The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…

Many current and future teachers have little experience with modeling and how to integrate it into their teaching. However, with the introduction of the Common Core State Standards for Mathematics (CCSSM) and its emphasis on mathematical modeling in all grades (CCSSI 2010), this integration has become paramount. Therefore, middle-grades teachers…

The pattern, which is a key concept in understanding the mathematical information and concepts, is the basis in comprehending mathematical relations and in understanding mathematical order and logic. The fact that students discover the relationships contained within the patterns and generalize them helps them develop their skills to better…

Many teachers experience the tension between using published curriculum materials and teaching in ways that are responsive to children. Teachers are often expected to use a particular mathematics curriculum series, but they still want to be able to build on and connect to children's multiple mathematical knowledge bases (MMKB).…

To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students…

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.

The topic of inhibition in mathematics education is both well timed and important. In this commentary, we reflect on the role of inhibition in mathematics learning through four themes that relate to how inhibition is defined, measured, developed, and applied. First, we consider different characterizations of inhibition and how they may shape the…

This paper explores students' ways of thinking about the average rate of change of a multivariable function and how they generalize those ways of thinking from rate of change of single-variable functions. I found that while students thought about the average rate of change of a multivariable function as the change in the independent quantity with…

In this paper I describe how I have used the classic buried treasure problem with prospective and practicing mathematics teachers to enhance their problem solving abilities and disposition to integrate interactive geometry software (IGS) into the learning environment. I illustrate how IGS may be used as a strategic tool to gain insight into the…

This paper is based on data gathered during visits to Uganda and Malawi, conducted by the International Math-teacher Professionalization Using Lesson Study (IMPULS) project and the Japanese International Cooperation Agency (JICA). The author's observations and experiences highlighted misconceptions about lesson study. The paper concludes that some…

A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.

In this article, we describe results of a reanalysis of two randomized studies that tested the effects of enhanced anchored instruction (EAI) on the fractions computation performance of students in special education resource rooms and inclusive mathematics classrooms. Latent class analysis and latent transition analysis classified students…

For the least-squares analysis of data having multiple uncertain variables, the generally accepted best solution comes from minimizing the sum of weighted squared residuals over all uncertain variables, with, for example, weights in x[subscript i] taken as inversely proportional to the variance [delta][subscript xi][superscript 2]. A complication…

Cognitive load theory was used to hypothesize that the effectiveness of collaborative learning is moderated by the completeness of the prerequisite knowledge bases of group members. It was predicted that when group members have gaps in their knowledge base that can be filled by other group members, collaborative is superior to individual learning.…