Abstract Teaching,mathematical,reasoning,is a challenge,for most,result-oriented,teachers.,In general, many strategies can be employed, including problem-based learning, technology-based learning, game-based learning, community-based learning, work- based learning, inquiry-based learning, project-based learning, team-based learning, web-based learning and participatory learning. However, none of these strategies may,address,the central,problem,of mistakes,made,with,inappropriate,application,of intuition,in mathematical,problem,solving. This paper,emphasizes,an agile method,of teaching,rapid,reconciliation,of intuition,and,controlled,mathematical,reasoning,to engineering,students,in order to overcome,inappropriate,use,of the intuitive,mode,of cognitive function. This emphasis is based on an extensive review of existing research,and,an emerging,understanding,of interactions,between,intuition,and,the controlled,mode,of cognitive,function. Key Words Intuition, agile teaching, access, metacognitive strategies, algebraic thinking