Math Knowledge Research Articles

Exploring First Semester Changes in Domain-Specific Critical Thinking

Critical thinking is a common aim for higher education students, often described as general competencies to be acquired through entire programs as well as domain-specific skills to be acquired within subjects. The aim of the study was to investigate whether statistics-specific critical thinking changed from the start of the first semester to the start of the second semester of a two-semester statistics course, where the curriculum contains learning objectives and assessment criteria related to critical thinking. The brief version of the Critical Thinking scale (CTh) from the Motivated Strategies of Learning Questionnaire addresses the core aspects of critical thinking common to three different definitions of critical thinking. Students rate item statements in relation to their statistics course using a frequency scale: 1 = never, 2 = rarely, 3 = sometimes, 4 = often, and 5 = always. Participants were two consecutive year-cohorts of full-time Bachelor of Psychology students taking a two-semester long statistics course placed in the first two semesters. Data were collected in class with a paper-pencil survey 1 month into their first semester and again 1 month into the second. The study sample consisted of 336 students (ncohort 1 = 166, ncohort 2 = 170) at baseline, the follow-up was completed by 270 students with 165 students who could be matched to their baseline response. To investigate the measurement properties of the CTh scale, item analysis by the Rasch model was conducted on baseline data and subsequently on follow-up data. Change scores at the group level were calculated as the standardized effect size (ES) (i.e., the difference between baseline and follow-up scores relative to the standard deviation of the baseline scores). Data fitted Rasch models at baseline and follow-up. The targeting of the CTh scale to the student sample was excellent at both timepoints. Absolute individual changes on the CTh ranged from −5.3 to 5.1 points, thus showing large individual changes in critical thinking. The overall standardized effect was small and negative (−0.12), with some variation in student strata defined by, gender, age, perceived adequacy of math knowledge to learn statistics, and expectation to need statistics in future employment.

Integrated Mathematical knowledge with other scientific knowledge and its role for Mathematics teaching at high school

In this paper, we present the following main contents: Emphasize the need, capacity, and opportunities to integrate mathematical knowledge with knowledge of other sciences in mathematics teaching at high school. Discovering the two-way connections between mathematical and other scientific knowledge when studying the situation of integrated teaching. Applying the above ideas to mathematics teaching at high school in the direction of discovering new knowledge in mathematics and providing ways to connect math knowledge with other sciences as well as their role in teaching mathematics.

Patterns of Using Multimodal External Representations in Digital Game-Based Learning

Although prior research has highlighted the significance of representations for mathematical learning, there is still a lack of research on how students use multimodal external representations (MERs) to solve mathematical tasks in digital game-based learning (DGBL) environments. This exploratory study was to examine the salient patterns problem solvers demonstrated using MERs when they engaged in a single-player, three-dimensional architecture game that requires the acquisition and application of math knowledge and thinking in game-based context problem solving. We recorded and systematically coded the behaviors of using MERs demonstrated by 20 university students during 1.5 hours of gameplay. We conducted both cluster and sequential analyses with a total of 2654 encoded behaviors. The study indicated that the maneuverable visual-spatial representation was most frequently used in the selected architecture game. All of the participants performed a high level of representational transformations, including both treatment and conversion transformations. However, compared to the students in the second cluster who were mostly non-game players, students in the first cluster (composed of mainly experienced video game players) displayed a higher frequency of interacting with various MERs and a more cautious and optimized reflective problem-solving process.

Efficacy of an Adaptive Game-Based Math Learning App to Support Personalized Learning and Improve Early Elementary School Students’ Learning

This study investigates whether using My Math Academy, which provides personalized content and adaptive embedded assessments to support existing curricula, can improve learning outcomes and engagement for kindergarten and first grade students (N = 505 treatment, 481 control). Findings indicate that students using My Math Academy made significant learning gains in math relative to children who did not. More skills mastered in My Math Academy was associated with greater learning gains on the external assessment, with the greatest impacts among students with lower levels of math knowledge, where there was more room for growth and on the most difficult skills. Teachers surveyed found My Math Academy easy to use in their classrooms and recognized it as a valuable learning resource that supplemented their existing curricula to improve students’ engagement, motivation, and confidence in learning math.

Analyzing the misperception of exponential growth in graphs

Exponential growth is frequently underestimated, an error that can have a heavy social cost in the context of epidemics. To clarify its origins, we measured the human capacity (N = 521) to extrapolate linear and exponential trends in scatterplots. Four factors were manipulated: the function underlying the data (linear or exponential), the response modality (pointing or venturing a number), the scale on the y axis (linear or logarithmic), and the amount of noise in the data. While linear extrapolation was precise and largely unbiased, we observed a consistent underestimation of noisy exponential growth, present for both pointing and numerical responses. A biased ideal-observer model could explain these data as an occasional misperception of noisy exponential graphs as quadratic curves. Importantly, this underestimation bias was mitigated by participants' math knowledge, by using a logarithmic scale, and by presenting a noiseless exponential curve rather than a noisy data plot, thus suggesting concrete avenues for interventions.

