Comparisons of U.S. and Japanese first graders' cognitive representation of number and understanding of place value.

1989 ◽  
Vol 81 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Irene T. Miura ◽  
Yukari Okamoto
2017 ◽  
Vol 23 (7) ◽  
pp. 404-412
Author(s):  
Aki Murata ◽  
Chana Stewart

This set of lesson examples demonstrates effective uses of magnets, number lines, and ten-frames to implement practice standards as first graders use place value to solve addition problems.


1990 ◽  
Vol 21 (3) ◽  
pp. 180-206 ◽  
Author(s):  
Karen C. Fuson ◽  
Diane J. Briars

A learning/teaching approach used base-ten blocks to embody the English named-value system of number words and digit cards to embody the positional base-ten system of numeration. Steps in addition and subtraction of four-digit numbers were motivated by the size of the blocks and then were carried out with the blocks; each step was immediately recorded with base-ten numerals. Children practiced multidigit problems of from five to eight places after they could successfully add or subtract smaller problems without using the blocks. In Study 1 six of the eight classes of first and second graders (N=169) demonstrated meaningful multidigit addition and place-value concepts up to at least four-digit numbers; average-achieving first graders showed more limited understanding. Three classes of second graders (N=75) completed the initial subtraction learning and demonstrated meaningful subtraction concepts. In Study 2 most second graders in 42 participating classes (N=783) in a large urban school district learned at least four-digit addition, and many children in the 35 classes (N=707) completing subtraction work learned at least four-digit subtraction.


2003 ◽  
Vol 10 (2) ◽  
pp. 78-82
Author(s):  
Amy R. Kari ◽  
Catherine B. Anderson

The problem 11 + 9 was written on the board at the front of the room. Eleven first graders and nine second graders sat on the carpet, their facial expressions intent as they thought about solutions. I had asked them to try to think of strategies they could use that did not involve counting on their fingers. They did not use paper and pencil because this was what we call “Mental Math” time at our school.


1999 ◽  
Vol 6 (3) ◽  
pp. 154-159
Author(s):  
Susan Hampton Auriemma

How much is a hundred?” How would your students respond to such a question? This article shares the experiences of my first graders as they participated in activities that develop number sense to answer this question. Teaching number sense to students in grades K–4 is an important goal of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The following activities are based on the Standards in many ways. They require problem solving, reasoning, communicating, and connecting mathematics to everyday situations that interest children. They provide opportunities to develop measurement and place-value concepts and to integrate reading, writing, drawing, and mathematics in ways that contribute to a cooperative learning environment.


1994 ◽  
Vol 17 (3) ◽  
pp. 401-411 ◽  
Author(s):  
Irene T. Miura ◽  
Yukari Okamoto ◽  
Chungsoon C. Kim ◽  
Chih-Mei Chang ◽  
Marcia Steere ◽  
...  

Cross-national comparisons of mathematics achievement have shown differences in favour of Asian students. This study examined the idea that the superior mathematics performance of students from Japan, Korea, and China may be due, in part, to differences in cognitive representation of number that is affected by numerical language characteristics differentiating Asian and non-Asian language groups. First-graders from the People's Republic of China, Japan, Korea, France, Sweden, and the United States were asked to construct various numbers using Base 10 blocks. Chinese, Japanese, and Korean children showed a preference for using a construction of tens and ones to show numbers; place value appeared to be clearly represented in those constructions. French, Swedish, and US children, in contrast, showed a preference for using a collection of units, suggesting that they represent number as a grouping of counted objects. More Asianlanguage speakers than non-Asian-language speakers were also able to make two correct constructions for each number, which suggests greater flexibility of mental number manipulation. Thus, the unique characteristics of the Asian number language system may facilitate the teaching and learning of mathematics, especially computation, for speakers of those languages.


Author(s):  
Lucia M. Flevares ◽  
Michelle Perry ◽  
Shereen Oca Beilstein ◽  
Neet Priya Bajwa

1957 ◽  
Vol 4 (5) ◽  
pp. 217-218
Author(s):  
Irene R. MacRae

Many teachers find that place value is one of the more difficult number concepts to explain to small children. The following game was devised to help reinforce the understanding of place value after it has been introduced by the use of the Hundreds, Tens and Ones Chart. This chart is familiar to primary teachers. The game uses the same pocket device used in the chart. Thus children can reinforce their initial learning by practice under conditions similar to those in which the learning took place.


2014 ◽  
Vol 30 (3) ◽  
pp. 231-237 ◽  
Author(s):  
Markus Quirin ◽  
Regina C. Bode

Self-report measures for the assessment of trait or state affect are typically biased by social desirability or self-delusion. The present work provides an overview of research using a recently developed measure of automatic activation of cognitive representation of affective experiences, the Implicit Positive and Negative Affect Test (IPANAT). In the IPANAT, participants judge the extent to which nonsense words from an alleged artificial language express a number of affective states or traits. The test demonstrates appropriate factorial validity and reliabilities. We review findings that support criterion validity and, additionally, present novel variants of this procedure for the assessment of the discrete emotions such as happiness, anger, sadness, and fear.


2014 ◽  
Vol 45 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Maya Machunsky ◽  
Thorsten Meiser

This research investigated whether relative ingroup prototypicality (i.e., the tendency to perceive one’s own ingroup as more prototypical of a superordinate category than the outgroup) can result from a prototype-based versus exemplar-based mental representation of social categories, rather than from ingroup membership per se as previously suggested by the ingroup projection model. Experiments 1 and 2 showed that a prototype-based group was perceived as more prototypical of a superordinate category than an exemplar-based group supporting the hypothesis that an intergroup context is not necessary for biased prototypicality judgments. Experiment 3 introduced an intergroup context in a minimal-group-like paradigm. The findings demonstrated that both the kind of cognitive representation and motivational processes contribute to biased prototypicality judgments in intergroup settings.


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