The focus of this study is on the role of achievement goals in students' persistence. The authors administered 5 puzzles to 96 college students: 4 unsolvable and 1 relatively easy (acting as a hope probe). They examined whether and how persistence may deteriorate as a function of failing the puzzles, as well as whether and how persistence may…

Teaching mathematics using graphic calculators has been an issue of didactic discussions for years. Finding ways in which graphic calculators can enrich the development process of creative activity in mathematically gifted students between the ages of 16-17 is the focus of this article. Research was conducted using graphic calculators with…

In the natural world, learning emerges from the joy of play, experimentation, and inquiry as part of everyday life. However, this kind of informal learning is often difficult to integrate within structured educational curricula. This report describes an educational program that embeds naturalistic learning into formal high school, college, and…

Although it is difficult to find any current literature that does not encourage use of multiple representations in mathematics classrooms, there has been very limited research that compared such practice to student achievement level on standardized tests. This study examined the associations between students' achievement levels and their (a)…

This study compared one lesson across four U.S. "traditional" textbook series, two U.S. reform-based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of…

How does early feedback change the programming problem solving in an online environment and help students choose correct approaches? This study was conducted in a sample of students learning programming in an online course entitled Introduction to C++ and OOP (Object Oriented Programming) using the ANGEL learning management system platform. My…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…

A quasi-experiment was conducted at an elementary school to investigate if guided collaboration would facilitate programming learning of 6 graders. Sixty-six students of two intact classes learned to program in KPL (kid's programming language) for 18 weeks during the experiment. One class was randomly assigned to the control group (i.e.,…

Learning about linear relationship with one unknown, middle school students may often demonstrate a certain degree of proficiency manipulating algebraic symbols. When encouraged, they can verbalize and explain the steps they perform, thereby demonstrating awareness of the procedures with symbols according to fixed rules. It is well known that…

A large body of research has shown that for novice learners, instruction that relies more heavily on worked examples than on problem solving, is more effective for learning as shown by higher test performance. Moreover, this beneficial effect is often obtained with less acquisition time and lower cognitive load during acquisition and test phase.…

A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th-, 9th-, and 10th-grade students in five different school systems over three consecutive…

The design of problems is crucial for the effectiveness of problem-based learning (PBL). Research has shown that PBL problems have not always been effective. Ineffective PBL problems could affect whether students acquire sufficient domain knowledge, activate appropriate prior knowledge, and properly direct their own learning. This paper builds on…

The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the…

Targeted as a highly desired skill for contemporary work and life, problem solving is central to game-based learning research. In this study, middle grade students achieved significant learning gains from gameplay interactions that required solving a science mystery based on microbiology content. Student trace data results indicated that effective…