Feedback influences children's reasoning about math equivalence: A meta-analytic review

ABSTRACT

Decades of research have focused on children's reasoning about math equivalence problems for both practical and theoretical insights. Not only are math equivalence problems foundational in arithmetic and algebra, they also represent a class of problems on which children's thinking is resistant to change. Feedback is one instructional tool that can serve as a key trigger of cognitive change. In this paper, we review all experimental studies (N = 8) on the effects of feedback on children's (ages 6–11) understanding of math equivalence. Meta-analytic results indicate that feedback has positive effects for low-knowledge learners and negative effects for high-knowledge learners, and these effects are stronger for procedural outcomes than conceptual outcomes. Findings highlight the variable influences of feedback on math equivalence understanding and suggest that models of thinking and reasoning need to consider learner characteristics, learning outcomes, and learning materials, as well as the dynamic interactions among them.     

Self-knowledge,belief, ability (and agency?)

Matthew Boyle [(2011). “Transparent Self-Knowledge.” Aristotelian Society Supplementary Volume 85 (1): 223–241. doi:10.1111/j.1467-8349.2011.00204.x] has defended an account of doxastic self-knowledge which he calls “Reflectivism”. I distinguish two claims within Reflectivism: (A) that believing that p and knowing oneself to believe that p are not two distinct cognitive states, but two aspects of the same cognitive state, and (B) that this is because we are in some sense agents in relation to our beliefs. I find claim (A) compelling, but argue that its tenability depends on how we view the metaphysics of knowledge, something Boyle does not consider. I argue that in the context of the standard account of knowledge as a kind of true belief – what I call the Belief Account of knowledge – the claim faces serious problems, and that these simply disappear if we instead adopt an Ability Account of knowledge, along the lines of that defended by John Hyman [(1999). “How knowledge Works.” The Philosophical Quarterly 49 (197): 433–451; John Hyman (2015). Action, Knowledge, and the Will. Oxford: Oxford University Press]. I find claim (B) less compelling, and a secondary aim of the paper is to suggest that once we reject the Belief Account of knowledge, and move over to an Ability Account, there is no explanatory role for (B) left to play.     

Carers’ beliefs about counselling: a community participatory study in Wales

This interpretivist community participatory study explores carers’ beliefs about the potential usefulness of counselling in relation to the caring role. Twenty semi-structured interviews with carers were transcribed and analysed thematically. All participants thought counselling could potentially be helpful to carers, but their ideas about the ways in which it would help varied according to whether or not they had personal experience of counselling. Only carers with counselling experience had an awareness of counselling as focussing on changing feelings, thoughts, attitudes and behaviours. The implications of the findings for the provision of counselling services are discussed.     

Why conceptual competence won’t help the non-naturalist epistemologist

Abstract

Non-naturalist normative realists face an epistemological objection: They must explain how their preferred route of justification ensures a non-accidental connection between justified moral beliefs and the normative truths. One strategy for meeting this challenge begins by pointing out that we are semantically or conceptually competent in our use of the normative terms, and then argues that this competence guarantees the non-accidental truth of some of our first-order normative beliefs. In this paper, I argue against this strategy by illustrating that this competence based strategy undermines the non-naturalist’s ability to capture the robustly normative content of our moral beliefs.     

Knowledge and availability

The mentioning of error-possibilities makes us less likely to ascribe knowledge. This paper offers a novel psychological account of this data. The account appeals to “subadditivity,” a well-known psychological tendency to judge possibilities as more likely when they are disjunctively described.     

Casuistic Reasoning in Expert Narratives on Healthy Eating

Individualisation of healthy eating is a broad tendency in Western culture and is becoming a popular ideal in nutrition science. Public perception of dietary knowledge is central to this individualisation and many experts now aim to present dietary knowledge in a way which relates to individual experience, as well as a casuistic style in which particular cases are discussed in relation to general, universal principles. Analysis of casuistic narrative styles in the public communication about healthy eating by experts makes explicit their flexible use of both particular cases and universal claims, in which clinical and personal cases are narratively employed by the experts to invite readers to personally consider dietary knowledge. Such casuistic narration by experts relates human agency and particular bodies to universal concepts in a way that has generative and critical functions with respect to dietary knowledge and understanding. The public articulation of clinical narratives by experts make salient the intersubjective emergence and accumulation of dietary knowledge between expert reasoning and lay understanding. Personal narratives have an essential role in presenting casuistic reasoning through experts’ personal lives and making their own bodies relevant to public communication about healthy eating. This emphasises the experts’ personal agency in relationship to common norms and general knowledge. Furthermore, both clinical and personal narratives are used by experts in their assessment of the shortcomings in public health messages. Experts’ casuistic narration thus does not merely construct credibility but has epistemic functions in constructing dietary knowledge tangible with respect to actual eating practices.     

A Confucian in Buddhist clothing? – Interpreting Nishida’s conception of the good as a realisation of the Mandate of Heaven

ABSTRACT

In this study, I examine the Confucian influence upon An Inquiry into the Good, the first publication of Nishida Kitarō. Nishida’s student Kōsaka Masaaki depicts his mentor’s conception of the good in terms of realising the 'Mandate of Heaven'. Taking this to be indicative of the importance of Confucianism for Nishida’s early thought, I compare his philosophy of pure experience and ethical project of ‘self-realisation’ with corresponding ideas found in the Confucian corpus. I especially focus on the Great Learning and Doctrine of the Mean as interpreted by the Neo-Confucian Wang Yang-Ming. This study builds upon the pioneering work of Michel Dalissier, Dermott Walsh and David Williams on the Kyoto School and Confucianism. My portrayal of Confucianism is indebted to the ‘philosophical’ translations of Roger Ames, David Hall and Henry Rosemont, Jr., which bring into relief the tradition’s ‘relational ontology’ that Graham Parkes teaches is shared by the Kyoto School.     

How Do We Acquire Moral Knowledge? Is Knowing Our Duty Ever Passive? – Two Questions for Martin Sticker

Martin Sticker's discussion of the common moral agent contains much that I find insightful, true and significant. As a response to his paper, I focus on two important issues that nevertheless separate us: (1) Sticker claims that knowing our duty can be mere passive awareness and that it indeed is passive as awareness of the special status of humanity. I deny that knowing our duty is ever passive. (2) He further claims that the common universalization test is the paradigmatic way active agents acquire moral knowledge. I argue that Sticker appears to construe universalization as a formal test that presupposes no moral knowledge and that so construed the test cannot serve for acquiring moral knowledge.