Deterministic or probabilistic: U.S. children's beliefs about genetic inheritance.

Do children think of genetic inheritance as deterministic or probabilistic? In two novel tasks, children viewed the eye colors of animal parents and judged and selected possible phenotypes of offspring. Across three studies (N = 353, 162 girls, 172 boys, 2 non-binary; 17 did not report gender) with predominantly White U.S. participants collected in 2019-2021, 4- to 12-year-old children showed a probabilistic understanding of genetic inheritance, and they accepted and expected variability in the genetic inheritance of eye color. Children did not show a mother bias but they did show two novel biases: perceptual similarity and sex-matching. These results held for unfamiliar animals and several physical traits (e.g., eye color, ear size, and fin type), and persisted after a lesson.

Like mother, like daughter: Adults' judgments about genetic inheritance.

Do adults think about genetic inheritance as a deterministic or probabilistic process? Do adults display systematic biases when reasoning about genetic inheritance? Knowing how adults think about genetic inheritance is valuable, both for understanding the developmental end point of these concepts and for identifying biases that persist even after formal education. In two studies, we examined adults' reasoning about genetic inheritance for familiar animals (Study 1) and unfamiliar animals (Study 2). First, participants were presented with animals that varied in eye color and were asked to judge whether each could be the offspring of a particular set of animal parents that had either the same or different eye colors. The potential offspring had eye colors that were either identical to the parents, blended the parents' eye colors, or differed from the parents. Next, participants predicted how six offspring of the animal parents would look. Participants judged a variety of choices as possible-not only the ones resembling the parents-suggesting that they thought genetic inheritance was a probabilistic process. Additionally, many participants thought that female offspring would look more like their mothers and male offspring would look more like their fathers. Thus, systemic biases in reasoning about inheritance persist into adulthood. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Is a substitute the same? Learning from lessons centering different relational conceptions of the equal sign.

Understanding of the equal sign is associated with early algebraic competence in the elementary grades and equation-solving success in middle school. Thus, it is important to find ways to build foundational understanding of the equal sign as a relational symbol. Past work promoted a conception of the equal sign as meaning "the same as". However, recent work highlights another dimension of relational understanding-a substitutive conception, which emphasizes the idea that an expression can be substituted for another equivalent one. This work suggests a substitutive conception may support algebra performance above and beyond a sameness conception alone. In this paper, we share a subset of results from an online intervention designed to foster a relational understanding of the equal sign among fourth and fifth graders (n = 146). We compare lessons focused on a sameness conception alone and a dual sameness and substitutive conception to each other, and we compare both to a control condition. The lessons influenced students' likelihood of producing and endorsing sameness and substitutive definitions of the equal sign. However, the impact of the lessons on students' approaches to missing value equations was less clear. We discuss possible interpretations, and we argue that further research is needed to explore the roles of sameness and substitutive views of the equal sign in supporting structural approaches to algebraic equation solving.