1. What are the main points of the article?
This article reveals how a preservice teacher was "able to take advantage of a situation on an April morning in prekindergarten. The main points of the article are to illustrate how children come to measure. It helps show how children may have clear ideas about what it means to use units when measuring length and how "the imcompleteness of their understanding of the formal properties of measurement units makes their exploration interesting."
The students all measured their snake using a different method. Some identified a use of units without knowing the type of unit while others identified the use that their snake was longer or shorter. The article illustrates how the students had experience with measuring and were therefore able to identify that something was used and were able to repeat their units and keep them more or less the same length while measuring. However, the article also makes the valid point that the students neglected to compare units of measurement. The students didn't notice that their units were different, but did notice that something was wrong. The students recognized that one child's snake was the longest but were confused because another student's snake measured to be longer than the snake that appeared to be the longest.
2. How does your article connect to early childhood?
This article connects to early childhood because it shows how children can generate interest to a solving a problem from the context of the problem itself. The article focuses on showing teachers the importance of attending to the problem solving strategies of young children. It helps teachers and others understand the importance of observing "the various learning trajectories through which children pass". In addition, the article helps teachers become more aware of children's mathematical thinking.
Teachers should understand the importance of a child's informal orgins of their first mathematical insights and the role that they play in the child's context of learning. The article helps teachers grasp the importance of being alert to learning opportuntities that may arise in the classroom. Teachers should listen to the mathematical discoveries made by students in the classroom so that he/she can build off of what is said and/or discovered.
Mathematical discoveries made within the classroom will help students in early childhood build off of previous knowledge so that the child can develop an understanding for mathematical processes that will be used in higher education.
3. What did you learn from the article that will help you as you teach measurement?
I learned that it is important to allow children to make their own discoveries about measurement and to allow students to generate their own thoughts and questions about measurement. In addition, I learned that it is important to take advantage of specific opportunities that may arise in the classroom for discussion. I began to understand that it is okay if a child doesn't understand and that as a teacher, we must become accustomed to attending to children's problem solving strategies.
When teaching measurement, it is important to build off of what children know and/or recognize. The teacher should scaffold when necessary but allow the student to think through the problem in an effort to solve the problem. In addition, it is important to recognize that a child's interests will lead them to other discoveries and insights. Provide children with different opportunities to explore measurement that will allow children to explore measurement through a different approach such as drawing shorter or longer lengths outside on the playground using chalk. This will help the teacher observe how the students approach a task they may be familiar with in a different context. This will also allow the teacher to scaffold during the process and attend to the problem-solving strategies of the student.
Saturday, November 13, 2010
Monday, October 25, 2010
Week 9: Geometry
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.
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.
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.
Monday, September 20, 2010
Reflection Question: Week 4
What are the key ideas presented in chapter 3?
Chapter 3 presented a range of important ideas that contribute to developing meaning for operations and solving story problems. Meanings, interpretations, and relationships to the four operations of addition, subtraction, mulitiplication, and division are each presented throughout chapter 3 and connected to help children establish an understanding of how they can use such operations in real-world settings. One important concept presented is that both addition and subtraction are connected. Another key idea within chapter 3 is that both addition and subtraction involve an action. One is a joining action of putting together where as the other is a separting action or taking away. Subtraction is the operation that names a missing part and addition is the operation that names the whole in terms of the parts. Important ideas regarding multiplication that were presented throughout the chapter include: multiplication involves counting groups of like size and figuring out how many are in all or the process of mulitplicative thinking, multiplication and division are connected/related. Division names a missing factor. In addition, models can be used to solve problems for all operations. They are also used to help figure out the operation involved in a problem despite number size and can be used to help number sentences have meaning.
How do these ideas inform your understanding of teaching numbers and operations?
