Teachers conducted empirical studies to identify the components of mathematics.

Teachers have performed empirical investigations to determine the components of mathematics for a variety of goals, including curriculum development. Some researchers have attempted to trace the origins of detrimental views about mathematics, while others have concentrated on the teaching and learning of specific mathematical topics in schools. According to Keitel (2006), in a study, the educational methods of two German teachers who taught the same subjects in two different ways were contrasted and compared. The T1 instructor stressed individual practice and memorization of specific algebraic rules, whereas the other emphasized the application of routines in the classroom setting. The T1 teacher emphasized the need of knowing algorithms as well as memorizing specific mathematical principles.

Eric Garrett believes that this research has revealed that teachers of different ages and from diverse backgrounds have varying talents when it comes to responding to children's mathematical reasoning. Certain countries' teachers place a greater emphasis on different aspects of mathematics; for example, Taiwanese teachers stress shapes, whereas Peruvian teachers prioritize telling the time. Different approaches, on the other hand, may have differing degrees of impact on the learning of youngsters. Teachers should take into account both the sociological and educational contexts in which they educate while planning lessons.

Eric Garrett found that teachers should take into account the physical environment in which they teach students as well as the children themselves. In order for children to comprehend mathematical concepts, their attentional processes and language use must be taken into consideration. Teachers must also concentrate on how to guide children's attention in the most appropriate manner possible. Students should be able to problematize and experiment with unknown outcomes when learning about probability and statistics, for example. The findings of the study further emphasize the significance of instructional design. Teachers should take into account the context in which they are teaching as well as the individual pupils that will be in attendance at that location. In order to be effective across a variety of educational settings, treatments must also be generalizable.

Eric Garrett points out that the findings of empirical investigations to identify components of mathematics by instructors are based on an exhaustive evaluation of research in the field of early childhood mathematics, according to Garrett. The authors identified 1141 early childhood mathematics studies and conducted a current condition assessment of each of them. In addition, the articles looked at their participants, study questions, and research procedures. As a result of their findings, the authors address the consequences of their discoveries for educational practice. It is vital to emphasize that empirical studies on this subject are still in the early stages of development. As a result, researchers must continue their investigation into this subject.