Early mathematics education presents middle-school students with the challenge of adding and subtracting negative integers. This paper reports on results from the experimental implementation of a proposed educational design for integer arithmetic that utilized the number-line (NL) form as a resource for students to enact simple addition and…

Place value competence in early years mathematics is a precursor for success in later grades. In this paper, we analyse the place value visual representations in workbooks from South Africa, Singapore and Australia. A cross-country comparison of curricula materials provides an opportunity to understand similarities and differences in use of visual…

The Reading and Appreciating Mathematical Proofs (RAMP) project seeks to provide novel resources for teaching undergraduate introduction to proof courses centered around reading activities. These reading activities include (1) reading rich proofs to learn new mathematics through proofs as well as to learn how to read proofs for understanding and…

This study explores secondary-school mathematics teachers' noticing of Critical Events Associated with Argumentation (CEAs), moments when students' reasoning or interactions become evident, offering teachers opportunities to promote argumentation in the classroom. Thirty-one teachers analyzed a written classroom scenario, identifying CEAs,…

This research aims to examine recent studies on the dimensions necessary for developing mathematical modelling instruction and established frameworks used in teaching mathematical modelling. The study followed the steps outlined as such: identification, screening, eligibility, inclusion, and data analysis throughout three search engines: ERIC,…

Self-regulated learning comprises cognitive, emotional, and behavioral dimensions. However, flipped classroom studies have mainly focused on behavioral self-regulation and overlooked their relationships with each other. This quasi-experiment was conducted to investigate whether implementing self-regulated cognitive strategies (SRCSs) in preclass…

This interpretive cross-case study investigates complexity in the ways teachers frame mistakes and the reasons behind their framing, challenging the assumption in the literature that productive beliefs about errors generate productive error-handling practices, while unproductive beliefs result in unproductive practices. The study draws on…

This paper reports on a novel corequisite design and implementation for College Algebra at Florida International University. The corequisite course uses online, just-in-time, prerequisite assignments delivered on an open-educational platform. Students get help from near-peer learning assistants inside a math emporium environment. The course…

A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…

When justifying a mathematical statement, textbooks often interweave several instances of justification, creating, what we term, "paths of justification." This study aims to characterize the paths of justification of mathematical statements that are offered in eight 7th grade Israeli mathematics textbooks. The study attended to context…

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

Since the introduction by Kermack and McKendrick in 1927, the Susceptible-Infected-Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious…

Students are required to have the ability to implement mathematics in solving everyday life problems. A good solving process will produce an excellent solving ability. The existing problem-solving stages cannot be used in solving problems with the Higher Order Thinking Skills (HOTS) category. The aims of this research are 1) to know students'…

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

The Great Mini-Golf Project requires students to use a ruler to identify measurements to the quarter-inch, with careful precision and accuracy, which supported the Standards for Mathematical Practice 5 and 6: using appropriate tools to solve mathematical problems with precision (NGA Center & CCSSO, 2010). This project also supported Standard…