Math Knowledge Research Articles

Correction to: Contextualizing Math-Related Strengths and Math Achievement: Positive Math Orientations, Social Supports and the Moderating Effects of Prior Math Knowledge

Correction to: Contextualizing Math-Related Strengths and Math Achievement: Positive Math Orientations, Social Supports and the Moderating Effects of Prior Math Knowledge

Math anxiety interferes with learning novel mathematics contents in early elementary school.

Whereas some evidence exists that math anxiety may interfere with math performance from the very beginning of primary school, no study to date has attempted to investigate whether math anxiety may also interfere with early math learning (i.e., the encoding of new math knowledge) and not only with recalling already mastered contents in test situations. Across 2 experiments carried out in 2 different countries (Study 1: N = 115, conducted in Italy; Study 2: N = 120, conducted in the United Kingdom), we addressed this question by presenting 6-year-old children with 2 math contents that had not been covered by their school curriculum before the study. Children were tested immediately before and immediately after the learning phase, and after a 1-week delay. Longitudinal models revealed that math anxiety was negatively related to initial level of knowledge in the case of 3 out of 4 math contents. More importantly, math anxiety was also negatively related to rate of learning in 2 out of 4 tasks (1 task in Study 1 and 1 in Study 2). These studies provide the first evidence that math anxiety may reduce the encoding of novel math contents in memory in very young children, potentially leading to cumulative gaps in math proficiency for children with math anxiety from the very beginning of their formal education. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

Elementary school teachers' math anxiety and students' math learning: A large-scale replication.

A solid foundation in math is important for children's long-term academic success. Many factors influence children's math learning-including the math content students are taught in school, the quality of their instruction, and the math attitudes of students' teachers. Using a large and diverse sample of first-grade students (n=551), we conducted a large-scale replication of a previous study (Proceedings of the National Academy of Sciences of the USA, 2010, 1860; n=117), which found that girls in classes with highly math anxious teachers learned less math during the school year, as compared to girls whose math teachers were less anxious about math. With a larger sample, we found a negative relation between teachers' math anxiety and students' math achievement for both girls and boys, even after accounting for teachers' math ability and children's beginning of year math knowledge, replicating and extending those previous results. Our findings strengthen the support for the hypothesis that teachers' math anxiety is one factor that undermines children's math learning and could push students off-track during their initial exposure to math in early elementary school.

Character Recognition By Implementing FPGA-Based Artificial Neural Network

A non-linear applied math knowledge modelling tool, Artificial Neural Networks (ANN) are predominantly used to model complicated interactions between inputs and outputs or to look for patterns within the data. Using VHDL coding, we developed a generic hardware-based ANN. This classifier has been trained to recognize letters on a 4x4 binary grid that a user fills out using 16 toggle switches. An LCD shows the most likely classification that the ANN proposed. The ANN was taught to recognize 20 English character patterns and 9 Arabic character patterns on a 4x4 grid to showcase the viability of the FPGA execution of ANN. The Altera DE2 development and education board use the generated design file to flash the Altera Cyclone II FPGA. A training supervisor is also included in the design, which is responsible for training the ANN to recognize a set of 29 standard characters drawn from the English and Arabic alphabets. Positive patterns were found, with the ANN successfully recognizing all training characters. Finally, this study demonstrates the adaptability and boundless possibility of hardware-based implementation of ANN and the infinite possibility of prototyping and building recent systems with VHDL coding on an FPGA platform.

Parent–child number application activities predict children’s math trajectories from preschool to primary school.