Spatial language during a household task with bilingual Latine families

Children's exposure to everyday math talk contributes positively to their early math development, yet little is known about family everyday math in culturally and linguistically diverse communities. The present study described the spatial language used by 75 low-income, bilingual, Latine caregivers as they taught their preschoolers to set a table for a birthday party. Forty percent of caregivers' content-rich utterances contained math references, half of which were spatial terms. “Where” spatial references were the most frequent and used to provide instructions. Analyses comparing Spanish and English interactions showed variations in spatial language types and manners of use, as well as in the relation between adult and child math talk. Results underscore the need to build foundational knowledge in early math with culturally and linguistically diverse families, and to encompass a wide range of everyday adult-child interactions, in an effort to forge equitable STEM initiatives and practices.

Computer discourse and use as determinants of student math outcomes: performativity and action at work in the lower school grades

There exists a tension between discussing the use of computers in the lower grade math curriculum and computer use outcomes, as achievement results fall behind the talk of use. Purpose: The purpose of this research was to explore this proposition on a large scale limited to a United States context. To that end, two studies emerged. Methods: In the first study, a large corpus of articles encouraging computer use from Teaching Children Mathematics was used to explore talk about how to use computers in the classroom using a content analysis method. The second study used weighted sample survey methods with corrections and jackknife replications for ANOVA tests to determine whether there were statistically significant differences between exposure time to computers during 4th grade math and standardized test scores on the TIMSS math knowledge and application subtests generalized to the United States population of students. Results: The results of the first study indicated that computer use talk fell under the domains of geometry, graphing functions, and base ten blocks. The second study indicated non-significant results on both tests, which was interpreted as a valuable finding. Conclusions: Several conclusions emerged for these studies. The most poignant ones included that common core standards do not require or mention technology use in obtaining math objectives in the 4th grade. It is concluded that the TIMSS survey results suggest that some of the findings might be due to lack of availability of computers for students and professional development opportunities for faculty. It is also concluded that there is a continuity between the recent 2000s and the use of computers in the lower grades during COVID-19, where reports show learning losses, despite talk of it as a teaching method.

HIIT and Resistance Training Effects on Learning-related Outcomes in Underserved School Children

Research has demonstrated associations between differing modalities of physical activity (PA) and behavioral and learning outcomes; however, little evidence exists in real world settings. To evaluate the effects of embedding high intensity interval training (HITT) and resistance training (RT) into physical education (PE) curriculum on PA, academic performance, and behavior in youth attending urban schools. Forty boys and 30 girls; ages 8-10 yrs. enrolled in an expanded public school supplemental learning program were assigned into one of three conditions using a pragmatic trial design: standard PE curriculum (n = 23), HITT (n = 25), and RT (n = 22). PA was measured using accelerometers; math achievement scores were conducted at baseline and post-intervention using the Math Knowledge Assessment (MKA); behavior was assessed using the Abbreviated Conners Rating Scale (ACRS) daily. Participation in HITT resulted in 1.86 additional vigorous PA minutes (p=0.04) and 0.76 additional very vigorous PA minutes (P=0.02) per session, but was not associated with increased moderate PA minutes compared to the control group. RT PA outcomes did not differ from regular PE. Participating in HIIT, but not RT, was associated with a 1.82-point improvement in math test scores compared to those in the same grade in the standard PE group (p=0.02). No group assignment was associated with behavioral ratings. Embedding HITT within PE has potential for improving vigorous PA levels and may affect learning outcomes in urban youth. This is consistent with prior studies which show how short bouts of intense exercise can improve cognitive outcomes.

New books & media

New books & media

The Influence of Origami on Mathematics Study

This study aimed to investigate the influence of origami on mathematics study. Origami artists have been studying origami since 1893 to find the secret of math in it. In the past years, according to the studies that past sages have done for the world, origami helps mathematicians to solve several math puzzles. In addition, it may help students to understand geometry. As a high school student, the researcher was interested in origami and mathematics. Therefore, research related to these two themes is made, and connected with math education, to discover how origami helps learn math. In this article, origami was seen as something that may greatly assist mathematics and the education of mathematics. For further support, research is done for some examples that past people have done about origami and mathematics. Theories proposed by the pioneers were put into practice. Additionally, some of the current study experiences in origami with math knowledge points were added to find the benefits of students learning math by using origami. Related theories are taken into practice by the researcher, to further discover how mathematics and origami have combined. This article concludes with the examples of origami that have greatly helped to solve math problems and my discovery of how learning origami may help better comprehension of math. Spatial awareness, logical execution, non-cognitive skills, and finger dexterity has been greatly improved.

