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This Concept Map, created with IHMC CmapTools, has information related to: cognitive-effects-of-arg-mapping, in the representation of an argument, the assumption that a reason warrants a claim is represented by the enabler therefore (ArgScheme: modus ponens) an argument’s enabler represents a crucial part of the arguer’s background assumptions, animals and children "are highly sensitive to surface markings and angular relationships in small pictures and objects" is "The other system applies to small-scale forms and allows for recognition and categorization of objects by their shapes" (870)., Spelke et al. (2010) argue that our basic knowledge of Euclidean geometry "that feels most natural to educated adults" (865) is, on one hand, "founded on at least two evolutionarily ancient, early developing, and cross-culturally universal cognitive systems that capture abstract information about the shape of the surrounding world: two core systems of geometry," and, on the other, "on uniquely human, culturally variable artifacts: pictures, models, and maps." (865) supports both the system of natural numbers and the system of natural geometry are hard-won cognitive achievement(s), constructed by children as they engage with the symbol systems of their culture" (Spelke et al., 2010, p. 865), "One system serves to represent numerically distinct individuals, supports the concept one, and allows for the operation of adding one to an array, but it includes no explicit, summary representations of other cardinal values (such as two) and has a capacity limit of about 3 individuals. The second system serves to represent sets and their approximate cardinal values, supports concepts such as about eight, and allows for operations of comparison and arithmetic on those concepts, but it has no successor function (one more) and is subject to a ratio limit on precision that rises from about .33 at birth to about .88 at maturity. (Spelke 2010, 874-5) describes Carey (2009) and others argue that children construct their knowledge of the system of natural numbers by combining two priorly given core cognitive systems: one system allows to distinguish and add individuals with no capacity of repre- senting sets and limited to about 3 individuals; the other system allows a rough representation of sets without successor function. There is evidence that this combination, however, is only possible when children engage "with devices for symbolizing and operating on exact numbers" (875), the fact that somebody provides a certain reason for a certain claim is either arbitrary, or it is based on the background assumption that this reason warrants the claim therefore (ArgScheme: disjunctive syllogism) the fact that somebody provides a certain reason for a certain claim is based on the background assumption that this reason warrants the claim, Spelke et al. (2010) suggest that the integration of both these systems--which is observable in the cognitive development of children starting at the age of 4 years-- "could" be explained by childrens' beginning understanding of the technologies "for making pictures, models, or maps of spatial layouts" (876) supports Spelke et al. (2010) argue that our basic knowledge of Euclidean geometry "that feels most natural to educated adults" (865) is, on one hand, "founded on at least two evolutionarily ancient, early developing, and cross-culturally universal cognitive systems that capture abstract information about the shape of the surrounding world: two core systems of geometry," and, on the other, "on uniquely human, culturally variable artifacts: pictures, models, and maps." (865), "One system applies to the large-scale spatial layout and guides navigation." (866) This system, however, does not capture 2D surface markers, only the shape of surrounding structures in their entirety, and it does not capture the Euclidean feature of angle, only distance and direction. (870) together "Together, the two systems capture all of the fundamental properties of Euclidean geometry: distance, angle, and directional relationships. Together, moreover, they allow for a common description of small-scale objects and of large-scale spatial layouts." (874), deductively valid arguments allow but one choice: Either accept its conclusion or defeat one of its premises therefore (ArgScheme: modus ponens) defeating a deductively valid arguments requires to demonstrate the unacceptability of one of the argument's reasons or of the enabler, a user thinks the more critical the more he or she is forced to reflect on his or her reasoning therefore (ArgScheme: modus ponens) Critical thinking can better be learned with argument visualizationtools that challenge the user to con- struct reasoning in the form of deductively valid argu- ments (=LAM tools) than with tools that constrain the freedom of expression less, IF deductively valid arguments allow but one choice: Either accept its conclusion or defeat one of its premises, THEN defeating a deductively valid arguments requires to demonstrate the unacceptability of one of the argument's reasons or of the enabler therefore (ArgScheme: modus ponens) defeating a deductively valid arguments requires to demonstrate the unacceptability of one of the argument's reasons or of the enabler, a deductively valid argument is always complete therefore (ArgScheme: modus ponens) LAM tools challenge the arguer to construct arguments that are complete and strong, LAM tools challenge the arguer to reflect on his or her back- ground assumptions therefore (ArgScheme: modus ponens) LAM tools force the user more to reflect on his or her reasoning than those tools that constrain the user's freedom of expression less, if a deductively valid argument is always complete, and if the conclusion of a deductively valid argument is necessarily true if all its premises are true LAM tools challenge the arguer to construct arguments that are complete and strong therefore (ArgScheme: modus ponens) LAM tools challenge the arguer to construct arguments that are complete and strong, "A child with access to the two core number systems could, in principle, construct the system of natural number concepts by combining together these concepts and operations. In practice, this construction takes many years, and it involves mastery of the counting system used in the child’s culture (Carey, 2009; Wynn, 1990). Although much remains to be learned about the steps by which children construct natural number from these core systems, there is evidence that experience in a numerate culture, with devices for symbolizing and operating on exact numbers, is critical for the development and exercise of natural number concepts. Children appear to acquire natural number concepts when they master their culture’s counting procedure (Carey, 2009). Moreover, adults who live in a culture lacking a verbal-counting procedure typically show only limited abilities to represent large, exact cardinal values (Frank, Everett, Fedorenko, & Gibson, 2008; Gordon, 2004; Pica, Lemer, Izard, & Dehaene, 2004; although see Butterworth, Reeve, Reynolds, & Lloyd, 2008). In numerate societies, symbolic systems other than language also support numerical reasoning (see Dehaene, 1997, for review), and many aspects of this reasoning are impervious to language impairments (Varley, Klessinger, Romanowski, & Siegal, 2005)." (875) supports Carey (2009) and others argue that children construct their knowledge of the system of natural numbers by combining two priorly given core cognitive systems: one system allows to distinguish and add individuals with no capacity of repre- senting sets and limited to about 3 individuals; the other system allows a rough representation of sets without successor function. There is evidence that this combination, however, is only possible when children engage "with devices for symbolizing and operating on exact numbers" (875), LAM tools force the arguer to reflect critically on the accept- ability of all the reasons and the enabler therefore (ArgScheme: modus ponens) LAM tools force the user more to reflect on his or her reasoning than those tools that constrain the user's freedom of expression less, if LAM tools challenge the arguer to reflect critically on the accept- ability of all the reasons and the enabler, then LAM tools force the user more to reflect on his or her reasoning than those tools that constrain the user's freedom of expression less therefore (ArgScheme: modus ponens) LAM tools force the user more to reflect on his or her reasoning than those tools that constrain the user's freedom of expression less, "One system applies to the large-scale spatial layout and guides navigation." (866) This system, however, does not capture 2D surface markers, only the shape of surrounding structures in their entirety, and it does not capture the Euclidean feature of angle, only distance and direction. (870) describes "The other system applies to small-scale forms and allows for recognition and categorization of objects by their shapes" (870)., the conclusion of a deductively valid argument is necessarily true if all its premises are true therefore (ArgScheme: modus ponens) LAM tools challenge the arguer to construct arguments that are complete and strong, children who can count up to six without any visible reference to external objects can count up to 22 when they count wooden blocks supports the internal structure of the externally given system of representation shapes--for better or for worse--the cognitive routines and strategies that the learner stores in long-term memory for use in further learning steps, LAM tools challenge the arguer to construct arguments that are complete and strong therefore (ArgScheme: modus ponens) LAM tools force the user more to reflect on his or her reasoning than those tools that constrain the user's freedom of expression less