The key ideas presented throughout the chapter help to establish meaning and purpose behind how to teach numbers and operations effectively to students. It is very important that as a teacher, I look at more than just the answer a student gets but instead, look at the techniques the child used to solve the problem. I should show students how operations are connected and help students develop the strategies needed to work through a problem and give it meaning. I realize that it is important to pay attention to how a student works through a problem or the strategies used so that it will give me the information that I need to understand their number development and the strategies being used. I also realize from the ideas presented that it is essential to pay attention to how a child solves a problem or the methods being used. This will help me grasp and understand as to what numbers should be used in problems for the next day.
From the points established throughout the chapter, I have become more aware of the connection and meaning between specific operations. I have also learned that it is important to encourage the use of problem analysis and avoid the use of key words such as "altogether" and "fewer" whem dealing with adddition or subtraction. Being able to provide good explanations behind specific mathematical operations is essential in the learning process. Rather than simply looking at specific "key terms" used throughout a problem, it is important to actually break the problem down and figure it out mathematically. This will help the child become more aware of how he/she was able to solve the problem and help give meaning to how the answer was found.
Chapter 3 presented a range of important ideas that contribute to developing meaning for operations and solving story problems. Meanings, interpretations, and relationships to the four operations of addition, subtraction, mulitiplication, and division are each presented throughout chapter 3 and connected to help children establish an understanding of how they can use such operations in real-world settings. One important concept presented is that both addition and subtraction are connected. Another key idea within chapter 3 is that both addition and subtraction involve an action. One is a joining action of putting together where as the other is a separting action or taking away. Subtraction is the operation that names a missing part and addition is the operation that names the whole in terms of the parts. Important ideas regarding multiplication that were presented throughout the chapter include: multiplication involves counting groups of like size and figuring out how many are in all or the process of mulitplicative thinking, multiplication and division are connected/related. Division names a missing factor. In addition, models can be used to solve problems for all operations. They are also used to help figure out the operation involved in a problem despite number size and can be used to help number sentences have meaning.
How do these ideas inform your understanding of teaching numbers and operations?
The key ideas presented throughout the chapter help to establish meaning and purpose behind how to teach numbers and operations effectively to students. It is very important that as a teacher, I look at more than just the answer a student gets but instead, look at the techniques the child used to solve the problem. I should show students how operations are connected and help students develop the strategies needed to work through a problem and give it meaning. I realize that it is important to pay attention to how a student works through a problem or the strategies used so that it will give me the information that I need to understand their number development and the strategies being used. I also realize from the ideas presented that it is essential to pay attention to how a child solves a problem or the methods being used. This will help me grasp and understand as to what numbers should be used in problems for the next day.
From the points established throughout the chapter, I have become more aware of the connection and meaning between specific operations. I have also learned that it is important to encourage the use of problem analysis and avoid the use of key words such as "altogether" and "fewer" whem dealing with adddition or subtraction. Being able to provide good explanations behind specific mathematical operations is essential in the learning process. Rather than simply looking at specific "key terms" used throughout a problem, it is important to actually break the problem down and figure it out mathematically. This will help the child become more aware of how he/she was able to solve the problem and help give meaning to how the answer was found.
Monday, September 13, 2010
Reflection Question: Week 3
How does the information and the tasks presented in chapter two connect to the videos of lessons you viewed as part of challenge 5?
Chapter two presented the task of using dot plates. As I recall, this task was presented by one of the first students in the videos. The child used the concept of counting dots to help them work through a counting task. Also, the concept of "one and two more, one and two less" is presented and used within the videos as an additional method when reflecting back on the way one number is related to another. This task is used through the activity "dot plate flash" that was mentioned throughout chapter two.
An additional concept that was used throughout the videos was the task of using missing-part activities. The activity "covered parts" that is metioned throughout chapter two was also seen throughout the videos using counting cows and a barn. The cows were hidden underneath the barn and either pulled out or taken away to provide the child with the task of being able to focus on a "single designated quantity as the whole".
As mentioned, there were several pieces of information and tasks presented throughout chapter two that connected to the videos viewed as part of challenge 5. It is evident that both the videos and the information presented are somehow connected, using the same concepts and providing students with similar tasks in order to understand the information being presented.
What task (activity) in chapter two was most interesting to you? Why?
