Students frequently struggled with the mathematizing process -- forging connections between implicit and explicit mathematical thinking -- when solving a context-rich applied problem. The current research investigated how students interact with and leverage purposively designed "mathematizing" supports when solving applied math problems…

The aim of this study is to determine the number sense skills of preschool (Kindergarten) children. In the study, survey design, one of the quantitative research methods, was used. The study group consists of a total of 114 children attending all the kindergartens (5 kindergartens) in the city center of Tunceli in the 2020-2021 school year. The…

Research into mathematics education at university level includes a wide range of theoretical approaches. This poses considerable challenges to researchers in terms of understanding and harmonizing the compatibility and commensurability of those approaches. The research community has already problematised and studied these challenges using…

The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…

In the first part, we investigate Birman, Ko, and Lee's left canonical form of a braid and give a new diagrammatic approach. We use the left canonical form to characterize almost strongly quasipositive braids. In the second part, we investigate students' confidence in mathematics and problem solving skills. Every math instructor has heard students…

Creative thinking transforms existing information, either from long-term memory or external sources, into new representations and innovative ideas. Creative thinking is an activity that processes received information to produce new representations and innovative ideas. Developing this skill is essential for students; however, recent research has…

Ever try to captivate students with real-world applications only to discover that they live in a very different world? Assigning an Extreme Word Problem activity to students alleviates this dilemma by placing the authorship of a problem squarely into the hands of learners. Rather than trying to be hip and finding word problems that resonate with…

The National Center for Leadership in Intensive Intervention (NCLII), a consortium funded by the Office of Special Education Programs (OSEP), prepares special education leaders to become experts in research on intensive intervention for students with disabilities who have persistent and severe academic (e.g., reading and math) and behavioral…

This study explores secondary mathematics teachers' attention to the three components of Jaworski's (1992) "teaching triad" (i.e., "mathematical challenge," "learning management," and "sensitivity to students") as they planned a lesson revolving around a rich mathematics problem and assessed pre-designed…

Often, straightforward notions from one mathematical domain, when altered even slightly, can become rich and rewarding investigations involving numerous additional domains -- particularly when the investigation includes rigorous proof. This study begins with a familiar high school geometry problem (namely finding the circumcentre of a triangle),…

The first calculus course in the province of Quebec (Canada) is taught in the first year of college (17-18 year-old students) before university. Statistics show that this course is the most difficult one for students at the collegial level and that it prompts many to drop out of school. The literature has highlighted the cognitive problems…

We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.

Manipulatives are an effective mathematical tool to support students with disabilities in the area of mathematics. Yet, there remain inconsistencies in terms of which type -- concrete or virtual -- is more effective for students with disabilities working on algebra related content and which type is preferred by students. The researchers used an…

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…

Proportional reasoning and knowledge of fractions are critical skills for completing algebra successfully, yet many students with mathematics learning disabilities (MLD) enter algebra classes without adequate prior knowledge of these skills. This study used a single-subject/case research, combined multiple-baseline and alternating-treatment design…