ABSTRACT

We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The research question is how teaching grounded on a structural approach and designed based on principles of variation theory is reflected in children’s learning of numbers. To answer this, three analyses were conducted, addressing: i) how the children’s ways of experiencing numbers changed after participating in the intervention, ii) how the theoretical ideas were afforded in the intervention program, and iii) synthesizing how the affordance was associated with the children’s arithmetic learning. One group of eight children participating in the intervention program was chosen for thorough analysis. Progression was observed in how the children changed their ways of experiencing numbers during the intervention that allowed them to enact more advanced arithmetic strategies, which was associated with the structural approach in teaching. The results also show how analysis focusing on aspects discerned in learning and aspects afforded in teaching provides a way of describing arithmetic learning with significant implications for teaching practices.

摘要

我们在这里报告了一项干预措施，该干预措施采用了一种结构性方法来解决学龄前儿童学习成果方面的算术问题。利用学习变异理论的基本原理来开发干预措施并作为分析框架，我们以相称的方式讨论教与学。研究的问题是如何在儿童的数字学习中反映出基于结构化方法并基于变异理论原理设计的教学。为了回答这个问题，进行了三项分析，涉及：i）儿童参与干预后的数字体验方式是如何改变的； ii）干预计划中如何提供理论思想； iii）综合如何将提供能力与孩子们的算术学习。选择参加干预计划的一组八个孩子进行全面分析。观察到儿童在干预期间如何改变他们的数字体验方式方面的进步，这使他们能够制定更高级的算术策略，这与教学中的结构方法有关。结果还表明，侧重于学习中识别的方面和教学中提供的方面的分析如何提供一种描述算术学习的方法，该方法对教学实践具有重要意义。这与教学中的结构化方法有关。结果还表明，侧重于学习中识别的方面和教学中提供的方面的分析如何提供一种描述算术学习的方法，该方法对教学实践具有重要意义。这与教学中的结构化方法有关。结果还表明，侧重于学习中识别的方面和教学中提供的方面的分析如何提供一种描述算术学习的方法，该方法对教学实践具有重要意义。