Assessment is a crucial part of the teaching and learning process. If prepared well and administered to the student at the right time and conditions, forms of assessments can be an aid to learning. If analysed and the data derived from the analysis are processed by the teacher, assessment can be an aid to teaching. In any case, assessment is an important part of any teacher’s work who is concerned about real learning.
This paper shall describe an assessment that was prepared to a fifth grade male student and was actually administered. There will be a discussion of the assessment results, the analysis done with the results, and the process of using the analysis to aid teaching towards improvement of learning.
The Assessment
The assessment that was prepared and administered to the fifth grade student was for the unit on ratio and proportion. It was consisted of three word problems and five number problems with diagrams for visual problem solving. The word problems were simple representations of common scenarios, such as the ratio of two kinds of farm animals, the ratio of children in a school with lacking classroom chairs, and the ratio of kilos of rice and families to receive them. The other set of problems was a combination of three pure number equations and two number equations with squares to visualize the problem.
The Assessment Results and Analysis
The fifth grade male student showed perfect accuracy of solution and precise answers to the five number problems. Whether with the use of squares to aid the solving process or with just pure numbers, the boy was able to answer them all correctly. But when it came to the three word problems, all final answers were wrong.
As I analysed the shocking performance with the word problems, I noticed that the student’s final answer was correct based on his solution. However, the error came even before the solving process. I then realized that his interpretation of the word problem was where the error started. The fifth grade student mixed up the meaning of the words in the problem and therefore assigned numbers wrongly. I noticed that this erroneous interpretation of word meaning and data was consistent for all three items. His coming up with the right answers based on the solution he made up was also consistent for all three word-problem items.
That observation made me realize that this boy had proficient comprehension skills of math concepts, especially in the concepts of ratio and proportion that is currently being assessed. The problem lies in this student’s deficient comprehension of the English language. Though English comprehension is not the central concern of Math subject, as a teacher, I see the important relation between these areas of comprehension. Words and numbers are actually two forms of language in with differing forms. Therefore, what this fifth grade male student needs to improve on is his comprehension skills of words, specifically the English language.
The Post-Analysis Process and Intervention
As a concerned teacher, I decided to find out more about the student. As soon as I traced that the student has a foreign descent and continues to speak the foreign language with the family at home, I started planning out some strategies that may help him with his specific difficulty. The main objective for the instructional strategies I plan to use as intervention is to indirectly improve his word comprehension that will eventually lesson his erroneous analysis of word problems in Math.
The strategies of instruction that I plan to use to support this student’s specific need include adding diagrams or illustrations to the word problems to help him visualize the meaning of the problem, providing translations for him whenever possible, and contextualizing word problems to the culture he is familiar with.
As I tried to learn more about the student, it came to my attention that he is a new student in the school as a result of his family moving in from abroad. The differentiation therefore, that he needs is that which is appropriate for culturally diverse groups and for English as Second Language students.
Along with the strategies I plan to use to help the student, informal and formative assessments would also be a big help. One of these informal assessments that can help both the teacher and the student is through class participation, recitation and small-group discussions. This student can be put in a group where there is another who may have the same cultural background and with students who have a proficient level of language comprehension. These small group discussions can be used as a helpful tool in learning Math problems, especially in understanding the context of the problem. As Wood and Kalinec (2012) claim in their empirical study, that mathematical learning can be improved through small group interactions. Much can be learned when students relate with their peers, and for this student of our concern, relating with others is definitely needed to ease his adjustment into the new language and culture.
Aside from small group discussions, another strategy of differentiated instruction that can be used for him and can also be used as a formative assessment is utilizing pair-grouping in authentic tasks. A student who shares his thinking process with a partner can positively help both of them. This strategy is supported by Iiskala, Vauras, Lehtinen, and Salonen (2011) who proved that metacognition – or higher thinking – naturally occurs within collaborative mathematical word problems.
For individual informal and formative assessment, the strategy to be used is to maximize the exercises in the student workbook and provide additional work sheets if needed. According to the cross-cultural study of Serrano (2012), it is proven that the practice of routine in mathematical calculations and problem-solving items helps a lot in increasing student performance.
Another way to help the student is to craft Math word problems with the context of the culture he is more familiar with. It would be more practical and relevant for him and therefore tap his natural interests as well. Another study supports this claim. Dewolf, Dooren, and Verschaeffel (2011) believe that children’s understanding of quantitative problems has a socio-cultural dimension into it.
References
Dewolf, T., Dooren, W. V., & Verschaffel, L. (2011). Upper elementary school children’s understanding and solution of a quantitative problem inside and outside the mathematics class. Learning and Instruction, 21, 770-780.
Iiskala, T., Vauras, M., Lehtinen, E., & Salonen, P. (2011). Socially shared metacognition of dyads of pupils in collaborative mathematical problem-solving processes. Learning and Instruction, 21, 379-393.
Serrano, A. M. (2012). A cross-cultural investigation into how tasks influence seatwork activities in mathematics lesson. Teaching and Teacher Education, 28, 806-817.
Wood, M. B., & Kalinec, C. A. (2012). Student talk and opportunities for mathematical learning in small. International Journal of Educational Research, 51 - 52, 109-127.
