Measurement Article

Perimeter: Which Measure is it?

1. What are the main points of the article?

• including measurement in mathematics curriculum in k-12 classrooms
• students use different techniques and approaches to solve problems related to perimeter and area
  
• sometimes students do not completely grasp a concept well enough to apply it to real life situations
• students need to examine the concept of area and perimeter simultaneously to clearly distinguish between the two
• the tasks should be meaningful
  
• just applying formulas to perimeter and area problems does not help students to understand the difference between the two
  

2. How does your article connect to early childhood?

This article connects to early childhood because it can be applied to early childhood concepts. Just because students know how to solve a problem does not mean they actually completely understand the concept and can apply it to other contexts or real life situations. Teachers must know that students compute answers using different methods and approaches, too. Solely applying formulas and not knowing exactly why they are applying the formulas is basically useless for the students to know how to apply the concept and how to use their knowledge to apply it to real life situations.

3. What did you learn from the article that will help you as you teach measurement?

I learned that teaching area and perimeter simultaneously can really help students to know the difference between the two and maybe help the students to apply the concepts to real life situations. Students do not just need to apply formulas to find solutions. When students have experience confronting the concepts in meaningful ways, the students can grasp the concept better. I will also keep in mind that students use different approaches as to how they will find solutions, so staying open minded to their methods will be important.

Week Nine: Geometry

After learnining 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?

I generally fit into the Level 3 of the Van Hiele framework. Geometry is honestly not my favorite part of math. I think several not-so-positive experiences in geometry have influenced the way I feel about geometry. I hope to help my students develop an appreciation for geometry rather than them feel the way I do about geometry. I understand most concepts of geometry, but that does not mean I truly appreciate the subject.

In my instructional practice I will make an extra effort to research and learn more about fun and meaningful activities for students in my early childhood classroom. Increasing my knowledge of geometry will help me better teach my students concepts of geometry. Making geometry meaningful and encouraging challenging experiences will help students to become more interested in geometry, hopefully giving students a chance to grow to level 4 of the Van Hiele framework.

Week Eight Reflection: Chapters 11 and 12

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

The task presented in class is parallel with the content covered in chapter 11. Chapter 11 mentions most of the practices and ideas we presented in class. In class and in the chapter, students are encouraged to contribute data about themselves. When children contribute data about themselves, it makes the data relevant to them, I think it makes things easier for them to understand. They also have a chance to realize that the information is coming from a familiar population, and they learn about themselves and their peers in the process. We also created a table and could have made a graphical representation of the data that we found. In class we used different methods to measure our wrists. The whole class was given a chance to decide what we would use to measure, how we would measure, which wrist we would measure, and other important aspects of the experiment to make sure all data was consistent among everyone. The ideas that were presented in class and the ideas in Chapter 11 were very similar and consistent.

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

In my third grade classroom, my teacher uses graphs and tables every day. Every day the students have a math review at the beginning of the day for standardized testing purposes. Each day the students have a portion where they analyze data in a table or graph or they have a portion about simple probability. My teacher also records the reading stamina of students during reading time by graphing the progress or lack of progress on a bar graph. The bar graph is displayed in the room so that students can refer to how they are progressing in reading stamina times throughout the year.

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 state standards and Chapters 11 and 12 are similar. Under the state standards students are expected to: interpret, analyze, and organize data, make graphical representations, demonstrate and understanding of simple probability, and make educated predictions about data. Each grade level builds off of the previous grade level's indicators. The concepts and lesson ideas require students to do all of the above. The suggestions in Chapters 11 and 12 are helpful and relevant to the South Carolina mathematics standards for data analysis and probability. The lesson ideas and concepts found in the chapter can be adapted appropriately to specific grade levels and appropriate indicators.

Chapter 3 Reflection

What are the key ideas presented in chapter 3?

• connecting meanings and relationships to addition, subtraction, multiplication, and division
• addition and subtraction are connected
• subtraction names a missing part
• addition names the whole in parts
• multiplication takes counting in groups, multiplication is repeated addition
• multiplication and division are connected
• division names a missing factor
• models can be used to solve any mathematical problem
• models can be used with any problem or any number size
• you can use models to make number sentences make sense

How do these ideas inform your understanding of teaching numbers and operations?

