Developing Students ' Mathematical Understanding

What effect did your teaching strategies have in terms of promoting student learning and keeping your students meaningfully engaged? (APS 5.A–C)

Engaging students in the classroom can be a difficult task. Understanding the process of how students learn can help a teacher adapt the lesson to meet the needs of all students. I will encounter students that are not intrinsically motivated so I will need to find different ways to motivate each and every student. Understanding how my students learn can provide me with insights as to how to help each student learn which will minimize classroom management problems.

The math concepts taught in this lesson are teaching the students how to use certain math formulas, and practice addition and multiplication. It is beneficial for students to know what tools to use for capturing and displaying information that is important to them (Davis, 2011). The science concepts taught in this

1 Using addition and substation within 20 to solve word problems involving situations of adding, taking from putting together, taking apart and comparing, with unknowns in all positions, e.g., by using objects, drawing, and equation with a symbol for unknown number to represent the problem.

At: Students at grade level will be expected to complete 6-8 of the three digit addition problems during the provided activity time. At grade level students will be expected to use at least one of the provided strategies to solve for the sum. Students who finish early will be asked to draw a picture or write and explanation of the strategy/strategies they used to find the sum. The teacher will direct students who are early finishers to complete this task individually. Slow finishes will be provided with three, two-digit addition problems

In order to successfully connect the data and the Focus Document, I have found a lesson that helps the students work with a variety of skills that they will need to know and work on. The lesson that I have chosen is adding and subtracting within 20. The objective for this lesson is to help students make a ten to add and subtract within 20. This lesson portrays a few of the

This is one unit in a yearlong 6th grade math course. In this unit, the students will learn about expressions and equations. Students will learn how letters stand for numbers, and be able to read, write, and evaluate expressions in which these letters take the place of numbers. In this unit, students will learn how to identify parts of an expression using various new terms. They will learn to solve both one- and two-step equations. Students will be able to distinguish between dependent and independent variables. They will be able to identify the dependent and independent variables of equations and in turn, be able to graph them. Various activities to be completed inside and outside of the classroom will be used to show

Throughout this year I have been given various amazing opportunities for professional development. Being a reading anchor classroom has given me a variety of opportunities to complete professional development. Two of the most impactful pieces of professional development that I received were, training on the architecture of a mini lesson and creating a demonstration notebook. These two pieces have significantly helped me to increase student engagement for my whole class as well as in small groups and individual conferences. I have also worked very hard to consistently be aware of the level of engagement in my classroom. When I notice students aren't engaged I try to change my approach in order to increase engagement. After a math observation

|Three ESL students- Reduce wordings on number labels and instead use digits to encourage ease of understanding |

According to Piaget’s theory of cognitive development, 4th graders between the ages of 9 and 10 are primed to begin exercising more complex logical conceptualizations of knowledge. To illustrate, one of his basic assumptions includes the idea that by this age group -- they should be able to generate (construct) and analyze patterns (Ormrod, 2017, 29). This is evidenced as their thought processes are organized into larger systems of mental processes and operations that allow them to conceptualize information in more logical or “adult-like” manner. Furthermore, the content presented in this lesson is appropriate for this age group of students by virtue of the idea that though they are not keen to the purposes of double-digit multiplication in real life/authentic settings -- they are starting to mature and will be more eager/ready to learn more advanced concepts (Ormrod, 2017, 31). Finally, we perused the Georgia State Standards of Excellence’s guide for instruction in fourth grade. Our lesson was based upon the following two standards:

1. Describe the content focus of the selected lesson and its importance in the overall context of the content area. (Rubric 1.2 B)

Good Moring class, today we are going to be learning about how to add with a number line. Raise you hand if you have ever used a number line to add? If not that perfectly acceptable because after today, you will know how! Your I can statement for to is “I can add numbers using a number line.” We will start out with a demonstration of a number line and vocabulary, then we will use our bodies to understand number lines, we will practice and then you all will complete a worksheet independently. Let get our thinking caps on and get ready to work hard! Teacher will play a video of the jumping jelly bean which demonstrates how to use the number line to add. After the video is complete the teacher will draw a number line and an equation. The teacher will tell students that a number line had arrows at each end, and dashes along it to show where each number goes. The number line will go to 20. The teacher will explain that 4+8= is an addition equation and that each number is called an addend, the + and = are signs and the answer is the sum. The teacher will then demonstrate how to use the number line to add two addends. Once this is complete students will line up to go outside.

Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.

Keeping students engaged and on task can be, at times, the most difficult part of being a teacher. You have to come up with new ways to engage them and keep them focused on learning, especially at the end of the day when all they can think about is going home.

Communication of mathematical ideas - Students learn the proper terminology associated with Math concepts and demonstrate their understanding in multiple ways (verbally, written, with the use of manipulatives, etc) I would give the students opportunities everyday to practice mathematical concepts verbally and in written form. Students could work on a problem and then go up to the SmartBoard to show what they did using the correct terminology.