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Addressing secondary three studentsโ difficulties with compound inequalities
Author
Wong, Shuk Wai
Supervisor
Ng, Swee Fong
Abstract
Singapore secondary students are familiar with two part linear inequalities such as ฮฑx + ๐ > ๐x + ๐, three part inequalities ฮฑx + ๐ < ๐x + ๐ < ๐x + ๐, and quadratic inequalities ฮฑx2 + ๐x + ๐ > 0. However compound linear inequalities with connective words such as and and or do not receive much attention. Such inequalities include ฮฑx + ๐ + ๐ and ๐x + ๐ < ๐ or ฮฑx + ๐ + ๐ or ๐x + ๐ < ๐. Depending on the conditions, some compound linear inequalities with the connective word and may not have any solutions and those with the connective word or may have solutions which are union of the two sets or the entire number line.
The objectives of this study are twofold. The first is to identify whether students were aware of these differences and if they were not, could they be helped to construct new understanding of compound inequalities. The study comprising two phases was conducted to identify the difficulties students have with compound linear inequalities. In Phase One, 57 Secondary Three Express provided written responses to a 14-item Written Task. In Phase Two, 20 of the 57 students were interviewed. The objective of Phase Two was to determine whether these students were able to construct a better knowledge of compound linear inequalities.
The study found that although students were able to solve compound linear inequalities involving connective word and, there was floor effect with compound linear inequalities involving the connective word or. However through appropriate prompts students constructed a better understanding of compound inequalities involving the connective words and and or. The study showed that the affordance of number line aided students in their construction of knowledge. The study argued that teachers and textbook writers should address studentsโ difficulties with compound linear inequalities.
The objectives of this study are twofold. The first is to identify whether students were aware of these differences and if they were not, could they be helped to construct new understanding of compound inequalities. The study comprising two phases was conducted to identify the difficulties students have with compound linear inequalities. In Phase One, 57 Secondary Three Express provided written responses to a 14-item Written Task. In Phase Two, 20 of the 57 students were interviewed. The objective of Phase Two was to determine whether these students were able to construct a better knowledge of compound linear inequalities.
The study found that although students were able to solve compound linear inequalities involving connective word and, there was floor effect with compound linear inequalities involving the connective word or. However through appropriate prompts students constructed a better understanding of compound inequalities involving the connective words and and or. The study showed that the affordance of number line aided students in their construction of knowledge. The study argued that teachers and textbook writers should address studentsโ difficulties with compound linear inequalities.
Date Issued
2017
Call Number
QA295 Won
Date Submitted
2017