This study examined whether learning with heuristic worked examples can improve students' competency in solving reality-based tasks in mathematics (mathematical modeling competency). We randomly assigned 134 students in Grade 5 and 180 students in Grade 7 to one of three conditions: control condition (students worked on reality-based tasks),…

Developing students' skills in solving mathematical problems and supporting creative mathematical thinking have been important topics of Finnish National Core Curricula 2004 and 2014. To foster these skills, students should be provided with rich, meaningful problem-solving tasks already in primary school. Teachers have a crucial role in equipping…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

The main aim of this research is to examine the effect of an instructional design based on the Algo-Heuristic Theory of Instruction (AHTI) on students' mathematics performance and logical thinking skills in the subject of 7th grade mathematics. The research is grounded in a mixed method. In the quantitative part of the research, a…

The Common Core State Standards for Mathematics highlight the importance of not only content standards for mathematics but also mathematical practices such as communication, representation, and reasoning, skills that are often difficult for students with autism spectrum disorder (ASD). Through a single-case multiple-probe-across-participants…

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

Distinguishing between sources of variability in mathematics performance may contribute to a more comprehensive theory of mathematics skills. Research has examined student differences based upon scores on achievement tests, which provide overall proficiency, but may not provide the detailed information for identifying and remediating difficulties.…

In teaching proportion, the teachers usually give the students a formal formula, such as cross-multiplication, without providing them the meaning of proportionality. Thus, the students just apply it in order to solve proportional problems. However, it does not connote that they understand what proportionality means. In this paper, the authors…

The purpose of this article is to address the lack of research on teachers' knowledge of probability. As has been the case in prior research, we asked prospective mathematics teachers to determine which of the presented sequences of coin flips was least likely to occur. However, instead of using the traditional perspectives of heuristic and…

Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

The current study demonstrates how conceptual and procedural knowledge can be used as a heuristic to better understand student math difficulties in order to develop interventions and lay the groundwork for future research. Math interventions were implemented with two elementary students using a nonexperimental single-case design. One student…

The authors compared a conceptual model-based problem-solving (COMPS) approach with a general heuristic instructional approach for teaching multiplication-division word-problem solving to elementary students with learning problems (LP). The results indicate that only the COMPS group significantly improved, from pretests to posttests, their…

In this article, the authors would like to look at a range of solutions submitted by Year 4-5 teams in the 2003 "Naturally Mathematical Challenge" to a question that involves no more than the numbers 1 to 6 and possible arrangements of them. In the context of other competition questions and in their elaboration of mathematical process,…