Algorithms are the essence of computational thinking, which refers to a set of problem-solving processes that help children become logical thinkers in this increasingly digital society. It is important for teachers of young children to carefully plan and implement algorithm design tasks that involve repeated step-by-step procedures to build strong…

This document describes the game ThunderHawk, intended for use in the first and second cycles of basic education (1st to 6th grade). The game was developed as didactic material to reinforce the fundamental operations of addition and subtraction.

In the context of a rapid digital transformation, digital competence is now regarded as a fourth cultural skill complementing reading, writing, and arithmetic. We argue that a well-structured and sound competence model is needed as a shared foundation for learning, teaching, pedagogical diagnostics and evaluative schemes in the school system.…

Analogical reasoning has played an important role in the development of modern mathematics. However, there has been critique of analogies for the purpose of learning new mathematics. In this article, I counter that students can productively reason by analogy to learn new mathematics and even develop new mathematics themselves. I display examples…

Mark Creager noticed that how we teach students to reason mathematically may be counter-productive to our teaching goals. Sometimes a linear approach, focusing on sub-processes leading to a proof works well. But not always. Students should be made aware that reasoning is not always a straight forward process, but one filled with false starts and…

Chemical reasoning takes many forms. The focus in this paper is on a reasoning process that facilitates using experimental evidence to make connections between macroscopic and submicroscopic domains, which we will refer to as "creating representation." It is a particular type of reasoning that has played a critical role in chemistry,…

What do cows drink? The correct answer is water, but many are tempted to say milk. The disposition to override an intuitive response (milk) with a more analytic response (water) is known as "cognitive reflection." Tests of cognitive reflection predict a wide range of skills and abilities in adults. In this article, we discuss the…

Science plays an important, if not central role, in the profession's mission of enhancing human well-being. The benefits that flow from science do not emerge in a vacuum, but rather are contingent upon the existence of a specific value-based milieu. Included among these values are an academic discourse that: 1) supports the free expression of…

"Productive Struggle" refers to a strategy that gives students an opportunity to increase their background mathematical knowledge. Productive Struggle helps students connect key concepts, determine how and where an error occurs, and supports students in figuring out how to use their own thinking and reasoning skills to correct an error.…

This paper, conceptual but with empirical support, fills in some blanks in Vygotsky's reworking of Spinoza's "Ethics." Here Vygotsky sought to develop a developmental theory of emotions that would fit his developmental theory of higher psychological functions; that is, one which used function to explain how structure changes (much as…

In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…

This chapter focuses on effective preparation for civic reasoning, discourse, and problem solving. It reviews literatures, including major synthetic reviews and studies from the science of learning and development (SoLD), civics education, and mathematics education. Based on these reviews, the authors make the case for a more comprehensive form of…

This article describes a teaching plan for a discussion-driven introduction to moral reasoning and explains its philosophical and pedagogical rationale. The teaching plan consists of a sequence of thought experiments that build on one another, and ends with participants addressing some morally complex, real-life issues. The plan rests on extensive…

Peirce made repeated attempts to clarify what he understood as abduction or creative reasoning in scientific discoveries. In this article, we draw on past and recent scholarship on Peirce's later accounts of abduction to put a case for how teachers can apply his ideas productively to elicit and guide student creative reasoning in the science…

The most obvious way that misinformation does damage is by causing people to believe misconceptions or reducing belief in accurate facts. One experiment found that just a handful of cherry-picked statistics about climate change confused people and reduced their acceptance that climate change was happening. After being shown the misinformation,…