Proof comprehension is an important skill for students to develop in their proof-based courses, yet students are rarely afforded opportunities to develop this skill. In this paper, we describe two implementations of an activity structure that was developed to give students the opportunity to engage with complex proofs and to develop their proof…

This paper highlights the pedagogical importance of gaps in mathematical proofs to foster students' learning of proofs. We use the notion of 'gap-filling' (Perry & Sternberg, 1986) from literary theory to analyze a task based on a Proof Without Words, which epitomizes the notion of gaps. We demonstrate how students fill in gaps in this…

Instructional design deals with the optimization of learning processes. To achieve this, three aspects need to be considered: (1) the learning task itself, (2) the design of the learning material, and (3) the activation of the learner's cognitive processes during learning. Based on Cognitive Load Theory, learners also need to deal with the task…

Many young people are unprepared to encounter misleading news and information that they find online. As civic educators, we are able to teach them the media literacy skills required to navigate this environment and critically evaluate the information. These lessons may be well-suited to the research methods classroom, where students will learn to…

This article describes the ICAP framework that defines cognitive engagement activities on the basis of students' overt behaviors and proposes that engagement behaviors can be categorized and differentiated into one of four modes: "Interactive," "Constructive," "Active," and "Passive." The ICAP hypothesis…

Choice theory identifies five psychological needs: survival, freedom, power, belonging, and fun (Glasser, 1998). There are close parallels with self-determination theory (SDT), which specifies autonomy, competence, and relatedness as essential needs (Deci & Ryan, 2000). This case study examines a very successful example of choice theory…

This paper draws on previous research to identify a specific set of criteria for evaluating assessments for learning which are not trialled and for which the teacher is the only rater. The paper suggests that four criteria be used for the evaluation of assessment for learning in the language classroom: impact, fairness, activity, and feedback. The…

Preschool environments can be critical to academic success and risk reduction but disruptive behaviors can have significant and lasting negative effects on students as well as teachers. These behaviors may be pervasive in some classrooms and effective interventions are needed. A combined delayed multiple baseline and withdrawal design across a…

In this writing it is my intention to show how using philosophy and creative thinking with junior school children has enabled me to identify gifts and talents of which I might otherwise have been unaware and to show the impact this has had on the children concerned in terms of their own awareness of themselves as learners. I will also question…

Ambitious teaching is a form of teaching that requires a high level of teacher responsiveness to what students do as they actively engage with the subject matter. Thus, a teacher enacting ambitious teaching is often confronted with uncertainties about how to advance students' learning while also building on students' contributions. In…

Although protocol analysis can be an important tool for researchers to investigate the process of collaboration and communication, the use of this method of analysis can be time consuming. Hence, an automatic coding procedure for coding dialogue acts was developed. This procedure helps to determine the communicative function of messages in online…

Recently, many insights have been gained into how to create powerful learning environments. The goal of learning how to teach in this way has important consequences for teacher training. Firstly, scholars indicate the necessity to work out a theoretical framework for the student-teachers which is sufficiently complete, but still manageable, and…