Students in secondary school often struggle with symbol sense, that is, the general ability to deal with symbols and to recognize the structure of algebraic formulas. Fostering symbol sense is an educational challenge. In graphing formulas by hand, defined as graphing using recognition and reasoning without technology, many aspects of symbol sense come to play. In a previous study, we showed how graphing formulas by hand could be learned. The aim of the study we present here is to explore the relationship between students’ graphing abilities and their symbol sense abilities while solving non-routine algebra tasks. A symbol sense test was administered to a group of 114 grade 12 students. The test consisted of eight graphing tasks and twelve non-routine algebra tasks, which could be solved by graphing and reasoning. Six students were asked to think aloud during the test. The findings show a strong positive correlation between the scores on the graphing tasks and the scores on the algebra tasks and the symbol sense used while solving these tasks. The thinking-aloud protocols suggest that the students who scored high on the graphing tasks used similar aspects of symbol sense in both the graphing and algebra tasks, that is, using combinations of recognizing function families and key features, and qualitative reasoning. As an implication for teaching practice, learning to graph formulas by hand might be an approach to promote students’ symbol sense.

中文翻译：

---

手绘公式与学生符号感的关系

中学生经常在符号感上挣扎，即处理符号和识别代数公式结构的一般能力。培养符号意识是一项教育挑战。在手工绘制公式中，定义为在没有技术的情况下使用识别和推理绘制图形，符号感的许多方面都发挥了作用。在之前的一项研究中，我们展示了如何手动学习绘图公式。我们在此介绍的研究的目的是探讨学生在解决非常规代数任务时的绘图能力与其符号感知能力之间的关系。对 114 名 12 年级学生进行了符号意义测试。测试由8个图形任务和12个非常规代数任务组成，可以通过图形和推理来解决。六名学生被要求在测试过程中大声思考。研究结果表明，绘图任务的分数与代数任务的分数以及在解决这些任务时使用的符号意义之间存在很强的正相关关系。大声思考的协议表明，在绘图任务中得分高的学生在绘图和代数任务中使用了相似的符号意义方面，即使用识别函数族和关键特征以及定性推理的组合。作为教学实践的启示，学习手工绘制公式可能是提高学生符号意识的一种方法。大声思考的协议表明，在绘图任务中得分高的学生在绘图和代数任务中使用了相似的符号意义方面，即使用识别函数族和关键特征以及定性推理的组合。作为教学实践的启示，学习手工绘制公式可能是提高学生符号意识的一种方法。大声思考的协议表明，在绘图任务中得分高的学生在绘图和代数任务中使用了相似的符号意义方面，即使用识别函数族和关键特征以及定性推理的组合。作为教学实践的启示，学习手工绘制公式可能是提高学生符号意识的一种方法。