Description of Implementation
Description of Implementation: Phase 2
Implementation, Data Collection and Analysis
I began Phase 2 by providing the students with a Pre-test. It was essentially a multiplication worksheet with 10 multiples numbers 6-9, in addition to space to do the work if necessary. The directions were as follows: “Solve for each problem. On the back, show me how to represent ONE (1) of these questions in two different ways. For example: explaining what this means in a sentence, drawing a picture/ diagram/ model, writing a word problem, etc.” These are very similar to directions the students have had on past worksheets that involved addition and each of the students I was working with were able to successfully solve the addition worksheets. I did not provide much outside help as I was looking for data that would give me a starting point of where to begin.
I knew some of these students had difficulty with multiplication, so I was not surprised by the data. Of the seven students, 1 student answered all 10 questions correctly, 5 students made between 2-4 errors, and 1 student made 5 plus errors. None of the students were able to correctly provide two correct ways of showing me how to explain the multiplication. Some attempted word problems, but they resembled addition statements instead of multiplication. Some tried to draw pictures, but they did not correctly represent the problems. I realized I would have to completely reteach and show them how to represent multiplication concepts. While this area of mathematics is not a standard for fifth grade, I believe it is an important stepping stone for understanding more complex math problems. By understanding and being able to explain multiplication problems, I am hoping this will make problem solving easier for my students.
I went onto teach 4 mini-lessons that dealt with concepts of multiplication. I used a poster activity that my students were excited to do. In the same manner of phase 1, the students did not feel as if they were participating in mathematics, but rather a fun activity. One student likened what we were doing to an art project. I was excited that this attitude towards the activity would enhance their understanding of the lesson on multiplication concepts. I had each student adopt a multiplication phrase at random, using numbers 6-9. They wrote this equation in the middle of their poster, and I explained that they would be using this expression for the remainder of the project.
The first mini lesson was on the Commutative Property. I had each student write the name of the property in the top left quadrant. We then discussed the definition, which I had written out onto a white board. My students then discussed how they could show their multiplication problem using the Commutative property, and then wrote it into the quadrant. I then showed the students how to create a fact family triangle using their equation, and the relationship between the numbers in the triangle. They students were all excited to get their information down on paper.
The second mini lesson was focused on the concept of Repeat Addition of multiplication. I showed them an example, using 6x9 as an equation: “6+6+6+6+6+6+6+6+6=6x9”. We discussed the idea of how multiplication is really just a way to describe 9 sets of 6, replacing 6 and 9 for the numbers in their equations. During this lesson, there were many “aha!” moments where students seemed to understand this particular idea.
Repeated addition led into the third mini lesson, which was looking at groups. I showed the students how to represent their equation in groups. Each student made a certain number of circles and then filled the circles with their necessary number of items. Some students used hearts, chocolate chips, and smiley faces. I then had the students write a statement about their groups. For example, using 6x9 the student would have written 6 groups of 9. We discussed how this related to repeated addition and the commutative property. I could tell they were adding to their foundation of Multiplication concepts.
The final mini lesson was on creating arrays. All of the students noted that they remember arrays from previous classes. I had each student create an array for their equation. Students noticed the relation without my prompting to the other concepts they had learned. I then had the students write statement for their arrays. For example, using 6x9, the students would have written “6 rows of 9”.
Once all lessons were completed, I had the students come up with a way to present their equation. I had each student come up with a word problem using their numbers. They then presented their posters and word problem to the group. The students did this verbally, and I recorded their word problems on the back of their posters. Each student came up with a correct word problem on the first try.
I then provided the students with a post test, using the same worksheet from the pre-test. This time around, 1 student made two errors, 2 students made one error, and 4 students made no errors on the multiplication problems. All students were able to illustrate and further define a way to show the problems, all using varying methods. I was very pleased with these results.
I provided a survey asking the questions detailed in my action and assessment plan for phase 2. Each student admitted on the survey that sometimes they are correct with multiplication and sometimes they have trouble. Some of the students thought that learning the concepts would help, but some said they weren’t sure how the concepts were helpful. Five of the students were able to correctly define multiplication, while two students only provided an example of an equation.
Results
Looking at my data, I realized that even with the concentrated instruction in multiplication concepts some of the students were going to make multiplication mistakes. However, I did notice a positive trend toward a higher comprehension in both the procedural and conceptual ability of my students. This was evidenced by the teacher notes I took during group work making the posters and subsequent results from both the survey and the post-test.
In the post-test, students made much fewer errors in the procedural computation of multiplication. Additionally, they were able to demonstrate a conceptual knowledge of the mathematics. I was able to see a definitive growth in their mindset and ability during Phase 2. Overall, the students grasped a better knowledge of both their procedural and conceptual after the instruction on different multiplication concepts.
