The National Council of Teachers of Mathematics (NCTM) emphasizes the teaching of "Big Ideas" in mathematics. This study focuses on the part-part-whole (PPW) relationship as a crucial aspect of word problem solving involving addition and subtraction. This study, conducted in the United States, evaluated the effects of conceptual…

The mathematical modeling process is also a powerful way to teach students the meaning of data. In mathematical modeling, students are collecting data to answer a question. Data collection is the means to an end and not the end in itself. The author was looking for an engaging way to introduce his third-grade mathematics class to the skill of…

This study invested 24 effective and 16 ineffective problem-solving kindergarten children's awareness of metacognitive self-regulated learning (MSRL) while watching other child's problem-solving behaviors. The model in a video performed a task with a trial-and-error approach and finally asked for help. After watching the video, children were asked…

The U.S. Nation's Report Card reveals that lower performing students exhibited greater achievement decline than their average/high performing peers based on 2022 long-term trend mathematics assessments for age 9 students. Technology, including computer-assisted instruction, plays an important role in today's dynamic learning environments.…

Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We…

This article presents the journey taken by staff at St. Patrick's Primary School in Kilmore to implement a consistent approach to the teaching of mathematics, using an instructional model to support student learning through structured inquiry pedagogies.

Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems. Given that current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, the purpose of this study was to evaluate the impact of a model-based…

This study presents a teaching experiment in which second-grade primary school students compared a city and a town according to population estimates. The activities were presented to them as Fermi problems and required an analysis of the reality to identify sub-problems that students could deal with. The students' products were analyzed from the…

Mathematical modeling involves using mathematics to represent, analyze, and make predictions or decisions about real- world situations. Garfunkel and Montgomery (2016) elaborate on six components of the mathematical modeling process, including identifying the problem, making assumptions and identifying variables, doing the math, analyzing and…

Background: A large evidence base suggests that without effective early intervention, young children who exhibit persistent challenging behavior often face a host of long-term social and academic challenges (Bulotsky-Shearer & Fantuzzo, 2011; Hauser-Cram & Woodman, 2016; Kazdin, 1995; Lane et al., 2008; Miller et al., 2017). Challenging…

The purpose of this study is to explore preservice teachers' (PTs') ability to implement multiple strategies using standard algorithms and alternative strategies and to investigate their conceptual knowledge of decimal operations. There were 37 PTs who participated in this study, all of whom attended a mathematics course in the K-8 Teacher…

Critical thinking when engaged in science problem solving around even simple tasks such as the Piagetian volume conservation task is a complex endeavor. Tasks such as the conservation task often require the interaction of multiple cognitive systems. Parity judgment, retrieval, and lateral thinking are three examples of such systems interacting…

The "Next Generation Science Standards" ("NGSS") have placed an emphasis on the incorporation of engineering practices into K-12 science instruction. This article details a sequence of physical science lessons that would be part of teaching matter in the second-grade classroom. The goals of these lessons are: (1) to be hands-on…

The International Technology and Engineering Educators Association's (ITEEA's) "Standards for Technological and Engineering Literacy" ("STEL") describes design thinking as an approach that allows students and educators to integrate other content areas by considering relevant contextual information to guide design and making…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…