A look at cooperative learning ventures in Math Education in Elementary Schools
Monday, July 25, 2011
Assessment in Cooperative Learning
Cooperative Learning Activities can be great tools to enhance the elementary classroom. Having focused objectives and goals for the activities are essential and helpful in guiding student learning and discovery. However, these activities can be difficult to assess. When students work together on projects or assignments, it can be hard to decipher who completed which task, and who understands the concepts the best. This post will aim to provide some tips for assessment when it comes to interactive learning activities.
To assess these activities, informal assessment strategies can be your best friend. Here are some tips that I use to informally assess my students:
1. Ask questions of each student during activities.
2. Check in with students who appear frustrated or overwhelmed.
3. Provide the group with different roles for each activity and assess them individually on their participation in these roles.
4. Evaluate their proper use of mathematical terms.
This link provides a good rubric for informal assessment.
Informal Assessment Rubric
This is another great rubric for assessing student progress informally.
Informal Assessment Rubric 2
Although informal assessment is useful, some formal assessment must be used to track student progress. Some tips for evaluating students formally include:
1. Have individual assignments due at completion of activity.
2. Tests/quizzes to assess learning.
3. Individual presentation of learning concepts.
4. Individual development of a similar problem utilizing the problem solving strategies learned.
This article provides great resources for assessing Cooperative Learning Activities.
Formal Assessment
Cooperative Learning can be a great tool to enhance your Math classroom. To be honest, it really enhances all content areas. By providing authentic and appropriate assessment, teachers can more accurately track their students' success.
Cooperative Learning for grades 4-6
The need for Cooperative Learning extends to the upper-elementary grades. Students at these higher levels still need to be engaged. At this age, students have more skills when it comes to staying focused and, provided they have worked cooperatively in the past, team work.
At this phase, students are developing as critical thinkers who are investigating and debating ideas with their classmates. Cooperative Learning Activities should be focused on developing students as higher-order thinkers and problem solvers. Due to the general increase in attention span at this stage, students can have a little more freedom in terms of their investigations. The objectives and goals of each activity should be clear and focused, but the methods can be a little more flexible.
The activity in this link, is for grades 1-6 and uses baking M&M cookies that can be adapted to reach several content areas including: Data Tracking, Graphs, Probability, and Measurement.
M&M Activity
The video below is a great resource for how to teach Math as a social activity. Students in grades 4-6 are exceptionally social. They are developing communities and learning how to be a productive part of a community. Integrating their social behaviors into their learning is extremely effective.
When it comes to learning Math at this age, enthusiasm of the teacher, and opportunities to work together to investigate knowledge go a long way. Students will gain excitement and become intrigued by Math and Problem Solving Strategies.
At this phase, students are developing as critical thinkers who are investigating and debating ideas with their classmates. Cooperative Learning Activities should be focused on developing students as higher-order thinkers and problem solvers. Due to the general increase in attention span at this stage, students can have a little more freedom in terms of their investigations. The objectives and goals of each activity should be clear and focused, but the methods can be a little more flexible.
The activity in this link, is for grades 1-6 and uses baking M&M cookies that can be adapted to reach several content areas including: Data Tracking, Graphs, Probability, and Measurement.
M&M Activity
The video below is a great resource for how to teach Math as a social activity. Students in grades 4-6 are exceptionally social. They are developing communities and learning how to be a productive part of a community. Integrating their social behaviors into their learning is extremely effective.
When it comes to learning Math at this age, enthusiasm of the teacher, and opportunities to work together to investigate knowledge go a long way. Students will gain excitement and become intrigued by Math and Problem Solving Strategies.
Cooperative Learning for K-3
Although there are 2 distinct sides to the cooperative learning debate, it is clear to me that the benefits definitely out-weigh the down sides. Children progress at a much fast rate when they are able to dig in and investigate together. Utilizing each other for resources and creating a community where building off of each other, students will grow exponentially in their understanding. In the professional world people have to work together in teams all of the time. Without training in cooperative and productive group work, many adults struggle with the skills it takes to produce quality and accurate work.
In this post, you will find resources and examples of Cooperative Learning activities for grades K-3. There are links and explanations. Enjoy!
In the beginning primary grades, it is important that cooperative learning activities be focused and fun. Students at this age have the hardest time paying attention and, from my experience, the easiest time getting distracted. Activities for this age group should have clear objectives and goals. Providing a check-list of procedures for the students can also help keep them focused. It is also important that the teacher be interacting with their students during the activities.
In this link, you will find 50 Cooperative Learning Activities for grades K-3. All of these activities focus on using Color Tiles, however a broad spectrum of content areas are explored. These content areas include: Patterns, Counting, Place Value, Addition and Subtraction, Geometry, Measurement, Graphing, and Probability.
Color Tiles Activities
In this link, you will find an additional 32 activities that are suitable for grades K-5. Several of these activities are already set up as Cooperative Learning activities. The ones in this list that aren't can easily be adapted.
Academy Curricular Exchange Activities
Finally, the article below explains how games in Math can help children, particularly those at a young age. It is important from the beginning that students find Math to be entertaining, practical, relevant, and engaging. Math activities and games are great ways to accomplish this.
How Do Math Games Help Children?
In this post, you will find resources and examples of Cooperative Learning activities for grades K-3. There are links and explanations. Enjoy!
In the beginning primary grades, it is important that cooperative learning activities be focused and fun. Students at this age have the hardest time paying attention and, from my experience, the easiest time getting distracted. Activities for this age group should have clear objectives and goals. Providing a check-list of procedures for the students can also help keep them focused. It is also important that the teacher be interacting with their students during the activities.
