Instructional Strategies
Teacher-CenteredModeling
Choice: I have chosen to use a teacher-centered approach to teaching for one of my lessons. I will model for students the correct way to solve systems of linear equations using the elimination method. The elimination method is a complex and confusing system so I will model the correct way to perform this task in an attempt to avoid any confusion that may be caused by having students do the work on their own. Description: As part of my direct instruction for this activity, I will be showing students a Prezi presentation that was created showing the steps of the elimination method and its application in a number of example problems. Although this Prezi was created for another class, it still has application in this class because it shows the essential steps of the elimination method. The teacher will have the power to go through this presentation as quickly or as slowly as he needs to based on how well students are understanding throughout the presentation. After the presentation, I can walk through more examples with the students if they still do not understand the elimination method. Technology: This direct-instruction lesson will require some form of laptop/projector combo or an Interactive Whiteboard in order to display the Prezi presentation. It would be helpful to have some technology where I can write on the board over top of the presentation so that I can go over examples on the board with the students. Rationale: I chose to use direct instruction in the form of a Prezi presentation to teach this method of solving systems of linear equations because the elimination is very complicated and difficult to understand. I feel that students will benefit the most and learn the most through seeing me model the correct steps of the method at the board in the form of a presentation. These students, as I pointed out in my learner analysis, need to first see how something is done correctly and then gradually be given responsibility to complete problems successfully on their own. The students would also benefit more from hearing me go through the presentation rather than just watching a video because they can stop the presentation and ask me questions if they don't understand something. Demonstration
Choice: The first day of the lesson will consist of a teacher-centered demonstration review activity for reviewing how to graph linear equations as well as an introduction to systems of linear equations.This is teacher-centered because the teacher will moderate the activity and direct the learning experience for the students. The students will have to come up with the equations, but the teacher will provide them with the information to help them understand the activity that they are doing. Description: This demonstration will require students to use a coordinate plane taped to the classroom floor which the students will practice on making their own linear lines with string and finding the equations of those lines. Students will see that by graphing multiple lines on the graph (i.e., creating a system of linear equations) that the lines will (most of the time) intersect each other. This point of intersection will correspond to the solution to the system of equations. Technology: Although this activity does not require students to use any technology, it would be helpful to use some form of technology that has graphing capabilities (such as a graphing calculator or Geogebra) to check and make sure the equations they come up with are correct. This will also help students see the connections between the graph they have created on the floor and the equations they have derived. Rationale: I chose to do this activity because it gives students a more hands-on review of graphing linear equations but is also structured enough so that students will receive support from the teacher while going through the activity. This activity is teacher-centered because the teacher will be guiding the students through the activity and moderating the students' learning. I believe by having students do this activity in person instead of just watching a video or a simulation about it they will gain more from it because of the hands-on application. |
Student-CenteredDiscovery Learning
Choice: One of the activities in my lesson involves having students use math-specific graphing software (Geogebra) to investigate systems of linear equations. This is student-centered because students are in charge of how fast or slow they work through the activity and how much practice they need in order to fully understand the material. The students are able to use the technology to manipulate equations in order to better understand systems. Description: Students will be given a number of linear equations in different forms (standard form, point-slope form, slope-intercept form) and will be asked to use the graphing program to graph these equations two at a time (therefore creating a system of linear equations). The students can choose which two equations to graph together and will be asked to use the technology to find the point of intersection of the two lines for each system they create. Students can go through this activity at their own pace and play around with the graphing software to get a better understanding of systems of linear equations by manipulating the equations they already have. Students will then document their learning in the form of a blog post where other students can see and review their posts. Technology: This activity will require each student to have some form of technology (e.g., a laptop, a computer, iPad, etc.). It might also be beneficial for the teacher to have a laptop/projector or an IWB in order to demonstrate how to correctly work the software or input the equations. Students will also be required to have their own personal blogs where they can report their findings and comment on and critique the work of their peers. Rationale: The graphing method of solving systems of linear equations is a great method for using technology. Students are able to manipulate equations and see what happens when they simultaneously graph more than one linear equation in the coordinate plane. Giving students the hands-on activity where they are free to use the technology to explore the mathematics will benefit them more than just being shown how to graph systems and estimate the point of intersection of the lines. This activity allows for students to move at their own pace and take control of their own learning while the teacher takes more of a backseat role and is there to answer questions for the students. |