*The onto-semiotic approach to research in mathematics education*

In this paper we synthesize the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. [1]

*A history of research in mathematics education.*

the history of research in mathematics education is part of the history of a field—mathematics education—that has developed over the last two centuries as mathematicians and educators have turned their attention to how and what mathematics is, or might be, taught and learned in school / from the outset, research in mathematics education has also been shaped by forces within the larger arena of educational research / like mathematics education itself, research in mathematics education has struggled to achieve its own identity / it has tried to formulate its own issues and its own ways of addressing them / look back at some of the people and events that have given form, direction, and substance to the field of research in mathematics education

roots in mathematics / roots in psychology [research on thinking, studies of teaching and learning] / emergence of a profession (PsycINFO Database Record (c) 2016 APA, all rights reserved) [2]

*Mathematics education as a ‘design science’*

Mathematics education (didactics of mathematics) cannot grow without close relationships to mathematics, psychology, pedagogy and other areas. However, there is the risk that by adopting standards, methods and research contexts from other well-established disciplines, the applied nature of mathematics education may be undermined. In order to preserve the specific status and the relative autonomy of mathematics education, the suggestion to conceive of mathematics education as a ‘design science’ is made. [3]

*A Mathematical Model of Rabies Transmission Dynamics in Dogs Incorporating Public Health Education as a Control Strategy -A Case Study of Makueni County*

Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virus [4]

*Mathematical Model of Cholera Transmission with Education Campaign and Treatment Through Quarantine*

Cholera, a water-borne disease characterized by intense watery diarrhea, affects people in the regions with poor hygiene and untreated drinking water. This disease remains a menace to public health globally and it indicates inequity and lack of community development. In this research, SIQR-B mathematical model based on a system of ordinary differential equations is formulated to study the dynamics of cholera transmission with health education campaign and treatment [5]

Reference

[1] Godino, J.D., Batanero, C. and Font, V., 2007. The onto-semiotic approach to research in mathematics education. *Zdm*, *39*(1-2), pp.127-135.

[2] Kilpatrick, J., 1992. A history of research in mathematics education.

[3] Wittmann, E.C., 1995. Mathematics education as a ‘design science’. *Educational studies in Mathematics*, *29*(4), pp.355-374.

[4] S. Musaili, J. and Chepkwony, I. (2020) “A Mathematical Model of Rabies Transmission Dynamics in Dogs Incorporating Public Health Education as a Control Strategy -A Case Study of Makueni County”, *Journal of Advances in Mathematics and Computer Science*, 35(1), pp. 1-11. doi: 10.9734/jamcs/2020/v35i130235.

[5] Nyaberi, H. O. and Malonza, D. M. (2019) “Mathematical Model of Cholera Transmission with Education Campaign and Treatment Through Quarantine”, *Journal of Advances in Mathematics and Computer Science*, 32(3), pp. 1-12. doi: 10.9734/jamcs/2019/v32i330145.