Understanding Math Research Articles

The role of self-math overlap in understanding math anxiety and the relation between math anxiety and performance.

Recent work has demonstrated that math anxiety is more than just the product of poor math skills. Psychosocial factors may play a key role in understanding what it means to be math anxious, and hence may aid in attempts to sever the link between math anxiety and poor math performance. One such factor may be the extent to which individuals integrate math into their sense of self. We adapted a well-established measure of this degree of integration (i.e., self-other overlap) to assess individuals’ self-math overlap. This non-verbal single-item measure showed that identifying oneself with math (having higher self-math overlap) was strongly associated with lower math anxiety (r = -0.610). We also expected that having higher self-math overlap would leave one especially susceptible to the threat of poor math performance to the self. We identified two competing hypotheses regarding how this plays out in terms of math anxiety. Those higher in self-math overlap might be more likely to worry about poor math performance, exacerbating the negative relation between math anxiety and math ability. Alternatively, those higher in self-math overlap might exhibit self-serving biases regarding their math ability, which would instead predict a decoupling of the relation between their perceived and actual math ability, and in turn the relation between their math ability and math anxiety. Results clearly favored the latter hypothesis: those higher in self-math overlap exhibited almost no relation between math anxiety and math ability, whereas those lower in self-math overlap showed a strong negative relation between math anxiety and math ability. This was partially explained by greater self-serving biases among those higher in self-math overlap. In sum, these results reveal that the degree to which one integrates math into one’s self – self-math overlap – may provide insight into how the pernicious negative relation between math anxiety and math ability may be ameliorated.

On the relation between math and spatial ability: The case of math anxiety

Engaging with math can be especially difficult for individuals who experience math anxiety. Interestingly, recent research has demonstrated a negative association between math anxiety and small-scale spatial ability (i.e., mental rotation). The aim of the present study is to better understand this fundamental link between individual differences in math and space in three ways. First, we investigated the relation between math anxiety and self-reported sense-of direction, a critical index of large-scale spatial ability thought to be distinct from small-scale spatial ability. Next, we investigated the relation between math anxiety and spatial anxiety (i.e., anxiety about environmental navigation). Then, we used behavioral measures of small- and large-scale spatial skills to further explore these abilities as a function of math anxiety. Results demonstrate that individuals high in math anxiety report a worse sense-of-direction, more spatial anxiety and general anxiety, and perform worse on behavioral tests of small- and large-scale spatial skills. Regression analyses suggest that spatial anxiety, general anxiety, and small-scale spatial skill are the most robust of the tested predictors of math anxiety. Implications for understanding math anxiety are discussed.

PENERAPAN MODEL PEMBELAJARAN CONTEXTUAL TEACHING AND LEARNING UNTUK MENINGKATKAN PEMAHAMAN MATEMATIS MAHASISWA DALAM MATA KULIAH PEMBELAJARAN MATEMATIKA KELAS RENDAH

To improve students' understanding of mathematical subjects low grade math learning, it is necessary to use a model of learning that can improve the process of teaching and learning process. One model used is the learning model Contextual Teaching and Learning (CTL). The problems examined in this study is whether the use of the learning model Contextual Teaching and Learning (CTL) can improve student learning outcomes in subjects low grade math learning the academic year 2013-2014 at the University of Sultan Agung Tirtayas Guidance and Counseling Department PGSD. The result is the achievement of students who use learning methods Contextual Teaching and Learning (CTL) is better than the achievement of students who use conventional teaching methods Keywords : Contextual Teaching and Learning (CTL), Learning Mathematics and Mathematical Understanding

Organization matters: Mental organization of addition knowledge relates to understanding math equivalence in symbolic form

Two quasi-experiments examined mental organization of addition knowledge as a potential source of individual differences in understanding math equivalence in symbolic form. We hypothesized that children who mentally organize addition knowledge around conceptually related groupings would have better understanding of math equivalence. In Quasi-experiment 1, we assessed 101 second and third grade students’ mental organization of addition knowledge based on their use of decomposition strategies to solve addition problems (e.g., 3+4=3+3+1=6+1=7). In Quasi-experiment 2, we assessed 94 second grade students’ mental organization based on their ability to generate a set of equations equal to a target value. In both quasi-experiments, children whose mental organization better reflected conceptually related groupings exhibited better understanding of math equivalence. Results thus support the hypothesis that mental organization of addition knowledge into conceptually related groupings based on equivalent values may influence understanding of math equivalence in symbolic form.

