Open Conference Systems, MISEIC 2018

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Students’ Number Sense of the 7th Grade based on Reflective and Impulsive Cognitive Styles
zainal zainal, masriyah masriyah, pradnyo wijayanti

Last modified: 2018-07-07

Abstract


Understanding of numbers refers to number sense. Number sense is basic for learning numbers. The ability to interpret numbers is also seen  as a characteristic of those with number sense: "Individuals are comfortable and confident with numbers, know how they are used, know how to interpret them and know when they make sense by Kaminski, (2002). Number sense is basic for learning numbers and an ability that if it practiced and develop correctly will useful for the students especially about number.

The aims of this study is to describe 7th students’ number sense, who have reflective and impulsive cognitive styles in fraction. The subjects were  students of the 7th grade of the SMPN 3 Bangkalan. All students’ were given Matching Familiar Figure Test and mathematical ability test. The subjects were two students were choosen based on reflective and impulsive cognitive styles and high mathematical ability and had to answer number sense test and they interviewed  based on their work. Test number sense and interviews based on the number of sense strands

Table 1. Number Sense Strands

Number sense strands

Indicator

Numbe Concept

1.1  able to determine decimal place value

1.2  able to compare  values of two ordinary or decimal fractions

1.3  able to order ordinary or decimal fractions

1.4   able to calculate values ​​of two ordinary or decimal fractions

1.5  able to show ordinary or other decimal fractions between two  ordinary or decimal fractions.

Multi representation

2.1. able to show ordinary or decimal fractions to other equivalent forms

2.2. able to state fractions to a shaded area.

Effect of operations

3.2  able to determine the results of operations on ordinary and decimal fractions.

3.3  able to conclude the result numbers obtained from operations on ordinary and decimal fractions.

Equivalent expressions

4.1  able to understand two equivalent expressions.

4.2  able to determine two mathematical expressions equivalent to the given mathematical expression.

Computing

and counting stretegies

able  to use strategies (estimation, counting on paper, mental counting) is effective in math problems.

The research results showed that: The number sense of reflective student was described as follow: (1) concept of number is shown by able to determine decimal place value, compared  values of two ordinary or decimal fractions, ordered ordinary or decimal fractions,and calculated values ​​of two ordinary or decimal fractions; but unable to show ordinary or other decimal fractions between two ordinary or decimal fractions; (2) Multiple Representation; able to show ordinary or decimal fractions to other equivalent forms; stated fractions to a shaded area; (3) Effect of operations ; able to determine the results of operations on ordinary and decimal fractions, concluded the result numbers obtained from operations on ordinary and decimal fractions; (4) equivalent expressions; able to understand two equivalent expressions, but was unable to determine two mathematical expressions equivalent to the given mathematical expression; (5) computing and counting strategies; unable  to use strategies (estimation, counting on paper, mental counting) is effective in math problems.

The number sense of impulsive student was described as follow: (1) concept of number is shown by able to compare  values of two ordinary or decimal fractions, ordered ordinary or decimal fractions,and calculated values ​​of two ordinary or decimal fractions; but unable to show ordinary or other decimal fractions between two ordinary or decimal fractions; but unable to determine decimal place value and unable to to showed ordinary or other decimal fractions between two ordinary or decimal fractions; (2) Multiple Representation; able to show ordinary or decimal fractions to other equivalent forms; stated fractions to a shaded area; (3) Effect of operations ; able to determine the results of operations on ordinary and decimal fractions, but unable to concluded the result numbers obtained from operations on ordinary and decimal fractions; (4) equivalent expressions; able to understand two equivalent expressions, but was unable to determine two mathematical expressions equivalent to the given mathematical expression; (5) computing and counting strategies; unable  to use strategies (estimation, counting on paper, mental counting) is effective in math problems.

The conclusion obtained show that there are various performance. It was found that, in general, reflective and impulsive students appear to have difficulties with all strands of number sense except those associated with the use of multi representation and operating effects. The fact that other strands requires a deeper understanding, but reflective student are better than impulsive student who are shown with the results of this study.


Keywords


number sense, cognitive styles, reflective and impulsive