The effect of using SOLO taxonomy on secondary mathematical competencies associated with quadratic equations

The data on the effect of using SOLO taxonomy on secondary mathematical competencies associated with quadratic equations was collected between May and June 2024 from three secondary schools in Mafinga district (Zambia). The sample involved 78 grade 11 students from three intact classes as experimental groups and 71 grade 11 students from three intact classes as comparison groups randomly selected. The researcher analyzed learning outcomes associated with quadratic equations in the Zambian secondary school mathematics syllabus and identified three expected competencies namely; algebraic graphing skills, algebraic reasoning skills and algebraic representation skills. With these competencies, four questions for testing students’ understanding of quadratic equations were formulated in line with the increasing complexity of the response structure reflected in the SOLO categories. Fifteen lessons were conducted to complete quadratic equations in five weeks. In each lesson, think-pair share, group and individual activities were implemented as formative assessments to monitor learning progress. Students from experimental groups completed formative assessments with formative feedback based on SOLO taxonomy that encouraged self-assessment and peer feedback. Students took the mathematics competence test within one-hour thirty minutes before and after learning quadratic equations. Students’ responses to quadratic tasks were analyzed using grading rubrics based on SOLO taxonomy that described the levels of understanding from pre-structural level (no understanding), uni-structural level and multi-structural level (surface understanding), relational level (deep understanding) to expended abstract level (conceptual understanding). The data set includes an Excel file named “Data set on students' competencies associated with quadratic equations based on SOLO taxonomy” with three sheets containing raw data for students before and after interventions: Graphing skills sheet, Reasoning skills sheet and Representation skills sheet. The levels of performance ranged from 0 = pre-structural level, 1 = uni-structural level, 2 = multi-structural level, 3 = relational level and 4 = uni-structural level. Students classified under relational and extended abstract level categories demonstrated higher order thinking skills while those under uni-structural and multi-structural levels demonstrated low order thinking skills. Students under pre-structural level demonstrated no understanding. Bar charts were used to present the proportion of students on each SOLO level in relation to algebraic graphing skills, algebraic reasoning skills and algebraic representation skills. SPSS v.25 was used to generate the outputs. Regardless of the levels of performance before interventions, the results showed that the proportion of students who achieved higher order thinking skills on expected mathematical competencies was higher for experimental groups than comparison groups after interventions.

本数据集采集了2024年5月至6月间，于赞比亚马芬加区（Mafinga district）三所中学开展的SOLO分类法（SOLO taxonomy）应用于与二次方程相关的中等数学能力培养的效果相关数据。研究样本包含随机选取的3个完整教学班共78名11年级学生作为实验组，以及另3个完整教学班共71名11年级学生作为对照组。研究者结合赞比亚中学数学教学大纲中与二次方程相关的学习成果，明确了三项核心预期能力，即代数绘图技能、代数推理技能与代数表征技能。基于这三项能力，结合SOLO分类法所反映的应答结构复杂度递增规律，研究者设计了4道用于测试学生对二次方程理解程度的试题。本次研究共开展15课时教学，在5周内完成二次方程相关内容的讲授。每节课均采用思考-配对-分享、小组及个人活动作为形成性评价手段，以实时监控学习进度。实验组学生的形成性评价作业将获得基于SOLO分类法的形成性反馈，以此鼓励自主评价与同伴互评。在二次方程教学前后，学生均需在1小时30分钟内完成数学能力测试。研究者采用基于SOLO分类法的评分量规对学生的二次方程任务作答情况进行分析，该量规将理解水平划分为前结构水平（无理解）、单结构水平、多结构水平（表层理解）、关联水平（深层理解）以及扩展抽象水平（概念性理解）。本数据集包含一个名为"基于SOLO分类法的学生二次方程相关能力数据集"的Excel文件，内含三个工作表，分别存储干预前后学生的原始数据：绘图技能工作表、推理技能工作表与表征技能工作表。绩效水平的编码规则为：0 = 前结构水平，1 = 单结构水平，2 = 多结构水平，3 = 关联水平，4 = 单结构水平。被归类为关联水平与扩展抽象水平的学生展现出高阶思维能力，而归属于单结构与多结构水平的学生则展现出低阶思维能力，处于前结构水平的学生未形成任何理解。研究采用柱状图呈现各SOLO水平学生在代数绘图、代数推理与代数表征三项技能上的占比情况。数据分析采用SPSS v.25软件完成。无论干预前的绩效水平如何，研究结果均显示，在预期数学能力上达成高阶思维能力的学生占比，实验组在干预后均高于对照组。