Relationships between 9-Year-Olds' Math and Literacy Worries and Academic Abilities

We investigated whether 9-year-olds experience math and/or literacy worries and, if they do, whether it is related to problem-solving abilities. Fifty-eight children judged the correctness of math, literacy, and mental rotation problems that differed in difficulty and rated their worry level about the correctness of judgments. Nonverbal IQ, general math, and literacy abilities were also assessed. Results showed children's worry ratings varied as a function of task and problem difficulty. Latent class analyses of math and literacy worry ratings revealed high-, moderate- and low-worry subgroups in both domains. The high-worry math subgroup exhibited poorer math performance than the other math subgroups, demonstrating a link between math worry and math performance. No relationship was found between worry literacy subgroups and literacy performance. Moreover, no relationship was found between teachers’ rating of children's academic and general worry and children’s own worry ratings. The relevance of the findings for understanding math and literacy worry is discussed.

Health numeracy in Japan: measures of basic numeracy account for framing bias in a highly numerate population.

BackgroundHealth numeracy is an important factor in how well people make decisions based on medical risk information. However, in many countries, including Japan, numeracy studies have been limited.MethodsTo fill this gap, we evaluated health numeracy levels in a sample of Japanese adults by translating two well-known scales that objectively measure basic understanding of math and probability: the 3-item numeracy scale developed by Schwartz and colleagues (the Schwartz scale) and its expanded version, the 11-item numeracy scale developed by Lipkus and colleagues (the Lipkus scale).ResultsParticipants’ performances (n = 300) on the scales were much higher than in original studies conducted in the United States (80% average item-wise correct response rate for Schwartz-J, and 87% for Lipkus-J). This high performance resulted in a ceiling effect on the distributions of both scores, which made it difficult to apply parametric statistical analysis, and limited the interpretation of statistical results. Nevertheless, the data provided some evidence for the reliability and validity of these scales: The reliability of the Japanese versions (Schwartz-J and Lipkus-J) was comparable to the original in terms of their internal consistency (Cronbach’s α = 0.53 for Schwartz-J and 0.72 for Lipkus-J). Convergent validity was suggested by positive correlations with an existing Japanese health literacy measure (the Test for Ability to Interpret Medical Information developed by Takahashi and colleagues) that contains some items relevant to numeracy. Furthermore, as shown in the previous studies, health numeracy was still associated with framing bias with individuals whose Lipkus-J performance was below the median being significantly influenced by how probability was framed when they rated surgical risks. A significant association was also found using Schwartz-J, which consisted of only three items.ConclusionsDespite relatively high levels of health numeracy according to these scales, numeracy measures are still important determinants underlying susceptibility to framing bias. This suggests that it is important in Japan to identify individuals with low numeracy skills so that risk information can be presented in a way that enables them to correctly understand it. Further investigation is required on effective numeracy measures for such an intervention in Japan.

Education and outreach bring NASA heliophysics to the public

Educating and inspiring students, teachers, and the public by communicating advances in heliophysics science is the objective of the education and public outreach (E/PO) specialists at the Heliophysics Science Division (HSD) at NASA Goddard Space Flight Center (GSFC) in Greenbelt, Md. The specialists carry out NASA's E/PO goal to enhance the nation's formal education system and contribute to the broad public understanding of science, math, and technology. HSD E/PO projects exploit community best practices to meet or surpass NASA's requirements, which include attention to quality; leverage through internal and external partnerships; and a focus on customer needs, project sustainability, and audience diversity. One key to the group's success is the involvement of enthusiastic HSD research scientists who directly interface with E/PO specialists and various audiences, verify scientific content, and/or provide data access or other resources. Scientists also mentor interns from high school to graduate school through NASA and GSFC programs, and several have shared their science with the public via appearances on national media, including the National Geographic and History channels as well as local news.

Why Do Taiwanese Children Excel at Math?

