After learning about the Van Hiele Geometric Levels of Thinking- Where do you think you generally fit into this framework? How will you use this information in your instructional practice?
In terms of Van Hiele's Geometric Levels of Thinking, I believe that I generally fit into the framework at a Level 2- Informal Deduction. When observing shapes, I pay attention to relationships among each shape and among the classes for each shape. I tend to pay attention to the fact that each shape makes up a group of shapes such as a rectangle and square make up a parallelogram with right angles. I informally observe shapes and tend to make "intuitive observations about certain shapes as they organize known properties" such as vertices, faces, angles, etc.
In my instructional practice, I will use this information to assess children in their levels of thinking. I understand that each child learns differently, but in regards to geometry and mathematical processes, I can use this information to distinguish each student among each other in terms of their level of thinking. In addition, I can use this framework to help assess each student and his/her individual needs. I can also use the framework when determining what areas of the lesson may need additional practice.
Monday, October 25, 2010
Sunday, October 17, 2010
Week 8 Reflection Questions
1. What does the task presented in class (examining fair tests) compare to the content covered in chapter 11?
Chapter 11, Helping Children Use Data, states that the goal of Data Analysis and Probability Standards says that students should "formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them". The chapter addresses the importance of how data gathered by students will become more and more meaningful as the students formulate the questions that they want to ask. In class, the task that was presented on examining fair tests had each of us measuring our wrists. Each of us had to measure our wrists and engaged in discussion to develop questions pertaining to our wrists. This allowed each of us to contribute through discussion and formulate questions that could be addressed through the use of data. Throughout the task, we were given the challenge to collect data on how wide our wrist was around and how to graph each student's measurement. Throughout chapter 11, it states that "young children can learn about themselves" which is how the task presented in class can compare to that mentioned throughout chapter eleven. In class, we were able to learn about ourselves by measuring the width around our wrists. We used a familiar body part to compare by collecting data. We were then able to display the data by determing which measurement was the most common or by determining the mode of all of the measurements. The chapter discusses how questions should be designed for students to contribute data about themselves. This will help children see "who they are as a class and how each fits into the class as an individual".
2. What are you seeing related to data analysis and probability in your own classroom settings?
In my first grade classroom, the children had the opportunity to bring in their favorite apple. Each child brought in their favorite apple and had the opportunity to present it to the class. The characteristics of each apple were discussed such as the color, size, height, and weight. Students were given an opportunity to generate their own questions about each apple and the teacher recorded each question on chart paper. Afterwards, the teacher chose one of the questions to represent using a graph. The teacher chose color and had each child state the color of their apple. Each child was given a picture of an apple that was the same color as their favorite apple. The teacher presented a pictograph for the students to display the color of their favorite apple. Each student was given the opportunity to attach the picture of their apple color onto the graph. After all of the apples were graphed, the teacher asked the students a series of questions. The teacher discussed with the students which color seemed to be the class favorite and which color apple was the least favorite. Students were able to graph something that they could relate to; the color of their favorite apple. Students were also able to engage in discussion opportunities and participate in the graphing process.
3. Examining the SC early childhood content standards (k-3) for data analysis and probability. How do the state standards compare to chapters 11 and 12?
The SC early childhood content standards (k-3) for data analysis and probability are relatively similiar to the content presented throughout chapters 11 and 12. In each chapter, data analysis and probability are presented in a way that both build off of each other. Chapter 11 states that "at the k-3 level, students can begin this understanding of data analysis by learning how data can be categorized and displayed in various forms." Chapter 12 states that "probability instruction at the k-3 level involves confronting students with the outcomes of simple experiments and games and discussing the reasons for these outcomes." Both chapters inform students on how to gather data or categorize data in an organized way that also allows students to develop an intuitive understanding of chance and grasp how to display data in the "context of real questions". Students are able to grasp how to display data effectively through a graph and take probability concepts and display them appropriately. The standards seem to present the concepts of data analysis and probability appropriately for each grade level. Through each grade level, both concepts continue to build off of the previous year in an effort to expand student learning.
Chapter 11, Helping Children Use Data, states that the goal of Data Analysis and Probability Standards says that students should "formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them". The chapter addresses the importance of how data gathered by students will become more and more meaningful as the students formulate the questions that they want to ask. In class, the task that was presented on examining fair tests had each of us measuring our wrists. Each of us had to measure our wrists and engaged in discussion to develop questions pertaining to our wrists. This allowed each of us to contribute through discussion and formulate questions that could be addressed through the use of data. Throughout the task, we were given the challenge to collect data on how wide our wrist was around and how to graph each student's measurement. Throughout chapter 11, it states that "young children can learn about themselves" which is how the task presented in class can compare to that mentioned throughout chapter eleven. In class, we were able to learn about ourselves by measuring the width around our wrists. We used a familiar body part to compare by collecting data. We were then able to display the data by determing which measurement was the most common or by determining the mode of all of the measurements. The chapter discusses how questions should be designed for students to contribute data about themselves. This will help children see "who they are as a class and how each fits into the class as an individual".
2. What are you seeing related to data analysis and probability in your own classroom settings?
In my first grade classroom, the children had the opportunity to bring in their favorite apple. Each child brought in their favorite apple and had the opportunity to present it to the class. The characteristics of each apple were discussed such as the color, size, height, and weight. Students were given an opportunity to generate their own questions about each apple and the teacher recorded each question on chart paper. Afterwards, the teacher chose one of the questions to represent using a graph. The teacher chose color and had each child state the color of their apple. Each child was given a picture of an apple that was the same color as their favorite apple. The teacher presented a pictograph for the students to display the color of their favorite apple. Each student was given the opportunity to attach the picture of their apple color onto the graph. After all of the apples were graphed, the teacher asked the students a series of questions. The teacher discussed with the students which color seemed to be the class favorite and which color apple was the least favorite. Students were able to graph something that they could relate to; the color of their favorite apple. Students were also able to engage in discussion opportunities and participate in the graphing process.
3. Examining the SC early childhood content standards (k-3) for data analysis and probability. How do the state standards compare to chapters 11 and 12?
The SC early childhood content standards (k-3) for data analysis and probability are relatively similiar to the content presented throughout chapters 11 and 12. In each chapter, data analysis and probability are presented in a way that both build off of each other. Chapter 11 states that "at the k-3 level, students can begin this understanding of data analysis by learning how data can be categorized and displayed in various forms." Chapter 12 states that "probability instruction at the k-3 level involves confronting students with the outcomes of simple experiments and games and discussing the reasons for these outcomes." Both chapters inform students on how to gather data or categorize data in an organized way that also allows students to develop an intuitive understanding of chance and grasp how to display data in the "context of real questions". Students are able to grasp how to display data effectively through a graph and take probability concepts and display them appropriately. The standards seem to present the concepts of data analysis and probability appropriately for each grade level. Through each grade level, both concepts continue to build off of the previous year in an effort to expand student learning.
Subscribe to:
Comments (Atom)