Acquisition of the counting principles during the subset-knower stages: Insights from children’s errors

Studies on children’s understanding of counting examine when and how children acquire the cardinal principle: the idea that the last word in a counted set reflects the cardinal value of the set. Using Wynn’s (1990) Give-N Task, researchers classify children who can count to generate large sets as having acquired the cardinal principle (cardinal-principle-knowers) and those who cannot as lacking knowledge of it (subset-knowers). However, recent studies have provided a more nuanced view of number word acquisition. Here, we explore this view by examining the developmental progression of the counting principles with an aim to elucidate the gradual elements that lead to children successfully generating sets and being classified as CP-knowers on the Give-N Task. Specifically, we test the claim that subset-knowers lack cardinal principle knowledge by separating children’s understanding of the cardinal principle from their ability to apply and implement counting procedures. We also ask when knowledge of Gelman & Gallistel’s (1978) other how-to-count principles emerge in development. We analyzed how often children violated the three how-to-count principles in a secondary analysis of Give-N data (N = 86). We found that children already have knowledge of the cardinal principle prior to becoming CP-knowers, and that understanding of the stable-order and word-object correspondence principles likely emerged earlier. These results suggest that gradual development may best characterize children’s acquisition of the counting principles, and that learning to coordinate all three principles represents an additional step beyond learning them individually.

Language effects in early development of number writing and reading

Reading and writing multidigit numbers requires accurate switching between Arabic numbers and spoken number words. This is particularly challenging in languages with number-word inversion such as German (24 is pronounced as four-and-twenty), as reported by Zuber, Pixner, Moeller, and Nuerk (2009, https://doi.org/10.1016/j.jecp.2008.04.003). The current study aimed to replicate the qualitative error analysis by Zuber et al. and further extended their study: 1) A cross-linguistic (German, English) analysis enabled us to differentiate between language-dependent and more general transcoding challenges. 2) We investigated whether specific number structures influence accuracy rates. 3) To consider both transcoding directions (from Arabic numbers to number words and vice versa), we assessed performance for number reading in addition to number writing. 4) Our longitudinal design allowed us to investigate transcoding development between Grades 1 and 2. We assessed 170 German- and 264 English-speaking children. Children wrote and read the same set of 44 one-, two- and three-digit numbers, including the same number structures as Zuber et al. For German, we confirmed that a high amount of errors in number writing was inversion-related. For English, the percentage of inversion-related errors was very low. Accuracy rates were strongly related to number syntax. The impact of number structures was independent of transcoding direction or grade level and revealed cross-linguistic challenges of transcoding multidigit numbers. For instance, transcoding of three-digit numbers containing syntactic zeros (e.g., 109) was significantly more accurate than transcoding of items with lexical zeros (e.g., 190). Based on our findings, we suggest adaptations of current transcoding models.

Cross-Format Integration of Auditory Number Words and Visual-Arabic Digits: An ERP Study

Converting visual-Arabic digits to auditory number words and vice versa is seemingly effortless for adults. However, it is still unclear whether this process takes place automatically and whether accessing the underlying magnitude representation is necessary during this process. In two event-related potential (ERP) experiments, adults were presented with identical (e.g., “one” and 1) or non-identical (e.g., “one” and 9) number pairs, either unimodally (two visual-Arabic digits) or cross-format (an auditory number word and a visual-Arabic digit). In Experiment 1 (N=17), active task demands required numerical judgments, whereas this was not the case in Experiment 2 (N=19). We found pronounced early ERP markers of numerical identity unimodally in both experiments. In the cross-format conditions, however, we only observed late neural correlates of identity and only if the task required semantic number processing (Experiment 1). These findings suggest that unimodal pairs of digits are automatically integrated, whereas cross-format integration of numerical information occurs more slowly and involves semantic access.

ANALISIS KESALAHAN PENGGUNAAN KATA BILANGAN UNIVERSAL “SEMUA, SEGALA, SELURUH DAN SEGENAP” PADA PEMULA PELAJAR MANDARIN INDONESIA

ABSTRAKPenelitian ini terutama ditujukan untuk analisis penguasaan dan kesalahan kata bilangan universal "semua", "segala" , “seluruh” dan "segenap" mahasiswa Indonesia dalam belajar bahasa Mandarin. Didalam Bahasa Indonesia juga memiliki kata bilangan yang serupa ini, tetapi kata bilangan tersebut masih berbeda dengan bilangan universal dalam bahasa mandarin. Oleh karena itu, mahasiswa Indonesia lebih cenderung membuat kesalahan saat mempelajari kata bilangan ini. Secara umum, tingkat terjadinya kesalahan lebih condong ke pembelajar pemula, penyebabnya yaitu pengaruh negatif dari bahasa ibu dan pemahaman bahasa mandarin yang tidak cukup dalam. Penulis menggunakan metode kualitatif dalam penelitian ini, dan didapatkan kesimpulan bahwa pelajar Indonesia mengalami kesulitan dalam menggunakan kata bantu bilangan universal bahasa Mandarin"semua", "segala" , “seluruh” dan "segenap" yaitu mereka tidak bisa membedakan pemakaian keempat kata bilangan tersebut.Kata Kunci: kesalahan penggunaan, kata bilangan se-, pelajar indonesia ABSTRACTThis article is mainly aimed at analyzing the mastery and errors of universal number words "所有，一切，全部” Indonesian students in learning Chinese. In Indonesian it also has a similar number word, but the number word is still different from the universal number in Chinese language. Therefore, Indonesian students are more likely to make mistakes when learning these number words. In general, the error rate is more likely for the beginner Chinese learners, the negative influence of the mother language and the insufficient understanding of the Chinese language. This analysis is based on the situation of beginner level students learning Chinese in Indonesia.Keywords: Usage errors, number words, Indonesian students