Taiwanese children excel in mathematics, often receiving top scores in international competitions. Fourth graders from Taiwan ranked third on the most recent Trends in International Mathematics and Science Study (2007) with only Hong Kong and Singapore scoring higher. Taiwanese 8th graders did even better, ranking first with an average scale score of 598. The average scale score for American 8th graders was 499, slightly below the TIMSS scale average of 500. So, why don't American children perform as well as Asian children on these international tests? Cultural differences Tsao's (2004) study of academic achievement discrepancies in children indicates that both intelligence and the learning environment influence academic achievement. Do these findings suggest that Taiwanese children are inherently more intelligent in mathematical reasoning than American children or that the learning environment in Taiwanese homes and classrooms is more supportive of mathematical learning? Because no scientific evidence indicates that American children are less intelligent than Taiwanese children, the key difference must be the mathematical learning environment, at home and at school. Parents, especially mothers, exert a strong influence on a child's early learning experiences. There is, however, a cultural difference in how Taiwanese mothers and American mothers view the connection between effort, intelligence, and learning. Research suggests that most American mothers believe a child's mathematical performance primarily depends on intelligence and innate math ability; Asian mothers believe effort is more important for academic success (Stevenson, Chen, & Lee, 1993; Stevenson & Lee, 1990; Stevenson, 1992; Stevenson & Stigler, 1992). This difference in maternal perception may affect the learning experiences mothers provide for their young children. In Taiwan, academic achievement is widely believed to hold the promise for a successful future. Taiwan is a small, densely populated island of over 23 million people. As a result, individual beliefs and values tend to be shaped by a socioeconomic context that often encourages competition. In Taiwan, parents, especially mothers, are highly involved in a child's schooling and play a key role in the child's academic achievement (Fejgin, 1995; Zellman & Waterman, 1998). This parental involvement may appear to be very intense, and Western observers often have difficulty comprehending the level of influence and control that Asian parents have on their children from an early age through college. For example, most Taiwanese mothers force their children to participate in after-school tutoring programs to enhance mathematical achievement; in addition, as Taiwanese students prepare for college, they usually select their university and major based on the preference of their parents. Given the cultural differences in parent involvement and competition, it's not surprising that Taiwanese parents approach learning with a sense of urgency and are often viewed as pushing children to learn academic subjects during preschool. Mathematical reasoning is highly valued and encouraged at a young age because it provides a foundation for a broad spectrum of future academic learning (Liu, 2006; Hess, Chang, & McDevitt, 1987). Taiwanese children begin a formal math curriculum in kindergarten. In addition to math instruction in school, over one-fifth of kindergartners receive after-school instruction (Huang, 2010) that usually focuses on preteaching and reteaching concepts and skills that are part of the classroom curriculum. The number of students attending after-school tutoring programs increases as children get older. Even in the United States, research indicates that after-school tutoring provides a significant increase in understanding math concepts, problem solving, computation, and overall math achievement for struggling math students (Lalley & Miller, 2006). …

Gender and Mathematics at Play: Parents’ Constructions of their Preschoolers Mathematical Capabilities

Using sociocultural learning theories and feminist post structural theories of gender, we explore how a diverse group of parents (n=28) construct their preschool sons and daughters as capable/not capable of doing mathematics. Our study examines the interactions between parents and children while playing an age appropriate board game. Following an analysis of the parents’ words and gestures, we found that on average, parents modeled mathematical procedures equally for daughters and sons, prompted their sons to complete mathematical procedures almost twice as frequently as they prompted their daughters, and enacted executive automany much more frequently with their daughters than with their sons. In other words, in the context of playing this board game the parents in this study appeared to construct their preschool sons and daughters as having a fairly equal potential for understanding math but constructed their sons as currently capable mathematicians more often than they constructed their preschool daughters this way. Implications for educators and researchers are considered.

Science, mathematics and technology education in the US: a perspective from the "frontlines of the classroom to national policy"

Abstract. In the past decade significant emphasis has been placed on increasing the involvement and influence of the professional scientific community in America's K-12 classrooms. The origins of this thrust have arisen from a variety of real and perceived crises occurring in America's K-12 classrooms. Projections for the nation's future workforce needs indicate an increased demand for science and technically literate workers, while fewer of the nation's students are pursuing advanced degrees in these academic areas of expertise. In an effort to address these issues and to impact the overall understanding and quality of science, math and technology education, several of the federal agencies have increasingly included a percentage of research funding devoted to the objective of improving the quality of kindergarten through Grade 12 (K-12, see Table 1) formal education and informal public outreach. To this end, NASA's Space Science Enterprise in particular has demonstrated a successful implementation approach and has been a national leader in forging strong partnerships with the education community to address these concerns.

