Children's mathematical skills were considered in relation to executive functions. Using multiple measures--including the Wisconsin Card Sorting Task (WCST), dual-task performance, Stroop task, and counting span-it was found that mathematical ability was significantly correlated with all measures of executive functioning, with the exception of dual-task performance. Furthermore, regression analyses revealed that each executive function measure predicted unique variance in mathematics ability. These results are discussed in terms of a central executive with diverse functions (Shallice & Burgess, 1996) and with recent evidence from Miyake, et al. (2000) showing the unity and diversity among executive functions. It is proposed that the particular difficulties for children of lower mathematical ability are lack of inhibition and poor working memory, which result in problems with switching and evaluation of new strategies for dealing with a particular task. The practical and theoretical implications of these results are discussed, along with suggestions for task changes and longitudinal studies that would clarify theoretical and developmental issues related to executive functioning.
Publicly funded prekindergarten programs have achieved small-to-large impacts on children's cognitive outcomes. The current study examined the impact of a prekindergarten program that implemented a coaching system and consistent literacy, language, and mathematics curricula on these and other nontargeted, essential components of school readiness, such as executive functioning. Participants included 2,018 four and five-year-old children. Findings indicated that the program had moderate-to-large impacts on children's language, literacy, numeracy and mathematics skills, and small impacts on children's executive functioning and a measure of emotion recognition. Some impacts were considerably larger for some subgroups. For urban public school districts, results inform important programmatic decisions. For policy makers, results confirm that prekindergarten programs can improve educationally vital outcomes for children in meaningful, important ways.
As students create and analyze mathematical knots, they develop their ability to reason spatially and engage in concepts not typically part of a geometry curriculum. Originally published in the May 2018 issue of TCM, this problem allows students to expand their understanding of mathematics by exploring knot theory.
As the staff and Editorial Panel of twenty-five-year-old Teaching Children Mathematics (TCM) prepare to retire the journal, we would be remiss if we failed to acknowledge that TCM would not have existed for a quarter of a century without the voluntary efforts of many, many mathematics educators who have served as department editors, reviewers, and referees as well as members of the editorial panel.
This study focuses on mathematics anxiety in nine- to eleven-year-old children and compares the mathematics anxiety of pupils taught in a traditional manner with that of pupils whose teachers adopted an alternative teaching approach emphasising problem-solving and discussion of pupils' own informal strategies. One finding is that pupils who were exposed to a traditional approach reported more mathematics anxiety than those who were exposed to the alternative approach, particularly with regard to the social, public aspects of doing mathematics. The question is raised whether it is these public aspects of doing mathematics in the presence of teachers and peers which actually evoke mathematics anxiety in many pupils, and not working with numbers or doing sums. However, the majority of pupils in this study reacted with either high or low anxiety to both aspects of doing mathematics.
Explore the new edition-including video clips, a sample chapter, and related blogs-at Heinemann.com/ChildrensMath The bestselling first edition of Children's Mathematics helped hundreds of thousands of teachers understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding. The highly anticipated Second Edition provides new insights about Cognitively Guided Instruction based on the authors' research and experience in CGI classrooms over the last 15 years. Highlights include:
A new expanded collection of over 90 online video episodes illustrating children's mathematical thinking, interactions between students and teachers, and classroom instruction that builds on children's mathematical thinking.
Together, the Second Edition and videos provide a detailed research-based account of the development of children's mathematical thinking and problem solving, and how teachers can promote this development in ways that honor children's thinking.
Thomas Carpenter was Professor Emeritus of Curriculum and Instruction at the University of Wisconsin-Madison, where he taught for twenty-five years. He is the former editor of the National Council of Teachers of Mathematics (NCTM) Journal for Research in Mathematics Education, and has received the NCTM Lifetime Achievement award for Distinguished Service to Mathematics Education (2004) among other awards. Tom passed away in August 2018, leaving behind a vast legacy to mathematics education thanks to his research into Cognitively Guided Instruction (CGI). That work, created by him and his team of researchers and authors, is available to all teachers in his influential and popular books Children's Mathematics, Thinking Mathematically, and Young Children's Mathematics. In addition, members of Tom's team have already begun the process of extending out from his work in CGI with Extending Children's Mathematics. Read more about Tom and his legacy, including warm remembrances from other influential members of the field of mathematics education.
Elizabeth Fennema is Emerita Professor of Curriculum and Instruction and Senior Scientist at the Wisconsin Center for Education Research at the University of Wisconsin-Madison. She has studied the teaching and learning of mathematics throughout her professional career, and is well known for her work on gender and mathematics.
Megan Loef Franke is a Professor in the Graduate Department of Education at UCLA where her research focuses on supporting teacher learning for both pre- and in-service teachers, diversity in mathematics education, and leadership in urban low performing schools. She was recently elected to the National Academy of Education. Megan is known for her work on Cognitively Guided Instruction (CGI), her leadership in UCLA's Center X, and her ongoing professional development work to support teachers, schools, and communities. Read a recent blog by Megan: What is Cognitively Guided Instruction Follow her on Twitter @meganlfranke
Linda Levi is the Director of the CGI Math Teacher Learning Center, an agency devoted to supporting teachers' understanding of children's mathematical thinking through Cognitively Guided Instruction. She works directly with schools, districts, education cooperatives, and State Departments of Education to provide CGI professional development. Linda is coauthor of three influential CGI books, all published by Heinemann: Children's Mathematics, second edition (2014), Extending Children's Mathematics (2011), and Thinking Mathematically (2003). These books have helped hundreds of thousands of teachers understand children's intuitive problem-solving strategies and computational skills. Learn more about Cognitively Guided Instruction here: Heinemann.com/CGImath Click here for updates about the CGI Math Teacher Learning Center. Follow Linda on Twitter: @LLeviCGIMath
Susan Empson is a professor and the Richard Miller endowed chair of mathematics education at the University of Missouri. Her research has consistently been supported by the National Science Foundation and the Spencer Foundation, including a recent NSF grant to study elementary teachers' learning and development centered on teaching in ways that are responsive to children's mathematical thinking in the domain of rational numbers. Susan is a coauthor of bestselling books focused on Cognitively Guided Instruction (CGI), including Children's Mathematics and Extending Children's Mathematics. Read a blog post adapted from Extending Children's Mathematics: How to Build Meaning for Fractions with Word Problems
The pandemic of coronavirus disease 2019 (COVID-19) has led to sudden and unexpected circumstances in education for all the involved people (pupils, teachers, education policymakers, parents). International organizations have paid attention to their responses in crises by using alternative modes of teaching. The typical teaching methods had to be replaced by e-learning processes and all the participants needed to adjust themselves and adapt innovative methods. Most studies concentrated on teachers' and students' difficulties, barriers and new challenges. However, a different role was given to parents as well, especially in the case of primary and the first grades of secondary education, as they were asked to facilitate their children to use the e-learning processes and support them during the learning process. The present study examined the change of parental involvement during the pandemic in comparison to the previous situation in the case of mathematical subject. A questionnaire was constructed and administered to parents from Cyprus at the first days of the school year 2019-2020 in order to examine their beliefs and self-efficacy beliefs about their parental role and involvement during homework at their children's mathematical understanding and the development of their children's perseverance strategies during mathematical problem solving. The same questionnaire was administered to them at the end of the e-learning teaching processes in May 2020, after they had alternative experiences in order to identify any differences at their respective beliefs. Only the sample of parents who took pa