I really liked the activity, "Fill the Chutes" that was presented to help children develop their understanding of counting by engaging each child in a game that involved both counts and comparisons. This is an activity that seems to be a fun learning activity that would provide children with a fun approach to counting. The game is very similar to the game, "Chutes and Ladders" that many children may already be familiar with. This is a way to get their attention and provide a fun alternative to worksheets. I found it both interesting and something that children would enjoy. Its a fun way to get children excited about counting!
Chapter two presented the task of using dot plates. As I recall, this task was presented by one of the first students in the videos. The child used the concept of counting dots to help them work through a counting task. Also, the concept of "one and two more, one and two less" is presented and used within the videos as an additional method when reflecting back on the way one number is related to another. This task is used through the activity "dot plate flash" that was mentioned throughout chapter two.
An additional concept that was used throughout the videos was the task of using missing-part activities. The activity "covered parts" that is metioned throughout chapter two was also seen throughout the videos using counting cows and a barn. The cows were hidden underneath the barn and either pulled out or taken away to provide the child with the task of being able to focus on a "single designated quantity as the whole".
As mentioned, there were several pieces of information and tasks presented throughout chapter two that connected to the videos viewed as part of challenge 5. It is evident that both the videos and the information presented are somehow connected, using the same concepts and providing students with similar tasks in order to understand the information being presented.
What task (activity) in chapter two was most interesting to you? Why?
I really liked the activity, "Fill the Chutes" that was presented to help children develop their understanding of counting by engaging each child in a game that involved both counts and comparisons. This is an activity that seems to be a fun learning activity that would provide children with a fun approach to counting. The game is very similar to the game, "Chutes and Ladders" that many children may already be familiar with. This is a way to get their attention and provide a fun alternative to worksheets. I found it both interesting and something that children would enjoy. Its a fun way to get children excited about counting!
Monday, September 6, 2010
Reflection Question- Week Two
How did each article help further your understanding for your topic area Mathematical Tools?
Thompson's article, "Concrete Tools and Teaching for Mathematical Understanding" allowed me look further into the importance of concrete tools and what teachers should be asking, "What, in principle, do I want my students to understand?" I also found that concrete materials are used appropriately for two purposes:
We cannot assume that each child knows the meanings of symbols and concrete objects but we must make sure that each child understands what the symbols represent in a mathematical expression.
Overall, the articles provided me with a better understanding on the role of concrete materials when teaching mathematics and the importance of fostering symbolic literacy.
Thompson's article, "Concrete Tools and Teaching for Mathematical Understanding" allowed me look further into the importance of concrete tools and what teachers should be asking, "What, in principle, do I want my students to understand?" I also found that concrete materials are used appropriately for two purposes:
- "they enable the teacher and the students to have grounded conversations about something concrete"
- they furnish something on which students can act
From this article, I learned that for concrete materials to be an effective aid to students' thinking and to successful teaching, "the effectiveness is contingent on what one is trying to achieve" and reflects upon the teachers ultimate goal. Meaning, it reflects on whether the teacher is asking, "What do I want my students to understand" rather than "What do I want my students to do". After reading Witherspoon's article, "And the Answer is Symbolic" I was able to grasp a better understanding behind the misconception of what a symbol means in terms of mathematics. I was also able to see the importance of fostering mathematical literacy and the communicative role of mathematical symbols in elementary school.
The use of concrete materials in early childhood education is essential. However, I have learned that it is very easy to misuse concrete materials and to use them incorrectly. As mentioned in the article, using concrete materials doesn't mean that a child will automatically grasp the understanding behind the mathematical meaning of the concrete object. While we must use concrete materials to teach math, it is also important to understand that children must know and understand the meaning and representation of the concrete materials being used.We cannot assume that each child knows the meanings of symbols and concrete objects but we must make sure that each child understands what the symbols represent in a mathematical expression.
Overall, the articles provided me with a better understanding on the role of concrete materials when teaching mathematics and the importance of fostering symbolic literacy.
