Phase 2: Action and Assessment Plan
Intervention and Rationale
For this study, I will be looking at how to teach multiplication procedures and concepts to my students. Based on the availability within my current classroom, I will be teaching a group of seven fifth graders during my second phase. Again, I will be teaching the students math in a different manner from their regular instruction, which is taught in individualized math contracts that provide content beneficial to their ability in math. I am interested in exploring their procedural and conceptual ability with multiplication because I believe it is a roadblock for my students as they are moving forward in more challenging mathematical curriculum, and especially as they begin to work through different multi-step math inquiry problems. I would like to provide instruction that is centered on how to utilize the concepts of multiplication in order to facilitate their procedural ability.
As I am progressing in my research, I have found that I am experiencing a narrowing of my topic versus a broader generalization. Instead of focusing on a multi-step math inquiry to test for procedural or conceptual ability, I will be targeting a single area with instruction. I want to see if students can learn multiplication by learning how to conceptualize the mathematics to aide in their ability of the procedures.
During this phase, seven of the fifth grade students in my classroom will be participating in interactive math activities where instruction and guided practice will be closely monitored and executed. They will be learning how to conceptualize multiples of numbers 6-9, which I informally assessed as the areas that students could use the most practice. The students will all work in a large group, with periods of either small group or partner talk to discuss ideas. I will use a small whiteboard to model concepts as we discuss them.
The lessons will consist of breaking down the multiplication procedures into concepts that can be interactively discussed with the students. I will be addressing:
· The definition of multiplication: I chose to do this first because I feel this is the most basic concept of multiplication. I will be defining the terms “product” and “factor”, and in the process develop an academic conversation on multiplication and what it means to multiply.
· The concept of grouping: I will begin by defining that a multiplication statement such as 6 X 8 = 42, and explains that it means 6 groups of 8. I will then go on to discuss how paralleling this equation into groups of (6 X 4 = 24) + (6 X 4 = 24), and then so on to (6 X 2 = 12) + (6 X 2 = 12) + (6 X 2 = 12) + (6 X 2 = 12). I want them to understand the idea of how multiples of the same number relate to one another.
· The ways to show multiplication: The third lesson will focus on a culmination of how we conceptualize. I will focus on the commutative property, arrays, grouping, fact family triangles, and repeated addition. I will have the students each create a small poster using manipulatives and markers, each representing a 6-9 multiplication equation. We will then share aloud the posters and discuss real life examples of the multiplication.
Throughout these lessons, I will be constantly checking for understanding as they go along. Again, I will slow down and help explain concepts further when necessary. Additionally, I will teach interactively in order to maximize modeling and conceptualization for students.
Data Collection and Assessment Methods
During this project I will collect (1) a pre- and post- test to determine understanding at different times of the implementation, (2) observations of student work through means such as physical examples and a teacher journal, and (3) student survey to assess student’s perception of how well they did and how they felt about the type of mathematical reasoning they were doing. I chose these tools because I feel that they will be effective in helping me monitor the implementation of math inquiry in the classroom.
Pre- and post- test: I will use the pre-test as a baseline for their understanding in areas that are relative to the multiplication. I will have the students solve for a list of 6-9 multiples. Then they will choose one question and illustrate two ways to show me how they solve this problem. After Phase 2 Implementation, I will then provide a post-test similar to the pre-test that will determine the academic outcomes of teaching math as an inquiry project and what type of effect the project had on their computational abilities.
Observations: At the end of their project, I will have worksheets and final posters as examples of students work. I will be using these samples to assess how well the students applied their computational and procedural ability for multiplication. I will also be looking at the student work to determine how effective the conceptualization was as providing a platform to work towards improving procedural abilities.
Additionally, I will be using a Clip-board approach to make notes on the things I observe during implementation. I will be observing the errors they make, their challenges and successes, and the different areas they become stuck on. This will provide me the ability to connect with all students and hopefully make the lessons as comprehensible as possible.
Survey: At the end of the beginning and culmination of Phase 2, I will give the students a survey to monitory three things:
• How the students feel they are at multiplication (strengths and weaknesses)
• Why is it either easy or hard?
• Does learning the concepts help?
• Can they define a multiplication equation?
I want to understand their points of view on the inquiry project and also see what their perception of themselves in math is like.
I will assess student learning based on their ability to perform during the math lessons and on the post-test assessment. The post-test will allow me to see if they can improve their procedural ability by creating a better conceptualization of multiplication.
