Diagnosing Acquisition of Cognitve Domain in Mathematics Curriculum: A Case of Malawi, Ghana, and Uganda

• In Event: Learning Foundations, STEM and Ethics

Proposal

Acquiring basic academic achievement is a significant issue in most low- and middle-income countries, particularly in sub-Saharan Africa. Approximately 87% of the children have not yet reached the minimum proficiency in sub-Saharan Africa, the highest percentage among regions. The ample study has focused on the quality of teachers, pedagogy, and developing teaching and learning materials, including curriculum and textbooks, to improve academic achievement. On the other hand, there is less attention to analyzing curriculum attainment by measuring student academic achievement.
By analyzing curriculum attainment, the application of Cognitive Diagnostic Models (CDMs) has been paid attention gradually. CDMs are psychometric models used in educational and psychological assessment. It improves academic achievement by diagnosing skills, strengths, and weaknesses in each area of the cognitive domain. Recently, it has been used to assess acquired skills in assessing academic achievement in high-income countries. In contrast, it has rarely been used in low- and middle-income countries.
To fill this gap, drawing data from Malawi, Ghana, and Uganga, this study aimed to assess the acquisition of cognitive domain in Mathematics curriculum attainment by applying cognitive diagnostic model.
To make mathematics tests, first, we developed the international curriculum, which is common contents in three coutries, by comparing the national curriculum. Then, 110 question items for mathematics tests were created based on the international curriculum and textbook in each country. Test forms were developed by selecting question items. Due to the different progress of the curriculum in the three countries, two test forms were developed: Test A for Malawi and Uganda and Test B for Ghana. The level of Test B was higher than Test A. To equate Test A and Test B, 18 common items were set up in tests. There were 40 question items in both tests. The implementation time was 90 minutes.
The sample was 900 grade 5 and 636 grade 6 students in 12 public primary schools in Lilongwe East and Nkhata Bay District, Malawi, 919 grade 5 and 981 grade 6 students in 23 public primary schools in the Lower Manya Krobo District, Eastern Region, Ghana, and 1049 grade 5 and 966 grade 6 students in 18 public primary schools in Mpigi District, Uganda. Data was collected in Malawi from October to November 2021, Ghana from January to February 2022, and Uganda from June to July 2022.
In analysis, first, we developed six attributes that classifying cognitive domain in mathematics: reading comprehension skills, natural numbers, rational numbers, four arithmetic operations (addition, subtraction, multiplication, and division), carrying and borrowing in arithmetic operations, and the concepts of graphs and units. Then, we created a Q matrix that explained whether the attributes required to get correct answer in each question item. Finally, we applied the generalized deterministic inputs noisy and gate model (GDINA) in cognitive diagnostic model in each grade and country to assess aqusition rates and its relationship of the attributes.
The results showed that the level of acquiring rational numbers tended to be lower than that of the other attributes in all countries. The levels of acquiring six attributes were different among the three countries. In Malawi, 58.0% and 95.2% of students in grades 5 and 6, respectively, acquired skills in natural numbers, while 11.0% and 43.0% of students in grades 5 and 6 acquired skills in rational numbers. In Uganda, 72.4% and 95.0% of students in grades 5 and 6, respectively, acquired skills in natural numbers, while 32.9% and 56.2% of students in grades 5 and 6 acquired skills in four arithmetic operations. In Ghana, 74.7% and 67.0% of students in grades 5 and 6, respectively, acquired skills in carrying and borrowing in arithmetic operations, while 8.9% and 25.7% of students in grades 5 and 6 acquired skills in rational numbers. In both grades, there was a strong relationship between rational numbers and the concepts of graphs and units in Malawi and Uganda. In Ghana, the tendency was different. There was a strong relationship between natural numbers and rational numbers in grade 5, while it was between natural numbers and the concepts of graphs and units in grade 6. The levels of acquiring six attributes were as follows: 1.0% in grade 5 and 20.7% in grade 6 in Malawi, 7.0% in grade 5 and 21.0% in grade 6 in Uganda, and 2.7% in grade 5 and 10.4% in grade 6 in Ghana. The results contribute to reconsider teaching methodlogy and guide learning points to improve basic mathematics skills in the three countries. Also, the methodology used in this study can apply to other countries.

Authors

• Kyoko Taniguchi, Hiroshima University

• Haruhiko Mitsunaga, Graduate School of Education and Human Development, Nagoya University

• Koji Watanabe, Miyazaki International University