Accelerating Early Math Learning with Research-Based Personalized Learning Games: A Cluster Randomized Controlled Trial

This study examines whether My Math Academy, a digital game-based learning environment that provides personalized content and adaptive embedded assessments, can improve math knowledge of Transitional Kindergarten and Kindergarten students. A cluster randomized study was conducted with 20 classrooms, 10 of which were randomly assigned to use My Math Academy for 12–14 weeks. Results of hierarchical linear models indicated that after using the app for about 5 hours, treatment students significantly outperformed the control group in math knowledge and skills as measured by TEMA-3. My Math Academy produced the greatest learning gains in students who began with a moderate level of math knowledge and on the most difficult skills assessed. Additionally, the more games students played, the greater the learning gains they experienced. Teacher surveys revealed that My Math Academy produced positive impacts on students’ interest and self-confidence in learning math. Teachers also recognized My Math Academy as a user-friendly, valuable learning resource that they will continue to use. The study results will inform ongoing development of My Math Academy, including tools to enable teachers to help children with low levels of prior math knowledge.

Pemberdayaan Masyarakat Terhadap Pendampingan Belajar Matematika Anak di Desa Batu Malenggang Kabuapten Langkat

This community empowerment activity is a breakthrough for math teachers and students who wish to share their math knowledge with small community organizations. This form of community empowerment is used to support and help the community implement mathematics teaching for children; help children with disabilities understand math; insights from DKM management and staff (Mushola Musyawarah Kemakmuran) on learning math fun for children; and develop familiarity and awareness. The DKM served as an impetus to integrate the da'wah program with the needs of the congregation in the education of children, especially in mathematics. The partner of this activity is the Musholla Prosperity Council, a non-profit organization committed to supporting the well-being and empowerment of mosques. In this case, parents who are members of the prayer hall church often find it difficult to guide their sons / daughters in their studies, especially in math due to their limited math skills. This activity aims to improve the understanding of managers and executives at DKM about fun math learning for kids by combining learning with math games and teaching aids. This activity in the process is very helpful in increasing interest in learning math for students and parents in Batu Malenggang Village, Langkat Regency. Keywords: Children, Parents, DKM, Mathematics, Learn

Children’s gesture use provides insight into proportional reasoning strategies

Children struggle with proportional reasoning when discrete countable information is available because they over-rely on this numerical information even when it leads to errors. In the current study, we investigated whether different types of gesture can exacerbate or mitigate these errors. Children aged 5–7 years (N = 135) were introduced to equivalent proportions using discrete gestures that highlighted separate parts, continuous gestures that highlighted continuous amounts, or no gesture. After training, children completed a proportional reasoning match-to-sample task where whole number information was occasionally pitted against proportional information. After the task, we measured children’s own gesture use. Overall, we did not find condition differences in proportional reasoning; however, children who observed continuous gestures produced more continuous gestures than those who observed discrete gestures (and vice versa for discrete gestures). Moreover, producing fewer discrete gestures and more continuous gestures was associated with lower numerical interference on the match-to-sample task. Lastly, to further investigate individual differences, we found that children’s inhibitory control and formal math knowledge were correlated with proportional reasoning in general but not with numerical interference in particular. Taken together, these findings highlight that children’s own gestures may be a powerful window into the information they attend to during proportional reasoning.

Socioeconomic status, home mathematics environment and math achievement in kindergarten: A mediation analysis.

Growing evidence suggests that parents' practices contribute to their children's cognitive development and that such practices may reflect SES disparities. This study investigated longitudinal interrelations between home mathematics environment (HME), children's math achievement, and two facets of SES (mother's educational attainment and household income-subsidy status) during the first year in kindergarten (n = 500 children; Mage at T1 = 57.3 months, SD = 3.8). Results revealed that these facets of SES operated through different mechanisms in kindergarten-the association between mothers' education and math growth at the end of K1 is fully mediated by HME and children's baseline math knowledge. Furthermore, only home math activities that explicitly supported the understanding of addition and subtraction contributed to children's math growth independently of SES background. The pattern of longitudinal associations suggests that the provision of home math activities may reflect children's mathematical abilities rather than SES disparities.

Conceptualizing STEM teacher professional knowledge for teaching ELs: Initial impact of subject matter and disciplinary literacy PD on content knowledge and practice

ABSTRACT This paper advances the conceptualization of STEM teacher professional knowledge reflecting the specialized knowledge needed to support English learner (EL) language development during science and mathematics instruction. What distinguishes this model is the integration of conceptual understanding, a key feature of subject matter knowledge, with disciplinary literacy knowledge (DLK). Several models have been proposed to capture the knowledge, skills, and dispositions of effective teachers. However, few studies have empirically investigated the model’s utility in producing effective EL instruction. Two professional development (PD) approaches were tested. One approach explicitly focused on developing subject matter knowledge and the second approach focused on developing pedagogical knowledge without an explicit attention to subject matter knowledge. Both approaches included PD on DLK. Outcome variables included teacher math and science content knowledge and instructional quality. Findings show overall science content knowledge score increased for both PD approaches, but no significant differences in overall math content knowledge score were found. This pattern suggests that for elementary teachers, prolonged PD can improve teacher science knowledge. Significant increases in instructional quality were found only for teachers who received PD with an explicit focus subject matter. PD focused on pedagogical knowledge did not improve overall teaching quality. Implications are discussed.

