When does the story matter? No evidence for the foregrounding hypothesis in math story problems

Math story problems are difficult for many solvers because comprehension of mathematical and linguistic content must occur simultaneously. Across two studies, we attempted to conceptually replicate and extend findings reported by Mattarella-Micke and Beilock (2010, https://doi.org/10.3758/PBR.17.1.106) and Jarosz and Jaeger (2019, https://doi.org/10.1002/acp.3471). Mattarella-Micke and Beilock found that multiplication word problems in which an irrelevant number was associated with the protagonist of the problem (i.e., foregrounded in the text) were solved less accurately than problems in other conditions. Jarosz and Jaeger used similar materials but tested the more general inconsistent-operations hypothesis that association with the protagonist would interfere with multiplication whereas dissociation would interfere with division. They found partial support: When division problems were primed with dissociative scenarios, solvers made more errors, but they failed to replicate the associative findings for multiplication. In the present research, we conducted two studies (Ns = 205 and 359), in which we similarly manipulated whether irrelevant content was associated with or dissociated from the story protagonist. In these studies, we did not find support for either the foregrounding or inconsistent-operations hypotheses. Exploratory error analyses suggested that solvers’ errors were most often the result of calculation difficulties or inappropriate operation choices and were unrelated to the presence of associative or dissociative story elements. Our careful implementation of this manipulation and much greater power to detect effects suggests that the association manipulation in irrelevant text does not influence adults’ performance on simple math story problems.

Effects of self-scoring their math problem solutions on primary school students’ monitoring and regulation

Preparing students to become self-regulated learners has become an important goal of primary education. Therefore, it is important to investigate how we can improve self-monitoring and self-regulation accuracy in primary school students. Focusing on mathematics problems, we investigated whether and how (1) high- and low-performing students differed in their monitoring accuracy (i.e., extent to which students’ monitoring judgments match their actual performance) and regulation accuracy (i.e., extent to which students’ regulation judgments regarding the need for further instruction/practice match their actual need), (2) self-scoring improved students’ monitoring and regulation accuracy, (3) high- and low-performing students differed in their monitoring and regulation accuracy after self-scoring, and (4) students’ monitoring and regulation judgments are related. On two days, students of 9 − 10 years old from 34 classes solved multiplication and division problems and made monitoring and regulation judgments after each problem type. Next, they self-scored their answers and again made monitoring and regulation judgments. On the multiplication problems, high-performing students made more accurate monitoring and regulation judgments before and after self-scoring than low-performing students. On the division problems, high-performing students made more accurate monitoring judgments before self-scoring than low-performing students, but after self-scoring this difference was no longer present. Self-scoring improved students’ monitoring and regulation accuracy, except for low- and high-performing students’ regulation accuracy on division problems. Students’ monitoring and regulation judgments were related. Our findings suggest that self-scoring may be a suitable tool to foster primary school students’ monitoring accuracy and that this translates to some extent into more accurate regulation decisions.

Examination of Semantic Structures Used by Teacher Candidates to Transform Algebraic Expressions into Verbal Problems

The aim of this study is to examine the semantic structures used by mathematics teacher candidates to transform algebraic expressions into verbal problems. The research is a descriptive study in the survey model, which is one of the quantitative research types. The study group of the research consists of 165 teacher candidates studying in the primary school mathematics teaching department of a state university in the south of Turkey in the 2019-2020 academic years. 73.2% of the teacher candidates in the study group are female and 26.8% are male. Criterion sampling method, one of the purposeful sampling methods, was used in the selection of teacher candidates in the study group. While the Algebraic Expression Questionnaire Form was used as the data collection tool, the evaluation rubric of verbal problems was used in the analysis of the data. As a result of the research, it has been revealed that pre-service teachers are more successful in transforming algebraic expressions into verbal problems, but they have problems in creating problems with algebraic expressions that make up systems of equations. Again in the study, it was concluded that pre-service teachers used addition and subtraction problems more than multiplication and division problems. On the other hand, when the problems in the type of addition and subtraction are examined in the study, in the type of combining and separating; It has been concluded that the category of equal groups is mostly used in the problems of multiplication and division.