The ideas set a foundation and give a deeper meaning and understanding to teaching numbers and operations. The chapter also metioned that addition is not "put together" and subtraction is not "take away". As a teacher I must remember that children should not have limited definitions or understandings for addition and subtraction because later they will have trouble understanding that addition and subtraction can be used in different forms. Connecting problems to children's lives and keeping the problems in context is very important. The ideas presented in chapter 3 helped open my eyes to new and different ways to solve math problems other than the traditional ways I learned. I must keep in mind that the children do not have the mathematical skills that I have developed, and solving problems in different ways and thinking about different ways to solve problems can help me facilitate students more efficiently. I liked how the text highlighted avoiding key words. When I was in elementary school, I was always taught to look for key words. After reading the explanations as to why key words should be avoided, I now understand why I should not stress using key words. Problem analysis and explanations are very important in mathematical processes. Explanations can be particularly helpful in understanding why a student solved a problem a certain way or how he or she got an answer to a problem.

Week Three Reflection

Your reflection question for this week relates to chapter 2. How does the information and the tasks presented in chapter two connect to the videos of lessons you viewed as part of challenge 5?

Much of the information and tasks presented in chapter 2 have to do with subitizing and quick number recognition. The tasks allow for math tools to be used. The tasks also allow for exploration and independent problem solving for all students. The tasks require more than just talking about numbers; they require children to analyze numbers and objects and compare them. The ideas and tasks presented provide a foundation for mathematical processes that can be used with larger numbers and computation of numbers.



What task (activity) in chapter two was most interesting to you? Why?

I liked activity 2.9 the Dot Plate Flash because the dot plates seem like they would be easy to make and use. Students could make their own and drill each other in a center to help develop pattern recognition skills. The dot plates can be used at any time of the year and any time during the day. They require little clean up and would not be a distraction to others if others were working on something different.

Week Two Reflection

How did each article help further your understanding of your topic area?

subitizing-instantly seeing how many
perceptual subitizing-recognizing a number without using mathematical processes
conceptual subitizing-viewing number and number patterns as units of units

• Subitizing is more accurate than counting
• Counting does not imply the understanding of numbers
• Subitizing is a precursor to counting
• There are two types of subitizing: perceptual and conceptual
• Some argue that subitizing cannot be taught

Subitizing is a very unfamiliar word to me. Subitizing is crucial in helping children recognize patterns, understand numbers, conserve, and understand arithmetic and place value.

• Children need to know how to decompose numbers
• Reasoning helps with working with large numbers
• Composing an decomposing are important for understanding parts and whole
• Dots and patterns should be used in a quick image format
• Seeing and describing quick images helps with flexible thinking and sharing of ideas
• Quick image activities are not a replacement for concrete activities
  

Quick image activities can help with number fluency. Students will learn more about number patterns and combinations through quick image activities rather than counting by ones to solve problems.

• Students should invent and examine ways to solve problems on their own
• Tasks make all the difference in students' abilities to solve problems
• Students should be given the chance to explore on their own rather than watching a teacher
• Students form their perceptions of subjects by the kinds of tasks they do
• Tasks should allow for reflecting and communicating
• Tasks should allow for students to use knowledge and skills they already possess
• Tasks should allow students to use tools; tools should be suitable

Tasks should allow for students to explore and think for themselves. Students will not be interested or completely compotent in math if the only way they learn math is by watching the teacher solve problems on the board. Students need to explore on their own and come up with their own ways and strategies to problem solve.

The articles showed me different ways to help enhance students' learning in math. I agree with all of the articles in that it is important that students learn to solve their own problems by first gaining an understanding of numbers and symbols. If students do not have the basic knowledge of numbers, symbols, and patterns, they will not know how to efficiently problem solve. Teachers need to do less teaching on the board and more scaffolding and mentoring to help children learn and explore math by making up their own ways to solve problems.

Week One Thoughts

What does the term early childhood mathematics mean to you?

Early Childhood Mathematics means that children are learning basic and practical math and thinking skills that will prepare them for more complex and real life math skills in the future. Children must have a very concrete knowledge of basic mathematics before trying to understand more abstract math.

What key points did you take from chapter one that inform your understanding of how to teach mathematics for young children?

• children construct their own knowledge
• connect any new information to information students already know
• children can learn from their peers when they share their ideas
• manipulatives are very important
• math should be challenging and taught through problem-solving
• math should be student-centered rather than teacher-centered
• students need to do more than solve the problem, they should explain how they got the answer
• give hints instead of answering problems for students, help them work through it rather than giving them an answer