Backward transfer is defined as the influence that new learning has on individuals' prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that quadratic functions instruction in real classrooms had on students' prior ways of reasoning about linear functions. Two algebra classes and their teachers…

Angularity is a persistent quantity throughout K-12+ school mathematics, and many studies have shown that individuals often conflate angularity with linear attributes (e.g., the length of an angle model's sides). However, few studies have examined the productive ways in which students might reason about angularity while attending to linear…

The aim of this study is to examine how algorithmatizing tasks engage mathematics students in algorithmic thinking. Structured, task-based interviews were conducted with eight Year 12 students as they completed a sequence of algorithmatizing tasks involving maximum flow problems. A deductive-inductive analytical process was used to first classify…

This study addresses the measurement of high school students' epistemic knowledge associated with scientific experimentation (EKSE) which concerns "how" scientific experimentation generates knowledge and "why" that knowledge is justified. Based on philosophical, educational standards, and literature analyses, an EKSE construct…

Semantic is associated with the relationship between symbol, reference, and the problem's context involved in the problem-solving process which also involves reasoning and decision-making. Hence, this study describes the characteristics of students' semantic reasoning to solve the double discounts problem. 51 high school students in Sidoarjo…

Background: In scientific inquiry learning, students often have difficulties conducting hypothetical reasoning with multiple intertwined variables. Concept maps have a potential to facilitate complex thinking and reasoning. However, there is little investigation into the content of student-constructed concept maps and its association with inquiry…

Proofs are attempts to conclusively demonstrate the validity of the claim for all cases indicated within its domain, which implies that proving should involve thoughtful consideration of the domain. This study analyzed the enactment of three general claim tasks, or tasks where the domain of the claim referred to an infinite number of cases, that…

Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that…

Adaptive comparative judgment (ACJ) has been widely used to evaluate classroom artifacts with reliability and validity. In the ACJ experience we examined, students were provided a pair of images related to backpack design. For each pair, students were required to select which image could help them ideate better. Then, they were prompted to provide…

We investigated how two didactical tools assist high school students in constructing knowledge about convergence and limits. The first tool is manual plotting of the terms of selected sequences, and the second, a technological applet. Student pairs worked in an interview setting on an activity designed for the purpose of this research. The…

Cosmology presents students with ideas that stimulate their curiosity and brings together various concepts from STEM that call on a variety of reasoning types across multiple representational modes, involving subtleties of spacetime relations, a variety of models and evidence requiring multiple lines of high precision observations. This study…

A key component of student mathematics achievement relates to the cognitive domains. This paper examines student mathematics achievement in three cognitive domains (knowledge, comprehension, reasoning) as per different achievement grades, across four years (2015, 2016, 2018, 2019), and by gender. This study used the Caribbean Secondary Education…

Critical and analytical thinking skills are included in higher-order thinking skills which become the focus of educational goals in recent era. This study aimed to determine the relationship between critical and analytical thinking skills in ecology learning at senior high school in East Jakarta. This research was conducted from March to June…

An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, award-winning researcher Dr. Nicole Fonger addresses the issue of how to support all learners to experience algebra as meaningful. In a highly visual approach, the book details four research-based lenses with examples from 9th-grade…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…