Trajectories of self-perceived math ability,utility value and interest across middle school as predictors of high school math performance

Although many studies have documented developmental change in mathematics motivation, little is known about how these trends predict math performance. A sample of 288 participants from the United States reported their perceived math ability, math utility value and math interest in 5th, 7th and 9th grades. Latent growth curve models estimated developmental trajectories in each of these constructs. Mathematics interest and utility value decreased across time, but there was no significant change in self-perceived math ability. Slopes and intercepts of all mathematics motivation variables correlated with one another. Even when controlling for prior mathematics performance, students who self-reported high math ability in 5th grade had higher standardised test scores than their peers in high school five years later. Neither math utility value nor math interest intercepts or slopes predicted later performance. Understanding the predictors of math performance is important for supporting students’ success in science, technology, engineering and mathematics careers.     

Technology, math, and the early learner: Models for learning

As today’s preschoolers become the school-age children of tomorrow, early learning educators are faced with a unique and exciting challenge of integrating technology into mathematics instruction. This article examines theory, standards, guidelines, and rationale that supports technology in the preschool environment. Examining practices at 12 diverse preschool sites, four designs emerge as the “typical” models that enable early learners to engage and experience technology within a developmentally appropriate learning environment. The designs outlined are viewed through the lens of preschool mathematics instruction and provide early learning educators as well as parents with models for replication.     

School belonging and math attitudes among high school students in advanced math

This study used the Trends in International Math Science (TIMSS) 2015 Advanced data from nine countries to examine the relationship between students’ sense of school belonging and their attitudes towards mathematics, and the extent to which student gender moderated these relationships. Results showed that students’ sense of school belonging emerged as a statistically significant, positive predictor of students’ liking and valuing of mathematics. For most countries, no significant moderating effect of student gender was observed. However, among Portuguese students, the relationship between students’ sense of school belonging and each attitude measure was stronger for males than for females.     

义务教育中数学教育功利化倾向的几种表现及危害

义务教育中的数学教育的功利化使数学教育的作用被扭曲地发挥，造成数学教育的异化．数学教育的功利化倾向通常表现为权威化、教条化、狭隘化、刻板化等，对数学教育功能的发挥和学生的发展造成比较大的危害．     

如何上数学课

课堂教学是学生获取知识的主渠道,数学知识在生活中应用广泛,如何上数学课,对于每一位小学数学老师来说,都有自己的经验和办法。但是,如何上好每堂数学课,使学生在课堂上最大限度地掌握知识,提高数学成绩,这就不仅需要我们备课精心设计,而且在教学过程中也要精益求精。现将如何上数学课的     

Effects of mathematics learning through children's literature on math achievement and dispositional outcomes

The purpose of this study was to analyze the effectiveness of using children's literature to promote mathematics learning. Fifty-seven kindergarteners were randomly assigned to either a control group or an experimental group. The experimental group received mathematics related storybook reading and discussion time and played with mathematics materials that were related to the storybook content during free play. The control group had ordinary storybook reading time and played with mathematics materials unrelated to the storybook content. The Learning Readiness Test and the Early Mathematics Achievement Test were administered. Four mathematics tasks were also given to compare the mathematics achievement of the two groups. The children's choice of favorite corners, the time spent, and the number of children who played in the mathematics corner were investigated also to measure children's disposition toward doing mathematics. The results showed that more children in the experimental group liked the mathematics comer, chose mathematics tasks, and spent more time in the mathematics corner. Furthermore, the experimental group did significantly better than the control group in the classification, number combination, and shape tasks, and there were qualitative differences in the content analysis.     

Reciprocal relationships between math self-concept and math anxiety

The present study examined the reciprocal relationships between self-concept and anxiety in mathematics. A sample of 495 grade 7 students (51% girls) completed self-report measures assessing self-concept and anxiety three times in a school year. Structural equation modeling was used to test a cross-lagged panel model of reciprocal effects between math self-concept and math anxiety. The analysis showed a reciprocal relationship between self-concept and anxiety in math (i.e., higher self-concept leads to lower anxiety, which in turn, leads to higher self-concept). However, the magnitude of the path from anxiety to self-concept is almost half of that from self-concept to anxiety. Overall, the results provide empirical support for the theoretical notion that math self-concept and math anxiety are reciprocally related.     

The Massachusetts math wars

This article recounts the battle in the “math wars” that took place in Massachusetts, United States in 1999–2000 over the scope, content and teaching of the state’s K-12 mathematics curriculum. Harsh controversies arose between the partisans of a “reform-math” movement stressing an undefined “conceptual understanding” and student-created algorithms and those, including the author, advocating an academically stronger mathematics curriculum as well as fluency in students’ computational skills with whole numbers and fractions. While “reform-math” supporters privileged and fought for a radical constructivist view of mathematics learning, the Massachusetts Board of Education decided to implement mathematics standards that linked strong academic content to the development of authentic computational competencies in students. Following the introduction of newly revised mathematic standards in 2000, real progress was reached in terms of student achievement. According to the results of the 2007 tests in reading and in mathematics for Grade 4 and Grade 8, reported by the National Assessment of Educational Progress (NAEP), Massachusetts ranked first nationwide in mathematics and tied for first place in reading, with its students having made significant gains from 2005 to 2007. The article makes a strong case for evidence-based curriculum design and implementation, freed, as much as possible, of mythologies and misconceptions. It explains why it was necessary to reject the theoretical assumptions and pedagogical strategies embedded in the National Council of Teachers of Mathematics’ 1989 and 2000 standards documents. It also highlights the importance of a strong personal life and working “principles” underpinning the mission of curriculum developers: successful reform “strategies” are indeed meaningless in the absence of such durable personal beliefs and values.

