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Article Excerpt
Spreadsheets can be a valuable tool for helping students construct a deeper understanding of statistical concepts. This investigation incorporated active-learning into the structure of an intermediate-level statistics course for doctoral students in education. Active-learning was implemented primarily by having students create learning playgrounds, which would instruct a novice about specific statistical concepts. This format led these doctoral-level education participants to become more fully involved in the process of mathematical storytelling with the beneficial consequence of a richer understanding of key analysis of variance concepts and techniques.
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One of the biggest problems in statistics education is that students tend to suffer from inert knowledge. Whitehead (1929) first used this term to describe knowledge, which can usually be recalled by students when explicitly asked to do so, but it is not used spontaneously in problem solving even though the knowledge is relevant. A new graduate student in the social sciences may take only two classes in statistical analysis and research design. A year or so later the student will then be expected to make use of that knowledge, either as a research assistant on a project or in their own research study. All too often students respond to these applied situations as if they had never taken a statistics or research design course. Although they likely remember key statistical concepts, the process of taking data and transforming it into meaningful information is frustrating and frightening to many. Of course this description is a general "best case" scenario. Using statistics goes beyond simply remembering knowledg e. Some of the ideas in statistics, and especially their connection to research design, are often never well understood by students.
In addressing the general problem of inert knowledge, Dewey made the case for an active-learning approach in which students are learning new material for some practical project or need in the present. As Dewey put it:
When preparation is made the controlling end, then the potentialities of the present are sacrificed to a suppositious future. When this happens, the actual preparation for the future is missed or distorted. The ideal of using the present simply to get ready for the future contradicts itself. It omits, and even shuts out, the very conditions by which a person can be prepared for his future. We always live at the time we live and not at some other time, and only by extracting at each present time the full meaning of each present experience are we prepared for doing the same thing in the future. This is the only preparation which in the long run amounts to anything. (1963, p. 49)
Benware and Deci (1984) hypothesized that active-learning where the student is "...learning material to teach it will lead to enhanced learning and to a more positive emotional tone than learning material to be tested on it, even when the amount of exposure to the material being learned is the same" (p. 756). Benware and Deci built their study upon the theoretical approaches of Bruner (1966) and Rogers (1969) who both suggested that students learn better if the content of the instruction is useful for a task they are undertaking. The "activity" would in turn result in a fuller engagement of the material. The logic behind this line of thinking is fairly simple: students approach the material with the anticipation of using it, so they become more fully involved.
This article presents an investigation into an active-learning approach to statistics through the use of spreadsheet software. The focus of the intermediate-level statistics course used in this study was on learning analysis of variance (ANOVA) techniques. In the past this course had been taught through a combination of lecture, computer-based activities with SPSS, and structured activities with Excel. The instructor (author) hypothesized that increasing the level of active-learning in the course through problem-based challenges would result in greater learning and higher student motivation. Indeed, previous research has indicated that active-learning approaches can be quite effective (Benware & Deci, 1984; Brophy & Alleman, 1991; Kafai, 1995; Mitchell, 1993; Mitchell, 1997).
Excel is a powerful spreadsheet software program that allows individuals to do more than simply crunch numbers. Through Excel's open-endedness, the ability to incorporate conceptual formulas, the use of intuitive naming of cells and arrays, dual coding features, and Excel's design tools, students can potentially create rich educational products. This full-featured software program appeared to offer a great way to pragmatically implement an active-learning curriculum. Specifically, students actively learned statistical concepts by creating learning playgrounds that would instruct a novice about particular statistical techniques. This kind of learning challenge was hypothesized to result in greater learning for the "constructors," or students, in the course.
In the present investigation, active-learning was used primarily for out-of-classroom activities that students completed. The classroom experience itself used instructor-led multimedia presentations, discussions, and computer-based examples. Indeed, the in-class experience could be described as being teacher-led because there was relatively little opportunity for true active-learning to take place. Instead it was the way students spent engaging with the course material outside of the classroom that incorporated the active-learning challenges.
Two studies previous to Benware and Deci tested the active-learning hypothesis and found positive indications that active-learning is effective (Bargh & Schul, 1980; Zajonc, 1960). However both of those studies used very short treatment periods. Benware and Deci's study represented the first systematic attempt to test the "learning-to-teach" hypothesis using a reasonable treatment period of three hours. Their results confirmed that students under the experimental "active" condition learned both rote and conceptual material significantly better than the control group. Just as importantly, the Benware and Deci study incorporated motivational variables and found that students in the experimental condition found the process of learning more interesting and enjoyable than those in the control group.
More recently, Mitchell (1997) described a classroom learning environment in which students learned about a computer-based approach to learning statistics through Microsoft Excel. The students in that study created educational worksheets. Mitchell highlighted five factors that helped explain the advantages of spreadsheet software in creating an active-learning based environment including creating multiple representations of statistical measures, making "number playgrounds," incorporating story lines, and the opportunity for student creativity. The result of making such products resulted in a type of active-learning in which students' thinking about basic statistical concepts grew much richer through the development of these products.
The present study sought to build upon the Benware and Deci (1984) and Mitchell (1997) studies with three important enhancements. First, like Mitchell, the study covers a time period of one semester as opposed to the three hour treatment used by Benware and Deci. Second, like Mitchell, the study used statistics as the content area, a subject that many students find difficult to understand and motivationally unappealing. However, unlike Mitchell, this study takes place in the context of a regular course focusing on statistical concepts rather than using a course that is primarily computerbased in its content. Thus this study hoped to address the more realistic concern of integrating technology into regular content courses. Finally the focus of this study is on a content analysis of students' products: did these products demonstrate significant understanding of the course concepts?
The challenge faced by intermediate-level students in this study was to create learning playgrounds that would instruct novice doctoral students about analysis of variance techniques. Students were told by the instructor that the best products resulting from the class would be used as learning aids in his beginning level statistics courses in the future. Since all the students were involved in education at the K-12 or higher education levels, there was the additional incentive for them to take advantage of their educational expertise to create a compelling set of learning playgrounds. This active-learning project took place within the context of using spreadsheet software as their instructional creation tool. The benefits of using spreadsheets, specifically Excel, to accomplish these goals was crucial.
THE POWER OF SPREADSHEETS
In this course spreadsheets were used as a pedagogical tool. For the purposes of statistical analysis only a software program such as SPSS or SAS would be much better choice. Excel is more akin to a numbers-based LOGO program. Just as Kafai (1995) and Papert (1980) had taken advantage of the relatively simple programming language called LOGO to teach elementary level kids about mathematics, so in this study Excel was used to help students learn about statistical concepts in a hands-on manner. Kafai's study was particularly relevant because she spent six months helping a fourth-grade class learn how to use LOGO. Those students had a special challenge: to create a learning environment that would teach younger students at their school about fractions. Kafai found significant results in both learning and motivation when students were faced with such a concrete and worthy...
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