This paper is intended to identify best instructional practices in the mathematics classroom by considering the relevance of several learning theorists, addressing various teaching and learning strategies, and by applying information based on cognitive science. The individual needs of students and families specific to my classroom experience will also be shared to identify solutions needed to concerns brought up by differences in family backgrounds.
Context
This paper is centered on my experiences teaching seventh through tenth grade honors Math courses. The courses include Pre-Algebra, Algebra I, Geometry, and Algebra II. Honors courses are designed to be academically challenging for students who are typically advanced proficient in their …show more content…
The students in my courses fall between the concrete operational stage and the formal operational stage (Huitt & Hummel, 2003). Both stages require the use of symbols and variables to represent either concrete or abstract concepts (Huitt & Hummel, 2003). This is most especially evident when students are working with real-world problems. They are required to “translate” a real-life observation into mathematical equations which accurately reflect the situation in order to obtain a solution, and often times, this one of the most challenging aspects of problem …show more content…
In accordance with Piaget’s constructivist ideologies, inquiry-based learning practices supports his proposal that “individuals must construct their own knowledge and that they build knowledge through experience” (Smith, n.d.). Inquiry-based learning encourages students to construct their own knowledge and is student-centered in contrast with direct instruction in which teachers transmit the knowledge to students and is teacher-centered (Smith, n.d.). Students become actively involved in their education as students must learn by doing, researching, and deliberately considering the real-world problems presented to them. Students learn to think critically and problem solve creatively, skills necessary for success in all levels of mathematics. Inquiry-based learning also requires students to constantly switch between Piaget’s two cognitive processes, assimilation and adaptation as they discover solutions to problems. Additionally, inquiry-based learning is also supported by Vygotsky’s social constructivist theory as this method of teaching relies heavily on student collaboration and learning in the proximal zone of development (Smith, n.d.). If students are given a task that is too far above their level, and
Context
This paper is centered on my experiences teaching seventh through tenth grade honors Math courses. The courses include Pre-Algebra, Algebra I, Geometry, and Algebra II. Honors courses are designed to be academically challenging for students who are typically advanced proficient in their …show more content…
The students in my courses fall between the concrete operational stage and the formal operational stage (Huitt & Hummel, 2003). Both stages require the use of symbols and variables to represent either concrete or abstract concepts (Huitt & Hummel, 2003). This is most especially evident when students are working with real-world problems. They are required to “translate” a real-life observation into mathematical equations which accurately reflect the situation in order to obtain a solution, and often times, this one of the most challenging aspects of problem …show more content…
In accordance with Piaget’s constructivist ideologies, inquiry-based learning practices supports his proposal that “individuals must construct their own knowledge and that they build knowledge through experience” (Smith, n.d.). Inquiry-based learning encourages students to construct their own knowledge and is student-centered in contrast with direct instruction in which teachers transmit the knowledge to students and is teacher-centered (Smith, n.d.). Students become actively involved in their education as students must learn by doing, researching, and deliberately considering the real-world problems presented to them. Students learn to think critically and problem solve creatively, skills necessary for success in all levels of mathematics. Inquiry-based learning also requires students to constantly switch between Piaget’s two cognitive processes, assimilation and adaptation as they discover solutions to problems. Additionally, inquiry-based learning is also supported by Vygotsky’s social constructivist theory as this method of teaching relies heavily on student collaboration and learning in the proximal zone of development (Smith, n.d.). If students are given a task that is too far above their level, and