In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

Background/purpose: In modern mathematical education, it is important to develop students' ability to understand the fundamental properties of geometric objects deeply. This makes it relevant to study the additivity of the area of triangles as a property inherent in various kinds of quantities and ways of representing it methodologically in the…

This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…

Traditionally, learning basic facts has focused on rote memorization of isolated facts, typically through the use of flash cards, repeated drilling, and timed testing. However, as many experienced teachers have seen, "drill alone does not develop mastery of single-digit combinations." In contrast, a fluency approach to learning basic addition…

Following the Migrant Student Record Transfer System skills list, this checklist, designed for non-English speaking students, is a system for rapidly evaluating a student's skill level and for keeping track of the student's mastery of suggested objectives at the fifth and sixth grade levels. Objectives to be mastered with 100% accuracy include:…

Following the Migrant Student Record Transfer System skills list, this checklist, designed for non-English speaking students, is a system for rapidly evaluating a student's skill level and for keeping track of the student's mastery of suggested objectives at the second grade level. Objectives to be mastered with 100% accuracy include: reading…

Following the Migrant Student Record Transfer System skills list, this checklist, designed for non-English speaking students, is a system for rapidly evaluating a student's skill level and for keeping track of the student's mastery of suggested objectives at the third grade level. Objectives to be mastered with 100% accuracy include: spelling…

Developed for non-English speaking grade 1 students, this skills check list was designed to evaluate rapidly and to monitor a student's mastery of suggested learning. Following the Migrant Student Record Transfer System skill's list, the check list is a suggested list of learning needs to be mastered, along with some helpful ideas for…