The sample group (year 10, co-educational, rural setting) would be mostly operating in either the Piagetian Formal Operational cognitive stage, however some students will still be at the Concrete Operational stage, progressing from problem-solving with actual (concrete) objects or events, to more abstract concepts and hypothetical tasks. (McLeod, 2010.) They will most likely be developing hypothetico-deductive reasoning (an individual's general theory of deducing possible factors that could affect an outcome, then creating and testing more specific hypotheses from this) (Woolfolk & Margetts, 2010, p. 45). Furthermore, adolescents working in the Formal Operational cognitive stage exhibit adolescent egocentrism, unable to differentiate between their concerns and the thoughts of others, however the ability to think abstractly allows the individual to have a broader perspective and to think beyond themself. (Hill & Lapsley, 2009)
However, statistics indicate that most students have not attained the formal operations stage by the time they finish high school, contrary to Piaget's reasoning (Lutz & Huitt, 2004), with gender and geographical location also contributing to cognitive development stage. Furthermore, the practical nature of the subject taught could indicate that the cognitive level of the students may not be set at purely formal operational stage but across stages, indicating that students who choose to study practical subjects are more likely to do so because of the concrete/hands-on nature of the subject, not for their ability to think abstractly with relative ease.
Learning Theory and Teaching Style
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The "Math Concepts in Construction" lesson plan primarily utilises constructivist learning theories, as it encourages students' critical thinking, active participation and provides relevant problem-solving tasks, thus allowing students to "construct" their own knowledge (Woolfolk & Margetts, 2010, p. 350).
Specifically, constructivist learning theories are employed in the lesson "Construction revision of complex learning environments (converting fractions to decimals, calculating volume), where "authentic" real-life situations are given that may not derive a neat numerical answer, with appropriate teacher support included into the lesson plan to allow all learners to access the tasks. The lesson plan also provides opportunities for social negotiation and discussion of how problems relate to the real-world, multiple representations of content (different analogies and examples provided for students to work through), "spiral curriculum" structures (students revisiting the same material that they may have encountered in actual maths classes- some skills having been acquired in their primary years, not an Industrial Technology class).
The teaching style by which the lesson is to be delivered is a combination of demonstration and guided discovery learning, focussing on student-centred activities. Within the lesson plan, specific examples of demonstration include "name different math concepts commonly used in construction "and guided discovery leaning include activities such as "together convert fractions to common denominator".
Evaluation of the plan before modifications
The conclusions reached from the reviewed articles in Assessment task A were to plan engaging, cross-curricular, "hands-on" self-guided learning activities; to consider individuals' needs in terms of gender, Piagetian cognitive developmental stage and potential post-school interests; to plan group work to maximise engagement for all students; to encourage senior classes to continue education and their chosen career path; to promote participation in groups beyond school and family to assist with students' self-worth and improved school retention. When relating these conclusions to the "Math Concepts in Construction" lesson plan, the sample lesson provides scope for cross-curricular, autonomous, relevant and engaging learning and group work.
However, the lesson plan fails to meet the differing abilities and needs of a class group, as the maths tasks could be considered too difficult for some students who may have "gaps" in maths skills, but too easy for others, highlighting the need for differentiated, supported tasks for students of all ability levels.
Similarly, by its nature, the lesson plan doesn't address the conclusions reached promoting positive careers guidance, encouraging further educating and career paths, or involvement social contexts including religion in a small community which may allow teaching to more effective due to positive student attitudes and achievement.
Modification to the plan
Three specific modifications that could be implemented to the "Math Concepts in Construction" lesson plan include:
Always on Time
Marked to Standard
Increasing relevance to an Australian setting by converting all units to metric equivalents.
research can be from your review of the literature or other references.
Relate to Wicked Problem
Define a 'wicked problem' based on referenced readings and explain why the selection of teaching strategies for your assigned group is a ''wicked problem' for teachers in planning their lessons