Got math attitude? (In)direct effects of student mathematics attitudes on intentions,behavioral engagement,and mathematics performance in the U.S. PISA

Academic performance is predicted by a multitude of demographic, contextual, cognitive, and noncognitive factors. The noncognitive factors predicting achievement in mathematics that have previously been investigated in depth are study skills, confidence, self-efficacy, and personality traits (Kyllonen, 2012). Limited applied research has explored the predictive value of attitudes and beliefs in mathematics achievement using representative data of U.S. students. The current study uses the theory of planned behavior (TPB) to explain high school students’ performance in mathematics in large-scale assessment data by using the PISA 2012. Along with key demographic factors, results indicated that students’ attitudes, subjective norms, and perceived behavioral control beliefs explained 21.1% of the variability in intentions to pursue and major in mathematics in the future, 59.4% of the variability in behavioral engagement with mathematics learning, and 30.7% of the variability in mathematics performance.The study results have implications on: (1) the applicability of an attitude-behavior framework in educational research for understanding academic performance, (2) the importance of perceived control and self-efficacy beliefs for predicting behavioral engagement in mathematics (e.g., paying attention in class, completing homework, studying for exams) and subsequent mathematics performance, and (3) the practical significance of students’ attitude towards mathematics on their intentions to pursue mathematics coursework in post-secondary education and possess math-relevant career aspirations.     

Groupitizing reflects conceptual developments in math cognition and inequities in math achievement from childhood through adolescence

Understanding the cognitive processes central to mathematical development is crucial to addressing systemic inequities in math achievement. We investigate the “Groupitizing” ability in 1209 third to eighth graders (mean age at first timepoint = 10.48, 586 girls, 39.16% Asian, 28.88% Hispanic/Latino, 18.51% White), a process that captures the ability to use grouping cues to access the exact value of a set. Groupitizing improves each year from late childhood to early adolescence (d = 3.29), is a central predictor of math achievement (beta weight = .30), is linked to conceptual processes in mathematics (minimum d = 0.69), and helps explain the dynamic between the ongoing development of non-symbolic number concepts, systemic educational inequities in school associated with SES, and mathematics achievement (minimum beta weight = .11) in ways that explicit symbolic measures may miss.     

Characteristic behaviors of students with LD who have teacher-identified math weaknesses

Mathematics learning disabilities (LD) have gained increased attention over the last decade from both researchers and practitioners. A large percentage of students receiving learning disability services experience difficulties with mathematics, but little research has examined the specific mathematics behaviors of students with LD who have teacher-identified math weaknesses. This study examines the literature on mathematics LD and identifies specific behaviors from that body of research for the purpose of determining the extent to which those behaviors are observed in students with LD. Data are presented from observations of 391 special education professionals on 1724 students with LD, 870 of whom had identified math weaknesses and 854 of whom did not. Our results validate the existing literature and provide implications for teachers, researchers, and others interested in studying mathematics LD.     

高职学生数学学习的心理障碍与教学对策

心理障碍是影响高职学生数学学习的一种消极心理现象。对这种心理现象进行分析和归纳,并在此基础上提出教学对策,对于提高高职数学的教学效率具有重要意义。本文从态度、能力、技能等4个方面分析了高职学生数学学习的心理障碍,并从建立动力系统和改进教学方法两方面给出了教学对策。     

Language factors associated with achievement grouping in math classrooms: a cross-sectional and longitudinal study

The study examines the effects of classroom achievement grouping (AG) practices on the early mathematics performance of language-minority students and compares their mathematics achievement to that of English-speaking majority students. Using a nationally representative database of the USA, both cross-sectional and longitudinal analyses were done. In the cross-sectional analyses we explored the direct effect of grouping practice on students performance, while in the longitudinal analysis we looked at the growth trajectory in mathematics learning. The results of cross-sectional analyses indicated that the effect of AG was negative on the math achievement in 1st and 5th graders. The longitudinal analysis showed a significant negative effect of AG for English Language Learners (ELL). The paper provides the basis for practical guidelines for the grouping practices in mathematics.     

Middle and high school math teaching for students with mild intellectual disability

The author briefly reviews studies on the math teaching of secondary school students with mild intellectual disabilities. Then, the author demonstrates ways to teach secondary-level mathematics to students with mild intellectual disabilities. In this article, readers will learn about how to use manipulatives, diagrams, and gestures to support students' thinking. Readers will also learn how to make connections between new and challenging math content to students' experiences inside and outside of school to support them as they think through mathematics.     

