This research aims to produce mathematics problems based on PISA level with valid and practical content of change and relationships and has potential effect for Junior High School students. A development research method developed by Akker, Gravemeijer, McKenney and Nieveen is used this research. This development research consists of three stages;…

Prior research shows that self-explanation promotes understanding by helping learners connect new knowledge with prior knowledge. However, despite ample evidence supporting the effectiveness of self-explanation, an instructional design challenge emerges in how best to scaffold self-explanation. In particular, it is an open challenge to design…

The OECD PISA (Programme for International Student Assessment) investigates whether students have acquired the applicable knowledge essential for full participation in a modern society (they measure how students can apply their knowledge to novel situations). Meaningful learning and understanding are basic aspects of all kinds of learning and they…

The present study examined indirect effects of principal leadership on the mathematics achievement of 254,475 15-year-old students from 10,313 schools in 32 OECD economies. Results showed that the students could be divided into three categories ("Disadvantaged," "Average," and "Privileged") differing in levels of…

Pythagoras' theorem in two and three dimensions appears in General Mathematics, Units 1-2, section 6 (Geometry and trigonometry: Shape and measurement) in the Victorian Certificate of Education Mathematics Study Design (Victorian Curriculum Assessment Authority, 2010). It also comes in Further Mathematics, Units 3-4 (Applications: Geometry and…

Computational estimation is an important skill necessary for students' mathematical development. Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem. In turn, good…

Many classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersections of points in these geometries. The dramatically different results we obtain illustrate the effect…

Teachers often look for good sources to find problems motivating students and stiffen the concepts they are going to teach and use in the classroom. This causes the question: "Where can we find good problems that can be used in classrooms?". History of mathematics presents many historical problems which can enrich the classroom…

In this study, ways in which 9-year old students from one Singapore school solved 1-step and 2-step word problems based on the three semantic structures were examined. The students' work and diagrams provided insights into the range of errors in word problem solving for 1- step and 2-step word problems. In particular, the errors provided some…

This paper reports on scaffolding that is situated within a research project that examined the ways mathematical thinking emerged from student-centred inquiry. The project utilised qualitative methods to investigate a case study of a year-10 class (14-15-year-olds), at a new purpose-built secondary school designed to facilitate inquiry learning.…

Research has found that students, particularly those in middle school and high school, believe that their participation in mathematics classrooms includes listening to teachers explaining, working in textbooks, and solving exercise problems quickly (Franke, Kazemi, and Battey 2007). In this article, the authors describe a classroom vignette and…

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

"Low threshold, high ceiling" tasks are accessible to diverse learners; invite a wide range of approaches; and hold the potential to further challenge, strengthen, and extend everyone's mathematical reasoning. In this article, the authors present a family of Brick Pyramid problems as examples of "low threshold, high ceiling"…

In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers'…