This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main…

Open-ended questions that can be solved using different strategies help students learn and integrate content, and provide teachers with greater insights into students' unique capabilities and levels of understanding. This article provides a problem that was modified to allow for multiple approaches. Students tended to employ high-powered, complex,…

The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…

Thirty-two students enrolled in one of four sixth-grade classrooms across two elementary schools participated in this study. Students receiving supplemental and intensive instruction in math and those with math-related disabilities were participants. A treatment and control, pre/postexperimental design was used to examine the effect of preteaching…

Despite the effort of teacher education programs, early childhood, and elementary preservice teachers often fear mathematics, have high mathematics anxiety, hold negative self-perceptions in relation to mathematics, find mathematics irrelevant, and have low mathematics achievement. The aim of this study was to implement and investigate the…

As a residential college within Michigan State University that focuses on STEM fields, Lyman Briggs College developed a STEM learning community to support students with low mathematics placement test scores, the Instilling Quantitative and Integrative Reasoning program (INQUIRE). INQUIRE serves some of those students considered historically…

"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP).…

An elementary proof using matrix theory is given for the following criterion: if "F"/"K" and "L"/"K" are field extensions, with "F" and "L" both contained in a common extension field, then "F" and "L" are linearly disjoint over "K" if (and only if) some…

Current reforms in mathematics education have called for a stronger emphasis on the teaching and learning of algebra for all students at all grade levels. Succeeding in algebra can prepare students to learn and understand more advanced mathematics in the future. One topic in algebra--the equal sign--has received considerable attention in middle…

Research on high school math course taking documents the advantages of starting high school at or beyond Algebra 1. Fewer studies examine differentiation into remedial, general, and honors Algebra 1 course types by course rigor. This study examines how course grades and course rigor are associated with math attainment among students with similar…

Across the United States, more than half of entering freshmen discover they are ineligible for college-level coursework each year, most commonly in math. The readiness gap is widest when considering students at nonselective two-year colleges, and students who are black, Hispanic, or from low-income families. It often spells disaster for students…

There have been many recent policy and program changes in K-12 education across the United States, particularly in area of mathematics. Changes, such as the Common Core State Standards for Mathematics and standards-aligned year-end summative assessments, require an increase in student-centered, cognitively demanding activities in the classroom.…

In order to improve problem-solving dispositions, a section of an inquiry-based math sequence for first-year business students was linked with a section of our general education English sequence. We describe how the linked classes worked and compare some preliminary results from linked and unlinked sections of the math sequence.

The aim of the study was to determine whether pre-service elementary mathematics teachers could write and use mathematical definitions. For this reason, the question sheet containing two questions, was given to 76 pre-service teachers in a public university who was taking general mathematics course. Qualitative research method was used during data…

This manuscript describes the study of an abstract algebra course for preservice secondary mathematics teachers (PSMTs). Often, courses in abstract algebra have not been viewed as productive, beneficial learning experiences for future teachers, both by researchers and PSMTs themselves. This despite calls for increased content knowledge for…