A challenge for teachers is to incorporate the Standards for Mathematical Practice (CCSSI 2010) throughout their teaching of mathematics so that the Common Core Standards do not revert back to a purely content-driven curriculum. One way to achieve this is through the use of mathematically rich, investigative tasks. These tasks encourage students…

The study reported on in this paper is an interview study conducted with 20 7th and 8th grade students whose purpose was to understand the generalizations they could make about non-linear meanings of multiplication (NLMM) and non-linear growth (NLG) in the context of solving combinatorics problems. The paper identifies productive challenges for…

The purpose of this study was to compare scores students received on the eighth grade EXPLORE test in math and English to scores received in English 9 and Algebra I on both the End-of-Course (EOC) test and the final average in those courses. These scores were taken from a rural East Tennessee High School and the middle schools that feed into the…

Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…

The indirect method for preparing the statement of cash flows, as described in many standard textbooks, involves an item-by-item approach, telling you to add to or subtract from the net income, the increases or decreases in the balance sheet items, such as accounts payable or accounts receivable. Many business students, especially at the…

The process of prime factor splicing to generate home primes raises opportunity for conjecture and exploration. The notion of "home primes" is relatively new in the chronicle of mathematics. Heleen (1996-97) first described a procedure called "prime factor splicing" (PFS). The exploration of home primes is interesting and…

The transition from preformal and propaedeutic generalization-actions to a symbolically explicit use of the concept of variable has been a matter of significant attention in mathematics education, for example in the context of generalization processes on a preformal level and regarding the specific nature of algebraic concepts. This contribution…

The goal of this article is to describe a university-community partnership sponsored by a university office of civic engagement. University-community partnerships are common, but many collaborations are fraught with challenges because of power inequities or differing goals and ways of operating. Aware of the potential pitfalls, the…

Assimilating multiple interactive elements simultaneously in working memory to allow understanding to occur, while solving an equation, would impose a high cognitive load. "Element interactivity" arises from the interaction between elements within and across operational and relational lines. Moreover, operating with special features…

Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers' beliefs about improving the transfer of algebraic skills from mathematics into physics. We interviewed 10 mathematics and 10 physics teachers using a…

This paper examines the process of instrumental genesis through which students develop their proficiency in making use of movable points and slider bars--two tools that dynamic mathematics software provides for working with variable coordinates and parameters in the field of functions. The paper analyses students' responses to task sequences…

It is estimated that the average student spends around 1200 USD on books and supplies every school year; thus, textbook affordability has become more and more of a challenge for students. Replacing traditionally expensive learning resources with open educational resources (OER) can have a great impact in the reduction of cost for post-secondary…

Improving the outcomes of students in developmental or remedial math remains a puzzle in higher education. Concerns with low persistence and completion rates have motivated proponents of reform to reconsider the delivery of developmental math. Lengthening the amount of time in math is thought to be an intervention that improves academic…

This study explored in a sample of 560 high level education students their judgment formation to perceived self-efficacy to solve mathematical tasks. Students had to read 36 experimental vignettes describing educative scenarios to learn mathematics. Each scenario presented four manipulated pieces of information (learning modality, task difficulty,…

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an…