Monday, August 30, 2010
Reflection Questions: Week One
What does the term early childhood mathematics mean to you?
The term early childhood mathematics refers to the basic mathematical skills and fundamentals that should be introduced and understood during the early years of a child's life. They are the building blocks for a child's understanding of mathematics. Early childhood mathematics introduce both skills and concepts that will later be used when a child begins to learn higher levels of mathematics.
What key points did you take from chapter one that inform your understanding of how to teach mathematics for young children?
A key point that stood out to me stressed the importance of not teaching students by telling, but implied that we must help them construct their own ideas using the ideas that they already own. However, it is important to understand that the manner in which you conduct your class plays a crucial role in what your students learn and how well the information they learn is understood. It is important that the teacher understands that the factors that influence learning are influenced by the teacher and will impact what and how well students learn the content being taught.
I also found that by having the children within the classroom engage in interactive classroom activities will provide the students with opportunities to learn from each other. It will also provide the students with "an enviornment to share ideas and results, compare and evaluate strategies, challenge results, determine the validity of answers, and negotiate ideas on which all can agree."
As a teacher, it is important that I understand the use of manipulatives and their role in either helping or failing to help students construct ideas. The use of tools is good when used correctly and appropriately. It is important that I provide students with the necessary tools, models, and materials to learn mathematics effectively but a key point mentioned within the chapter stressed the importance of knowing how to use such tools correctly. The chapter mentioned the importance of the teacher introducing the models appropriately and "perhaps conducting a simple activity that illustrates this use".
From the reading of chapter one, I also found that it is important for the teacher to understand the value of teaching with problems and the effectiveness of problem solving. Problem-based teaching seems to be an approach that can be quite confusing or difficult yet highly rewarding for the students and teacher. I also found that there is a 3-Part fomat for problem-based lessons that can be followed.
A helpful point made when discussing how to deal with a class that doesn't understand the content being taught was to "not give into the temptation to show them but rather regroup and offer students a simpler related problem that will help them prepare for a more difficult one." It stated that the teacher should first find out what ideas the student of group has and try and provide hints on ideas that you hear are being considered within the group of students.
The term early childhood mathematics refers to the basic mathematical skills and fundamentals that should be introduced and understood during the early years of a child's life. They are the building blocks for a child's understanding of mathematics. Early childhood mathematics introduce both skills and concepts that will later be used when a child begins to learn higher levels of mathematics.
What key points did you take from chapter one that inform your understanding of how to teach mathematics for young children?
A key point that stood out to me stressed the importance of not teaching students by telling, but implied that we must help them construct their own ideas using the ideas that they already own. However, it is important to understand that the manner in which you conduct your class plays a crucial role in what your students learn and how well the information they learn is understood. It is important that the teacher understands that the factors that influence learning are influenced by the teacher and will impact what and how well students learn the content being taught.
I also found that by having the children within the classroom engage in interactive classroom activities will provide the students with opportunities to learn from each other. It will also provide the students with "an enviornment to share ideas and results, compare and evaluate strategies, challenge results, determine the validity of answers, and negotiate ideas on which all can agree."
As a teacher, it is important that I understand the use of manipulatives and their role in either helping or failing to help students construct ideas. The use of tools is good when used correctly and appropriately. It is important that I provide students with the necessary tools, models, and materials to learn mathematics effectively but a key point mentioned within the chapter stressed the importance of knowing how to use such tools correctly. The chapter mentioned the importance of the teacher introducing the models appropriately and "perhaps conducting a simple activity that illustrates this use".
From the reading of chapter one, I also found that it is important for the teacher to understand the value of teaching with problems and the effectiveness of problem solving. Problem-based teaching seems to be an approach that can be quite confusing or difficult yet highly rewarding for the students and teacher. I also found that there is a 3-Part fomat for problem-based lessons that can be followed.
A helpful point made when discussing how to deal with a class that doesn't understand the content being taught was to "not give into the temptation to show them but rather regroup and offer students a simpler related problem that will help them prepare for a more difficult one." It stated that the teacher should first find out what ideas the student of group has and try and provide hints on ideas that you hear are being considered within the group of students.
