This work analyses the changes in the relationship between arguing and images from the mathematics textbooks for the secondary school in Argentina (students 12-17 years old) along 67 years. The textbooks have been published in the period 1940 thru 2007. The analysis is done by (N = 137) textbooks based on three metacategories in an inductive way.…

Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

This study examines different factors' relative importance for students' performance in the transition to university mathematics. Students' characteristics (motivation, actions and beliefs) were measured when entering the university and at the end of the first year. Principal component analysis revealed four important constructs:…

This investigation explored pre-service teachers' mathematics content knowledge (MCK) and beliefs associated with mathematics education practices. An Exploratory Factor Analysis, conducted on a beliefs and attitudes questionnaire, produced three common attitude factors associated with (1) inquiry-based teaching; (2) how mathematics knowledge is…

In this study, we aimed at examining Indonesian In-Service primary Teachers' Mathematics Content Knowledge (MCK) and Mathematics Pedagogical Content Knowledge (MPCK) for teaching ratio and proportion. The instruments were administered to 271 in-service primary teachers with various education background. There were three underlined factors on MCK…

Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?" In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the…

Positive self-assessment of ability in the quantitative domains is considered critical for student participation in science, technology, engineering, and mathematics field studies. The present study investigated associations of gender compatibility (gender typicality and contentedness) and math-gender stereotypes with self-concepts in math and…

The current study aimed to construct a questionnaire that measures students' personality traits related to "striving for understanding" and "learning value of geometry" and then examine its psychometric properties. Through the use of multiple methods on two independent samples of 402 and 521 middle school students, two studies…

Student academic self-assessment engages the students in deliberate reflection about what they are learning and how they are learning it. This intervention study investigated the effects of self-assessment training on students' perceptions towards self-assessment in two Singaporean primary schools. The study, which used a pretest-posttest design,…

The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…

The present study investigated the relative importance of executive functioning, parent-child verbal interactions, phonological awareness and visual skills on reading and mathematics for Chinese children from low-versus middle-socio economic status (SES) backgrounds. A total of 199 kindergarten children were assessed on executive functioning,…

In this paper, we provide evidence of the impact of early algebra (EA) over time. We document this impact in the following ways: (a) by showing the performance over time of an experimental group of 15 children on an algebra assessment, from 3rd to 5th grade; and (b) by showing how the performance on an algebra assessment of children from an…

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students' attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students'…

The Mathematical Resilience Scale measures students' attitudes toward studying mathematics, using three correlated factors: Value, Struggle, and Growth. The Mathematical Resilience Scale was developed and validated using exploratory and confirmatory factor analyses across three samples. Results provide a new approach to gauge the likelihood of…

After a test is developed, most content validation analyses shift from ascertaining domain definition to studying domain representation and relevance because the domain is assumed to be set once a test exists. We present an approach that allows for the examination of alternative domain structures based on extant test items. In our example based on…