ASMĀ' AL-A'DĀD WA KINĀYĀTUHA FĪ AL-QUR'AN AL-KARĪM (DIRĀSAH TAHLĪLIYYAH NAHWIYYAH)

In the types of words there is a chapter on numerals and their kinayah. It is widely used in Arabic, either in conversation or in Arabic texts. The purpose in this research is to describe the number words and their kinayah, as well as the form of the number word phrase and the position of the number word and its kinayah in the verse of the holy Quran. The type in this research is library research with a content analysis design (adapted from Krippendorf) because it is based on the data sources in this study in the form of documents. The primary data in this study was the holy Quran and the secondary data in this study were taken from books related to the research. And the results of this study, 1. Quantity of number word 37 words in the Quran 2. Quantity of kinayah number in the Quran 4 words 3. Quantity of position number 17 verse in the Quran 4. Quantity of position kinayah number 6 verse in the Quran.

Measuring Emerging Number Knowledge in Toddlers

Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children’s cardinal number knowledge and understanding of exact number words but does not capture children’s preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., “Which has three?”). Two- to three-year-old toddlers (N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children’s emerging number knowledge and capturing nuances in children’s number-word knowledge that Give-N may miss.

Student-generated learning objectives and curricular innovation

Introduction Recent focus from accrediting bodies emphasizes learning objectives as a means of mapping and standardizing content coverage. While most educational training centers on faculty-derived learning objectives that are geared towards didactic lectures, student-centered teaching modalities like problem-based learning continue to gain popularity. One opportunity is the integration of student-generated learning goals in curriculum development. The educational philosophy at the Penn State College of Medicine University Park Regional Campus centers on discussion-based Inquiry Groups that focus on students’ experiential case learning which leads to student-generated learning objectives. This study examined a student-centered approach to learning objectives. Methods Our quantitative analysis explored student-generated learning objectives during the first-year curriculum. Primary outcome measures included process variables investigating the growth and change of objectives across the year that include Bloom’s taxonomy-based verb scores, verb numbers per session, and learning objective word lengths. Knowledge-based content coverage variables were compared with existing curricular models. Results Student-derived learning objectives changed substantially over the year. Taxonomy scores decreased while the learning objective verb number, word length, and calculated value per session increased significant. Content and comparator analyses showed that coverage and verb quality met or exceeded existing curricular models. Discussion Student-generated learning objectives are not only plausible and achievable, they also provide distinct pacing and engagement benefits. Our findings serve as a model for student-centered educational innovations.

How Reliable is the Give-a-Number task?

The Give-a-Number task has become a gold standard of children’s number word comprehension and has been increasingly used to organize debate in developmental psychology. In this task, the experimenter asks children to give specific numbers of objects (e.g., 1 to 6), and based on their pattern of responses, children are classified into stages that can be readily related to other developmental milestones. The increasing popularity of Give-a-Number raises the question of how reliable it is, since the size of a correlation between two different tasks cannot reliably exceed the test- retest reliability of either measure taken individually. In Experiment 1, 2- to 4-year-old children were tested twice in a single session with Wynn’s (1992) version of the Give-a- Number task, which features a titrated design. In Experiment 2, we tested a second group of children with an alternative version that uses a larger number of trials in a non-titrated design. We found that in both cases the task was highly reliable in differentiating children who could accurately count from those who could not, but that reliability differed for specific numbers, and was more reliable for very small numbers (i.e., “one” and “two”) than for slightly larger ones (i.e., “three” and “four”). We discuss practical implications of these results for researchers studying numeracy and discuss further directions to assess the validity of the task.

The Acquisition of French Un

How does cross-linguistic variation in grammatical structure affect children’s acquisition of number words? In this study, we addressed this question by investigating the case study of young speakers of French, a language in which the number one and the indefinite article a are phonologically the same (i.e., un). We tested how French-speaking children interpret un, and whether it more closely resembles the English word a or one. We found that French-speaking children almost always accepted sets of 1 for un, but that their responses for sets of 2 were more equivocal, with many children saying “Oui” (Yes) when asked whether there was un. Overall, French children’s interpretation of un differed from how English-speaking interpret both a and one. This suggests that French-speaking children’s interpretation of un reflects the ambiguity of the input that they are exposed to. We conclude that French morphological structure may pose a challenge to French- speaking children in acquiring an exact numerical meaning for the word un, potentially causing a delay in number word learning.