Examination of Semantic Structures Used by Teacher Candidates to Transform Algebraic Expressions into Verbal Problems

The aim of this study is to examine the semantic structures used by mathematics teacher candidates to transform algebraic expressions into verbal problems. The research is a descriptive study in the survey model, which is one of the quantitative research types. The study group of the research consists of 165 teacher candidates studying in the primary school mathematics teaching department of a state university in the south of Turkey in the 2019-2020 academic years. 73.2% of the teacher candidates in the study group are female and 26.8% are male. Criterion sampling method, one of the purposeful sampling methods, was used in the selection of teacher candidates in the study group. While the Algebraic Expression Questionnaire Form was used as the data collection tool, the evaluation rubric of verbal problems was used in the analysis of the data. As a result of the research, it has been revealed that pre-service teachers are more successful in transforming algebraic expressions into verbal problems, but they have problems in creating problems with algebraic expressions that make up systems of equations. Again in the study, it was concluded that pre-service teachers used addition and subtraction problems more than multiplication and division problems. On the other hand, when the problems in the type of addition and subtraction are examined in the study, in the type of combining and separating; It has been concluded that the category of equal groups is mostly used in the problems of multiplication and division.

Picking Sequences and Monotonicity in Weighted Fair Division

We study the problem of fairly allocating indivisible items to agents with different entitlements, which captures, for example, the distribution of ministries among political parties in a coalition government. Our focus is on picking sequences derived from common apportionment methods, including five traditional divisor methods and the quota method. We paint a complete picture of these methods in relation to known envy-freeness and proportionality relaxations for indivisible items as well as monotonicity properties with respect to the resource, population, and weights. In addition, we provide characterizations of picking sequences satisfying each of the fairness notions, and show that the well-studied maximum Nash welfare solution fails resource- and population-monotonicity even in the unweighted setting. Our results serve as an argument in favor of using picking sequences in weighted fair division problems.

Optimal Interval Division

This paper provides a simple unified analysis of optimal interval division problems. My primitive is a cell function that assigns a value to each subinterval (cell). Submodular cell functions conveniently imply the property of decreasing marginal returns. Also, for coarse decision problems, optimal cutoffs commonly increase as prior belief shifts upward. Its implications on language and efficient menus are discussed.

Effects of Persistent Undernutrition During Adolescence on Learning Skills: Findings From a Longitudinal Study of 16,000 Adolescents in India

Objectives Limited evidence exists on longitudinal impacts of undernutrition on learning skills as adolescents mature. This study aimed to examine the effect of undernutrition in early adolescence on learning skills in late adolescence. Methods We used longitudinal data from a project called UDAYA that surveyed 16,929 adolescents aged 10–19 years from Bihar and Uttar Pradesh, India in 2015–16 (wave 1) and again in 2018–19 (wave 2). Adolescents’ ability to read a story and solve division problems at age 19–22 years was assessed using the Annual Status of Education Report tools. We characterized adolescents’ nutrition status into 4 groups: never undernourished (e.g., not stunted in wave 1 and 2), recovered (e.g., stunted in in wave 1 but not stunted in wave 2), faltered (e.g., not stunted in wave 1 but stunted in wave 2), and persistent (e.g., stunted in both waves). These 4 groups were created for stunting, thinness, and anemia. We used multivariable logistic regression models adjusted for key demographics, environmental factors, and sampling design. Results Undernutriton was high (51% were anemic, 19% thin, and 36% stunted) in both survey rounds. Nearly one third of adolescents had persistent stunting or anemia, and 11% had persistent thinness. Compared to those who were never stunted, adolescents with persistent stunting had poorer reading (adjusted odds ratio: 0.66, 95% confidence interval: 0.53–0.83) and math (0.70, 0.56–0.89) skills. Reading ability was also poorer in adolescents who experienced growth faltering (0.61, 0.42–0.90) or who were stunted in wave 1 but not stunted in wave 2 (0.64, 0.44–0.93). Persistent thinness was negatively associated with reading (0.71, 0.54–0.93) but not math skills. Persistent anemia was also negatively associated with reading skills, but the association did not remain significant in the fully adjusted model. Conclusions In a high poverty sample of Indian adolescents, persistent undernutrition during adolescence was associated with poor learning skill. Promisingly, most of those who recovered from undernutrition in the 2–3 year period between surveys showed catch-up in learning. Ensuring appropriate nutrition during this period of rapid physical and cognitive maturation will yield long-term dividends for wellbeing. Funding Sources Bill & Melinda Gates Foundation.

