Children's Mathematics Research Articles

By Way of Introduction: Moving beyond show & tell: Intentional math discourse

Welcome to the 2018 Teaching Children Mathematics (TCM) Focus Issue. Engaging students in meaningful mathematical discourse has long been identified as an essential component of students' mathematics learning. Principles to Actions: Ensuring Mathematical Success for All calls for teaching practices that—

Reflecting on the Cloud Clock problem

This problem scenario explores the analog clock, a rich source of tasks associated with angles and angle measures. The Cloud Clock problem is an opportunity for students to deepen their understanding of analog clocks, angles, and time and angle measurement. To access the full-size activity sheet, go to http://www.nctm.org/tcm, All Issues. Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics.

Economic disadvantage and math achievement: The significance of perceived cost from an evolutionary perspective

Children growing up in poverty tend to perform worse in school than their more economically advantaged peers. The current study integrates an educational theory of motivation and an evolutionary theory of life history strategies to examine how economic disadvantage predicts children's mathematics achievement through their academic beliefs and values. Participants were 1,536 students (Mage =12.88) in a large metropolitan city in the United States. Economic disadvantage was assessed via school reports of the student being eligible to receive free or reduced-price lunch during the 2014-2015 school year (i.e., at or below 185% of the federal poverty line). Students reported on their perceived interest, usefulness, and cost of learning mathematics during the first half of the 2015-2016 school year (August to December). Mathematics achievement for both school years was assessed via school reports of mathematics grades. Children receiving free or reduced-price lunch showed higher perceived cost of learning mathematics, and this in turn predicted changes in mathematics achievement over time, indirect effect=-0.57, 95% CI (-0.97, -0.23). However, neither interest nor perceived usefulness or ability in mathematics mediated the association between economic disadvantage and changes in mathematics achievement. Results underscore the potential for interventions to target students' perceived cost of learning as a way to increase school engagement, particularly among disadvantaged students.

Effectiveness of Kumon Teaching Method for Academic Achievement of Children in Mathematics

The experimental study was designed to investigate the effectiveness ofKumon method in comparison with traditional lecture method in theteaching of Mathematics to grade-5. Kumon is a math and readingenrichment program, which provides practice and instruction to eachindividual. This helps to think and work independently. The hypothesisof this study was that in Mathematics, Grade-5 students have nosignificant difference in their academic achievement treated by Kumonmethod and by traditional lecture method. The objective of the study wasto determine the effectiveness of Kumon method for academicachievement of children in Mathematics. All grade-5 students of Fazaiainter colleges of Rawalpindi and Islamabad was the population. Clustersampling technique was used. One of the three Fazaia colleges (juniorsection) was selected randomly. All grade-5 students of the selectedcluster formed the sample of the study. Data was collected and analyzedby applying t-test and recommendations were given on the basis offindings of the study. This study shows that Kumon method is moreeffective for teaching mathematics to Grade 5 students in comparisonwith traditional lecture method and equally helpful in teachingmathematics effectively to boys and girls.

Letters to the editor

Lyrics from the ever-so-popular 1980 song by Kool and the Gang seem to be a fitting way to kick off the twenty-fifth year of Teaching Children Mathematics (TCM). This milestone volume year will be one of joyous celebration as we commemorate the journal's numerous contributions to elementary school mathematics education during the past quarter of a century.

Revisiting the Bean Counting, Fog, and Snow problem

The problem scenario explores analog clocks, a rich source of tasks associated with angles and angle measures. To access the full-size activity sheet, go to http://www.nctm.org/tcm, All Issues. Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics.

The Developing Mental Number Line: Does Its Directionality Relate to 5- to 7-Year-Old Children's Mathematical Abilities?

Spatial representations of number, such as a left-to-right oriented mental number line, are well documented in Western culture. Yet, the functional significance of such a representation remains unclear. To test the prominent hypothesis that a mental number line may support mathematical development, we examined the relation between spatial-numerical associations (SNAs) and math proficiency in 5- to 7-year-old children. We found evidence of SNAs with two tasks: a non-symbolic magnitude comparison task, and a symbolic “Where was the number?” (WTN) task. Further, we found a significant correlation between these two tasks, demonstrating convergent validity of the directional mental number line across numerical format. Although there were no significant correlations between children’s SNAs on the WTN task and math ability, children’s SNAs on the magnitude comparison task were negatively correlated with their performance on a measure of cross-modal arithmetic, suggesting that children with a stronger left-to-right oriented mental number line were less competent at cross-modal arithmetic, an effect that held when controlling for age and a set of general cognitive abilities. Despite some evidence for a negative relation between SNAs and math ability in adulthood, we argue that the effect here may reflect task demands specific to the magnitude comparison task, not necessarily an impediment of the mental number line to math performance. We conclude with a discussion of the different properties that characterize a mental number line and how these different properties may relate to mathematical ability.

