Measurement Articles

1. This article focuses on Perimeter. To study perimeter, this article gives students sample items to measure, and then finds the success rate of the students. It gives us sample work from students, to see their work, and successes and mistakes. By seeing these examples of student work, teachers are able to study it and understand how they can better teach their students. The article gives an explanation to the teachers that students could learn better if their instruction was related to real-world experiences. Teachers should build on their students knowledge of real life experiences to ask them measurement questions in order for them to really understand what they're measuring. This article also discusses reasoning. It describes how students are able to complete some problems with success, however they're not able to explain or justify why they responded the way that they did.
2. The sample problems were conducted by middle school grade students. However, I have experienced working with perimeter in my 3rd grade class, and I've found that students do have a hard time justifying their answers, as well as applying it to real life. This article helps teachers (in any grade) to understand the thought processes of their students and how they can adapt their teaching to better suit their students.
3. I learned that it is very important to question my students when teaching them measurement. They might be able to "understand" the concept, or complete problems dealing with measurement, however, unless they can explain their learning process, then they don't truly understand. I will be sure to ask them to justify their actions, and talk and walk out their work, so they truly know how to do the concept.

Week Nine Reflection

I think that I'm definitely at a Level 2. Because I understand these concepts at a more complex and developed level, I believe that as a teacher, I'll be able to help my students understand shapes and geometry at a basic level, but with the opportunity to improve and grow on what they already know. Geometry, like any math, is such a fundamental building block skill that has to be slowly learned through more and more information being grasped. As an instructor, it's important to understand your skill and content area at a deep and complex level before trying to teach them to students without a basis of knowledge at all.

Week 8 Reflection Questions

1. In class, we worked with collecting data through measurements. When we were collecting this data, we had to be very specific about what tools we were using, units of measurement, where exactly we were measuring to and from, and what we were rounding to. We found that everyone in class was doing different things, and we weren't all on the same page, therefore, our data couldn't be presented to the class accurately. In Chapter 11, the book discusses different ways and styles of collecting data. Chapter 11 shows that not only are there different styles of collecting the data, but also very different ways to present the data. At the end of the chapter, it discusses how to describe a set of data, and lists the different ways that data can be described and explained to an outside eye.

2. I am very fortunate to have been able to teach my math lesson on data collecting, and building graphs. The students were very attentive, and listened carefully to learn how to collect the data. I've noticed that they're very good at it, and really like to ask questions and write down responses. As third graders, they are very inquisitive, and they also like to compare their answers, and work with their classmates. It's good to allow this from a mathematical standpoint, so that they can collect information, and be able to see the differing ways a problem can be solved. Each day, a lunch count is taken by the class "helper" and they take a count of who is going to eat what each day. I like that they do this in class so that they can really collect data and record it on a daily basis. It will help them in the long run not to forget how to do this task.

3. Looking at the SC Kindergarten Standards, it tells us that data is organized in the form of drawings and pictures. As the grades get higher, data is displayed more numerically, and is represented more accurately. Chapters 11 and 12 describe more completely how to teach this concept of data collection and representation, and gives ideas for teachers on how to approach these standards in a tangible way in their classrooms. I really like having this book relate directly to the standards by giving us ideas to work with after we've reviewed and read the standards.

Week Four Reflection Questions

In chapter 3, they discussed strategies of addition and subtraction. I was encouraged by the descriptions of each type of problem, as well as the sample problems given to the reader. The chapters also discussed how to write problems for your students, and within that told us what students were learning within their specific grade levels. I really liked all the sample problems that the book set up, and I found it really helpful that they mapped out exactly how to write out and make the problem functional for the grade level discussed.

Reflection Question Week Three

How does the information and the tasks presented in chapter two connect to the videos of lessons you viewed as part of challenge 5?
I saw a lot of different things in this chapter that correlated with the videos. The first thing I noticed were the relationships among numbers 1-10 as well as numbers 10-20. We learned about place value relationships and learning what numbers are more and less.


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

I loved the activities with dominos. These objects are such an easy and helpful tool in the classroom. I think that it is very important for students to be able to have that visual and tactile opportunity to learn the value and quantity of the numbers and how to show more and less, addition and subtraction.

Reflection Question Week Two

How did each article help further your understanding of your topic area (Classroom Discourse, Mathematical Tools, Mathematical Tasks, Role of the Teacher, Student Thinking, or Classroom Norms)?

In the Fraivillig article I learned a lot from the Venn Diagram about Eliciting, Supporting, and Extending. Fraivillig talked about when eliciting, the teacher should really practice active listening to each students response towards problems, and as these responses are presented to the class, also think about varying ways she or he can present the information to the class. Also, when recieving responses, teachers should be sure to accept and evaluate each students answer, whether correct or incorrect. When supporting students, teachers should be familiar with and offer the option to students to have assistance in their work as well as lead them through the process. When extending the problem, teachers should offer reflection questions, to give the students the opportunity to take the problem a step further and understand more of what the problem is asking.

In the Mewborn Hewberty article, I really liked the initial comments on Question-listen-question-this method talks about teachers providing good questions to students, and then after recieving their responses, following up with other questions. I like the fact that this article tells us HOW to question our students, without putting them down or lowering their self-esteem. It gives us the opportunity to help our students learn while they might be incorrect in an answer, it also promotes collaboration with the other students.

Reflection Questions Week One

1. What does the term "early childhood mathematics" mean to you?
I believe that early childhood mathematics is the most important mathematics that children have. It sets the foundation for all of their math knowledge for their academic future. This is the time that students learn the most and that their brains are the most absorbent. Setting the foundation for math includes teaching the students their numbers, what each number represents, and how to add and subtract their numbers.

2. What key points did you take from chapter one that inform your understanding of how to teach mathematics for young children?
-p. 4- Three Factors that Influence Learning
-student reflective learning
- social interaction with other students in the classroom
-use of models or tools for learning.
I like this because it teaches me what factors are important to implement in my students learning every day.
-p.7-9- These few pages talk about Models, and how important they are in teaching math. All students need to see things visually and be able to manipulate objects and models help accomplish this task.
-p.14-19 describe problem based approaches to teaching. Each of these pages discuss a different part of the problem solving approach. Before, During, and After. These pages are very important to teach me HOW to approach problems with the children, and what steps to take before assigning the problem, as well as after.
-p.20-21-I loved how these pages answered frequently asked questions. It was helpful to know how to assess different strategies and types of responses I'll get from the students.