In this paper, I discuss undergraduate students' engagement in basic Python programming while solving combinatorial problems. Students solved tasks that were designed to involve programming, and they were encouraged to engage in activities of prediction and reflection. I provide data from two paired teaching experiments, and I outline how the task…

In this study, we used multivariate decoding methods to study processing differences between canonical (montring and count) and noncanonical finger numeral configurations (FNCs). While previous research investigated these processing differences using behavioral and event-related potentials (ERP) methods, conventional univariate ERP analyses focus…

Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by…

Are there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an…

Mastery of mathematics depends on the people's ability to manipulate and abstract values such as negative numbers. Knowledge of arithmetic principles does not necessarily generalize from positive number arithmetic to arithmetic involving negative numbers (Prather & Alibali, 2008, https://doi.org/10.1080/03640210701864147). In this study, we…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…

This research investigates positive future expectancies, particularly hope in children, which is comprised of agency thinking, perceiving oneself as capable of achieving goals, and pathways thinking, perceiving oneself as capable of discovering methods toward the desired goals. Two studies (n = 82) were conducted in the United States to examine…

The ability to project oneself forward in time and imagine a future episode, known as episodic foresight (EpF), is an important aspect of future thinking. EpF tasks often involve children choosing an item for a future episode, yet the degree to which future projection is required to succeed -- versus memory or semantic associations -- has been…

The present research examined whether U.S. infants can recognize in others a pattern of helping or hindering after watching such behaviors across multiple scenarios. Infants at 17 months watched three familiarization events in which a person (recipient) failed to achieve various goals and another person (actor) always helped or hindered the…

Rhyme awareness is a varied skill emerging consistently only in late preschool, yet children respond to rhythmic and phonological patterns to spontaneously complete rhymes in everyday settings. Our study replicates and extends previous work using a modified preferential looking task to test whether preschoolers can efficiently use rhyme to…

Children have traditionally been viewed as less reliable witnesses than are adults. More recently, a concept known as developmental reversals, has brought this view into question. Developmental reversals have demonstrated that in certain contexts, children produce fewer false memories than adults. The primary paradigm used to demonstrate…

Parents who vary in their experience with formal schooling are likely to use different types of informal guidance with their children. However, rather than assuming a deficit approach we need evidence regarding how parents with limited schooling support their children's learning. Forty U.S. families of Mexican-heritage, from two levels of…

Adults conceptualize God as particularly knowledgeable -- more knowledgeable than humans -- about moral transgressions. We investigated how younger (4- to 5-year-old) and older (6- to 7-year-old) children view God's moral knowledge. Cultural narratives in the United States portray God as omniscient, which could lead children growing up in the…

Evidence of processing costs for unexpected words presented in place of a more expected completion remains elusive in the eye-movement literature. The current study investigated whether such prediction error costs depend on the source of constraint violation provided by the prior context. Participants' eye movements were recorded as they read…