Challenge 4
The children seemed to possess higher level thinking during the second set of interviews. The children overall seemed more capable of counting in their head or understanding the concept behind addition and subtraction. They were able to use information that they already understood or had previously learned and used it in their thinking when solving the addition or subtraction problem presented. For example, Lauren understood that 7+6=13 because she already knew that 7+7=14 and knew that if it were 7+6 then it should equal up less than 14 so she thought it should be 13.
The children also appeared to understand what they were being asked and were more open to answering the questions. During the first set of interviews, the children seemed more confused when asked particular questions and would simply answer that they didn't know or wouldn't have a good explanation behind their reasoning. Even if a child didn't know the answer to a question asked, the child would at least think about the question being asked and try and figure out the answer rather than give up like they seemed more likely to do in the first set of interviews.
The children also appeared to understand what they were being asked and were more open to answering the questions. During the first set of interviews, the children seemed more confused when asked particular questions and would simply answer that they didn't know or wouldn't have a good explanation behind their reasoning. Even if a child didn't know the answer to a question asked, the child would at least think about the question being asked and try and figure out the answer rather than give up like they seemed more likely to do in the first set of interviews.
Challenge 3
I think it is important to understand that each child doesn't learn things the same way or at the same rate. It is important to provide those who learn best visually with a visual activities so that they can understand the concept of addition and subtraction better. It is important to understand how each child does learn material so that I could provide the child with an activity that would accomodate for his/her needs. From the videos, I had the opportunity to see that some children within the class performed subtraction by counting backwards while others just guessed or based their answer on a "pattern" that they had previously seen. If this were my classroom of students, I would seperate each child into a group of students that seemed to perform addition or subtraction using the same method. I would also find lesson ideas and activities that incorporated all methods of perfoming addition and subtraction so students could understand that there is more than one way to figure out the answer. I believe it is important to address each child's needs and by having a child exposed to different learning styles or options, the child is more likely to catch on and figure out the style that works best for them.
If I were a teacher of this class, I would build on the concept of what it means to subtract from a higher number or simiply add to it. I would explain the idea of combining numbers and how to distinguish between when it is necessary to count forwards or backwards. I would incorporate the use of a visual but also have the child practice solving simple math problems using their fingers or by counting in their head without having to use their fingers. I would provide the child with mulitple options and slowly take them away until they have reached the point where they do not need a visual aid to help them solve the problem.
If I were a teacher of this class, I would build on the concept of what it means to subtract from a higher number or simiply add to it. I would explain the idea of combining numbers and how to distinguish between when it is necessary to count forwards or backwards. I would incorporate the use of a visual but also have the child practice solving simple math problems using their fingers or by counting in their head without having to use their fingers. I would provide the child with mulitple options and slowly take them away until they have reached the point where they do not need a visual aid to help them solve the problem.
Tuesday, August 24, 2010
Challenge 2
It is important to provide students with an array of activities that allow the child to become actively engaged in learning. Providing students with the use of pattern blocks, counting bears, and hands-on activities will allow the students to get engaged with the activity. It will give them the opportunity to practice basic counting, adding/subtracting numbers, grouping and will help them build on what they already understand so that they can begin to recognize more complex shapes, patterns, addition/subtraction problems and will also have the opportunity to understand how basic shapes can be used to make other shapes. It is important to incorporate group and student led instructions so that the students can work cooperatively with others to build on information they already know. It is important for students to work together so that they can begin to think critically and have the opportunity to build on what other students may know. It is also important to integrate math into other subjects and provide students with fun learning games that catch their attention.
Challenge 1
Coming into first grade, students are capable of doing basic addition and subraction skills. They have the ability to add and subtract single digit numbers and understand the concept of "taking away". They have the ability to understand and develop basic patterns using numbers, colors, and shapes. They understand and have the ability to perform basic number counting; counting up to 20. Also, they can recognize basic shapes. They understand the concept of "multiples" and how to group items by number.
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