problems (one-step and multistep) in which the fraction has a meaning as an operator. Preservice teachers showed some difficulties when working with this content, difficulties that were intensified when they solved multistep problems. The most common error founded in both types of problems is related to the meaning of fraction as operator. The results show a weak prior mathematical content knowledge and as a consequence, it is necessary to establish preventive actions in the training degrees since an insufficient mathematical content knowledge prevents them having a proper didactic knowledge.

Pengaruh Model Eliciting Activities (MEA’s) terhadap Higher Order Thinking Skills (HOTS) dan Self Esteem Siswa Sekolah Menengah Pertama

This research aims to know the effect of Model Eliciting Activities (MEAs) and Conventional Learning Models to Higher Order Thinking Skills (HOTS) in mathematics and students self-esteem.The research was conducted at SMPN 200 and SMPN 53 Jakarta in the academic year 2020/2021. Design of this research is a post-test only experiment and control group design. The method used in this research was a quasi experiment. The instruments consist of the Higher Order Thinking Skills test, prior knowledge of mathematics test, and a questionnaire of mathematics self-esteem. The instruments have been checked in terms of validity and reliability. Two-way Anova was used for data analysis. The results show that: (1) Higher Order Thinking Skills of students who are given MEA’s is higher than the students who are given conventional Learning Models. (2) There is an enhancement of Higher Order Thinking Skills of students effected by prior knowledge of mathematics and Mathematics Learning Models. (3) Higher Order Thinking Skills of students with high KAM who are given MEA is higher than the students who are given Conventional Learning Model. (4) There is no significant difference in terms of Higher Order Thinking Skills between students with low KAM given MEA treatment and students given Conventional Learning Model treatment. (5) Mathematics Self Esteem of students given MEA treatment is higher than those given Conventional Learning Model treatment.

Mathematical problem-solving ability: The effect of numbered head together (NHT) model and mathematical prior knowledge

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 EFFECT OF APPLICATION OF SEARCH, SOLVE, CREATE, AND SHARE (SSCS) LEARNING MODEL ON STUDENTS' MATHEMATICS COMMUNICATION ABILITY BASED ON PREVIOUS KNOWLEDGE IN MATHEMATICS IN JUNIOR HIGH SCHOOL

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.