Lesson Reflection
Lesson Plan Reflection
Description: Students often have difficulty graphing quadratics, and frequently struggle understanding the connection between a table of values, a graph, and an equation. My lesson was centered on providing students with an understanding of the transformations that quadratic functions undergo. My lesson plan revolved around the use of graphing calculators and Excel to model graphing to students, and featured a class wiki to foster student collaboration. As I used think-aloud techniques, students were scaffolded through the process of graphing quadratic functions and describing the transformations taking place. I modeled how to graph quadratics with a calculator, with Excel, and by hand. After modeling the parent function, I coached students through various other quadratic functions, and eventually withdrew all supports.
Narrative: The students that I implemented this lesson with were tenth grade honor’s geometry students. The class did not feature any students with learning disabilities for me to accommodate. The students were definitely engaged during the lesson with the graphic calculators and Excel. Incorporating TI-Smartview so that students could follow the buttons pressed was extremely helpful, as some were relatively unfamiliar with a graphing calculator. Viewing student computer screens through the master computer also was beneficial in coaching students and catching misconceptions prior to them becoming ingrained. The students were quick to understanding the three methods of graphing, and therefore did not really need the assistance I provided through a graphic organizer and notes. Their ability to comprehend the concepts made the modeling and guided practice portions of the lesson seem unnecessary and too lengthy. The lesson took over two full class periods, which again demonstrates that perhaps I was too thorough with the number of examples and guided practice questions. Nonetheless, the students were very successful in the independent practice and scored well on the assessment.
Reflection: This experience was beneficial. The students learned how to graph quadratic functions and how the function itself relates to the transformations of a parabola. I learned the worth of modeling concepts in multiple manners, and my belief in the power of technology in education was reinforced. I based the lesson on the assumption that knowledge is best gained when individuals discover and classify it themselves. With my guidance, the students were able to discover how a shift, stretch, and reflection appear in a function. Another assumption taken in this lesson is that knowledge is best obtained when it is represented in multiple forms. In this lesson students compared graphs, tables, and function through Excel and graphing calculators. This was an affordance because it allowed students to compare the parent function and the given quadratic function through calculators, and enabled students to manipulate graphs through Excel. Likewise, focusing on the assumption that students learn best when cooperating with peers was an affordance because it allowed authentic dialogue through a wiki. Unfortunately, both of these affordances are linked to constraints. All of these multiple avenues for learning created a lengthy lesson, which would not be feasible to implement on a regular basis.
This lesson was definitely hinged upon learning theories. Social constructivism can be seen through the scaffolding and inductive learning that is present through the lesson. Students were internalizing cultural tools, such as calculators and spreadsheets. Cognitive apprenticeship is another learning theory I employed. I strived to make my thinking visible, provide a range of tasks for the learners, and enable students to problem solve in small groups. Behavioralism was not a major theory present in the lesson. There was no conditioning, although students did seem to feel rewarded by posting correct responses on the wiki. Alongside the theories present, the lesson did address the needs of diverse learners. Through graphic organizer, paragraph notes, the manipulation of graphs, and the various methods of graphing promoted, the needs of students with different learning styles were addressed. Furthermore, there were accommodations made for students with disabilities. Students with learning disabilities and cognitive impairments were able to focus on the graphing and transformations of functions with calculators, so that they were not being dragged down by the arithmetic of creating tables. All learners were able to enhance their skills of graphing through the use of technology, and develop new understandings of quadratics.
For this lesson to be a success, teachers need to have a strong understanding of graphing calculators and their settings, as well as Microsoft Excel. Furthermore, a teacher implementing this lesson should be aware of how to monitor student understanding through the wiki and through the use of a master computer in a lab. As far as the students are concerned, a prerequisite would be the ability to evaluate powers and expressions, and to place coordinate pairs in a plane. There are accommodations made for students without this prior knowledge, yet that prior knowledge would be best in order to get the most out of the lesson. To judge the success of this lesson, monitoring the students is imperative. To hold students accountable, a teacher should be able to verify their answers through the wiki as well as check their comprehension by viewing their computer screen. Furthermore, a comprehensive assessment must be given at the end of the lesson so that students may individually demonstrate their understanding of the material without the use of the graphic organizer, calculator, or Excel.
This lesson is contingent upon the use of technology. Excel and graphing calculators allow students to compare graphs of quadratics and manipulate them by altering equations, while TI Smartview enables students to clearly follow calculator steps. Additionally, collaboration is possible through the use of a wiki. Technology fosters scaffolding and puts students in the driver’s seat as they explore the relationships among quadratic functions. Without such technology students would not be able to compare such graphs and manipulate them dynamically. I expected students to thoroughly enjoy the technology in the lesson. They certainly did enjoy the technology and found the lesson much more engaging than a traditional approach. There were a couple frequent questions posed by the students. The first was “how does Excel recalculate formulas when the cell changes?” I explained to the students the difference between relative and absolute Excel formulas. The second question revolved around not being able to see portions of a graph. To address this question, I gave a brief tutorial of how to adjust a graphing calculator window. Otherwise, the students embraced the technology and used it to gain a deeper understanding of the mathematics. The intersection of technology, learning theories, self-discovery, and student collaboration proved to be instrumental, as students forged a deep understanding of transformations of quadratics.
