The study aimed to assess the impact of the KWDL technique on the learning achievement of grade 9 students in quadratic function and their satisfaction with this instructional approach. Forty-four ninth-grade students from a Thai public secondary school participated, recruited by cluster random selection. The instruments comprised a KWDL learning…

In this paper I analyze a problem solving event in a secondary mathematics classroom. As the event unfolds, the teachers, including me, understand the event as involving interactions that were not related to learning. By adopting an expansive view of learning, I advance a different interpretation, that the interactions tell a story of student…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

In the present study, we tested the hypotheses that: a) there are individual differences in secondary students' conceptual and procedural fraction knowledge, and b) these differences are predicted by students' approach (deep vs. surface) to mathematics learning. We used two instruments developed and evaluated for the purposes of the study which…

Classroom activities using an inquiry approach often feature students working in small groups to reduce teacher-centeredness and maximize student autonomy. Within science classrooms, group work may mirror modern scientific research: successful interaction among team members (social/relational) that engages probing questioning and creativity…

Teachers constantly struggle to get students actively engaged and invested in their own learning. It can be even more difficult to engage those students in critical thinking and 21st century skills. Problem-based learning (PBL) provides a student-led format with real-life learning experiences, offering a purpose for instruction. By relinquishing…

This research aims to produce a Learning Trajectory Based Instruction (LTBI) that can help the ninth grade students understand the concept of congruence of the two-dimensional shape by examining Lawang Sewu as one of Central Java historical buildings. LTBI is defined as a teaching and learning trajectory that uses Hypothetical Learning Trajectory…

Learning analysts often consider whether learning processes across time are related (1) to one another or (2) to learning outcomes at higher levels. For example, are a group's temporal sequences of talk (e.g., correct evaluation [right arrow] correct, new idea) during its problem solving related to its group solution? I show how to address these…

This study examined the types of learning behaviors students demonstrated while performing inquiry tasks. It also explored the relationship between the learning behaviors and students' domain knowledge. We observed fourteen students in five groups during a ninth-grade biology course. Three types of learning behaviors (inquiry, collaborative, and…

This article continues to challenge the robust myth that mathematical smartness is exemplified in individuals who consistently complete mathematics problems quickly and accurately. In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

Cognitive interest is a vital learning motive for the successful learning process. Nowadays students' interest about science and mathematics are decreasing. The aim of the study is to explore the cognitive interest of Grade 9 students in science and mathematics. Students were surveyed and it helped to explore the respondents' cognitive activity…

Problem solving is not simply a process that ends when an answer is found; it is a scientific process that evolves from understanding the problem to evaluating the solution. This process is affected by several factors. Among these, one of the most substantial is belief. The purpose of this study was to evaluate the beliefs of high school students…

Researchers are skeptical about the role of authoritative sources of information in a constructivist learning environment for fear of usurping students' critical thinking. Taking a social semiotics perspective in this study, authoritative sources are regarded as inscriptions of cultural artifacts, and science learning involves meaning-making of…