This study (N = 196) examined the extent to which the frequency of parent–child math activities in preschool was associated with children’s developmental trajectories of math skills from preschool to primary school. Parents reported the frequency of their involvement in a variety of math activities with their preschool children. Children were tested individually on their formal (i.e., math knowledge that involves verbal or written symbolism, such as rote counting and written computation) and informal (i.e., object-based numeration and operations, such as number line concepts and object-based calculation) math skills from preschool to first grade. The results showed that the frequency of parent–child formal math activities, including number skill and book activities, was not associated with children’s formal or informal math trajectories. In contrast, the frequency of informal math activities, including number game and application activities, was associated with formal math skill levels in preschool. More important, parental involvement in application activities in preschool significantly predicted the rate of growth in formal math skills through first grade. This predictive relation persisted after controlling for the other three types of math activities and other child- and family-level variables. The findings underscore the importance of early parent–child application activities in engendering possible long-term effects on children’s math skill development. (PsycInfo Database Record (c) 2020 APA, all rights reserved)

Nursing students’ perspectives on learning math for medication calculations in a Canadian nursing program in Qatar

This study describes nursing students' perspectives on learning math for medication calculations in a Canadian baccalaureate nursing program in Qatar. There is a dearth of guidance within the nursing literature to support teachers to develop pedagogical methods to help improve students' math competence. Moreover, the challenge of teaching math skills to student nurses in Qatar is particularly difficult because there is little standardization of curricula in secondary education. Data collected from focus groups was analyzed using interpretive description. Focus groups included, Group 1 those students who were beginning to learn math for medication calculations and had not completed the required math module and Group 2, students who had not yet completed the math module. Themes emerging from the data included from first year students, 1. Fear of math resulting in resistance to learning math for medication administration. 2. Student success is dependent on good instructors. 3. Student resentment towards perceived ‘complicated’ math in the nursing program. Themes from second year students included 1. Lack of nursing student's confidence with medication calculation within the clinical settings 2. Lack of self-directedness to uptake math knowledge 3. Incongruence amongst clinical instructors with applied math practice whilst in the clinical setting.

Math Self-efficacy and the Likelihood of Pursuing a STEM-Based Career: a Gender-Based Analysis

The attitudes teenagers have towards Math, as well as their knowledge of Science, Technology, Engineering and Math (STEM)–based careers will affect their likelihood of pursing these careers in the future. The purpose of this study was to examine the attitudes that youth (girls and boys) aged 12–14 hold towards Math, their knowledge of Math, and Science requirements for future careers as well as their likelihood of choosing a STEM-based career. This research also examined the responses of girls who attended a week-long intensive Science summer camp compared with those who did not attend this camp. To do this, students’ attitudes and knowledge were explored using a gender-based analysis (GBA) in four sample groups: (1) public school boys, (2) public school girls, (3) public school girls who do well in math, and (4) a specialized sample of girls who had attended a female-only Science summer camp. Our results show that more grade 7 girls in Nova Scotian public schools feel tense doing Math problems compared with similarly aged boys, yet the average self-rating of getting good marks, learning Math quickly, and looking forward to Math were similar for girls and boys. Furthermore, girls had a better knowledge of careers that required Math and/or Science than boys. In relation to the Science camp, significantly more girls attending the Science camp indicated that they would be very likely to pursue a STEM career in the future, compared with girls, with equally good Math grades, in the non-camps group. These findings show that enabling girls to interact with female STEM professionals and to attend an all-girls Science dedicated camp significantly impacts their interest in STEM professions and is a concrete way in to break down stereotypes in male-dominated fields.

Finding patterns in objects and numbers: Repeating patterning in pre-K predicts kindergarten mathematics knowledge

Both recent evidence and research-based early mathematics curricula indicate that repeating patterns—predictable sequences that follow a rule—are a topic of major importance for mathematics development. The purpose of the current study was to help build a theory for how early repeating patterning knowledge contributes to early math development, focusing on development in children aged 4–6 years. The current study examined the relation between 65 preschool children’s repeating patterning knowledge (via a fast, teacher-friendly measure) and their end-of-kindergarten broad math and numeracy knowledge, controlling for verbal and visual-spatial working memory (WM) skills as well as end-of-pre-K (pre-kindergarten) broad math knowledge. Relations were also examined between repeating patterning and specific aspects of numeracy knowledge—knowledge of the count sequence to 100 and the successor principle. Children’s repeating patterning knowledge was significantly predictive of their broad math and general numeracy knowledge, as well as one specific aspect of their numeracy knowledge (counting to 100), even after controlling for verbal and visual-spatial WM skills. Further, repeating patterning knowledge remained a unique predictor of general numeracy knowledge and counting to 100 after controlling for end-of-pre-K broad math knowledge. The relation between repeating patterning and mathematics may be explained by the central role that identifying predictable sequences based on underlying rules plays in both. Theories of math development and early math instruction standards should thus give even greater attention to the role of children’s repeating patterning knowledge.