Innate spatial–temporal reasoning and the identification of genius

The teaching of mathematics is invariably language-based, but spatial-temporal (ST) reasoning (making a mental image and thinking ahead in space and time) is crucial to the understanding of math. Here we report that Big Seed, a demanding ST video game, based upon the mathematics of knot theory and previously applied to understanding DNA structure and function, can be used to reveal innate ST reasoning. Big Seed studies with middle and elementary school children provide strong evidence that ST reasoning ability is not only innate but far exceeds optimistic expectations based on age, the percentage of children achieving exceptional ST performance in less than 7 h of training, and retention of ability. A third grader has been identified as a genius (functionally defined) in ST performance. Big Seed may be used for training and assessing 'creativity' (functionally defined) and ST reasoning as well as discovering genius.

Math Learning Disability and Math LD Subtypes

The present study examined whether indicators of math learning disability are observed in 5- and 6-year-olds with neurofibromatosis type 1 (NF1) and in 5- to 6-year-old girls with Turner syndrome or fragile X syndrome. Data from 14 girls with Turner syndrome, 9 girls with fragile X syndrome, and 11 children with NF1 were compared to data from control participants matched on age, sex, IQ score, and grade level. The results indicate that girls with fragile X syndrome or Turner syndrome are significantly more likely to have specific math difficulties relative to their control group, with a larger effect size demonstrated by the group with Turner syndrome. Young children with NF1 had a heterogeneous profile not suggestive of specific math disability. The results are discussed in terms of their implications for understanding math disability subtypes and the identification of math difficulty in the early school years.

From Desk Set to The Net: Women and Computing Technology in Hollywood Films

Like a number of Hollywood producers who have received grants from the Sloan Foundation “to encourage more thoughtful treatment of science,” I am interested in looking closely at representations of scientists and scientific discovery (Pollack). As the National Science Foundation documents, science and technology hold important places in our lives, but public understanding of science continues to lag (Hill; Olson; National Science Foundation [NSF], “Overview”). Politicians and educators frequently argue that US students need to improve their standing in world rankings of student understanding of math and science. One economic reason to educate children and the general public is clear: the transformation from a cold war culture that contributed money to the scientific infrastructure via defence research to a world power eager to expand trade in world markets via electronic means and premier medical research. In the 1990s, defence research shrank while health and telecommunications research received increased support in the federal budget.

Understanding of mathematics and science: efficient models for student assessments

Student self-reports provide information that is invaluable in assessing student backgrounds and achievements. These critical student inputs can be used to help place students in beginning courses; to identify high-risk and honors students; to evaluate the quality of courses, services, and resources; to initiate and evaluate existing and new programs; and to help students make career decisions. Faculty members can also use self-reports to efficiently examine student perceptions of their understanding of key content at the beginning and end of the courses for which they are responsible. This paper uses as a model: self-reports of first-year engineering students using the Mathematics Science Inventory (MSI). The MSI is used in placing students in beginning mathematics and chemistry courses and to evaluate their perceptions of their understanding of the key content of these courses. Significant, but differential self-reported gains in mathematics and chemistry knowledge are reported in twelve different math and chemistry courses, completed by 1995 and 1996 beginning engineering students. Complex, but generally positive, relationships are observed between course grades and pre-test and post-test self-reports of understanding of math and science content.

The Humanities and Chaos Theory: A Response to Steenburg's “Chaos at the Marriage of Heaven and Hell”

In an article in the fall 1991 issue of the Harvard Theological Review, David Steenburg proposes “to consider the potential significance of chaos theory for modern culture.” This important issue has not received adequate attention because the understanding of math and the physical sciences necessary to be able to speak cogently about chaos theory can be intimidating for nonscientists. Those who are not scientists, however, have at their disposal the popular and effective summary of chaos theory by James Gleick. While Gleick's work is solid, it has led some to be captivated by chaos theory's fecund metaphorical terminology and elegant computer-aided graphical images. Although those images, particularly the logistic map, show striking instances of order hidden within chaotic systems, too often they are used to forward the thesis that there are other systems, ranging from modern literary theory to stock market fluctuations, that also house deep structure amid their apparent disorder. The result is, on occasion, analysis that is based only upon metaphor.

Affective Variables and Mathematics Education

to general feelings such as liking/disliking of mathematics, nor is it meant to exclude perceptions of the difficulty, usefulness, and appropriateness of mathematics as a school subject. There are several ways affective variables are related to mathematics learning. It is likely that a student who feels very positive about mathematics will achieve at a higher level than a student who has a negative attitude toward mathematics. It is also likely that a high achiever will enjoy mathematics more than a student who