Educational Psychology (Mathematics)

Psychology 2220
12/4/2012

Part One

Illinois standards for mathematics A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings. 1. Identify whole numbers and compare them using the symbols <, >, or = and the words “less than”, “greater than”, or “equal to”, applying counting, grouping and place value concepts. 2. Identify and model fractions using concrete materials and pictorial representations. B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships. 3. Solve one- and two-step problems with whole numbers using addition, subtraction, multiplication and division. C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers. 4. Select and perform computational procedures to solve problems with whole numbers. 5. Show evidence that whole numbers computational results are correct and/or that estimates are reasonable. D. Solve problems using comparison of quantities, ratios, proportions and percents. 6. Compare the numbers of objects in groups.

Standards Aligned Classroom Lessons 1. Represent and solve problems involving multiplication and division. Interpret products of whole numbers. 2. Represent and solve problems involving multiplication and division. Interpret whole-number quotients of whole numbers. 3. Represent and solve problems involving multiplication and division. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. 4. Represent and solve problems involving multiplication and division. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. 5. Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. 6. Understand properties of multiplication and the relationship between multiplication and division. Understand division as an unknown-factor problem. 7. Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. 8. Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 9. Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Part Two

There are three instructional goals that I have for my lesson plan. 1. By the end of my lesson, I would like my third graders to be able to multiply and divide on their own. This meaning that they will be able to do these tasks without the help of a teacher or a parent. They will be able to multiply and divide in their heads without the use of paper and pencil. They will also be able to do this without the use of a calculator. The only calculator they will be using is their brain.

2. During my lesson plan, they will also be learning the concepts behind multiplication and division. One way I can explain to the children is to write out, for example, 3 + 3 + 3 + 3 = 12. This will not only help the kids to review addition but this will also show them that there is a faster way to solve 3 + 3 + 3 + 3 by the means of multiplication. I will show them that 3 x 4 = 12 by having 3 rows and 4 columns using balls. You can have 3 groups of 4 balls together or 4 groups of 3 balls together and they will arrive at the same exact answer. This will help them visualize what 3 x 4 looks like.

3. There are several things I plan on doing when it comes down to learning experiences and instructional activities. There’s a game of “around the world” is where there are flashcards with multiplication and division problems are on them. I will be holding these flashcards and showing it to two students at a time. One student will be on the move as the other student is sitting in his or her seat. Whoever gets the correct answer gets to stand and move “around the world”, as in go around the classroom and the winner gets a prize. This is not only fun for the students but this can help the students to practice on how to get better and faster at solving these problems.

Another activity that comes to mind is a school project. This project will be assigned as soon as they know how to multiply and divide on their own. This project is called “be a teacher for a day” project. This is where the students can be the teacher and they have to be able to stand in front of a group of crowd that does not know anything about multiplication and or division and be able to teach them how to do so. This includes the explanation of what a whole number is, what a multiplication symbol looks like, and etcetera. This is both beneficial to me as a teacher and to the student. This is beneficial to me because I will be able to know who knows how to multiply and divide and be able to focus on the students that have trouble with the subject. This is beneficial to the student because they will learn how to teach and be creative with their project as well. This will also help me to know how the students learn and how they attack the problem.

Part Three

I will definitely be using the most common type of assessment geared towards mathematics which is the paper-pencil assessment. This is very critical to mathematics because as they go to higher levels of math, it is required for them to show work. For example, when they get to geometry, which is a whole different world of math compared to algebraic math, they need to write a proof for a triangle being isosceles, or a proof for two sides being equivalent. If they do not practice using paper and pencil they will never be able to show work properly. Another example of showing your work is in Algebra. If there is a problem given such as, 2x + 5 = 11, the students need to learn how to get to x = 3. If they just write x = 3 on the test, we as teachers will not know how they have gotten to that solution. Another reason why it is so critical for students to learn to write everything out is that as teachers we don’t know if the student understands the concept or if he or she is just randomly guessing the answers.

Another assessment I will be using is a Performance Assessment. As I stated earlier, I will be playing a game with the students called “Around the World”. This is an example of a Performance Assessment. This is where the students demonstrate their abilities without paper and pencil. This also shows me as a teacher and the student how much they can do using mental math. This will also help them to know how fast they can solve these problems without the help of the teacher and students.

Another assessment I may consider using is Authentic Assessment. This will contain real life scenarios with basic addition and subtraction on there so this will test their whether they are true masters of basic mathematical calculations such as addition and subtraction. One example is,

“Tara and Doug have a total of twenty apples. If Doug takes eight apples, how many apples does Tara have left?”

This assessment will also contain multiplication and division questions that are used in real-life situations. These types of problems will help both the student and the teacher that they are able to use these concepts outside of the classroom use. An example of a multiplication problem would go something like this,

“Hannah and David are getting married today, and they are trying to fit about 300 people for their wedding reception. The room for their wedding reception can only fit about 40 tables. Each table can fit eight people. Will they have enough room for 300 people for their wedding reception?”

Part Four

Dear ____’s Parent/Guardian:

I am here to inform you that as the teacher of your son or daughter, he or she will be learning how to multiply and divide in class. By the end of this year they will be able to multiply and divide on their own. This will be accomplished through assessments and activities distributed in class. One of the activities will be called “Around the world” where I will be holding flashcards with multiplication and division problems so that they will be able to answer these questions through mental math rather than paper and pencil. I will be holding these flashcards and showing it to two students at a time. One student will be on the move as the other student is sitting in his or her seat. Whoever gets the correct answer gets to stand and move “around the world”, as in go around the classroom and the winner gets a prize. This is not only fun for the students but this can help the students to practice on how to get better and faster at solving these problems.

Another activity that I will be distributing is a project called “be a teacher for a day”. This is where the students can be the teacher and they have to be able to stand in front of a group of crowd that does not know anything about multiplication and or division and be able to teach them how to do so. This includes the explanation of what a whole number is, what a multiplication symbol looks like, and etcetera. This is both beneficial to me as a teacher and to the student. This is beneficial to me because I will be able to know who knows how to multiply and divide and be able to focus on the students that have trouble with the subject. This is beneficial to the student because they will learn how to teach and be creative with their project as well. This will also help me to know how the students learn and how they attack the problem.

During my lesson plan, they will also be learning the concepts behind multiplication and division. One way I can explain to the children is to write out, for example, 3 + 3 + 3 + 3 = 12. This will not only help the kids to review addition but this will also show them that there is a faster way to solve 3 + 3 + 3 + 3 by the means of multiplication. I will show them that 3 x 4 = 12 by having 3 rows and 4 columns using balls. You can have 3 groups of 4 balls together or 4 groups of 3 balls together and they will arrive at the same exact answer. This will help them visualize what 3 x 4 looks like.

Each child will receive an achievement test score through each assessment I will distribute to them. These scores will help me as a teacher to see where each student lies within the distribution amongst the children in my class. Each test score will be a number and it will then be graphed on a distribution.

These scores will be obtained through paper-pencil assessment and authentic assessment. Paper-pencil assessment is where the students have problems on paper and they have to work through the problems by showing their work. An authentic assessment is where they use the multiplication and division in real-life problems. These will then be grades by me and will then be calculated into their achievement test score.

There will be three different categories: below average, average and above average. For the students that is in the below average category, I will keep an eye on them and try to help them through the process. For the students that are in the average category, they are at the level of an average third grader. For the students that are in the above average category, I will likely challenge them with more challenging work through homework.

If you have any questions or concerns, please do not hesitate to give me a call.