Quantitative Research Method Assignment

The Effect of Calculator-Based Ranger Activities on

Students’ Graphing Ability

Pamela R. Hudson Bailey

George Mason University

The Effect of Calculator-Based Ranger Activities on Students’ Graphing Ability

Purpose

The study explored the impact of CBR activities on high-school students’ to model, interpret, and transform graphical information of real-life situations. Middle school students in Korea were investigated by Kwon (2002) revealing an increase in conceptual understanding of graphs. Participants in Kwon’s study were middle and high school students without previous graphing knowledge. The middle school students showed a better conceptual understanding of graphs after the study than the high school students who were taking upper level mathematics courses.

Research Questions

CBR activities encouraging students’ graphing abilities was the overall idea analyzed. Previous student knowledge of the Cartesian plane, graphing, and differentiation was considered when determining student growth. These considerations led to three research questions. Does the use of a CBR improve a students’ ability to model, interpret, or transform graphs illustrating real-life situations? Is a students’ ability to graph using CBR activities affected by prior knowledge of graphing on the Cartesian plane? Is a students’ ability to graph affected by the teacher instructional method (lecture vs. student-centered investigations)?

Method

Participants and setting.

The participants in this study were 295 students in 4 different high schools, all located in Spotsylvania County, Virginia. Students were taking two different levels of mathematics courses, 245 students taking Algebra I and 50 students taking Calculus. The classes were selected randomly at each of the schools. All levels of socioeconomic status were represented within the group of students who were considered to be of average scholastic ability. Two of the four schools did not make AYP in mathematics the previous school year. Emphasis, county wide, was on meeting the needs of all students therefore alternative instructional methods were being considered. All high schools in the county are on an A/B block schedule with each class period being 90 minutes.

Some of the students in both courses had used the CBR and graphing calculators in a previous course. All of the students participating in this research took a pretest and posttest but only the Algebra I students used the CBR and graphing calculators in four investigations. Students had experience with graphing on the Cartesian plane in middle school mathematics courses as well as instruction on functions, evaluating, determining and plotting points, and relating tables to graphs. Past CBR usage was limited to gathering data to obtain a table of values that students used to practice plotting points on the Cartesian plane. The Algebra I students were separated in to two groups, those with experience, the CBG (CBR Before Graphing) group, and those without experience, the CAG (CBR After Graphing) group. The 50 Calculus students had studied graphing functions and their derivatives using an algebraic approach. Instruction was delivered by lecture to the Calculus students without the aid of technology or any type of motion graphing.

Instruments.

The same instruments employed by Kwon (2002) were also used in this study, the modified GIST, The Graphing Interpretation Skill Test, and the modified MCT, Motion Content Test. A pretest and posttest, also used by Kwon, assessed graphing ability of students. The GIST, the MCT, and the pretest and posttest were originally constructed by Michael (1995) as stated by Kwon. The posttest was an alternative version of the pretest with both assessments consisting of 27 items, including seven free-response and 20 multiple-choice questions. Scoring rubrics established by teachers in the Kwon study were also used to assess student knowledge in the current study. Four teachers, divided into groups of two, assessed the free-response questions. The tests were divided in half with each group grading their portion. In order to be objective, teachers graded the first problem of all tests prior to proceeding to the second question, repeating the process till all seven were assessed. If the teachers did not agree on the score, all four were consulted and an agreement was obtained with the approval of the researcher. The groups switched papers and repeated the process. The multiple-choice problems were worth 3 points, free-response problems received scores of 3, 2, 1, or 0, determined by the quality of student response.

Procedures.

The study was conducted in October 2007 and took half of six class periods for students to take a pretest, to undergo the investigative activities, and take the posttest. The CBR was used by the Algebra I students to collect and analyze real time data related to distance and velocity and their corresponding graphs. The investigations involved four in-class labs created to actively engage students in learning and understanding graphs conceptually as they related to real-life situations. Students were lead through the investigations using worksheets that guided their actions. The effect of speed on distance-time and velocity-time graphs using the CBR was the focus of all four investigations.

During the first day of the lab student focus was on position graphs and using the CBR correctly. Comparing and contrasting distance and velocity graphs was the focus of the activity for the second day. Balls were bounced and remote control cars moved at varying speeds while teams of students watched the graphs being drawn simultaneously on the graphing calculators. Connecting movement of the ball or remote control car to the graph was acknowledged. Teams exchanged graphing calculators and then attempted to replicate the newly received graph by manipulating the ball or remote control car to match. The third day was spent with students attempting to physically move their bodies to replicate graphs illustrating distance-time and velocity-time representations. Students, using the CBR, walked with varying speeds to produce a distance-time graph and the related velocity-time graph. Both were then projected on a screen for the entire class to view with the remaining students attempting to determine the movement of the walkers. The focus of the last day of investigations was on predicting and explaining graphs illustrating real-life situations. Given graphs of either distance-time or velocity-time, students were asked to replicate the movements. The posttest was given to all students following the last day of investigation.

Proposed Preliminary Data Analysis

The study concentrated on helping students learn interpretation of graphs, relate real-life situations to graphs, and to transform between distance-time graphs and velocity-time graphs. The modified GIST and MCT were analyzed to determine differences in student graphing ability. The results of the Algebra I students were then compared to the results of the Calculus students. Predictions would show that the mean posttest results would be significantly higher than the mean pretest results for the Algebra I students as well as higher than the mean results for the Calculus students. The proposed outcome of the investigations involving the CBR will reveal that the Algebra I students will have a better understanding of modeling data graphically, interpreting graphical results, and relating distance-time graphs to velocity-time graphs. Prior knowledge of graphing on the Cartesian plane did not influence or effect the outcome of the investigations. Lastly, students’ knowledge gained through active learning far exceeded learning by the traditional lecture approach.

References

Kwon, O.N. (2002). The effect of Calculator-Based Ranger activities on students’

graphing ability. School Science and Mathematics, 102(2), 57-67.

Michael, T. S. (1996, April). Effect of microcomputer based laboratory on graphing

interpretation skills and understanding of motion. Paper presented at the annual

meeting of the National Association of Research in Science Teaching, San Francisco, CA.