Geometry

Here is your reflection question for the week:

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?

After learning about the Van Hiele Geometric Levels of Thinking, I think I generally fit into Level 2: Informal Deduction. I can see relationships between shapes and recognize that some shapes are "subclasses of other shapes." I remember a significant portion of the vocabulary that I have been taught about geometry and shapes. I am able to determine relationships between shapes using the information I know about their properties.

I will use this in instructional practice by pointing out similarities and differences between shapes. I will try to guide students to think about relationships between shapes. For example, I might ask what a square and a rectangle have in common (equal angles) and what they have different (length of sides). I will assess what level of thinking students are in and will determine my instruction to meet their understanding. When students are in Level 0, I will begin to gradually introduce vocabulary and provide 3-D manipulatives. When students are in Level 1, I will also introduce ideas about relationships to help students begin to think about concepts that are understood in the 2nd level. I will use the Van Hiele Geometric Levels of Thinking to guide my instructional practice in mathematics. By using this system, I can determine what students understand about shapes and I can guide them to more complex understandings.

Chapters 11 & 12

Chapters 11 and 12 deal with content related to data analysis and probability.

1. How does the task presented in class (examining fair tests) compare to the content covered in chapter 11?

The task presented in class where we measured our wrists is suggested in Ch. 11, because each student got to contribute "one piece of data." The task presented in class was also a comparison, because we compared our wrist circumferences. We discussed that we could make a bar graph from the measurements we obtained. Chapter 11 also discusses Descriptive Statistics, which we related to our task in class. We determined the range of our wrist measurements, the average wrist circumference, the mode, and the median. We discussed what these terms meant and how we determined them.

2. What are you seeing related to data analysis and probability in your own classroom settings?

The Kindergarten class I am in incorporates data analysis and probability into daily activities. The class uses a bar graph to analyze weather conditions. There are about 5 different weather categories that students can pick from to add on to the graph every day. Then the class counts how many are in the selected conditions and determines which weather occurs the most frequently for that month. Bar graphs were also recently used to compare which type of apple students preferred. They could choose between 3 varieties and stacked an apple picture above their selection. Cluster graphs are also used in my Kindergarten classroom. For example, during a science lesson, students sorted items into two categories on the SmartBoard: "living" and "not living." I have not seen too much related to probability yet. The teacher does ask some questions to introduce students to the idea of probability, such as: "Juice and Popsicles are both offered at lunch today but you can only take one. So if you take a juice, can you take a Popsicle too?" The class also sometimes determines whether or not something is likely to happen, similar to Activity 12.1. For example, during weather, the teacher may ask students in August if it's likely to snow tomorrow.

3. Examine 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 for data analysis and probability are directly related the concepts found in chapters 11 and 12. The Kindergarten standard states that "The student will demonstrate through the mathematical processes an emerging sense of organizing and interpret data." In chapters 11 and 12, different ways to organize data, such as bar graphs and cluster graphs, are described. In the text, there are also assessment suggestions that suggest how the teacher can guide students towards interpreting data. For example, the teacher may ask the students to explain what their graph tells them. The first grade standard, which states is the same as the Kindergarten standard with the addition that the student will "make predictions on the basis of data." Probability is related to making predictions. Determining whether the likelihood of something is "certain, impossible, or possible" is a probability concept. When students determine the likelihood of an event, they are also making a prediction about whether or not it will happen. The standard for 2nd grade has the same core as the K and 1st, with the addition of that the student will describe trends of a data set. After students begin to make their own graphs, as described in Ch. 11, they can analyze the information and eventually observe trends and patterns.