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"Place value (Mathematics)"
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What's the place value?
Introduces young children to the use of place values in mathematics-- Source other than Library of Congress.
Book
Place value at playtime
\"During recess, friends learn about place value by working together to add and subtract by tens on the playground at school\"-- Provided by publisher.
Book
Odd squad. Season 2, Episode 5, Oscar strikes back
Oscar Strikes Back - In this two-part episode, Oscar attends a gathering of Odd Squad scientists called Lab-Con at Odd Squad Academy. Curriculum: Place value and multi-addend addition.
Streaming Video
Countries with Higher Levels of Gender Equality Show Larger National Sex Differences in Mathematics Anxiety and Relatively Lower Parental Mathematics Valuation for Girls
Despite international advancements in gender equality across a variety of societal domains, the underrepresentation of girls and women in Science, Technology, Engineering, and Mathematics (STEM) related fields persists. In this study, we explored the possibility that the sex difference in mathematics anxiety contributes to this disparity. More specifically, we tested a number of predictions from the prominent gender stratification model, which is the leading psychological theory of cross-national patterns of sex differences in mathematics anxiety and performance. To this end, we analyzed data from 761,655 15-year old students across 68 nations who participated in the Programme for International Student Assessment (PISA). Most importantly and contra predictions, we showed that economically developed and more gender equal countries have a lower overall level of mathematics anxiety, and yet a larger national sex difference in mathematics anxiety relative to less developed countries. Further, although relatively more mothers work in STEM fields in more developed countries, these parents valued, on average, mathematical competence more in their sons than their daughters. The proportion of mothers working in STEM was unrelated to sex differences in mathematics anxiety or performance. We propose that the gender stratification model fails to account for these national patterns and that an alternative model is needed. In the discussion, we suggest how an interaction between socio-cultural values and sex-specific psychological traits can better explain these patterns. We also discuss implications for policies aiming to increase girls' STEM participation.
Journal Article
The influence of theoretical mathematical foundations on teaching and learning: a case study of whole numbers in elementary school
This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform -which was eventually itself replaced in the longer term - provides some keys to understanding the influence of mathematical theories on teaching and learning. The paper studies changes related to place value, a notion that was deeply impacted by the introduction of numeration bases other than ten in 1970, and their subsequent removal in the 1980s. What the author terms 'numeration units' (ones, tens, hundreds, thousands, etc.) and 'powers-often written in figures' (1, 10, 100, 1000, etc.) are key tools for describing and understanding changes. The author identifies two theories that have formed the basis for place value teaching in the twentieth century, and examines some aspects of their influence. The paper also addresses epistemological issues in the relation between academic mathematics and school mathematics, and highlights the role of units in the teaching of basic arithmetic.
Journal Article
Validation of a Model of Sustainable Place Value Understanding in Turkey
Research has shown that a profound place value understanding is crucial for success in learning mathematics. At the same time, a substantial number of students struggles with developing a sustainable place value understanding. In this regard, two aspects of the place value system appear especially relevant: First, the knowledge of the decimal structure of numbers, and second, the relation between the bundling units. To support teaching place value understanding, a developmental model of place value understanding focusing on both aspects has been constructed and validated in Germany. The model comprises five levels of place value understanding that build upon each other hierarchically. This study aims at validating the level hierarchy in Turkey to prepare the usage of the developmental model as learning trajectory for Turkish primary schools. N=437 Turkish students from Grades 2 through 4 completed a translated version of the item collection of the German validation study as well as a Turkish place value test that is not based on a developmental model. In a Rasch analysis, most items of the translated item collection showed item difficulties as predicted by the model. In a regression analysis, item difficulties were well predicted by their allocation within the level hierarchy, while other item characteristics did not inform about the item difficulties. Substantial correlations between the translated item collection and the Turkish test underpin the claim that the model is appropriate to assess Turkish students’ place value understanding as well as structuring place value instruction in Turkish primary schools.