Early Emotion Knowledge and Later Academic Achievement Among Children of Color in Historically Disinvested Neighborhoods.

This study examined longitudinal relations between emotion knowledge (EK) in pre-kindergarten (pre-K; Mage =4.8years) and math and reading achievement 1 and 3years later in a sample of 1,050 primarily Black children (over half from immigrant families) living in historically disinvested neighborhoods. Participants were part of a follow-up study of a cluster randomized controlled trial. Controlling for pre-academic skills, other social-emotional skills, sociodemographic characteristics, and school intervention status, higher EK at the end of pre-K predicted higher math and reading achievement test scores in kindergarten and second grade. Moderation analyses suggest that relations were attenuated among children from immigrant families. Findings suggest the importance of enriching pre-K programs for children of color with EK-promotive interventions and strategies.

The Role of Gender on the Associations among Children’s Attitudes, Mathematics Knowledge, Digital Game Use, Perceptions of Affordances, and Achievement

This study explored associations among children’s prior attitudes, prior mathematics knowledge, and frequency of digital game use, with children’s perceptions of game affordances, and transfer to out-of-game performance when interacting with digital math games, with respect to gender. Participants were 187 children (ages 8–12). An SEM mediation path analysis using MPLUS software showed significant direct effects for all pathways for all children, and significant indirect effects on all pathways for male children and five of six pathways for female children. More favorable attitudes, prior math knowledge, and perception of the helping affordances were associated with increased posttest performance, while increased frequency of digital game use and stronger perception of the hindering affordances was associated with decreased posttest performance. The model showed stronger connections for male children between frequency of digital game use, prior mathematics knowledge, and hindering affordances to the posttest, while female children showed stronger connections between attitude and perception of helping affordances to the posttest.

Investigating Factors that Influence Math Homework Expectancy: A Multilevel Approach

The present study investigated several clusters of variables influencing students’ math homework expectancy based on 3018 students in grade 8 in China. Results revealed that math homework expectancy was positively associated with homework quality at both the individual and class level. At the individual level, math homework expectancy was positively associated with prior math knowledge, parent education, homework interest, homework favorability, parent autonomy support, mastery-approach, and homework value. Meanwhile, math homework expectancy was negatively associated with homework time, parent help quantity, and performance-approach. Finally, compared with females, males tended to have higher math homework expectancy.

Math-word embedding in math search and semantic extraction

Word embedding, which represents individual words with semantically fixed-length vectors, has made it possible to successfully apply deep learning to natural language processing tasks such as semantic role-modeling, question answering, and machine translation. As math text consists of natural text, as well as math expressions that similarly exhibit linear correlation and contextual characteristics, word embedding techniques can also be applied to math documents. However, while mathematics is a precise and accurate science, it is usually expressed through imprecise and less accurate descriptions, contributing to the relative dearth of machine learning applications for information retrieval in this domain. Generally, mathematical documents communicate their knowledge with an ambiguous, context-dependent, and non-formal language. Given recent advances in word embedding, it is worthwhile to explore their use and effectiveness in math information retrieval tasks, such as math language processing and semantic knowledge extraction. In this paper, we explore math embedding by testing it on several different scenarios, namely, (1) math-term similarity, (2) analogy, (3) numerical concept-modeling based on the centroid of the keywords that characterize a concept, (4) math search using query expansions, and (5) semantic extraction, i.e., extracting descriptive phrases for math expressions. Due to the lack of benchmarks, our investigations were performed using the arXiv collection of STEM documents and carefully selected illustrations on the Digital Library of Mathematical Functions (DLMF: NIST digital library of mathematical functions. Release 1.0.20 of 2018-09-1, 2018). Our results show that math embedding holds much promise for similarity, analogy, and search tasks. However, we also observed the need for more robust math embedding approaches. Moreover, we explore and discuss fundamental issues that we believe thwart the progress in mathematical information retrieval in the direction of machine learning.

