Abstract
This chapter looks into the MCK performance of future teachers by in-depth analyses which go beyond the overall MCK scores provided by the international TEDS-M study. The purpose is to identify factors that may describe the differences and similarities of performance between countries. Many new findings are revealed through a multifaceted analysis of cognitive subdomains and individual items on both the country and the cultural level. Our analysis identified six performance patterns based on the relative achievement in knowing, applying, and reasoning as cognitive subdomains. The performance distribution has a tendency to cluster culturally similar countries in the same group, but exceptions do appear.
We constructed a variable that models the difficulty of the cognitive subdomains. Based on this model, we identified the impact of cognitive elements on countries’ performance. For example, we found that the two developed European countries, Norway and Switzerland, and almost all Eastern countries are strong on the reasoning element of items, which indicates a focus of their mathematics teacher education on reasoning.
The in-depth item analysis reveals new findings as well. Russia and the Philippines tend to employ uniform methods to solve problems, while the United States, Germany, Norway, Poland, and Taiwan tend to employ multiple methods. A tendency that the Western culture embodies an open and creative nature in their mathematics education is inferred. This study also finds a different philosophy in mathematics education relating to the rigor and formalism of acceptable mathematics solutions between the Eastern and the Western countries.
This chapter includes certain content from two articles: (1) Hsieh, F.-J., Lin, P.-J., & Wang, T.-Y. (2012). Mathematics related teaching competence of Taiwanese primary future teachers: Evidence from the TEDS-M. ZDM—The International Journal on Mathematics Education, 44(3), 277–292. doi:10.1007/s11858-011-0377-7; (2) Hsieh F.-J., & Wang, T.-Y. (2012). 
[Mathematics competence of future secondary mathematics teachers]. In F.-J. Hsieh (Ed.), 
—Taiwan TEDS-M 2008 (pp. 93–118). Taipei: Department of Mathematics at National Taiwan Normal University.
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- 1.
In the primary study, the combined participation rates of Chile, Poland, Norway, and the United States were between 60 % and 75 %. Analyses for Norway were conducted by combining the two data sets available. In the lower-secondary level, the combined participation rates of Chile, Georgia, Poland, and the United States were between 60 % and 75 %. The combined participation rate of Norway was 58 %, which only slightly missed the threshold of 60 % and therefore was still included. Datasets of four Norwegian program types were available, which were combined for analysis in an attempt to accurately represent the situation in Norway. Poland limited its participation to institutions with concurrent programs. Switzerland limited its participation to German-speaking regions. The United States limited its participation to public universities.
- 2.
For example, a response with a code 20 or 21 was scored as 2 points, whereas a code 10 or 11 was scored as 1 point.
- 3.
The higher-achieving countries include Taiwan, Russia, Singapore, Poland, Switzerland, Germany, and the USA at the secondary level; and Taiwan, Singapore, Norway, Switzerland, Russia, Thailand, the USA, and Germany at the primary level.
- 4.
Norway, though not strictly adhering to this pattern, was close to it by a non-significant deviation between the percent corrects of knowing and applying.
- 5.
Though the Philippines did not show a significant difference between knowing and reasoning at the 0.05 level, the p=0.07 was close to 0.05 and was regarded as acceptable for the purpose of testing our approach.
- 6.
Suppose a country’s percent corrects for items across the four curricular levels are: IAp, IAl, IAu, and IAt for primary, lower-secondary, upper-secondary, and tertiary; and the percentages of items for a cognitive subdomain, say knowing, for the four curricular levels are P % (dividing number of items in primary level by number of total items), L %, U %, and T %. The CPCE for the knowing subdomain for this country is obtained as IAp×P %+IAl×L %+IAu×U %+IAt×T %, which represents the content difficulty degree of the knowing subdomain for this particular country.
- 7.
There were no tertiary-level MCK items in the primary-level study.
- 8.
This result is consistent with the chi-square test result expressed in Hsieh et al. (2012).
- 9.
For A1, more than 90 % of the future teachers from the mentioned countries employed the method receiving code 11; for A2, more than 80 % of the mentioned countries receiving code 11.
- 10.
For both A1 and A2, countries in this group had less than 70 % same-method responses. For A2, all Western countries in this group had less than 55 % same-method responses.
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Acknowledgements
We gratefully acknowledge the following: the IEA, the International Study Center at Michigan State University, the Data Processing Center, the ACER, the U.S. NSF, the Taiwan TEDS-M team, and all TEDS-M national research coordinators for sponsoring the international study and providing information and data. Taiwan TEDS-M 2008 was supported by the National Science Council and Ministry of Education.
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Hsieh, FJ., Chu, CT., Hsieh, CJ., Lin, PJ. (2014). In-depth Analyses of Different Countries’ Responses to MCK Items: A View on the Differences Within and Between East and West. In: Blömeke, S., Hsieh, FJ., Kaiser, G., Schmidt, W. (eds) International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6437-8_6
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