Keto-enol tautomerization is paramount to understanding the mechanisms involved in many organic reactions and biochemical transformations. Isomerization of an enol to a carbonyl compound is typically introduced during the discussion of the acid-catalyzed electrophilic addition of water to alkynes. The tautomerization of carbonyl compounds to enol…

We propose a simple computational model that describes potential mechanisms underlying the organization and development of the lexical-semantic system in 18-month-old infants. We focus on two independent aspects: (i) on potential mechanisms underlying the development of taxonomic and associative priming, and (ii) on potential mechanisms underlying…

The same and different routine offers an opportunity to build a strong foundation for future grades while also deepening the experiences of prekindergarten and transitional kindergarten students. Students have opportunities to make sense, share ideas, and engage in the ideas of others. We conjecture this type of experience supports students and…

Concepts and practices are widely used to assess students' development in computational thinking (CT). However, less is known about how the development of each construct relates to that of the other. With a sample of 997 grade 6 students (average age = 11.43 at the beginning of the school year) from 14 primary schools, we examined the…

There is growing interest in mathematics learning progressions in early childhood education. Counting is a skill usually developed early in life. The application of the counting principles in early childhood typically entails counting objects. This poses challenges for learning about zero. Indeed, the word "zero" is seldom used in the…

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

Background and Context: In order to fully include learners with visual impairments in early programming education, it is necessary to gain insight into specificities regarding their experience of and approach to abstract computational concepts. Objective: In this study, we use the model of the layers of abstraction to explore how learners with…

This qualitative case study investigated how computational models can help students engage in scientific practice and influence their emotional, epistemic, and conceptual aspects. Twenty-four sixth-graders were guided to conduct scientific practices as they predicted and modified the computational models on food web using StarLogo Nova. Three…

Circulatory system is a challenging subject for middle school students to learn and understand conceptual relationships. To address these challenges, this study developed plugged (computational thinking activities using computer) and unplugged (computational thinking activities without using computer) teaching modules that integrated computational…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Children vary widely in their number knowledge by the time they enter kindergarten, and this variation is related to their future academic success. Although talk about number predicts children's early understanding of foundational number concepts, we know little about whether interventions can increase this talk nor about the types of number talk…

Students in Appalachia have a heritage of problem-solving. We explore how computational thinking (CT) relates to and complements this heritage by analyzing 34 local ingenuity stories, and perspectives from 35 community members about the relevance of CT. We found the two problem-solving approaches are meaningfully different, but can be used in…

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students' conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools…

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics…