Transcoding of French numbers for first- and second-language learners in third grade.

Transcoding is the process of translating between spoken and written numbers, and it is correlated with other mathematical skills. In the present study, we investigated the link between French number writing of 49 students in the third grade (aged 7-9 years) and their language skills. Transcoding in French is of particular interest because the spoken number language system does not completely correspond to that of the written digits (e.g., quatre-vingt-dix [four-twenty-ten] and 90). We hypothesised that the complex linguistic structure of spoken numbers in French would be challenging for students who are learning to transcode. First and second French-language learners' accuracy and errors were recorded during a writing task of 3- to 7-digit numbers. Children also completed linguistic tests (e.g., receptive vocabulary, receptive syntax). Results showed that first- and second-language learners did not differ in their transcoding accuracy. Number size, decade complexity of stimulus number words in French (i.e., numbers containing a complex decade, operationalized as a number between soixante-dix, 70, and quatre-vingt-dix-neuf, 99), and receptive vocabulary predicted children's French transcoding skills. Students were more likely to produce errors (e.g., 68 or 6018 for 78) when they transcoded complex decade numbers compared with simple decade numbers. When an error was made on the complex decade portion of a number, it was likely a lexical error. In conclusion, third graders, both first- and second-language learners, found complex decade numbers challenging and their performance was related to their general vocabulary skills.

Does Conceptual Transparency in Manipulatives Afford Place-Value Understanding in Children at Risk for Mathematics Learning Disabilities?

We investigated the effect of conceptual transparency in the physical structure of manipulatives on place-value understanding in typically developing children and those at risk for mathematics learning disabilities. Second graders were randomly assigned to one of three manipulatives conditions: (a) attachable beads that did not make the denominations or ones in the denominations transparent, (b) pipe cleaners that made only the denominations transparent, and (c) string beads that made both the denominations and the ones in the denominations transparent. Participants used the manipulatives to represent double- and triple-digit numerals. Statistical analyses indicated that the transparency of the denominations, but not the transparency of the ones in the denominations, is responsible for children's number representation and place-value understanding. Descriptive analyses of their responses revealed that the at-risk children were at a greater disadvantage than their typically developing peers with the attachable beads, failing to use place-value concepts to interpret their representations.

Individual differences in the development of children's arithmetic fluency from grades 2 to 3.

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In Grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In Grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in Grade 3, whereas addition fluency did not. In Grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Addressing the struggle to link form and understanding in fractions instruction.

BACKGROUND: Although making explicit links between procedures and concepts during instruction in mathematics is important, it is still unclear the precise moments during instruction when such links are best made. AIMS: The objective was to test the effectiveness of a 3-week classroom intervention on the fractions knowledge of grade 5/6 students. The instruction was based on a theory that specifies three sites during the learning process where concepts and symbols can be connected (Hiebert, 1984): symbol interpretation, procedural execution, and solution evaluation. Sample. Seventy students from one grade 5/6 split and two grade 6 classrooms in two public elementary schools participated. METHOD: The students were randomly assigned to treatment and control. The treatment (Sites group) received instruction that incorporated specific connections between fractions concepts and procedures at each of the three sites specified by the Sites theory. Before and after the intervention, the students' knowledge of concepts and procedures was assessed, and a random subsample of 30 students from both conditions were individually interviewed to measure their ability to make specific connections between concepts and symbols at each of the three sites. RESULTS: While all students gained procedural skill (p < .001), the students in the Sites condition acquired significantly more knowledge of concepts than the control group (p < .01) and were also better able to connect fractions symbols to conceptual referents (p < .025). CONCLUSIONS: The current study contributes to the literature because it describes when it might be important to link concepts and procedures during fractions instruction.