Assessing Students’ Mathematical Knowledge with Fuzzy Logic

Abstract

Assessing student mathematical knowledge is an important factor in the mathematics learning process because students obtain important feedback to improve their knowledge and learning. Despite the importance of student assessment, several researchers have shown that student grades comprise noncognitive and metacognitive factors and teachers’ prejudices and beliefs. One method to obtain a more objective view of student mathematical knowledge is through standardized assessments. In this paper, we analyze two methods of assessing student mathematical knowledge by considering their written and oral grades and achievements on the Italian National Assessment of Knowledge (INVALSI). The final grade was produced using the fuzzy logic inference system. It was tested on a sample of 2279 Grade 13 Italian high school students, who had both an oral and written grade in mathematics and who took the INVALSI assessment in the school year 2020–2021. Both tested fuzzy-logic-based assessment methods lowered the mean grades.

Enhancing Learners’ Performance in Grade 7 Mathematics Through 50-30-20 Exercise

“…It is a decision-making process using information obtained through measuring learning outcomes [17,18] . Assessing students' mathematical knowledge is vital because students obtain essential feedback to improve their knowledge and learning [19] . In addition, assessment strategies are approaches used by teachers to evaluate learners' progress and create course content.…”

Fuzzy Application (Mamdani Method) in Decision-Making on Led Tv Selection

“…These rules are expressions of the type: IF <condition> THEN <consequence> (7) The condition part, the antecedent of the expression, represents the state of the input variables, and the consequence part describes the state of the output variable. Fuzzy inference rules are built with the help of the binary logic operators AND, OR, and NOT because the antecedent of the expression can be a combination of many circumstances related to input variables that represent realistic situations.…”

“…This logic is the result of the development of Boolean Logic and has become the basis for various computer applications. Iranian mathematician Lofti A. Zadeh created Fuzzy Logic, a branch of mathematical logic, in 1965 [7]. He realized that classical Logic or Boolean Logic could not be applied effectively in various complex conditions and problems.…”

Beyond Traditional Assessment: A Fuzzy Logic-Infused Hybrid Approach to Equitable Proficiency Evaluation via Online Practice Tests

“…We considered five functions that stand for the fuzzy membership ones to the sets of marks. We would like to mention that in very recent years there has been a large increase in the usage of fuzzy logic in the evaluation of students' performance [16][17][18][19][20][21][22][23][24][25][26].…”

“…By comparing the results of second exam in terms of overall points (78, 76, 80, 63, 67, 61, 68, 75, 13, 72, 74, 76, 72, 79, 70, 58, 57, 66, 66, 59, 74, 67, 36, 35, 75, 38, 36, 52, 47, 55, 25,47,73,35,31,70) and points on the open questions (15,14,15,7,6,8,9,13,0,13,13,14,11,15,15,3,9,11,8,9,13,12, 0, 3, 14, 0, 0, 6, 7, 8, 0, 3, 13, 0, 0, 7) to those first exam in terms of overall points (57,74,58,58,22,65,19,70,21,63,42,42,62,42,63,23,47,62,66,74,59,56,69,59,67,55,48,41,…”