New semiotic approaches to elementary number theory have emerged in recent times in the forms of diagonal arithmetic (DA) and rectangular arithmetic (RA). These new forms of arithmetic which view numbers as entries in a matrix, were juxtaposed with the conventional arithmetic (CA) with a view to determining their effects on pupils’ arithmetical achievement when treated with ethno-cultural pedagogical instruments. The study was a post-test, quasi experiment involving two groups of pupils in a population of 300 pupils. Out of this population a sample of 120 pupils was used for the study and for statistical analysis using descriptive and inferential statistics. The study showed that there are significant differences among the three semiotic approaches to arithmetic, with diagonal and rectangular arithmetic gaining the upper hand. The study also showed that the use of ethno-cultural pedagogy amplified the arithmetical achievement of pupils exposed to diagonal and rectangular arithmetic. The study further revealed that it is safe to adopt diagonal and rectangular arithmetic as independent parallel curricula alongside conventional arithmetic.