Similarly, the relationship patterns of OTL and PSTs’ MCK differed between the institutions in the three countries. In the United States, the more the programs provided OTL to show why a procedure works, the higher the average PSTs’ MCK. Additionally, the patterns of the relationships in the Russian programs were positive, whereas, in the Polish programs, the relationships among these variables were negative.
The relationships between the OTL how to make distinctions between procedural and conceptual knowledge differed in the generalist programs in the three countries. Specifically, the higher the frequency of this OTL, the higher the average...
... middle of paper ...
...relationships were positive for the Polish generalist programs, but negative for the Polish specialist programs. However, in the United States, the relationships between the OTL how to make distinctions between procedural and conceptual knowledge was positive, but not significant.
Finally, the relationships between the OTL how to explore multiple solution strategies and average PSTs’ MPCK between the programs also differed across the three countries. The relationships between this OTL and the average PSTs’ MCK across the programs in the United States and Russia were positive (ns) whereas, the relationships between this OTL and the average PSTs’ MPCK were negative for the Polish programs. A summary of the relationships between the OTL mathematics instruction for conceptual understanding and PSTs MPCK within and between the institutions are presented in Tables 5 and 6.
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