Background: Dealing with uncertainties is inherent in the engineering design process and often poses challenges for young learners. This necessitates providing learners with adequate support to navigate their uncertainties effectively. However, achieving this requires a deeper understanding of the factors influencing learners' uncertainty…

Empirical evidence demonstrates the effect of productive failure (Kapur, 2008) on disciplinary knowledge. However, there is no clear theoretical explanation for why this is the case. Empirical evidence on argumentation and education shows the impact of curricular embedded deliberative argumentation on learning. However, these two trends of…

Background: Learning to program and success in computer science requires persistence in the face of challenges. This study contributes to research on the social context of learning by describing how children's peer interactions can support or hinder the pair's problem solving on the computer. Methods: Video recordings from eight pairs of middle…

Educators aim to equip students with learning strategies they can apply when approaching new problems on their own. Teaching design-thinking strategies may support this goal. A first test would show that the strategies are good for learning and that students spontaneously transfer them beyond classroom instruction. To examine this, we introduce…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

This study investigated how interaction with peers influenced the ways students managed uncertainty during collaborative problem solving in a 5th-grade class. The analysis focused on peer responses to individuals' attempts to manage uncertainty they experienced while engaged in collaborative efforts to design, build, and program robots and…

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…

In this article, we describe the design principles undergirding "productive failure" (PF; M. Kapur, 2008). We then report findings from an ongoing program of research on PF in mathematical problem solving in 3 Singapore public schools with significantly different mathematical ability profiles, ranging from average to lower ability. In…

This article presents a designed learning environment intended to engage students in learning about the relationships among multiple representations as they work together on a shared task. Over the course of several extended problem-solving sessions, groups developed several successive alignments of participants and representations as they learned…

There is a growing national recognition that teachers and teaching are at the heart of successful educational reform. However, few tools exist for measuring classroom instruction. The primary purpose of this article is to describe methods we developed to measure and study teaching, specifically while teachers were using a multimedia intervention…

We describe how 1 Algebra I teacher and her 8th-grade students used meta-representational knowledge when generating and evaluating equations to solve word problems. Analyzing data from a sequence of 4 lessons, we found that the teacher and her students used criteria for evaluating equations, in addition to other types of knowledge (e.g., different…

This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did…

Learning in a socially mediated context like a classroom places emphasis on the ability of learners to communicate their ideas to others, and for members of a class to achieve shared meaning or intersubjectivity (IS). We take a participatory view of IS, where both consensual agreement and disagreement are regarded as aspects of a common set of…