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"Decimal system."
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On beyond a million : an amazing math journey
Explores counting by powers of ten all the way up to the largest numbers that exist.
Book
Locating Indian knowledge in modern libraries: Incorporating the traditional classification of knowledge in India
Historically, Indian Knowledge, has been classified into
Aṣṭādaśa-vidyāsthānas
(अष्टादशविद्यास्थान), eighteen abodes of knowledge. This classification scheme assigns an appropriate place for all components of Indian knowledge in a consistent system. In modern libraries, based mainly on the Dewey Decimal Classification (DDC), there is no natural place for the corpus of Indian Knowledge (IK), and different components of IK get split over widely separate diverse classes. In this article, we describe India’s traditional classification of knowledge and propose a national modification of the DDC to incorporate the former. The proposed scheme shall ensure that the diverse corpora of IK are compactly brought together in Indian libraries. This shall help the students and scholars appreciate the breadth and depth of IK and also the interconnectedness of its different components. It is impossible to understand the history of any element of IK, including Indian Sciences and Technologies, without comprehending the interconnectedness of the entire corpus.
Journal Article
When Numbers Whisper Their Names – Number Word Processing in Multi-Digit Number Magnitude Comparison in French Speakers
French number words provide a unique window into the relationship between numerical cognition and language, because numbers above 60 follow a vigesimal (base-20) word structure (e.g., 72 = “60–12”). In a two-digit magnitude comparison task with sixty French native speakers, we replicated the classic unit-decade compatibility effect (UDCE; slower responses when unit and decade comparisons conflict) and within-decade effect (faster responses when decades are identical), reflecting the place-value structure of Arabic numerals. Given the French vigesimal system, we expected not only the classic UDCE and within-decade effect but also their vigesimal counterparts driven by magnitudes of number words: a unit-vigintade compatibility effect (UVCE) and a within-vigintade effect, in which pairs sharing the same decade word (e.g., “soixante” for the 60s and 70s) are processed faster than other between-decade pairs. Linear mixed models revealed both a UDCE for numbers larger than 60 and a UVCE, indicating that number words were accessed during processing. Participants also responded faster to within-vigintade items (86 vs. 95) than to between-vigintade items (76 vs. 85) and as fast as to within-decade items (82 vs. 85), indicating a verbal equivalent of the within-decade effect. This effect is unaffected by decade distance and can only be explained by access to number words so that the decades were identical (“80–6” vs. “80–15”). Overall, our data indicate that verbal representations can shape basic numerical judgments and that number processing may be more closely tied to language than previously assumed.
Journal Article
How 15 Hundred Is Like 15 Cherries: Effect of Progressive Alignment on Representational Changes in Numerical Cognition
How does understanding the decimal system change with age and experience? Second, third, sixth graders, and adults (Experiment 1: N = 96, mean ages = 7.9, 9.23, 12.06, and 19.96 years, respectively) made number line estimates across 3 scales (0-1,000, 0-10,000, and 0-100,000). Generation of linear estimates increased with age but decreased with numerical scale. Therefore, the authors hypothesized highlighting commonalities between small and large scales (15: 100:: 1500: 10000) might prompt children to generalize their linear representations to ever-larger scales. Experiment 2 assigned second graders (N = 46, mean age = 7.78 years) to experimental groups differing in how commonalities of small and large numerical scales were highlighted. Only children experiencing progressive alignment of small and large scales successfully produced linear estimates on increasingly larger scales, suggesting analogies between numeric scales elicit broad generalization of linear representations.
Journal Article
Inhibitory control and decimal number comparison in school-aged children
School-aged children erroneously think that 1.45 is larger 1.5 because 45 is larger than 5. Using a negative priming paradigm, we investigated whether the ability to compare the magnitude of decimal numbers in the context in which the smallest number has the greatest number of digits after the decimal point (1.45 vs. 1.5) is rooted in part on the ability to inhibit the \"greater the number of digits the greater its magnitude\" misconception derived from a property of whole numbers. In Experiment 1, we found a typical negative priming effect with 7th graders requiring more time to compare decimal numbers in which the largest number has the greatest number of digits after the decimal point (1.65 vs. 1.5) after comparing decimal numbers in which the smallest number has the greatest number of digits after the decimal point (1.45 vs. 1.5) than after comparing decimal numbers with the same number of digits after the decimal point (1.5 vs. 1.6). In Experiment 2, we found a negative priming effect when decimal numbers preceded items in which 7th graders had to compare the length of two lines. Taken together our results suggest that the ability to compare decimal numbers in which the smallest number has the greatest number of digits is rooted in part on the ability to inhibit the \"greater the number of digits the greater its magnitude\" misconception and in part on the ability to inhibit the length of the decimal number per se.
Journal Article
Saving the Toughest for Last: 50th Completers’ Final U.S. State High Points
This paper finds that the most difficult U.S. state high point climbs are saved for the end. 50th completers are significantly more likely to save more difficult U.S. state high points for their final high point ascent. There is also some more limited evidence that 50th completers save more distant high points for their final ascent.
Journal Article
Happiness Underestimated
In this paper, an exploratory study was conducted to investigate a potential measurement bias in happiness studies using 0-10 Likert scales. A total of 121 college students from a public university in California participated in the study by completing a hypothetical subjective well-being survey. The survey consisted of 23 scenarios with varying levels of happiness or unhappiness, and the students were asked to rate their level of happiness/unhappiness on the 11-point Likert Scales. The results showed that there was an inconsistent understanding of the scale when the expected value was between 7 and 8 on the 0 to 10 Likert scale, which leads to a higher variance and lower observation values. Based on these findings, it is suggested that an alternative scale length or a -5 to 5 scale should be considered to improve data quality.
Journal Article
Numeros y Operaciones: Sistema Decimales y valor posicional
Obten una mayor comprension sobre los decimales y el valor posicional con este atractivo recurso. Los conceptos incluyen: bloques de decimales, sumar, contar, tabla de valor posicional, resta. Este recurso, redactado para los estudiantes de tercer a quinto grado, se divide en tres secciones: Hojas de tarea con problemas de texto, seguido por Hojas de simulacro para practicar la competencia de los estudiantes en las habilidades procesales, y finalmente una prueba de evaluacion. La clave de respuestas esta incluida. Sus estudiantes tendran una amplia oportunidad de aprender todas las expectativas de los Conceptos Basicos Comunes del Curriculo de los Capitulos de Matematicas de Numeros y Operaciones de NCTM.
eBook