The mediating effect of the home environment for mathematics on the relationship between mothers' attitude toward mathematics and young children's mathematical ability

The mediating effect of the home environment for mathematics on the relationship between mothers' attitude toward mathematics and young children's mathematical ability

"알고리즘 기반의 수학활동이 유아의 수학적 문제해결력에 미치는 영향"

"알고리즘 기반의 수학활동이 유아의 수학적 문제해결력에 미치는 영향"

Mediated learning experience and its role in teaching fractions to pupils with learning difficulties

AbstractThis research focuses on studying the effect of mediated learning experience in children with learning difficulties in terms of deeper understanding of mathematical concepts. The main objective of the mediation method is to improve the cognitive skills of the participants through its close mediator' children interaction. This paper analysed the term "knowledge" and how it is often interpreted mistakenly by many teachers. In the survey participated 10 pupils with learning disabilities, aged 10, who attended the fifth class of primary school in Athens, Greece. Here, the action research methodology was used because the researcher took the role of mediator and worked with the students to explore the fractions. Research findings show that mathematical concepts are easier and deeper understood through practical activities and active participation of all members of the class. The mathematical abilities of children with learning difficulties and their self-confidence towards lesson have been boosted during the survey to a remarkable extent.

TCM index, volume 24 (September 2017–May 2018)

The 2017—2018 index for Teaching Children Mathematics contains both author and subject categories and appears online only.

Thank you

Teaching Children Mathematics (TCM) would not exist without the voluntary efforts of many mathematics educators. This journal benefits from the experience of those who have served as department editors, reviewers, and referees as well as members of the TCM Editorial Panel.

Does single parenthood put children’s school performance at risk?

With a good future for their children in mind, parents follow several strategies to invest in their children’s skills, education, norms and values. Some strategies, such as choosing a school or reading to children, require time commitments. For other strategies parents need money. Examples of such expensive strategies are extra-curricular classes or living in a ‘good’ neighborhood. Investing in children is thus a time-consuming and expensive process. Whereas parents who live together can often assist each other in this task, making all these investments could be harder for single parents. Should we therefore be worried about their children’s opportunities in life? How about children living with single parents from lower socioeconomic backgrounds? And if so, what can be done about it? We aim to answer these questions for Spain here, where single motherhood has become increasingly more common. We first use Census data to document the rise in single motherhood and show that in 1991 6% of children lived with a single mother, but that by 2011 this percentage had risen to 15%. We subsequently look at data from the PISA project of the OECD to look at the mathematical abilities of children living with single parents. Even though children living with single parents have slightly lower mathematics scores than those who live with two parents, these differences appear substantively barely relevant upon closer inspection. We argue that if we want to equalize opportunities in Spain we should not focus on family structure, but rather on other sources of inequality of opportunity such as income, neighborhoods and schools

S'more Fraction Fun

This article presents solutions to the April 2017 problem scenario, which offers students the opportunity to explore many ways to partition a square. Students can generate ideas about halves, thirds, and fourths through the exploration of squares and rectangles. Students can also recognize that equal shares do not necessarily have to be congruent. Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics.

Interactive Apps Promote Learning of Basic Mathematics in Children With Special Educational Needs and Disabilities.

Interactive apps delivered on touch-screen tablets can be effective at supporting the acquisition of basic skills in mainstream primary school children. This technology may also be beneficial for children with Special Educational Needs and Disabilities (SEND) as it can promote high levels of engagement with the learning task and an inclusive learning environment. However, few studies have measured extent of learning for SEND pupils when using interactive apps, so it has yet to be determined if this technology is effective at raising attainment for these pupils. We report the first observational study of a group of 33 pupils with SEND from two primary schools in Malawi that are implementing a new digital technology intervention which uses touch-screen tablets to deliver interactive apps designed to teach basic mathematical skills. The apps contain topics that align to the national curriculum. To assess learning gains, rate of progress (minutes per topic) for each pupil was determined by calculating the average time taken to complete a topic. Progress rate was then correlated with teacher ratings of extent of disability and independent ratings of pupil engagement with the apps. Results showed SEND pupils could interact with the apps and all pupils passed at least one topic. Average progress rate for SEND pupils was twice as long as mainstream peers. Stepwise regression revealed extent of disability significantly predicted progress rate. Further exploratory correlations revealed pupils with moderate to severe difficulties with hearing and/or language made slower progress through the apps than those with greater functionality in these two domains because the use of verbal instructions within the apps limited their capacity to learn. This original quantitative analysis demonstrates that interactive apps can raise learning standards in pupils with SEND but may have limited utility for pupils with severe difficulties. Software modifications are needed to address specific areas of difficulty preventing pupils from progressing.

