This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children's fluency, as well as the strategies used to create equal groups,…

Spatial thinking permeates much of our lives and is an asset when solving problems involving well-structured visual information or imagining solutions in physical or digital space. However, an estimated three million US school children have spatial talents that go unrecognized because of the tools commonly used for identification of academic…

Spatial thinking permeates much of our lives and is an asset when solving problems involving well-structured visual information or imagining solutions in physical or digital space. However, an estimated three million US school children have spatial talents that go unrecognized because of the tools commonly used for identification of academic…

The paper aims to propose an instrument to identify students' metacognitive strategies in mathematical modelling activities. The items were designed from a review regards metacognition and instruments already recognised in literature. This design comprises an instrument that differs from others in which the data were the self-reported students'…

Self-Regulated Learning (SRL) is important to solve learning problems. This research aimed to determine the effect of the problem-solving based Self-Regulated Learning (SRL) strategy on simple harmonic motion material toward the metacognitive abilities of student's senior high school. This research applied a quasi-experimental method with a…

In this report we show an investigation of how high-school students learn strategies to find intermediate numbers in an interval to understand the property of numerical density. Research has shown that some high-school students have difficulty in understanding this property. To mitigate this difficulty, we proposed a Hypothetical Learning…

Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…

As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

Our research aimed to investigate the potential learning benefits to young children of implementing digital interactive multimodal technologies that provide both visual and haptic experiences in elementary mathematics classrooms. We studied the ways in which fourth-grade students collaboratively create collective strategies for solving…

Background: Data on children's ability to answer assessment questions correctly paints an incomplete portrait of what they know and can do mathematically; yet, it remains a common basis for program evaluation. Indeed, pre-post-assessment correctness is necessary but insufficient evidence for making inferences about learning and program…

Problem-solving tasks form the backbone of STEM (science, technology, engineering, and mathematics) curricula. Yet, how to improve self-monitoring and self-regulation when learning to solve problems has received relatively little attention in the self-regulated learning literature (as compared with, for instance, learning lists of items or…

Extant research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and extent of this relationship requires a detailed elaboration. This is especially true when adidactical problem-posing arises within a problem-solving context. In this study, we analyze the scripting journey used by two…

Considering the low achievement of Indonesian students in international studies (PISA), which measures Higher-Order Thinking Skill (HOTS) in solving the problem, improving the quality of mathematics learning in Indonesia is very important. The purpose of this research was conducted to explore the variations in students' learning strategies and…

The study aimed to investigate the impact of incorporating deep learning strategies in mathematics instruction on students' problem-solving abilities, critical thinking skills, academic achievement, and mathematical skills development. The study population consisted of 280 students, with a sample size of 162 participants. Employing a purely…

The growing use of generative AI (GenAI) has sparked discussions regarding integrating these tools into educational settings to enrich the learning experience of teachers and students. Self-regulated learning (SRL) research is pivotal in addressing this inquiry. One prevalent manifestation of GenAI is the large-language model (LLM) chatbot,…