There have been many attempts to reform mathematics teaching in Australia to encourage teachers to use more cognitively demanding tasks that focus on problem solving and reasoning. However, there is limited specific advice for teachers on how best to do this. This paper reports on one set of survey items that examines 52 teachers' responses to…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

Considering the update of curricula and the importance of problem solving skills in mathematics education; the need for examining the problems in mathematics textbooks in the context of presentation, content, and solution becomes a current issue. In this study, it was aimed to designate the problem types used in middle school mathematics textbooks…

Highly capable mathematics students are not usually considered strugglers. This paper reports on a case study of a Year 6 student, Debbie, her response to a lesson, and her learning involving a challenging mathematical task. Debbie, usually a highly capable student, struggled to complete a challenging mathematical task by herself, but as the…

The purpose of this paper is to explore and explain students' achievements in solving context-based gas exercises comprising the macroscopic and submicroscopic levels of chemical concepts. The influence of specific variables, such as interest in learning, formal-reasoning abilities, and visualisation abilities, is a significant factor that should…

Owing to the popularity of tablet computers and smart phones, e-books have become an important medium for both formal and informal learning. However, conventional e-books are mainly designed to provide information in the form of multimedia, implying that students spend most of their time memorizing and comprehending what they read from e-books,…

Data are becoming increasingly important in science and society, and thus data literacy is a vital asset to students as they prepare for careers in and outside science, technology, engineering, and mathematics and go on to lead productive lives. In this paper, we discuss why the strongest learning experiences surrounding data literacy may arise…

Children in the elementary grades are expected to solve equations to demonstrate prealgebraic proficiency. Prealgebraic differences may emerge based equation type (i.e., standard vs. nonstandard), the operation shown or required for solution (i.e., addition or subtraction), and the position of the unknown. Prealgebraic differences may also be…

Purpose: The purpose of this paper is to present an algorithm to generate story problems via controlled parameters in the domain of mathematics. The generation process is performed in the problem generation module in the context of an intelligent tutoring system suggested in this paper. Controlling the question parameters allows for adapting the…

Previous experiments have shown a deleterious effect of visual representations on college students' ability to solve total- and joint-probability word problems. The present experiments used conditional-probability problems, known to be more difficult than total- and joint-probability problems. The diagram group was instructed in how to use tree…

An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…

The Common Core State Standards for Mathematics (CCSSM) highlight the importance of students' conceptual understanding, mathematical reasoning, and problem solving in order to prepare students for college and careers. However, the success of this reform effort largely depends on how teachers actually design and implement instruction based on the…

The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that…

Worked examples have proven to be effective for knowledge acquisition compared with problem solving, particularly when prior knowledge is low (e.g., Kalyuga, 2007). However, in addition to prior knowledge, executive functions and fluid intelligence might be potential moderators of the effectiveness of worked examples. The present study examines…

Many educational data mining studies have explored methods for discovering cognitive models and have emphasized improving prediction accuracy. Too few studies have "closed the loop" by applying discovered models toward improving instruction and testing whether proposed improvements achieve higher student outcomes. We claim that such…