Challenging the Students‘ Sense of Mathematics Via Decoding Problems in Chernorizec Hrabar Tournament

Under consideration is a thematic branch from the Chernorizec Hrabar (ChH) math tournament, which aims to check and develop the student’s sense of mathematics. The ChH competition papers include several types of test items related to codes. These test items require just basic math knowledge but a high level of nonstandard reasoning and a kind of synthetic mathematical abilities. The authors’ standing point is to present by examples how the idea of (de)coding evolves in competition papers for students in different ages.

Parent Math Anxiety Predicts Early Number Talk

ABSTRACT Differences in children’s math knowledge emerge as early as the start of kindergarten, and persist throughout schooling. Previous research implicates the importance of early parent number talk in the development of math competency. Yet we understand little about the factors that relate to variation in early parent number talk. The current study examined the relation of parent math anxiety and family socioeconomic status (SES) to parent number talk with children under the age of three (n = 36 dyads). For the first time, we show preliminary evidence that parent math anxiety (MA) predicts the amount of number talk children hear at home, beyond differences accounted for by SES. We also found a significant SES by parent MA interaction such that parent MA was predictive of higher-SES parents’ number talk but not that of lower-SES parents. Furthermore, we found that these relations were specific to parents’ cardinal number talk (but not counting), which has been shown to be particularly important in children’s math development.

Parent and child spontaneous focus on number, mathematical abilities, and mathematical talk during play activities

The mathematical talk that parents use when engaging with their children is important for children’s early math development. However, parents vary in the amount and type of mathematical input they provide. Because early math knowledge is predictive of later achievement, understanding contributors to this variation has implications for children’s math development. The current study examined how individual parent and child cognitive factors, including math ability and spontaneous focus on number (SFON), relate and contribute to math talk during parent-child play. Findings indicate that SFON relates to math ability for both parents and children. SFON was not a significant predictor of math talk, but parent and child math ability related to talk about advanced math concepts and numbers in context. These results suggest that the relation of SFON and math ability is consistent in adulthood, and that more research is needed to understand factors that contribute to variation in math talk.

Linking inhibitory control to math achievement via comparison of conflicting decimal numbers

The relationship between executive functions (EF) and academic achievement is well-established, but leveraging this insight to improve educational outcomes remains elusive. Here, we propose a framework for relating the role of specific EF on specific precursor skills that support later academic learning. Starting from the premise that executive functions contribute to general math skills both directly – supporting the execution of problem solving strategies – and indirectly – supporting the acquisition of precursor mathematical content, we hypothesize that the contribution of domain-general EF capacities to precursor skills that support later learning can help explain relations between EF and overall math skills. We test this hypothesis by examining whether the contribution of inhibitory control on general math knowledge can be explained by inhibition's contribution to processing rational number pairs that conflict with individual's prior whole number knowledge. In 97 college students (79 female, age = 20.58 years), we collected three measures of EF: working memory (backwards spatial span), inhibition (color-word Stroop) and cognitive flexibility (task switching), and timed and untimed standardized measures of math achievement. Our target precursor skill was a decimals comparison task where correct responses were inconsistent with prior whole number knowledge (e.g., 0.27 vs. 0.9). Participants performed worse on these trials relative to the consistent decimals pairs (e.g., 0.2 vs. 0.87). Individual differences in the Stroop task predicted performance on inconsistent decimal comparisons, which in turn predicted general math achievement. With respect to relating inhibitory control to math achievement, Stroop performance was an independent predictor of achievement after accounting for age, working memory and cognitive flexibility, but decimal performance mediated this relationship. Finally, we found inconsistent decimals performance mediated the relationship of inhibition with rational number performance, but not other advanced mathematical concepts. These results pinpoint the specific contribution of inhibitory control to rational number understanding, and more broadly are consistent with the hypothesis that acquisition of foundational mathematical content can explain the relationships between executive functions and academic outcomes, making them promising targets for intervention.

Using Math in Physics: Overview

The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even the way we interpret mathematical equations. Learning to think about physics with math instead of just calculating involves a number of general scientific thinking skills that are often taken for granted (and rarely taught) in physics classes. In this paper, I give an overview of my analysis of these additional skills. I propose specific tools for helping students develop these skills in subsequent papers.