Students exhibiting mathematical promise or mathematically talented students understand mathematics differently than other students. Lester and Schroeder 1 listed twelve cognitive characteristics of mathematically talented students. One of the attributes was the ability to reverse the reasoning process (switch from a direct to a reverse train of thought) which talented students performed with relative ease. Thus, the students’ thinking was not only different, it resembles the way that professional mathematicians work with the only difference is in the degree of sophistication 2 .

In order to address the learning needs of mathematically talented students’, experts in gifted education suggested accelerative programs, enrichment programs and modified curriculum. Enrichment programs are recommended for moderately talented students as the programs give students motivation. 1 indicates that when pupils were motivated to carry out a complex and in-depth investigation, they often sought new and more advanced knowledge. 3 designed an inquiry-based enrichment program and discovered that using higher-level math concepts engaged students and kept them excited about learning. Besides that, 4 developed and field tested advanced curriculum for mathematically promising elementary students. They found that the curriculum which focused on disciplinary thinking 5 had positively affected the students’ achievement.

School holiday enrichment program organized by PERMATApintar National Gifted Centre was a program to uncover hidden talents in science and mathematics. Each course in the program was handled by course instructors and teaching assistants. One of the courses offered in this program was Introduction to Cryptology course. Students who attend this course were from different schools in Malaysia and had passed UKM 1 and UKM 2 identification tests. They have already mathematical knowledge learned at primary school level. In this Introduction to Cryptology course, students were introduced to the higher level of mathematical concepts behind cryptology which were integers and matrices. Thus, in this study we would like to determine whether or not students have mastered each concept in the integers and matrices.

This study was carried out to 34 12-year old students attending Introduction to Cryptology course in the school holiday enrichment program. During this 3-week program, students were taught some basic mathematical concepts and elements of cryptology based on a module. After learning all mathematical concepts, students were being given a set of questions to assess their achievement in mathematics.Table 1 displays the distribution of mathematical concepts covered in each questions.

Student scores in the examination were tabulated in Table 2 .

From the above table, most students scored 80 – 100 while only one student scored 45 – 49 in the examination. This shows that 73.6% students have mastered all mathematical concept learned in this course. Scores for each questions in the examination were displayed in Table 3 to determine scores for each mathematical concept using the following formula.

students mark in the related questionstotal marks for that questionsx 100%

From Table 3 , all students scored 50 – 100 on the concept of integers which shows that this concept dominates the matrices. For the concept of integers, 2 students have difficulty in solving the division problems while 2 students have difficulty in solving operation on integer modulo n problems. Meanwhile, for the concept of matrices, 11 students scored 0 – 34 in finding the inverse of a matrix, 2 students scored 0 – 34 in subtracting matrices, 1 student scored 0 – 34 in adding matrices modulo n and 3 students scored 0 – 34 in multiplying matrices.

From Table 3, all students scored 50 – 100 on the concept of integers which shows that this concept dominates the matrices. For the concept of integers, 2 students have difficulty in solving the division problems while 2 students have difficulty in solving operation on integer modulo n problems. Meanwhile, for the concept of matrices, 11 students scored 0 – 34 in finding the inverse of a matrix, 2 students scored 0 – 34 in subtracting matrices, 1 student scored 0 – 34 in adding matrices modulo n and 3 students scored 0 – 34 in multiplying matrices.

From the results, it is observed that students have mastered the concept of integers but were deficient in the concept of matrices. Integers were the extension of natural numbers hence the concept can be easily understood by the students. Matrices were new to students, thus interesting activities relating to matrices should be included in the module to intensify students’ motivation in mathematics.