This paper focuses on the emergence of abstraction through the use of a new kind of motion detector--WiiGraph--with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their…

The authors question how hermetic texts in mathematics, history, and philosophy of mathematics, specifically those referring to abstract algebra, can be open to the understanding of researchers, teachers and students who are intentionally willing to understand them. This discussion suggests that the openness may happen through hermeneutic…

Co-teaching is a widely-used service delivery model to support students with disabilities in accessing the general curriculum in the United States. The pairing of a special educator and general educator is meant to produce substantively different instruction than when the general educator teaches alone. Research into these instructional…

Algebra is the foundational mathematics course that students take as they begin their high school career and is often difficult for the average learner. In order for students with disabilities and those with mathematics difficulties to meet the high expectations of future mathematical courses, providing quality instruction by implementing…

Due to low success of traditional, postsecondary remediation mathematics, The Maryland Mathematics Reform Initiative First in the World Grant (MMRI-FITW) sought to develop and implement a statistics pathway as an alternative to traditional algebra-based math, to accelerate developmental mathematics students' progress into credit-bearing…

When students solve an algebra problem, students try to deduce the facts in the problem. This step is imperative, students can draw conclusions from the facts and devise a plan to solve the problem. Drawing conclusions from facts is called reasoning. Some kinds of reasoning are deductive, inductive, and abductive. This article explores the…

Students in secondary school often struggle with symbol sense, that is, the general ability to deal with symbols and to recognize the structure of algebraic formulas. Fostering symbol sense is an educational challenge. In graphing formulas by hand, defined as graphing using recognition and reasoning without technology, many aspects of symbol sense…

Jefferson Education Accelerator contracted with Empirical Education to study the effectiveness of the implementation of Agile Mind's "Agile Assessment" in an urban school district in the Northeast United States during the 2016-17 school year. "Agile Assessment" is a system for building formative assessments that includes…

Research indicates that a large percentage of students have misconceptions of the equal sign and that this can be detrimental to their mathematical pursuits as they progress through algebra. In order for students to develop a strong understanding of the meaning of the equal sign, algebra teachers must be aware of the viewpoints their students will…

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

Mathematical proof is a logically formed argument based on students' thinking process. A mathematical proof is a formal process which needs the ability of analytical thinking to solve. However, researchers still find students who complete the mathematical proof process through intuitive thinking. Students who have studied mathematical proof in the…

In the United States, the prevailing high school mathematics course sequence begins with a year of Algebra I, followed by a year of geometry and a year of Algebra II. Educators and others have raised concerns about the extent to which this sequence, which prioritizes the mastery of algebra, is appropriate for the longer-term education and career…

Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students…

Within a study of student reasoning in abstract algebra, we encountered the claim "division and multiplication are the same operation." What might prompt a student to make this claim? What kind of influence might believing it have on their mathematical development? We explored the philosophical roots of "sameness" claims to…

This study examined if and how thinking time, defined as the time from the start of the problem to the students' first action to solve, influences their problem-solving efficiency, defined as the number of steps taken to solve the problem, using Graspable Math, a web-based mathematical tool. We found that: (1) students who took longer to think…