Published as: Roth, W.-M., & Bowen, M. (1993, February). The unfolding vee. Science Scope, 16(5), 28-32.
Last month we discussed the benefits of using concept maps to understand concepts and the relationships between them This month we will talk about the benefits of using Vee maps to drive those investigations. Like concept maps, Vee maps are less structured than conventional teaching methods. A Vee map guides students through investigations that they choose themselves. This less-structured investigative arrangement allows students to actively learn the principles of investigation.
In following the Vee map, through their investigations, students work to penetrate the structure and meaning of a branch of knowledge. The Vee map helps students to better organize their thinking, investigate more efficiently, and create guidelines for learning. Furthermore, using the Vee map makes students feel better about themselves because they are in control of their own learning and therefore know what they are doing. Figure 1 represents our version of the Vee map, a version adapted specifically to suit middle level students.
The left and right sides of the Vee emphasize two interdependent aspects of science learning: knowing and doing, respectively. What students know at any one moment--their existing conceptions, the investigative tools available to them, and their ideas--will determine the quality and quantity of the questions they ask. Conversely, the answers students obtain to their questions will affect what they know, by changing, adding to, refining, or reconfiguring their knowledge. The Vee should lead students to discover the relationship between doing and knowing science. The following six questions lead students through the discovery process, guiding them toward what they need to think about in order to complete their investigation. (Italicized phrases correspond to associated phase names.)
The six guiding questions encourage students to reflect in an orderly manner, providing them with a sort of road map toward new knowledge. Supporting questions to each of the six major headings encourage students to consider the questions more specifically in the process of acquiring information to complete their maps.
The focus question, which drives the investigation, is situated at the top of the Vee. The ability to ask the right kinds of questions and to find the answers to those questions distinguishes scientists from run-of-the-mill thinkers. The focus question "What do I want to find out?" therefore becomes central to an investigation. Before beginning their investigations, it's good for students to ask themselves "What do we know about the topic?" "What experimental techniques are relevant to the question?" and "How is what I already know inter-connected?" as well as to list associated words on the left, or knowing, side of the Vee. These questions inspire students to assess their knowledge before they design and plan their investigations.
The investigative activities take their place beneath the point of the Vee, an appropriate position antithetical to the focus questions, for the bottom of the Vee points to the question "How do I go about finding the answer to my question?" This question focuses on the details of the investigation. To allow student investigations to unfold as in real-life science, students should be allowed to follow contingencies as they develop during the investigation, with intermediary results leading to further focus questions. From this point, the investigation will lead us back up the right side of the Vee.
Under the heading of Data and Data Transformations, students report their observations and provide any maps, data tables, and graphs resulting from the question "What did I observe?" Students should ask themselves such questions as "Did I list all my data and observations?" "Can I represent any of the data in the form of graphs?" "Is there any better way of graphing my data?" and so forth to complete this work.
Next, students formulate claims from their data and graphs; for example, they should ask themselves "What can I make of my findings?" Resulting claims should not be restricted to simple factual statements. All knowledge, in some way, has implications for society at large. Students may even need to do research to find out what these implications are. For example, students should consider ways the information can be put to use in practical situations and the value of their newly obtained knowledge. Afterward, students investigate the doing side of the investigation or right side of the Vee and reflect on what they learned.
Creating a relevant concept map encourages students to reflect on vocabulary-building words they've encountered during the activity and how these different words are interconnected. Because a concept map reflects students' current level of knowledge, it is located on the left side of the Vee. Students can increase their productivity in this task by asking themselves such questions as "Are there any other concepts/investigative activities that we can add?" "Are there any possible cross-links between different parts of the concept map?" and "Is there a better way of connecting our words or concepts?"
The Vee map in Figure 2 was prepared by a group of students during the same eight-week open-inquiry unit on biomes mentioned in our preceding article on concept maps that appeared in the January issue. Figure 2 shows how sophisticated investigations can become when students are given the freedom to frame their own questions. Following self-planned research agendas stimulated students' interest in related courses, increased their motivation to find out on their own, and encouraged them to link their classroom experience to the real world outside of school.
At Appleby College, a prep school, students in grades six through ten work on individual projects throughout the year for their science classes. As with most types of assignments that teachers must evaluate, there are different ways of scoring Vee maps. Figure 3 shows a scoring scheme that has worked for Appleby faculty in the past, but the weights given to each of the areas on the Vee map are arbitrary and can be changed to fit individual needs. For example, when the teacher gives a focus question at the beginning of a unit to get students started, less weight may be assigned to this part. On the other hand, given that the data and data transformations, claims, and concept map take more time and intellectual effort, we like to weight them more heavily.
For teachers who like to give marks as percentage points, the following grading system is a possible suggestion. Weight the areas of concept map, data and data transformation, and claims twice as heavily as associated words and investigative activities, yielding 24 points (6, 6, 6, 3, and 3) for a perfect map. If you include one point for overall outlook and presentation, then multiplying a student's score by 4 would yield a percentage score. Using a chart like that in Figure 4, a student's progress can be monitored for each of the areas of the Vee map over the period of a term, or possibly even an entire year.
In spite of concerns about rigid assessment practices and the practice of assigning value to students' work in the form of letter grades, teachers must not forget that all assessment necessarily requires some judgment and thus contains elements of subjectivity. We have found, as have others before us, that in general there is good agreement among scorers of Vee maps [1]. However, so many alternatives exist for constructing a concept map on a given topic that we must remain flexible in scoring to do justice to a student's learning style and way of expression. Over time, after scoring several sets of Vee's, one can develop a set of criteria to consistently and quickly evaluate an entire class of students work. When students work in groups of two to three students, the actual number of Vee maps marked is much smaller than number of students. In these situations, students indicate on the top right-hand side of the Vee the individual roles they will be taking or have taken during a Vee-map-directed investigation.
1. Novak, J., and Gowin, D. (1984). Learning How to Learn. Cambridge, England: Cambridge University Press.
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