Considering the low achievement of Indonesian students in international studies (PISA), which measures Higher-Order Thinking Skill (HOTS) in solving the problem, improving the quality of mathematics learning in Indonesia is very important. The purpose of this research was conducted to explore the variations in students' learning strategies and…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

Supporting students' in-the-moment perseverance is a vital objective in mathematics education because it promotes learning with understanding. Yet, little is written about if and how student perseverance can improve over time. I examine the specific ways in which secondary students improved their perseverance as they engaged with challenging…

Rich mathematical modeling activities are crucial to giving students agency and making mathematics meaningful. Proportional reasoning and transitional algebraic reasoning are the primary topics in the prealgebra curriculum, so a need exists for meaningful modeling activities using proportional reasoning in addition to geometric modeling. In…

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…

How can geometry teachers design great tasks that allow students to make connections among interrelated concepts and expand their geometric reasoning skills? Many curricular materials provide problems for students to apply a single geometric concept. However, these problems do not always promote reasoning opportunities for students, because…

This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: "language of generalisation," "language of comparison," "language of proportional reasoning," and…

Students must be encouraged to think for themselves by tapping into their imaginations. Only when mathematical concepts are presented in an imaginative way will students fully benefit from their experience. Both teachers and students must engage themselves in this creative realm of thinking, where imagination plays a vital part in learning and…

Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…