NPTNC1628: Week 5 Knowledge & Cognitive Developmental Processes

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NPTNC1628: Week 5 Knowledge & Cognitive Developmental Processes

“Yet Piaget seems to have overestimated what adolescents can do. Formal operational thinking processes (e.g., proportional reasoning, separation and control of variables) emerge much more gradually than Piaget suggested, and even high school students don’t necessarily use them regularly (Flieller, 1999; Schliemann & Carraher, 1993; Tourniaire & Pulos, 1985; Zohar & Aharon-Kraversky, 2005). In fact, even adults don’t always reason in the logical ways that supposedly characterize formal operational thought (X. D. Lin & Lehman, 1999; Morra et al., 2008; Pascarella & Terenzini, 1991). For instance, when adults draw conclusions and inferences about real-world events, they may overrely on their existing knowledge about the world—thus having the same difficulty in separating logic from reality that children in concrete operations do (D. Kuhn & Franklin, 2006). Perhaps the rules of formal logic—the kind you might learn in a philosophy class—don’t reflect the typical ways in which children or adults reason. To some degree, Piaget’s formal operations stage may capture people’s capabilities under the best of circumstances rather than their normal, day-to-day reasoning processes (Halford & Andrews, 2006; D. Kuhn & Franklin, 2006; R. J. Sternberg, 2003).”

The video on “Constructivism in the Classroom” shows many students engaged in one of the hallmarks of Neo-Piagetian theories, engagement in hands-on activities(p. 305). In many of the images displayed students are using tangibles or interacting with objects to better understand concepts they’re learning. This allows for elementary students to work out a problem physical or for adolescents to tie abstract concepts to concrete tools and the physical world mainly using tools and technology(p. 306). Within my own class I always like describing the concept of kerf to my students. When processing material on various tools, one must account for kerf or the amount of material the tool destroys when processing material. With any saw one can account for kerf by measuring the thickness of the blade. At first, students don’t understand why this is so important. However, they quickly figure out when working with hand saws or power saws that if they place the blade on the wrong side [or on] the measurement their piece is cut to the wrong dimension. It is truly only when they work with a physical object that they understand the initially abstract concept of kerf. What’s great is throughout the rest of the year we can apply that same concept to tolerance or sizing of physical objects printed on a 3D printer, or to the kerf that we must account for when cutting on a laser cutter. I find it amazing to always reference back to that first moment a student measures and cuts a piece of wood throughout their time in the shops with me. It goes hand in hand with “Measure Twice, cut once”!

Students who are capable formal operational thinking are capable of planning for the future, and thinking abstractly based on prior knowledge(p. 306). Students at a concrete operational stage struggle with the abstract. For example students with formal operational thinking are better capable of assessing fractions of a whole than students who are still at a concrete operational level. As such, one with either formal or concrete operational capabilities can understand that when they cut lumber down, they’ll have a certain amount of lumber from a whole sheet. However, if a student is asked to calculate how much lumber they’ll have and to account for kerf, or the amount of material removed by the blade cutting the material [into sawdust], the student capable of formal operational thinking can apply the general principle of kerf to the outcome of cutting wood. A student at the concrete operational thinking stage will struggle with or be incapable of this reasoning.