| The purpose of this study was to prepare and evaluate instructional units in mathematics to teach the concepts of equivalency and addition to first graders. The units were designed to introduce informal mathematical knowledge into the classroom as well as to establish connections between informal and formal mathematical knowledge, as defined by the researcher.; Protocols conducted by other interviewers were synthesized to determine how children comprehend equivalency and addition. The definition of connection and GIS (general impressive scoring) were used to analyze mathematics textbooks, categorized as Series A, B, and C. Cohen's Kappa coefficients were measured to ensure objectivity of analysis.; As an answer to the first research question, it was found that children's informal understanding and use of equivalency and addition differed from the traditional meanings of those concepts in a mathematical sense. It was found that textbooks encourage children to misunderstand these concepts as well.; The analysis of the textbook series introduced informal mathematics. However, several limitations were found. First, the number of pages assigned to informal procedures is larger than that for informal concepts. Second, only a few informal mathematical concepts were found in the texts. Consequently, it is difficult to expect that formal concepts are connected with informal concepts. Distinct models were used to present informal mathematical knowledge, formal mathematical knowledge, and a combination of informal and formal mathematical knowledge for equivalency and addition. It was difficult to determine whether the models used to represent informal and formal mathematical knowledge were appropriate. In Series A and B, the consistency of the models in a chapter as well as across chapters was low, except for the model “Fictional Story.” The consistency of models in Series C was high, appearing in and across units.; The instructional units emphasized teaching informal and formal conceptual knowledge, introducing equivalency first instead of addition, connecting procedures and concepts between informal and formal knowledge, and using “Story Problems” as a frequent model. |