Journal Article
Investigating prospective mathematics teachers’ use of concrete materials in place value concept in different bases: addition and subtraction with whole numbers
The aim of this study is to examine how prospective mathematics teachers (PMTs) conceptualize the place value concept in different number bases and how they utilize concrete materials in this process. To achieve this aim, a case study design was utilized. The participants of this study consist of 24 PMTs from a public university in Turkey. The participants of this study were asked to answer activity questions that required them to perform addition and subtraction operations on numbers written in base ten, base six and base three using at least two concrete materials. Participants completed this activity as a group, with four weeks to provide written responses and the freedom to use any type of concrete material. The findings revealed that PMTs employed not only proportional and non-proportional models, as stated in related literature, but also a mixed model approach. The use of the mixed model emerged as an effective strategy, allowing PMTs to leverage the strengths of both proportional and non-proportional models. Another finding indicated that PMTs were limited in generating solutions using a second concrete material. This limitation highlights the difficulties PMTs face in maintaining material diversity when working with different base systems, which in turn affects their ability to construct mathematical meaning.
Bu çalışmanın amacı, ortaokul matematik öğretmeni adaylarının (OMÖA) farklı sayı tabanlarında basamak değeri kavramını nasıl anlamlandırdıklarını ve bu süreçte somut materyalleri nasıl kullandıklarını incelemektir. Bu amacı gerçekleştirmek için durum çalışması deseni kullanılmıştır. Çalışmanın katılımcıları, Türkiye’deki bir devlet üniversitesinde öğrenim gören 24 OMÖA’dan oluşmaktadır. Katılımcılardan, onluk, altılık ve üçlük tabanlarda yazılmış sayılarla toplama ve çıkarma işlemlerini içeren etkinlik sorularını en az iki farklı somut materyal kullanarak yanıtlamaları istenmiştir. Katılımcılar bu etkinliği grup hâlinde tamamlamış, yazılı yanıtlarını dört hafta içinde sunmaları istenmiş ve herhangi bir tür somut materyal kullanma konusunda özgür bırakılmışlardır. Bulgular, OMÖA ‘ların basamak değeri için ilgili literatürde belirtilen orantısal ve orantısal olmayan modellere ek olarak karma model yaklaşımını da benimsediklerini ortaya koymuştur. Karma model kullanımı, öğretmen adaylarının orantısal ve orantısal olmayan modellerin güçlü yönlerinden yararlanmalarını sağlayan etkili bir strateji olarak öne çıkmıştır. Ayrıca, OMÖA’ların ikinci bir somut materyali kullanarak çözüm üretmede sınırlı kaldıkları ortaya çıkmıştır. Bu sınırlılık, OMÖA’ların farklı taban sistemleriyle çalışırken materyal çeşitliliğini sağlama konusunda karşılaştıkları zorlukları vurgulamakta ve bunun matematiksel anlam inşa etme süreçlerini etkilediğini ortaya koymaktadır.
Journal Article
Enhancing Established Counting Routines to Promote Place-Value Understanding: An Empirical Study in Early Elementary Classrooms
Understanding place value is a critical and foundational competency for elementary mathematics. Classroom teachers who endeavor to promote place-value development adopt a variety of established practices to varying degrees of effectiveness. In parallel, researchers have validated models of how young children acquire place-value understanding. Faced with competing demands, teachers may resist abrupt, disruptive, or time-intensive changes to existing practices. In this study, we explore ways of introducing changes in pedagogical supports that minimally disrupt existing classroom routines that nonetheless offer potential gains in children’s understanding of base-ten number concepts. Specifically, we examine the impact of modifying how teachers demonstrate and discuss representations of the ten-for-one structure during the familiar “Days in School” counting routine on young children’s place-value understanding. We report on a 2-year longitudinal study of a cohort of students beginning in grade one, conducted in nine classrooms across a control school and a treatment school. We describe the modifications in the counting routine and report the results of children’s development of base-ten number concepts. The percentage of children who identified base-ten number concepts was three times higher for the children in the treatment group than for the children in the control group. Moreover, nearly twice as many children in the treatment group as compared with the control group advanced beyond a concatenated single-digit conception by the end of second grade when counting two-digit quantities. We conclude with a discussion of the implications of our findings for early elementary mathematics education more generally.
Journal Article