Contextualizing Math-Related Strengths and Math Achievement: Positive Math Orientations, Social Supports and the Moderating Effects of Prior Math Knowledge

Ongoing policy discussions emphasize the need for more STEM professionals to keep the United States internationally competitive in scientific fields and industry. From a K-16 perspective, it is important to note that students’ trajectories into STEM professions are often shaped by their high school experiences—especially in mathematics. Accordingly, this study employs a strength-based framework to examine students’ high school math achievement with an emphasis on the role of their math-related personal and social strengths. This research uses data from the NCES High School Longitudinal Study, a large-scale national study that emphasizes students’ math outcomes. Moderated regression was utilized to examine associations between students’ high school math-related strengths and their math achievement, as well as how these relationships may differ based upon students’ prior math achievement. The findings suggest that a number of students’ strengths in math were positively related to their math achievement; however, some of these relationships differed base upon prior math achievement levels. Accordingly, while math-related strengths can be equally beneficial for students in some instances, in other instances there is a need to better understand these relationships with some nuance. Implications for K-16 STEM education policy, practice and research are discussed.

Assessing math attitude through the Attitude Toward Mathematics Inventory – Short form in introductory statistics course students

Math attitude refers to emotional responses, beliefs, and behaviors towards mathematics. Several studies measured the relation with math learning and related variables, but very few with statistics learning. To better investigate this relation has become increasingly relevant to have a measure that ensuring multidimensionality and shortness. The aim of the present paper was to confirm the factor structure of the Lin and Huang (2014)'s ATMI - Short Form (ATMI - SF) when administered to Italian college students attending introductory statistics course, and to test its measurement invariance applying a multigroup confirmatory analysis. We also assessed the reliability and the incremental validity of the ATMI - SF by verifying whether it predicted statistics achievement over and above the effect of math knowledge. The overall findings provide that ATMI - SF is a reliable and valid measure to assess math attitude among college students who attend introductory statistics courses in non-mathematical courses.

Preschoolers’ broad mathematics experiences with parents during play

The current study broadens our understanding of preschoolers’ early math experiences with parents, recognizing that math knowledge and experiences are inclusive of numeracy as well as non-numeracy domains. Parents and preschoolers (N = 45) were observed exploring three domains of early mathematics knowledge (i.e., number, space, and pattern) during play in three activities (playing cards, building with blocks, and stringing beads, all with activity suggestions). Children were administered a broad math and numeracy measure and individual measures of spatial and patterning skills concurrently and 7 months later. Dyads explored math broadly across most activities but emphasized number more than space or patterning. In addition, there was more overall math exploration during card and bead play than during block play, with the greatest parent support during card play. Parent support was not linked to children’s skills, although children’s exploration of space and patterns related moderately to their concurrent spatial and pattern skills. Overall, parents and young children explored a variety of early math domains in guided play contexts, with an emphasis on numeracy. Future work should aim to increase the breadth and rigor of individual concepts that parents and preschoolers explore during play.

Preschool children's math exploration during play with peers

Young children are strongly encouraged to engage with math-related materials in early childhood classrooms; however, little is known about how preschoolers explore math during play with a peer. The current study examined 86 preschoolers' (Mage = 4 years, 5 months, SD = 7 months) math exploration during peer play, the characteristics and social participation of dyads associated with this exploration, and child-level factors in relation to their own and their play partner's math discovery. Math exploration was mostly nonverbal, focusing on spatial, pattern, and shape play; however, dyads who engaged in more cooperative play tended to explore more advanced math concepts and engage in more verbal math exploration. Dyadic analyses revealed that children's math knowledge contributed to their own and their play partner's nonverbal math exploration. Findings support the important contributions of peers to math exploration during play, and help us to better understand the nature of math-related play during early childhood.

