Development and Validation of an Instrument to Measure the Effect in respect to Error Commission in Mathematics

Abstract Mistakes may have a negative connotation and can cause negative affects in students toward mathematics. The objective of this research is to develop and validate an instrument which measures the affect of making mistakes in mathematics, and the affect towards mathematics due to errors. The instrument items are based on the relation between the error commission and the three affectivity components: emotions, beliefs, and attitudes. It was administrated to 319 freshmen in the Business School at a private university in Guadalajara, Mexico. The instrument showed strong reliability with an alpha Cronbach of 0,9. Factor analysis confirmed its validity with five constructs related to errors, that explain 52,73% of the total variance: 1) negative emotions and affects on making mistakes, 2) favorable conduct towards the use of errors as a learning tool, 3) mistaken conceptions in regards to usefulness of errors, 4) negative beliefs and emotions towards mathematics due to making mistakes, and 5) the belief that one can learn mathematics from errors. To be able to measure the affectivity students have developed towards errors in mathematics and towards mathematics due to making mistakes as well as their conceptions about errors, may offer a clearer view about of the error culture they have experienced during their school time. Due to this experience, beliefs and attitudes were formed and their behavior may tend to be favorable or not favorable towards their mathematics learning.

摘要 错误往往带有负面内涵，且可能会使学生对数学产生消极情感。本研究旨在开发并验证一款测评工具，用于测量学生在数学学习中犯错时的情感体验，以及因犯错产生的对数学的情感倾向。该工具的条目基于犯错行为与三类情感性成分（情绪、信念与态度）之间的关联构建。研究以墨西哥瓜达拉哈拉一所私立大学商学院的319名大一新生为施测对象，结果显示该工具具有良好的信度，克朗巴赫α系数（Cronbach's α）为0.9。因素分析验证了其效度，共得到5个与错误相关的构念，累计解释总方差的52.73%：1. 犯错时产生的负面情绪与情感体验；2. 将错误视为学习工具的积极行为倾向；3. 对错误价值的错误认知；4. 因犯错而对数学产生的负面信念与情绪；5. 认为可通过错误学习数学的信念。通过测量学生对数学学习中错误的情感体验、因犯错产生的对数学的情感倾向，以及他们对错误的认知，能够更清晰地展现学生在校期间所经历的错误文化生态。此类经历会塑造学生的信念与态度，进而影响其在数学学习过程中的行为倾向，使其或积极或消极地对待数学学习。