Beyond Rhetoric: Authentically Supporting a Growth Mindset

Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at http:/www.nctm.org/WriteForTCM.

Top Tips for Being Your Best

Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at http:/www.nctm.org/WriteForTCM.

The Traveling Caterpillar

This article describes how students in first, third, and firth grade worked on the traveling caterpillar task with Katie Hurckes; it includes an analysis of students' thinking. Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. Find detailed submission guidelines for all departments at http://www.nctm.org/WriteForTCM.

Investigating the relationship between two home numeracy measures: A questionnaire and observations during Lego building and book reading.

Home numeracy has been defined as the parent-child interactions that include experiences with numerical content in daily-life settings. Previous studies have commonly operationalized home numeracy either via questionnaires or via observational methods. These studies have shown that both types of measures are positively related to variability in children's mathematical skills. This study investigated whether these distinctive data collection methods index the same aspect of home numeracy. The frequencies of home numeracy activities and parents' opinions about their children's mathematics education were assessed via a questionnaire. The amount of home numeracy talk was observed via two semi-structured videotaped parent-child activity sessions (Lego building and book reading). Children's mathematical skills were examined with two calculation subtests. We observed that parents' reports and number of observed numeracy interactions were not related to each other. Interestingly, parents' reports of numeracy activities were positively related to children's calculation abilities, whereas the observed home numeracy talk was negatively related to children's calculation abilities. These results indicate that these two methods tap on different aspects of home numeracy. Statement of contribution What is already known on this subject? Home numeracy, that is, parent-child interactions that include experiences with numerical content, is supposed to have a positive impact on calculation or mathematical ability in general. Despite many positive results, some studies have failed to find such an association. Home numeracy has been assessed with questionnaires on the frequency of numerical experiences and observations of parent-child interactions; however, those two measures of home numeracy have never been compared directly. What does this study add? This study assessed home numeracy through questionnaires and observations in the 44 parent-child dyads and showed that home numeracy measures derived from questionnaires and observations are not related. Moreover, the relation between the reported frequency of home numeracy activities and calculation on the one hand, and parent-child number talk (derived from observations) and calculation on the other hand is in opposite directions; the frequency of activities is positively related to calculation performance; and the amount of number talk is negatively related to calculation. This study shows that both measures tap into different aspects of home numeracy and can be an important factor explaining inconsistencies in literature.

MATHEMATICAL ABILITIES AND EDUCATIONAL STRATEGIES FOR CHILDREN WITH AUTISM SPECTRUM DISORDER

The exploration of mathematical abilities in children with Autism Spectrum Disorder (ASD) reveals a diverse and complex landscape, highlighting both strengths and challenges. Structured mathematics education plays a vital role in the cognitive development of these children by offering tailored, predictable methods that address their unique learning needs. King, Lemons, and Davidson (2016) stress the importance of evidence-based practices to help students with disabilities meet rigorous mathematical standards. Their review underscores the necessity of targeted interventions, particularly for students with co-occurring intellectual disabilities. Iuculano et al. (2014) further explore the cognitive strengths of children with ASD in mathematics, revealing that these individuals often employ sophisticated problem-solving strategies, despite differences in brain activation patterns compared to their typically developing peers. This suggests that specialized educational approaches could leverage these strengths effectively. Oswald et al. (2016) address the spectrum of mathematical achievement within ASD, from mathematical disabilities to giftedness, and the influence of cognitive and clinical factors such as test anxiety and perceptual reasoning. Their findings emphasize the need for interventions that consider individual differences in mathematical ability. Chiang and Lin (2007) and Titeca, Roeyers, and Desoete (2017) highlight the variability in mathematical skills among children with Asperger Syndrome (AS) and high-functioning autism (HFA), showing that while some have average abilities, others may exhibit significant weaknesses or exceptional skills. Early numerical competencies were found to be similar between children with ASD and typically developing peers, suggesting that early educational strategies should focus on foundational skills. Wei et al. (2015) examine longitudinal growth and achievement profiles, identifying distinct categories such as hyperlexia and hypercalculia, and noting how socioeconomic factors impact mathematical development. These studies collectively advocate for a nuanced understanding of ASD and suggest that tailored, evidence-based educational strategies are crucial for supporting the diverse needs of students with autism.