Смешанное предметно-интегрированное обучение русскому как иностранному обучающихся физико-математического модуля на этапе довузовской подготовки

The article describes main difficulties that prevent from effective content integration of mathematics and natural science subjects into teaching Russian as a foreign language for academic purposes. Over-coming these difficulties is the main objective of the presented complex two-phase content-integrated model of blended RFL learning at a pre-university level. The paper reveals main results of a three-phase teaching experiment in the course of which this model was tested in groups of students of a pre-university level with majors in mathematics and physics. It is concluded that application of such an approach provides for the improvement of students’ speaking and listening skills, enhances lexico-grammatic skills and increases their motivation, making an educational process more flexible and easy in use (teachers of Russian as a Foreign lan-guage do not need to have any fundamental knowledge of Math and Physics).

Teachers’ belief in mathematics teaching: a case study of early childhood education teachers

This article aims to analyze teachers’ belief in mathematics teaching. Furthermore, this article will be used as a reference for a professional development program that the researcher is going to develop. This research is a case study with five respondents in a city in West Java, Indonesia. Semi-structured interviews towards five respondents were conducted using an interview guideline that refers to the instrument The Mathematical Development Beliefs Survey. The thematic analysis was used for data processing in this research. The result of the research revealed all respondents agreed that mathematics is a substantial part of early childhood education curriculum, contributes to the confidence of the students, development activities could be carried out, and early childhood is ready for mathematics. However, they are unsure and less confident in teaching mathematics and basic math knowledge. This research suggests that professional programs given should aim to boost teachers’ belief in teaching mathematics.

In-Game Actions to Promote Game-Based Math Learning Engagement

Game-based learning (GBL) has increasingly been used to promote students’ learning engagement. Although prior GBL studies have highlighted the significance of learning engagement as a mediator of students’ meaningful learning, the existing accounts failed to capture specific evidence of how exactly students’ in-game actions in GBL enhance learning engagement. Hence, this mixed-method study was designed to examine whether middle school students’ in-game actions are likely to promote certain types of learning engagement (i.e., content and cognitive engagement). This study used and examined the game E-Rebuild, a single-player three-dimensional architecture game that requires learners’ application of math knowledge. Using in-depth gameplay behavior analysis, this study sampled a total of 92 screen-recorded and video-captured gameplay sessions attended by 25 middle school students. We adopted two analytic approaches: sequential analysis and thematic analysis. Whereas sequential analysis explored which in-game actions by students were likely to promote each type of learning engagement, the thematic analysis depicted how certain gameplay contexts contributed to students’ enhanced learning engagement. The study found that refugee allocation and material trading actions promoted students’ content engagement, whereas using in-game building tools and learning support boosted their cognitive engagement. This study also found that students’ learning engagement was associated with their development of mathematical thinking in a GBL context.

Math acceleration in elementary school: Access and effects on student outcomes

This paper examines curricular acceleration in mathematics during elementary school using administrative data from a large, diverse school district that recently implemented a targeted, test-based acceleration policy. We first characterize access to advanced math and then estimate effects of acceleration in math on measures of short-run academic achievement as well as non-test-score measures of grit, engagement with schoolwork, future plans, and continued participation in the accelerated track. Experiences and effects of math acceleration differ markedly for girls and boys. Girls are less likely to be nominated for math acceleration and perform worse on the qualifying test, relative to boys with equivalent baseline performance. We find negative effects of acceleration on short-run retention of math knowledge for girls, but no such performance decay for boys. After initial exposure to accelerated math, girls are less likely than boys to appear in the accelerated track during late elementary school and at the start of middle school.