The Effect of Multiple Internal Representations on Context Rich Instruction

This paper presents n-coding, a theoretical model of multiple internal mental representations. The n-coding construct is developed from a review of cognitive and imaging studies suggesting the independence of information processing along different modalities: verbal, visual, kinesthetic, social, etc. A study testing the effectiveness of the n-coding construct in classrooms is presented. Four sections differing in the level of n-coding opportunities were compared. Besides a traditional instruction section used as a control group, each of the remaining three treatment sections were given context rich problems following the “cooperative group problem solving” approach which differed by the level of n-coding opportunities designed into their laboratory environment. To measure the effectiveness of the construct, problem solving skills were assessed as was conceptual learning using the Force Concept Inventory. However, a number of new measures taking into account students’ confidence in concepts were developed to complete the picture of student learning. Results suggest that using the developed n-coding construct to design context rich environments can generate learning gains in problem solving, conceptual knowledge and concept-confidence. In his Nobel lecture, Richard Feynman stated: “Perhaps a thing is simple if you can describe it fully in several different ways without immediately knowing that you are describing the same thing”. The converse may also be true as the ability to represent an object or phenomenon in multiple ways may simplify one’s understanding of it. Consistent with this idea, several studies have addressed the importance of multiple representations in learning physics. However, previous studies have defined representations primarily as external representations used in practice such as mathematical, diagrammatic or graphical representations. The present paper shifts the focus to internal mental representations to provide insights into optimizing student learning and potentially explain the effectiveness of external representations. Just as multiple external representations can enhance problem solving, previous cognitive studies have shown that the construction of multiple mental representations can also enhance problem solving abilities. Multiple mental representations complete each other, resulting in a more authentic portrayal of a problem than any single source of uni-modal information. The present paper has three parts. The first consists of a survey of the cognitive literature to build a coherent model of internal representations that is simple enough to be used in classrooms. The second part presents a physics instructional study testing the effectiveness of the proposed model of internal representations. To achieve a comprehensive picture of effectiveness, an objective of this paper is to develop new measures of learning in physics. By shifting the focus away from a Boolean view of students’ conceptual states (i.e. away from a perception that “they either get it or they don’t”), these new measures acknowledge the complexity of students’ conceptions by taking into account affective factors such as students’ confidence in concepts. The third part will discuss the findings, their limitations and provide recommendations on maximizing physics learning. From encoding to n-coding Within the brain, the mind is currently seen as a set of specialized information processors that are spatially independent but functionally interrelated. Local brain areas have different processing functions and although spatially independent, these processors interact with each other, a collaboration of separate entities that Minsky has poetically called the Society of Mind. Cognitive scientist and Nobel laureate Herbert Simon had argued that this type of modular design of the mind is but a special case of modular, hierarchical design of all complex systems. The process through which information is taken from the external environment and “coded” for the mind is called encoding. Encoding can take place in several modes. Consider for instance Dual-Coding Theory (DCT). The DCT approach attempts to give equal weight to verbal and visual processing. The reasoning behind this approach is that both the visual and the auditory system can be activated independently although the two systems are interconnected. In the neuro-cognitive literature these independent systems are referred to as the auditory or phonological loop and the visuospatial sketchpad. This independence can be easily demonstrated by asking subjects to perform two simultaneous tasks. If both tasks are auditory (or both visual), an interference occurs prohibiting their simultaneous completion. However, when one is visual and the other auditory, simultaneous tasks can be performed. It has been suggested that the connectedness of both systems allows individuals to cue from one system to the other which facilitates interpreting the environment. The inference is that since there are two distinct ways of encoding and representing information in our mind, the use of both representations allows parallel processing to occur thus reducing computational time. 1 On possible candidate for this interaction mechanism is coherent gamma wave synchrony (Crick & Koch, 1995). This process shows how different parts of the brain can be united by allowing local high frequency brain waves (i.e. gamma waves) to be synchronized with other parts of the brain. Corollaries of this hypothesis have also been observed as disorganized though in schizophrenia has been correlated to gamma asynchrony (Haig et al, 2000). Fig 1. Reproduced with consent from TIP database Evidence of specialized processing is abundant. Through studies of injured patients, it has been known for over a century that the processing of language is located in what are now called Broca and Wernicke’s areas in the brain (see Figure 2). However, in the past 15 years, the use of neural imagery such as PET and fMRI scans has revealed an increasingly clear picture of localized processing. The impact of current advances in imaging has been likened to Santiago Ramon y Cajal’s first observation of an individual nerve cell. Imaging data of localized processing shows that visual and auditory words activate (a largely left sided) set of areas of the anterior and posterior cortex and the cerebellum; while simple arithmetical tasks activate left and right occipital and parietal areas. There is now also information on spatial tasks, on understanding of the minds of others and of oneself and even on the processing of musical tasks. Thus, encoding information from the environment is a parallel process: one part of the brain does not wait in sequence to start processing if another part is activated; more than one part can be activated at once. This survey of neuro-imaging studies suggests that multiple forms of encoding can take place. In a similar way that dual-coding theory urged us to consider two encoding modes, these imaging findings urge us to reconsider encoding as n-coding. The term n-coding is coined here to emphasize that ‘n’ is no longer two (as in dual coding) but the number of encoding dimensions identifiable, which may increase with further imaging studies. Fig 2. Visual processing areas in orangeverbal processing areas in blue N-coding modes need not be strictly perceptual. For instance, imaging data on understanding the minds of others