Implementation, Data Collection and Analysis
I began Phase 2 by providing the students with a Pre-test. It was essentially a multiplication worksheet with 10 multiples numbers 6-9, in addition to space to do the work if necessary. The directions were as follows: “Solve for each problem. On the back, show me how to represent ONE (1) of these questions in two different ways. For example: explaining what this means in a sentence, drawing a picture/ diagram/ model, writing a word problem, etc.” These are very similar to directions the students have had on past worksheets that involved addition and each of the students I was working with were able to successfully solve the addition worksheets. I did not provide much outside help as I was looking for data that would give me a starting point of where to begin.
I knew some of these students had difficulty with multiplication, so I was not surprised by the data. Of the seven students, 1 student answered all 10 questions correctly, 5 students made between 2-4 errors, and 1 student made 5 plus errors. None of the students were able to correctly provide two correct ways of showing me how to explain the multiplication. Some attempted word problems, but they resembled addition statements instead of multiplication. Some tried to draw pictures, but they did not correctly represent the problems. I realized I would have to completely reteach and show them how to represent multiplication concepts. While this area of mathematics is not a standard for fifth grade, I believe it is an important stepping stone for understanding more complex math problems. By understanding and being able to explain multiplication problems, I am hoping this will make problem solving easier for my students.
I went onto teach 4 mini-lessons that dealt with concepts of multiplication. I used a poster activity that my students were excited to do. In the same manner of phase 1, the students did not feel as if they were participating in mathematics, but rather a fun activity. One student likened what we were doing to an art project. I was excited that this attitude towards the activity would enhance their understanding of the lesson on multiplication concepts. I had each student adopt a multiplication phrase at random, using numbers 6-9. They wrote this equation in the middle of their poster, and I explained that they would be using this expression for the remainder of the project.
The first mini lesson was on the Commutative Property. I had each student write the name of the property in the top left quadrant. We then discussed the definition, which I had written out onto a white board. My students then discussed how they could show their multiplication problem using the Commutative property, and then wrote it into the quadrant. I then showed the students how to create a fact family triangle using their equation, and the relationship between the numbers in the triangle. They students were all excited to get their information down on paper.
The second mini lesson was focused on the concept of Repeat Addition of multiplication. I showed them an example, using 6x9 as an equation: “6+6+6+6+6+6+6+6+6=6x9”. We discussed the idea of how multiplication is really just a way to describe 9 sets of 6, replacing 6 and 9 for the numbers in their equations. During this lesson, there were many “aha!” moments where students seemed to understand this particular idea.
Repeated addition led into the third mini lesson, which was looking at groups. I showed the students how to represent their equation in groups. Each student made a certain number of circles and then filled the circles with their necessary number of items. Some students used hearts, chocolate chips, and smiley faces. I then had the students write a statement about their groups. For example, using 6x9 the student would have written 6 groups of 9. We discussed how this related to repeated addition and the commutative property. I could tell they were adding to their foundation of Multiplication concepts.
The final mini lesson was on creating arrays. All of the students noted that they remember arrays from previous classes. I had each student create an array for their equation. Students noticed the relation without my prompting to the other concepts they had learned. I then had the students write statement for their arrays. For example, using 6x9, the students would have written “6 rows of 9”.
Once all lessons were completed, I had the students come up with a way to present their equation. I had each student come up with a word problem using their numbers. They then presented their posters and word problem to the group. The students did this verbally, and I recorded their word problems on the back of their posters. Each student came up with a correct word problem on the first try.
I then provided the students with a post test, using the same worksheet from the pre-test. This time around, 1 student made two errors, 2 students made one error, and 4 students made no errors on the multiplication problems. All students were able to illustrate and further define a way to show the problems, all using varying methods. I was very pleased with these results.
I provided a survey asking the questions detailed in my action and assessment plan for phase 2. Each student admitted on the survey that sometimes they are correct with multiplication and sometimes they have trouble. Some of the students thought that learning the concepts would help, but some said they weren’t sure how the concepts were helpful. Five of the students were able to correctly define multiplication, while two students only provided an example of an equation.
Results
Looking at my data, I realized that even with the concentrated instruction in multiplication concepts some of the students were going to make multiplication mistakes. However, I did notice a positive trend toward a higher comprehension in both the procedural and conceptual ability of my students. This was evidenced by the teacher notes I took during group work making the posters and subsequent results from both the survey and the post-test.
In the post-test, students made much fewer errors in the procedural computation of multiplication. Additionally, they were able to demonstrate a conceptual knowledge of the mathematics. I was able to see a definitive growth in their mindset and ability during Phase 2. Overall, the students grasped a better knowledge of both their procedural and conceptual after the instruction on different multiplication concepts.