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Statistical graphs: understanding and attitude of Singapore secondary school students and the impact of a spreadsheet exploration
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Type
Thesis
Author
Wu, Yingkang
Supervisor
Wong, Khoon Yoong
Abstract
This study sought to investigate Singapore secondary school students’ understanding of and attitude toward statistical graphs, and the impact of an EXCEL exploration on these two outcomes. The six main research questions guiding the study were: (1) What is students’ Understanding of Statistical Graphs (USG)? (2) What is students’ Attitude toward Statistical Graphs (ASG)? (3) What is the relationship between USG and ASG? (4) How does the use of EXCEL affect students’ USG? (5) How does the use of EXCEL affect students’ ASG? (6) What is students’ attitude toward using EXCEL to learn statistical graphs? In order to answer these questions, two studies, Study I (an investigation of students’ USG and ASG) and Study II (an EXCEL exploration), were conducted.
A framework of Understanding of Statistical Graphs (USG) was built based on the relevant literature on graphical understanding. USG was operationally defined from four aspects: graph reading (GR), graph interpretation (GI), graph construction (GC), and graph evaluation (GE). Attitude toward Statistical Graphs (ASG) was defined from five aspects: enjoyment, confidence, usefulness, critical views, and learning preferences. A Test on Understanding of Statistical Graphs (TUSG) and a Questionnaire of Attitude toward Statistical Graphs (QASG) were constructed for this study.
A total of 907 secondary school students from four streams (Special, Express, Normal Academic, and Normal Technical) and three grade levels (Secondary 1 to Secondary 3) in five Singapore schools participated in Study I from February to July in 2003. They completed the TUSG and QASG. Fifty-six students were interviewed on their responses to TUSG based on a pre-constructed interview schedule.
These students performed best in GC, followed by GR, GE, and GI in a descending order. Their performance in TUSG and the four aspects of USG varied considerably with grade level and stream. There were statistically significant and strong relationships among GR, GI, GC, and GE. Seven error categories emerged from the students’ responses to TUSG. They were: comprehension errors E1, graph convention errors E2, association errors E3, use of information errors E4, mathematics errors E5, communication errors E6, and miscellaneous errors E7.
These students expressed a neutral to positive view toward enjoyment, confidence, and usefulness, and a moderate level of critical views about statistical graphs. For learning preferences, these students expressed a favorable view toward teacher clear explanations, doing a lot of practices, and group work, a neutral view toward teacher using computer, teacher using everyday example, and student collecting own data, and a dislike toward writing a short report for a given statistical graph. Grade level and stream had interaction effects on students’ attitude toward enjoyment, confidence, and usefulness but not critical views. Confidence and usefulness had statistically significant and positive relationships with the four aspects of USG, i.e., GR, GI, GC, and GE.
Four EXCEL templates were designed for Study II. Each template dealt with one common error in graphs. These four templates were zero in scale, effect of scale, size pictogram, and cumulative line graph. A case study research design was adopted in Study II. Twenty students, selected from the subjects of Study I, participated in Study II from March to August in 2003. They worked in pairs with two to four of the four EXCEL templates.
The results show that the four templates provided a platform for the students to develop their understanding of the topics involved through their exploratory activities. The detailed descriptions of the students’ interaction processes with the templates illustrate how the use of the templates had changed their understanding about the topics involved. Two approaches, a relational approach and an isolated approach, were identified to describe how the pairs worked with the templates. A relational approach appeared to be associated with better achievement in the templates, whereas an isolated approach seemed to be related to poor achievement in the templates. The result of pre and post tests on students’ USG shows statistically significant increases in these students’ overall scores, GR scores, and GI scores before and after the EXCEL exploration. There were no statistically significant differences in the students’ attitude toward ASG with respect to enjoyment, confidence, usefulness, critical views, and learning preferences. The students generally expressed a positive view toward using EXCEL to learn statistical graphs.
This study was embedded in Singapore educational context where research on students’ understanding of and attitude toward statistical graphs is lacking. This study can inform practices of teaching, teacher training, and curriculum development to be reflective of the realities of students, and provide some interesting questions for further research in the area of statistical graphs.
A framework of Understanding of Statistical Graphs (USG) was built based on the relevant literature on graphical understanding. USG was operationally defined from four aspects: graph reading (GR), graph interpretation (GI), graph construction (GC), and graph evaluation (GE). Attitude toward Statistical Graphs (ASG) was defined from five aspects: enjoyment, confidence, usefulness, critical views, and learning preferences. A Test on Understanding of Statistical Graphs (TUSG) and a Questionnaire of Attitude toward Statistical Graphs (QASG) were constructed for this study.
A total of 907 secondary school students from four streams (Special, Express, Normal Academic, and Normal Technical) and three grade levels (Secondary 1 to Secondary 3) in five Singapore schools participated in Study I from February to July in 2003. They completed the TUSG and QASG. Fifty-six students were interviewed on their responses to TUSG based on a pre-constructed interview schedule.
These students performed best in GC, followed by GR, GE, and GI in a descending order. Their performance in TUSG and the four aspects of USG varied considerably with grade level and stream. There were statistically significant and strong relationships among GR, GI, GC, and GE. Seven error categories emerged from the students’ responses to TUSG. They were: comprehension errors E1, graph convention errors E2, association errors E3, use of information errors E4, mathematics errors E5, communication errors E6, and miscellaneous errors E7.
These students expressed a neutral to positive view toward enjoyment, confidence, and usefulness, and a moderate level of critical views about statistical graphs. For learning preferences, these students expressed a favorable view toward teacher clear explanations, doing a lot of practices, and group work, a neutral view toward teacher using computer, teacher using everyday example, and student collecting own data, and a dislike toward writing a short report for a given statistical graph. Grade level and stream had interaction effects on students’ attitude toward enjoyment, confidence, and usefulness but not critical views. Confidence and usefulness had statistically significant and positive relationships with the four aspects of USG, i.e., GR, GI, GC, and GE.
Four EXCEL templates were designed for Study II. Each template dealt with one common error in graphs. These four templates were zero in scale, effect of scale, size pictogram, and cumulative line graph. A case study research design was adopted in Study II. Twenty students, selected from the subjects of Study I, participated in Study II from March to August in 2003. They worked in pairs with two to four of the four EXCEL templates.
The results show that the four templates provided a platform for the students to develop their understanding of the topics involved through their exploratory activities. The detailed descriptions of the students’ interaction processes with the templates illustrate how the use of the templates had changed their understanding about the topics involved. Two approaches, a relational approach and an isolated approach, were identified to describe how the pairs worked with the templates. A relational approach appeared to be associated with better achievement in the templates, whereas an isolated approach seemed to be related to poor achievement in the templates. The result of pre and post tests on students’ USG shows statistically significant increases in these students’ overall scores, GR scores, and GI scores before and after the EXCEL exploration. There were no statistically significant differences in the students’ attitude toward ASG with respect to enjoyment, confidence, usefulness, critical views, and learning preferences. The students generally expressed a positive view toward using EXCEL to learn statistical graphs.
This study was embedded in Singapore educational context where research on students’ understanding of and attitude toward statistical graphs is lacking. This study can inform practices of teaching, teacher training, and curriculum development to be reflective of the realities of students, and provide some interesting questions for further research in the area of statistical graphs.
Date Issued
2005
Call Number
QA276.3 Wu
Date Submitted
2005