Number Sense Makes All the Difference: Calculation Using Number Sense by Pupils With and Without Learning Difficulties in Math

The research examined the calculation methods used by pupils in Grades 3–6 when they were presented with problems that could be worked out efficiently and flexibly by applying number sense. The study was conducted with a convenience sample of 179 pupils between the ages 7 years and 10 months to 12 years and 10 months. in mainstream education in Israel, who attended schools belonging to different sectors and situated in different areas of the country with varied socioeconomic profiles. The test included addition, subtraction, multiplication, and division problems that pupils were asked to solve mentally, in writing and by identifying correctly and incorrectly solved problem. Some of the problems presented pupils with opportunities to apply number sense. As expected, the research findings showed significant differences in calculation accuracy between pupils with and without learning difficulties, especially in multiplication and division tasks. Still, the performance of pupils with difficulties in the accuracy variable was above average, and there was high variance within this group. We found significant differences between pupils with and without difficulties in the calculation-speed variable in all tasks and in all calculation modalities. One of the implications is that pupils, and especially those with difficulties, should be afforded enough time to work out problems, and should be presented with tasks that would enable them to use number sense in order to retrieve prior knowledge and apply it.

PROSPECTIVE TEACHERS UNDERSTANDING FRACTION DIVISION USING RECTANGLE REPRESENTATION

Fraction division is one of the most difficult subjects in elementary school. Not only elementary students but many prospective teachers don’t understand the fraction division concept yet—most of them using a keep-change-flip algorithm to solve fraction division problems. A study using rectangle representation was conducted by us to prospective teachers. This study aims to see whether this rectangle representation will make prospective teachers understand or not. To do so, we made a mixed-method study with 80 prospective teachers as participants. The results show that 53,75% of prospective teachers use the keep-change-flip algorithm without understanding the concept of fraction division, and just 15% of prospective teachers understand fraction division. We assume that most prospective teachers still can’t imagine how fraction division works in a real-life context. They remember what they used to do to finish the fraction division problem that their teacher has introduced in primary school. Based on the results, we conclude that the study with rectangle representation still needs an improvement, whether the teacher’s explanation or the rectangle media.

Strategies of Pre-Service Early Childhood Teachers for Solving Multi-Digit Division Problems

Unlike previous research, this study analyzes the strategies of pre-service early childhood teachers when solving multi-digit division problems and the errors they make. The sample included 104 subjects from a university in Spain. The data analysis was framed under a mixed-method approach, integrating both quantitative and qualitative analyses. The results revealed that the traditional division algorithm was widely used in problems involving integers, but not so frequently applied to problems with decimal numbers. Often, number-based and algebraic strategies were employed as an alternative to the traditional algorithm, as the pre-service teachers did not remember how to compute it. In general, number-based strategies reached more correct solutions than the traditional algorithm, while the algebraic strategies did not usually reach any solution. Incorrect identifications of the mathematical model were normally related to an exchange of the dividend and divisor roles. Most pre-service teachers not only failed to compute the division, but also to interpret the obtained solution in the problem context. The study concludes that, during their schooling, students accessing the Degree in Early Childhood education have not acquired the necessary knowledge and skills to solve multi-digit division problems, and thus the entrance requirements at the university must be rethought.