Analysis of Learners
General Characteristics
This lesson was designed to be used in an 8th grade mathematics classroom. A typical 8th grade classroom will consist of approximately 30 students age 13 to 14 years old. In any classroom, there will likely be a mix of students of varying races and differing ethnic backgrounds. I will use my teacher assisting classroom as a sample classroom for this lesson. In the class, there were 17 boys and 12 girls in the classroom. 10 of those students were Caucasian, 11 were African American, 6 were Hispanic, and 2 were Asian. There were also two students with mild forms of Autism, two students with Reading Learning Disorders, and three English Language Learners (ELL).
As is the case in any middle school mathematics classroom, many of the students show low motivation levels and low achievement in mathematics. Students appear to be most motivated when the material they are working with is engaging and they can see a direct connection with the mathematics and how it can be used in real life. They also become more motivated when they are given the chance to use hands-on tools and share their experiences with their peers. More about these general characteristics can be found here.
Entry Competencies
This lesson is aligned with the 8th grade Common Core Mathematics Standards. Students should have a large bank of prior knowledge from previous grades that will help them in the current lesson. Here is a list of some of the prior knowledge that students should possess before coming into the current lesson:
Learning Styles
Middle school students tend to not have very long attention spans, especially when it comes to learning mathematics. The lesson I have created will break students' learning activities up to make them shorter and more manageable in the hopes that they will be as engaged as possible in the activities. Some of the tasks will require students to move around throughout the class period. Other activities will require students to get out of their seats from time to time and work with their peers to accomplish something. This is done in order to break the monotony of sitting through one class period the entire time. Students will be moving around periodically and collaborating with their peers, not doing some boring drill and practice problem at their desks.
Middle school students, and students in general, need a fair amount of guidance when it comes to learning. I can't just give an activity to a student and tell them to go learn. They must experience some form of modeling or demonstration before they are expected to be able to work on it on their own. With this in mind, many of the activities that are included in this activity begin with the teacher (or someone in a video) modeling how to perform the mathematical operations and then gradually giving students more responsibilities. This is known as gradual release of responsibility. For example, in one of my more teacher-centered lessons, I will begin by first modeling the steps of the elimination method for solving systems of linear equations. After the presentation that I give, I will then be giving students practice problems that we will go through together as a group. Then I will give students more control by working independently on practice problems. In this way I am first giving students the tools they need to work independently and when they have shown that they are capable, I will hand over control to them.
Many students are motivated by an external reward in the classroom which usually at the middle and high school level is a grade. Students put forth their best effort when they know they are going to be given a grade. I want students to move away from that mindset and instead be motivated intrinsically. By giving students more control and letting them work with peers, the hope is that the students will shift their motivation from wanting a good grade to instead wanting to do well in order to contribute to their own understanding and the understanding of their students. By allowing students to express their learning in a variety of ways (in a blog, through a video, etc.) these lessons will hopefully help students become more internally motivated.
This lesson was designed to be used in an 8th grade mathematics classroom. A typical 8th grade classroom will consist of approximately 30 students age 13 to 14 years old. In any classroom, there will likely be a mix of students of varying races and differing ethnic backgrounds. I will use my teacher assisting classroom as a sample classroom for this lesson. In the class, there were 17 boys and 12 girls in the classroom. 10 of those students were Caucasian, 11 were African American, 6 were Hispanic, and 2 were Asian. There were also two students with mild forms of Autism, two students with Reading Learning Disorders, and three English Language Learners (ELL).
As is the case in any middle school mathematics classroom, many of the students show low motivation levels and low achievement in mathematics. Students appear to be most motivated when the material they are working with is engaging and they can see a direct connection with the mathematics and how it can be used in real life. They also become more motivated when they are given the chance to use hands-on tools and share their experiences with their peers. More about these general characteristics can be found here.
Entry Competencies
This lesson is aligned with the 8th grade Common Core Mathematics Standards. Students should have a large bank of prior knowledge from previous grades that will help them in the current lesson. Here is a list of some of the prior knowledge that students should possess before coming into the current lesson:
- Students should have a good understanding of what linear equations are and what they look like (graphically, in a table, in an equation, etc.)
- Students should be able to manipulate an equation of one variable in order to solve for the other variable (e.g., solve the equation 3x+y=4 for x).
- Students should be able to graph linear equations by hand and using some form of technology (such as a graphing calculator or a graphing software such as Geogebra).
- Students should be able to work with tables and graphs to identify the intersection of lines and what they mean in the context of the problem.
- Students should understand the basics of a computer and the internet
- Students should be able to run math-specific software such as Geogebra or Desmos
- Students should know the basics of Microsoft Office and/or Google Drive.
- Students should know how to post and comment on a blog.
Learning Styles
Middle school students tend to not have very long attention spans, especially when it comes to learning mathematics. The lesson I have created will break students' learning activities up to make them shorter and more manageable in the hopes that they will be as engaged as possible in the activities. Some of the tasks will require students to move around throughout the class period. Other activities will require students to get out of their seats from time to time and work with their peers to accomplish something. This is done in order to break the monotony of sitting through one class period the entire time. Students will be moving around periodically and collaborating with their peers, not doing some boring drill and practice problem at their desks.
Middle school students, and students in general, need a fair amount of guidance when it comes to learning. I can't just give an activity to a student and tell them to go learn. They must experience some form of modeling or demonstration before they are expected to be able to work on it on their own. With this in mind, many of the activities that are included in this activity begin with the teacher (or someone in a video) modeling how to perform the mathematical operations and then gradually giving students more responsibilities. This is known as gradual release of responsibility. For example, in one of my more teacher-centered lessons, I will begin by first modeling the steps of the elimination method for solving systems of linear equations. After the presentation that I give, I will then be giving students practice problems that we will go through together as a group. Then I will give students more control by working independently on practice problems. In this way I am first giving students the tools they need to work independently and when they have shown that they are capable, I will hand over control to them.
Many students are motivated by an external reward in the classroom which usually at the middle and high school level is a grade. Students put forth their best effort when they know they are going to be given a grade. I want students to move away from that mindset and instead be motivated intrinsically. By giving students more control and letting them work with peers, the hope is that the students will shift their motivation from wanting a good grade to instead wanting to do well in order to contribute to their own understanding and the understanding of their students. By allowing students to express their learning in a variety of ways (in a blog, through a video, etc.) these lessons will hopefully help students become more internally motivated.