A Case Study of Students' Mastery Level and Level of Understanding of the Domain and Range of a Function

Date of Award


Document Type


Degree Name

Master of Science in Mathematics Education (Thesis Option)



First Advisor

Angela Fatima H. Guzon, PhD


This case study involved an in-depth investigation of six Grade 12 students’ procedural and conceptual understanding of the domain and range of functions expressed in three different representations: as a set of ordered pairs (tabular form), in graphical form, and in algebraic form. Data were collected through questionnaires and interviews. Students' answers in the questionnaires were analyzed using a scoring rubric and their mastery levels and levels of understanding were categorized using a mastery level scale and the SOLO taxonomy rubric. Results of the study show that students have varied mastery levels and levels of understanding in finding the domain and the range of a function. Among the three representations, students exhibited higher mastery levels and levels of understanding in the graphical representation of a function. The visual representation of the function aided the students in identifying the values of the two variables to be included in the domain and the range. Students displayed poor understanding and mastery in algebraic forms as they tend to use memorized formulas or procedures to solve for the domain or the range. Students who belonged to the higher spectrum of the mastery level scale displayed competency in finding the domain and range in any of the three representations while those in the lower spectrum expressed very few ideas of the topic. Regarding their levels of understanding, students with higher levels of understanding were able to get the correct responses and could explain the meaning behind the process in finding the domain and range while students with lower levels of understanding failed to give the correct responses and explanations. v Students with higher levels of understanding tend to master the concept as well while students under the lower levels of understanding tend to have a poor acquisition of the concepts. It is recommended that the study be replicated to consider a larger sample size in order to make a more generalized result. It is also recommended that teachers and subject coordinators use different teaching strategies and tasks that involve connections among the three representations. Furthermore, textbook writers are encouraged to create materials that involve different activities and exercises that will help students understand and connect the three function representations, as well as allow students to achieve the higher levels of understanding provided by the SOLO taxonomy.

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