Description: Students often have difficulty graphing quadratics, and frequently struggle understanding the connection between a table of values, a graph, and an equation. My lesson was centered on providing students with an understanding of the transformations that quadratic functions undergo. My lesson plan revolved around the use of graphing calculators and Excel to model graphing to students, and featured a class wiki to foster student collaboration. As I used think-aloud techniques, students were scaffolded through the process of graphing quadratic functions and describing the transformations taking place. I modeled how to graph quadratics with a calculator, with Excel, and by hand. After modeling the parent function, I coached students through various other quadratic functions, and eventually withdrew all supports.
Narrative: The students that I implemented this lesson with were tenth grade honor’s geometry students. The class did not feature any students with learning disabilities for me to accommodate. The students were definitely engaged during the lesson with the graphic calculators and Excel. Incorporating TI-Smartview so that students could follow the buttons pressed was extremely helpful, as some were relatively unfamiliar with a graphing calculator. Viewing student computer screens through the master computer also was beneficial in coaching students and catching misconceptions prior to them becoming ingrained. The students were quick to understanding the three methods of graphing, and therefore did not really need the assistance I provided through a graphic organizer and notes. Their ability to comprehend the concepts made the modeling and guided practice portions of the lesson seem unnecessary and too lengthy. The lesson took over two full class periods, which again demonstrates that perhaps I was too thorough with the number of examples and guided practice questions. Nonetheless, the students were very successful in the independent practice and scored well on the assessment.
Reflection: This experience was beneficial. The students learned how to graph quadratic functions and how the function itself relates to the transformations of a parabola. I learned the worth of modeling concepts in multiple manners, and my belief in the power of technology in education was reinforced. I based the lesson on the assumption that knowledge is best gained when individuals discover and classify it themselves. With my guidance, the students were able to discover how a shift, stretch, and reflection appear in a function. Another assumption taken in this lesson is that knowledge is best obtained when it is represented in multiple forms. In this lesson students compared graphs, tables, and function through Excel and graphing calculators. This was an affordance because it allowed students to compare the parent function and the given quadratic function through calculators, and enabled students to manipulate graphs through Excel. Likewise, focusing on the assumption that students learn best when cooperating with peers was an affordance because it allowed authentic dialogue through a wiki. Unfortunately, both of these affordances are linked to constraints. All of these multiple avenues for learning created a lengthy lesson, which would not be feasible to implement on a regular basis.
This lesson was definitely hinged upon learning theories. Social constructivism can be seen through the scaffolding and inductive learning that is present through the lesson. Students were internalizing cultural tools, such as calculators and spreadsheets. Cognitive apprenticeship is another learning theory I employed. I strived to make my thinking visible, provide a range of tasks for the learners, and enable students to problem solve in small groups. Behavioralism was not a major theory present in the lesson. There was no conditioning, although students did seem to feel rewarded by posting correct responses on the wiki. Alongside the theories present, the lesson did address the needs of diverse learners. Through graphic organizer, paragraph notes, the manipulation of graphs, and the various methods of graphing promoted, the needs of students with different learning styles were addressed. Furthermore, there were accommodations made for students with disabilities. Students with learning disabilities and cognitive impairments were able to focus on the graphing and transformations of functions with calculators, so that they were not being dragged down by the arithmetic of creating tables. All learners were able to enhance their skills of graphing through the use of technology, and develop new understandings of quadratics.
For this lesson to be a success, teachers need to have a strong understanding of graphing calculators and their settings, as well as Microsoft Excel. Furthermore, a teacher implementing this lesson should be aware of how to monitor student understanding through the wiki and through the use of a master computer in a lab. As far as the students are concerned, a prerequisite would be the ability to evaluate powers and expressions, and to place coordinate pairs in a plane. There are accommodations made for students without this prior knowledge, yet that prior knowledge would be best in order to get the most out of the lesson. To judge the success of this lesson, monitoring the students is imperative. To hold students accountable, a teacher should be able to verify their answers through the wiki as well as check their comprehension by viewing their computer screen. Furthermore, a comprehensive assessment must be given at the end of the lesson so that students may individually demonstrate their understanding of the material without the use of the graphic organizer, calculator, or Excel.
This lesson is contingent upon the use of technology. Excel and graphing calculators allow students to compare graphs of quadratics and manipulate them by altering equations, while TI Smartview enables students to clearly follow calculator steps. Additionally, collaboration is possible through the use of a wiki. Technology fosters scaffolding and puts students in the driver’s seat as they explore the relationships among quadratic functions. Without such technology students would not be able to compare such graphs and manipulate them dynamically. I expected students to thoroughly enjoy the technology in the lesson. They certainly did enjoy the technology and found the lesson much more engaging than a traditional approach. There were a couple frequent questions posed by the students. The first was “how does Excel recalculate formulas when the cell changes?” I explained to the students the difference between relative and absolute Excel formulas. The second question revolved around not being able to see portions of a graph. To address this question, I gave a brief tutorial of how to adjust a graphing calculator window. Otherwise, the students embraced the technology and used it to gain a deeper understanding of the mathematics. The intersection of technology, learning theories, self-discovery, and student collaboration proved to be instrumental, as students forged a deep understanding of transformations of quadratics.
Labels: Lesson, mathematics, reflection
posted by Brian Ericson at
2:27 PM
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