Abstract—The graphical elements as parts of concept map construction are employed to assess both learning and teaching. Augmenting the use of concept maps, this study examines the graphical elements, such as, nodes, edges, cliques, diameters, travelling paths and structures of the graphs to relate to ones’ understanding to a topic, in this case, polynomials for middle school. In the aspect of teaching assessment, the teacher’ concept map drawn according to the lesson plan is served as the master map, which echoes the teacher’s expectation of students’ learning. On the other hand, students’ maps also reveal their understanding through the nodal relationship, which can be the definitions of terms, related examples, graph representation and algebraic manipulation. Data collection includes a focus group of 10 students and 1 teacher undergoing the concept map assessment task with restricted node terms. Graphically analyzed, students’ concept maps reveal some common elements as in the teacher’s map. In addition, the interview with the teacher also suggests that concept map as the assessment tool is an effective teaching reflection for which the teacher can see what to fulfill for future classes. Index Terms—Concept mapping, learning assessment, teaching assessment, graphical information, polynomials. I. INTRODUCTION Concept maps have received a great deal of attention in science education as a learning strategy since 1990 [1]. The continuing research about this further suggests that the concept map construction is based on the epistemological assumption that the concept-concept relationship is the building block of knowledge [2]. However, structuring knowledge can be diverse, yet hard to visualize, particularly for abstract mathematical concepts. Therefore, use of concept mapping becomes handy to extract learners‟ knowledge construction and to reflect their understanding. In accordance with this argument, McGowen and Tall claims that a concept map is a diagram representing the conceptual structure of a subject discipline as a graph in which nodes represent concepts and lines connecting them represent cognitive links [3]. With the beneficial structures, some research extends the application of concept maps as an assessment tool, for which the comparison between a teacher and students‟ concept maps can be considered as a form of a lesson evaluation to assess the lesson‟s objectives [4], [5]. According to multiple reviews, the previous work about concept mapping assessment has involved around concept recognition, organization of concept in branching structure, graph alignment, similarity, and scoring scheme for learning Manuscript received March 17, 2020; revised June 10, 2020. The authors are with Mahidol University, Thailand (e-mail: chuechote@gmail.com). assessment [6]-[10]. Yin et al.‟s research offers the comparison between two models of a concept map construction; one model is a concept map construction assignment with only node terms restricted—students self-create linking phrases—and another is just a map assembling task where both node terms and linking phrases are provided [10]. From this work, it suggests that the first model is better for knowledge capturing, whereas the latter fits better for large scale scoring. Clearly seen in the map assembly task, the scoring could be bipolar; matching is either right or wrong. On the other hand, in the open-ended approach, the constructed concept maps can diversify and generate more complication in scoring. Since this study emphasizes on learning assessment, we therefore have embraced the first model of concept map construction with node terms about polynomials provided. To tackle with the complication of scoring, we have explored the graphical elements and features, such as, nodes, edges, diameters, cliques, travelling paths and structures, for potential use in map scoring scheme. With awareness of reasoning behind the map construction process, the collection of concept maps from students will be compared with the teacher‟s map to make a better vision of how the teacher has expected and what students have achieved. Analyzing graphical data, we have considered how these graphs are formed and how the elements are linked. The graphical result and its interpretation provide interesting angle in learning and teaching assessment. Remarkably, concept map similarity among students engaging in the same lesson can mirror prior knowledge of students and the effectiveness of the teaching approach. This research gives another purposeful use of the concept maps and suggests diagnostic scheme that could be beneficial to both learning and teaching assessment. II. CONCEPT MAP CONSTRUCTION Since knowledge construction process is the integral part for this study, we designed the experiment to include 3-hour training of concept map construction following the adapted scheme from Malone & Dekkers [11]. The protocol is described as follows. - First task: List the key terms and find all possible terms that can be associated with the key terms. - Second task: Rank the strength in association of the key terms and other node terms. Arrange the key terms on top and the closest or strongly associated node terms with the key terms are one level below. If node terms have the same relationship with the key terms, put them on the same level. - Third task: Add edges or linking phrases according to the Utilizing Graphical Elements for Concept Map Analysis to Design Teaching and Learning Assessment Suparat Chuechote and Parames Laosinchai International Journal of Information and Education Technology, Vol. 10, No. 8, August 2020 557 doi: 10.18178/ijiet.2020.10.8.1424