‘Slaughtering this beautiful math’: graduate women choosing and leaving mathematics

The quality of graduate students' relationships with faculty are crucial for students' success. Unfortunately, negative relationships with faculty are common for women in the sciences and mathematics. Six women doctoral students in one mathematics department in the US were interviewed to better understand the nature of their relationships with faculty members, and the effects of those relationships on their decisions to persist or to leave. These women described the limited or negative relationships they had with faculty. They spoke of ways in which they felt ignored, the lack of mentoring, advising, and other guidance, poor teaching, and a general lack of moral support. Each of them described ways in which they felt they did not ‘fit in’ in the department. These findings are interpreted through two lenses: the idea of participation in a community of practice and all that that entails, and Noddings' notions of caring. Implications for women in mathematics at all levels are discussed.     

Identifying children with persistent low math achievement: The role of number-magnitude mapping and symbolic numerical processing

Although an increasing number of research studies have investigated the cognitive deficits related to difficulties in learning mathematics, little is known about whether these cognitive deficits longitudinally predict low mathematics achievement over time. The current 6-year longitudinal study was conducted to address this issue. A sample of 101 students was tested on various numerical and cognitive competencies when they were in kindergarten and in Grade 1. They were then followed until they were in Grade 6, and their mathematics achievement was assessed bi-annually. A group of persistent low mathematics achievers (PLA) who scored consistently below the 25th percentile was identified. This group of PLA showed difficulties in most of the numerical tasks as early as kindergarten. More importantly, three of the early predictors correctly identified 79% of the PLAs. The current findings provide valuable information concerning the core cognitive deficits underlying difficulties in learning mathematics as well as an important tool for educators for identifying children who are at risk of persistent math learning difficulties in the elementary school years.     

Preservice education of math teachers using paradoxes

This is a report on a naturalistic study of the role mathematical paradoxes can play in the preservice education of high school mathematics teachers. The study examined the potential of paradoxes as a vehicle for: (a) sharpening student-teachers' mathematical concepts; (b) raising their pedagogical awareness of the constructive role of fallacious reasoning in the development of mathematical knowledge. Course material development and data collection procedures are described. Results obtained in parts of the study through written responses and class-videotapes are analyzed and discussed. The findings indicate that the model of dealing with paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions and constructive learning.This is a second report on this study. The first report (Movshovitz-Hadar, 1988) was a brief one, and focused on the problem, the procedures and findings in a general way. The present report is focused in details on one task. The authors intend to present an across tasks analysis in a third report to be presented at AERA 90.     

Hemispheric laterality in music and math

Hemispheric laterality may be a useful concept in teaching, learning, training, and in understanding more about human development. To address this issue, a measure of hemispheric laterality was compared to musical and mathematical ability. The Human Information Processing Survey (HIPS) instrument, designed to measure hemispheric laterality, was administered to 101 participants who were then asked to provide a measure of their conceptual aptitude for mathematics and music. Scores were then compared through canonical correlation to test the hypothesis that perceived mathematical ability may be explained by left-brain hemisphere preference and musical by the right hemisphere. A relatively strong correlation was found between music ability and right-brain hemisphere preference. A relationship between math and left-brain hemisphere preference or integrated brain processing scores was found to be marginal. Ramifications to learning are discussed.     

Preschool children's math-related behaviors mediate curriculum effects on math achievement gains

This study used a mediational model to examine the effect of curriculum condition on student behaviors and how those behaviors related to math achievement gains. The student behaviors examined were children's participation in learning-related activities, talking during learning activities, and level of engagement with the materials. Conducted as part of a larger project involving the implementation and evaluation of a preschool mathematics curriculum, this study involved twenty urban prekindergarten sites with 57 classrooms randomly assigned to the new curriculum or a practice-as-usual condition. The final analytic sample included 675 children, predominately from low-income homes. Results showed that the greater gains made by children in curriculum classrooms were mediated by the number of times children were observed focused on mathematics and the number of times they were observed talking during mathematics. Findings from this study demonstrate the importance of focusing on children's actual responses to a new curriculum in determining its effects.     

Dynamics of classroom motivation: Teacher enthusiasm and the development of math interest and teacher support

Interest is important for successful student learning, but little is known about the developmental dynamics between interest and social support in classrooms. Based on the stage-environment fit theory, this study investigated the interrelation of developmental changes in student class-level interest and perceived teacher support in mathematics classes over one school year after the students transitioned to secondary school. We also examined how teacher-reported enthusiasm was related to these changes. Data of 1000 students (53.6% male) and their classroom teachers (N = 42), who were surveyed at the beginning of Grades 5 and 6, were analyzed. The results showed a significant decline in class-level mathematics interest and perceived teacher support. Teacher-reported enthusiasm buffered the decline in class-level mathematics interest. When including bidirectional relationships between perceived teacher support and the students’ interest, perceived class-level teacher support in Grade 5 positively predicted the change in student interest and, thus, buffered the decline.