For this study, I will be looking at how to teach multiplication procedures and concepts to my students. Based on the availability within my current classroom, I will be teaching a group of seven fifth graders during my second phase. Again, I will be teaching the students math in a different manner from their regular instruction, which is taught in individualized math contracts that provide content beneficial to their ability in math. I am interested in exploring their procedural and conceptual ability with multiplication because I believe it is a roadblock for my students as they are moving forward in more challenging mathematical curriculum, and especially as they begin to work through different multi-step math inquiry problems. I would like to provide instruction that is centered on how to utilize the concepts of multiplication in order to facilitate their procedural ability.
As I am progressing in my research, I have found that I am experiencing a narrowing of my topic versus a broader generalization. Instead of focusing on a multi-step math inquiry to test for procedural or conceptual ability, I will be targeting a single area with instruction. I want to see if students can learn multiplication by learning how to conceptualize the mathematics to aide in their ability of the procedures.
During this phase, seven of the fifth grade students in my classroom will be participating in interactive math activities where instruction and guided practice will be closely monitored and executed. They will be learning how to conceptualize multiples of numbers 6-9, which I informally assessed as the areas that students could use the most practice. The students will all work in a large group, with periods of either small group or partner talk to discuss ideas. I will use a small whiteboard to model concepts as we discuss them.
The lessons will consist of breaking down the multiplication procedures into concepts that can be interactively discussed with the students. I will be addressing:
· The definition of multiplication: I chose to do this first because I feel this is the most basic concept of multiplication. I will be defining the terms “product” and “factor”, and in the process develop an academic conversation on multiplication and what it means to multiply.
· The concept of grouping: I will begin by defining that a multiplication statement such as 6 X 8 = 42, and explains that it means 6 groups of 8. I will then go on to discuss how paralleling this equation into groups of (6 X 4 = 24) + (6 X 4 = 24), and then so on to (6 X 2 = 12) + (6 X 2 = 12) + (6 X 2 = 12) + (6 X 2 = 12). I want them to understand the idea of how multiples of the same number relate to one another.
· The ways to show multiplication: The third lesson will focus on a culmination of how we conceptualize. I will focus on the commutative property, arrays, grouping, fact family triangles, and repeated addition. I will have the students each create a small poster using manipulatives and markers, each representing a 6-9 multiplication equation. We will then share aloud the posters and discuss real life examples of the multiplication.
Throughout these lessons, I will be constantly checking for understanding as they go along. Again, I will slow down and help explain concepts further when necessary. Additionally, I will teach interactively in order to maximize modeling and conceptualization for students.
Data Collection and Assessment Methods
During this project I will collect (1) a pre- and post- test to determine understanding at different times of the implementation, (2) observations of student work through means such as physical examples and a teacher journal, and (3) student survey to assess student’s perception of how well they did and how they felt about the type of mathematical reasoning they were doing. I chose these tools because I feel that they will be effective in helping me monitor the implementation of math inquiry in the classroom.
Pre- and post- test: I will use the pre-test as a baseline for their understanding in areas that are relative to the multiplication. I will have the students solve for a list of 6-9 multiples. Then they will choose one question and illustrate two ways to show me how they solve this problem. After Phase 2 Implementation, I will then provide a post-test similar to the pre-test that will determine the academic outcomes of teaching math as an inquiry project and what type of effect the project had on their computational abilities.
Observations: At the end of their project, I will have worksheets and final posters as examples of students work. I will be using these samples to assess how well the students applied their computational and procedural ability for multiplication. I will also be looking at the student work to determine how effective the conceptualization was as providing a platform to work towards improving procedural abilities.
Additionally, I will be using a Clip-board approach to make notes on the things I observe during implementation. I will be observing the errors they make, their challenges and successes, and the different areas they become stuck on. This will provide me the ability to connect with all students and hopefully make the lessons as comprehensible as possible.
Survey: At the end of the beginning and culmination of Phase 2, I will give the students a survey to monitory three things:
• How the students feel they are at multiplication (strengths and weaknesses)
• Why is it either easy or hard?
• Does learning the concepts help?
• Can they define a multiplication equation?
I want to understand their points of view on the inquiry project and also see what their perception of themselves in math is like.
I will assess student learning based on their ability to perform during the math lessons and on the post-test assessment. The post-test will allow me to see if they can improve their procedural ability by creating a better conceptualization of multiplication.