Many students consider mathematics as the most dreaded subject in their curriculum, so much so that the term “math phobia” or “math anxiety” is practically a part of clinical psychological literature. This symptom...Many students consider mathematics as the most dreaded subject in their curriculum, so much so that the term “math phobia” or “math anxiety” is practically a part of clinical psychological literature. This symptom is widespread and students suffer mental disturbances when facing mathematical activity because understanding mathematics is a great task for them. This paper described the students’ cognitive skills performance in Basic Mathematics based on the following logical operations: Classification, Seriation, Logical Multiplication, Compensation, Ratio and Proportional Thinking, Probability Thinking and Correlation Thinking as it serves a critical element of teaching and learning, that is determining the current position of the learners’ mathematical capacity. Its implications for mathematics education were also revealed. A descriptive quantitative design was used in this study. The study included 1011 first-year college students from six state universities in the Philippines who were enrolled in the Bachelor of Science of Secondary Education Program during the first semester of the Academic Year 2019-2020. This study made use of the teacher-made test called the Test on Logical Operations. Findings revealed that the cognitive skills achievement of the first year BSE students from different state universities in the Philippines falls under the category of late concrete operational stage. As a result, students are unable to perform the logical operational skills expected of their age. At their age level, they are expected to be under the formal operational stage based on Piaget’s stages of cognitive development. These findings revealed a weak mathematical education foundation among students which requires immediate attention. This reality should be recognized by educational planners and implementers when making curricular and other instructional decisions.展开更多
The simulation of indentations with so called “equivalent” pseudo-cones for decreasing computer time is challenged. The mimicry of pseudo-cones having equal basal surface and depth with pyramidal indenters is exclud...The simulation of indentations with so called “equivalent” pseudo-cones for decreasing computer time is challenged. The mimicry of pseudo-cones having equal basal surface and depth with pyramidal indenters is excluded by basic arithmetic and trigonometric calculations. The commonly accepted angles of so called “equivalent” pseudo-cones must not also claim equal depth. Such bias (answers put into the questions to be solved) in the historical values of the generally used half-opening angles of pseudo-cones is revealed. It falsifies all simulations or conclusions on that basis. The enormous errors in the resulting hardness H<sub>ISO</sub> and elastic modulus E<sub>r-ISO</sub> values are disastrous not only for the artificial intelligence. The straightforward deduction for possibly ψ-cones (ψ for pseudo) without biased depths’ errors for equal basal surface and equal volume is reported. These ψ-cones would of course penetrate much more deeply than the three-sided Berkovich and cube corner pyramids (r a/2), and their half-opening angles would be smaller than those of the respective pyramids (reverse with r > a/2 for four-sided Vickers). Also the unlike forces’ direction angles are reported for the more sideward and the resulting downward directions. They are reflected by the diameter of the parallelograms with length and off-angle from the vertical axis. Experimental loading curves before and after the phase-transition onsets are indispensable. Mimicry of ψ-cones and pyramids is also quantitatively excluded. All simulations on their bases would also be dangerously invalid for industrial and solid pharmaceutical materials.展开更多
文摘Many students consider mathematics as the most dreaded subject in their curriculum, so much so that the term “math phobia” or “math anxiety” is practically a part of clinical psychological literature. This symptom is widespread and students suffer mental disturbances when facing mathematical activity because understanding mathematics is a great task for them. This paper described the students’ cognitive skills performance in Basic Mathematics based on the following logical operations: Classification, Seriation, Logical Multiplication, Compensation, Ratio and Proportional Thinking, Probability Thinking and Correlation Thinking as it serves a critical element of teaching and learning, that is determining the current position of the learners’ mathematical capacity. Its implications for mathematics education were also revealed. A descriptive quantitative design was used in this study. The study included 1011 first-year college students from six state universities in the Philippines who were enrolled in the Bachelor of Science of Secondary Education Program during the first semester of the Academic Year 2019-2020. This study made use of the teacher-made test called the Test on Logical Operations. Findings revealed that the cognitive skills achievement of the first year BSE students from different state universities in the Philippines falls under the category of late concrete operational stage. As a result, students are unable to perform the logical operational skills expected of their age. At their age level, they are expected to be under the formal operational stage based on Piaget’s stages of cognitive development. These findings revealed a weak mathematical education foundation among students which requires immediate attention. This reality should be recognized by educational planners and implementers when making curricular and other instructional decisions.
文摘The simulation of indentations with so called “equivalent” pseudo-cones for decreasing computer time is challenged. The mimicry of pseudo-cones having equal basal surface and depth with pyramidal indenters is excluded by basic arithmetic and trigonometric calculations. The commonly accepted angles of so called “equivalent” pseudo-cones must not also claim equal depth. Such bias (answers put into the questions to be solved) in the historical values of the generally used half-opening angles of pseudo-cones is revealed. It falsifies all simulations or conclusions on that basis. The enormous errors in the resulting hardness H<sub>ISO</sub> and elastic modulus E<sub>r-ISO</sub> values are disastrous not only for the artificial intelligence. The straightforward deduction for possibly ψ-cones (ψ for pseudo) without biased depths’ errors for equal basal surface and equal volume is reported. These ψ-cones would of course penetrate much more deeply than the three-sided Berkovich and cube corner pyramids (r a/2), and their half-opening angles would be smaller than those of the respective pyramids (reverse with r > a/2 for four-sided Vickers). Also the unlike forces’ direction angles are reported for the more sideward and the resulting downward directions. They are reflected by the diameter of the parallelograms with length and off-angle from the vertical axis. Experimental loading curves before and after the phase-transition onsets are indispensable. Mimicry of ψ-cones and pyramids is also quantitatively excluded. All simulations on their bases would also be dangerously invalid for industrial and solid pharmaceutical materials.