supports cognitive “theories of mind” positing the existence of an internal “mind reading system”. This modality can be seen as rooted both in genetic and environmental settings as illustrated by its dysfunction in autistic disorders and its normal developmental trajectory in children. However, encoding information about the mind of others is done somewhat independently from its related visual perceptual process. Indeed, autistic individuals can recognize people without being able to tell their emotional state; something autistic professor of animal studies Temple Grandin has likened to being as an anthropologist on Mars, constantly trying to figure out how different behaviors translate into emotional states. In a nutshell, the possibility to n-code is the possibility to represent information mentally along multiple dimensions (verbal, logico-mathematical, visual, kinesthetic, social, etc.). The remaining question is: How can these findings be applied to instruction? From theory to Practice It is always necessary to err on the side of caution when going from a “descriptive learning theory” to a “prescriptive instructional theory”. It would be ill-advised to take imaging findings and make clear conclusions and recommendations as to what instructional environments should be like. Current educational trends, such as “Brain-based” learning, have been severely critiqued for inferring one-to-one relationships between fundamental research findings and instructional practices. Before jumping into tentative applications, one is reminded of the wise comments of a founding father of American psychology, William James: “You make a great, a very great mistake if you think that psychology, being a science of the mind’s laws, is something from which you can deduce definite programmes and schemes and methods of instruction for immediate schoolroom use” Although one must be wary of translating neuroscience findings directly into educational practice, it would be unconscionable not to use neuroscience findings as a guide for empirically driven educational development. The current paper will thus present a classroom quasiexperiment where students in different sections were assigned to activities based on context rich problems consistent with the Cooperative Group Problem Solving (CGPS) approach but that varied in n-coding opportunities. The CGPS approach was chosen because of its demonstrated effectiveness and because it constitutes an exemplary Interactive Engagement approach using context rich problems. The classroom experiment presented attempts to test whether increasing ncoding opportunities in CGPS has even more beneficial effects on learning. Description of treatment conditions Students enrolled in an algebra-based mechanics course in a Canadian 2-yr community college were given homomorphic CGPS problems. The classroom study consisted of 4 sections differing by the level of n-coding built into the environment and the problem structure. To get a better picture of the difference between these treatment sections it may be useful to briefly describe one CGPS activity and its implementation across the different groups. One problem was based on a popular TV show (CSI: Crime Scene Investigators) and put the student in the shoes of a detective trying to solve a murder. The objective of this ballistics problem was to help students better acquire and synthesize notions of 2D kinematics. The first section, labelled high n-coding group (nCodHi), incorporated multiple representations in the problem presentation and required n-coding in the problem solution as well. Thus, in the first treatment section (nCodHi), the text problems were accompanied by rich visuo-spatial presentations. Besides diagrams, an actual scene reconstitution included an outline of a victim taped on floor and chalk dust emulating gun powder distribution so as to locate the initial horizontal position of the gun. Furthermore, kinesthetic data was also available such as a bloc of wood in which a stray bullet was found and an actual 9mm slug (graciously provided by the police technology program of the college). Students were then given a table of muzzle speeds (i.e the initial speed of the bullet as it exits the gun) for various calibres. Once extracted from the bloc of wood it had supposedly been shot in, the slug’s angle of entry was to be measured (a 9+mm hole was drilled at 5 from horizontal and the slug was inserted prior to lab). Using all the information available students had to collaboratively determine which variable they were ultimately looking for. In this particular case, the initial vertical position of the bullet was to be found so as to find the approximate shoulder height of the shooter to later identify him from a line-up. The second section, labelled medium n-coding group (nCodMed), did not include emulated environments that required elaborate setups. Problems were presented in text format. However, the solution of these problems required students to inquire about the objects of the emulated environment and make some measurements. Thus, the second group (nCodMed) was presented neither with an emulated environment nor with physical props. However, to solve the problem students had to enquire about the props. For instance, the actual 9mm slug was not presented but was available on student request and its measurement was essential to the problem solution (without the information that this was a 9mm slug, student could not know for instance the initial speed of the bullet). Thus, although the same problem was given and similar measurements had to be carried through in both groups, only one group had the props presented with the problem while the other had to enquire about them. Note that the lab problems for the two first treatment conditions were designed to use measurement instruments that were familiar to students (everyday tools such as a bathroom scale or a measuring tape, stop watches etc.). The third section, labelled low n-coding group (nCodLo), was comprised of conventional CGPS context rich problems presented in text format without transforming the environment. This section had less opportunities for multiple representations as none of the props were available and all data gleaned along visual or tactile dimensions were obtainable in text form. For instance, the problem stated: “a 9mm slug was recovered from the scene”. Given the calibre of the bullet the students can figure out its muzzle speed from a table. As in the other two treatment conditions, all the information was not available in the initial problem description. However, students could not measure the missing information from various props. Finally, the control group was comprised of traditional highly-structured “cookbook” labs assessing the same learning outcomes (eg. 2D kinematics). All sections of the course (treatments and control) had the same instructor (N.L.) so as to minimize, if not control for interinstructor differences and macro-differences in classroom culture. Furthermore, all three treatment sections required students to collaboratively solve problems in groups of three or four. Students in the control section however were assigned to groups of two. The table below summarizes the presence or absence of characteristics across all groups. Table 1: Schema of various treatment sections Control nCodLo nCodMed nCodHi Cooperative group N Y Y Y n-coding/multiple representation required for task solution N N Y Y n-coding in task presentation and task solution N N N Y