In this link, you will find 50 Cooperative Learning Activities for grades K-3. All of these activities focus on using Color Tiles, however a broad spectrum of content areas are explored. These content areas include: Patterns, Counting, Place Value, Addition and Subtraction, Geometry, Measurement, Graphing, and Probability.
Color Tiles Activities
In this link, you will find an additional 32 activities that are suitable for grades K-5. Several of these activities are already set up as Cooperative Learning activities. The ones in this list that aren't can easily be adapted.
Academy Curricular Exchange Activities
Finally, the article below explains how games in Math can help children, particularly those at a young age. It is important from the beginning that students find Math to be entertaining, practical, relevant, and engaging. Math activities and games are great ways to accomplish this.
How Do Math Games Help Children?
Tuesday, July 5, 2011
13 x 7 = 28...maybe??
For this week's post, I watched this video on YouTube. It's an Abbott and Costello clip illustrating how 13 x 7 = 28...or does it?? Here's the video:
This video, is very interesting. It shows us as educators how some students may rationalize the process of multiplication. There are several different techniques that can be used to determine a product of a multiplication problem. Several approaches are demonstrated in this video.
Students learn techniques for all things we teach, particularly mathematics, in different ways. This video shows us that while some students may understand key concepts and have basic understanding, they may be missing key components in the steps they take to solve problems. In this video, it looks as though single digit multiplication is understood, however when adding a second digit, it gets treated like single digit multiplication which is not correct.
In the film, this is how the standard algorithm is presented
13
x 7
______
21 (7x3)
+ 7 (7x1)
__________
28
However, the correct way to perform this algorithm is:
2
13
x 7
_________
91 (7x3=21; carry the 2; 7x1=7 then add the carry number of 2. 7+2=9. That number goes in the tens space. The solution is 13 x 7 = 91)
Here we see that by not correctly understanding where to place the numbers, how to carry, or failure to comprehend the significance of the face value of numbers, you will get the wrong solution.
Understanding and recognizing where students are struggling and tracing it back to what specific part they don't understand, teachers will be able to better correct habits and get students on track. Without digging in and investigating where the errors occur, teachers will only see wrong answers, and students will be frustrated and discouraged because in their mind, they are correct.
One thing that I liked about this video is that it showed the group of 3 men working together to try to teach and learn from each other and come up with the correct solution. This is collaborative learning. They had a real life problem that needed a solution. They worked together to develop a series of algorithms to rationalize their findings. In a classroom setting, we would have them reach an agreement and develop a system that would lead to the correct solution and group understanding.
This video below shows another way to teach children how to multiply with double digit numbers. I've never seen this approach before and I find it interesting.
This video, is very interesting. It shows us as educators how some students may rationalize the process of multiplication. There are several different techniques that can be used to determine a product of a multiplication problem. Several approaches are demonstrated in this video.
Students learn techniques for all things we teach, particularly mathematics, in different ways. This video shows us that while some students may understand key concepts and have basic understanding, they may be missing key components in the steps they take to solve problems. In this video, it looks as though single digit multiplication is understood, however when adding a second digit, it gets treated like single digit multiplication which is not correct.
In the film, this is how the standard algorithm is presented
13
x 7
______
21 (7x3)
+ 7 (7x1)
__________
28
However, the correct way to perform this algorithm is:
2
13
x 7
_________
91 (7x3=21; carry the 2; 7x1=7 then add the carry number of 2. 7+2=9. That number goes in the tens space. The solution is 13 x 7 = 91)
Here we see that by not correctly understanding where to place the numbers, how to carry, or failure to comprehend the significance of the face value of numbers, you will get the wrong solution.
Understanding and recognizing where students are struggling and tracing it back to what specific part they don't understand, teachers will be able to better correct habits and get students on track. Without digging in and investigating where the errors occur, teachers will only see wrong answers, and students will be frustrated and discouraged because in their mind, they are correct.
One thing that I liked about this video is that it showed the group of 3 men working together to try to teach and learn from each other and come up with the correct solution. This is collaborative learning. They had a real life problem that needed a solution. They worked together to develop a series of algorithms to rationalize their findings. In a classroom setting, we would have them reach an agreement and develop a system that would lead to the correct solution and group understanding.
This video below shows another way to teach children how to multiply with double digit numbers. I've never seen this approach before and I find it interesting.
Monday, June 20, 2011
Varying views on Cooperative Learning
Many experts believe, and research has shown that there can be extraordinary success in cooperative learning environments. Education has shifted from the days of the teacher as the lecturer, to the teacher as a guide to education. This shift has enabled students to construct their knowledge based on their experiences. Students who work in groups, tend to get more out of their learning experiences. This can accomplished by providing opportunities for students to engage in critical thinking and exploration. They are able to bounce ideas off of each other, and investigate different perspectives.
Below is a video designed by a student, based on research, stating that cooperative learning is right for all students, regardless of their knowledge levels:
Due to these experiences that students are having during their primary education, they are learning from the beginning how to interact in the "real world." During their careers, people have to interact in groups and work with their peers to get ahead. Being successful in working with others is a developed skill and providing students with the opportunity to learn how to do this, from a young age. Students learn how to ask questions and conduct learning in a way that moves a group forward, therefore making them more marketable and successful in their professional and educational goals.
The only opposing view I have found is that some students may suffer from primarily learning in cooperative learning groups. Without proper preparation, structure, and guidance from the teacher, some students may end up doing most, or on the other hand, none of the work. I myself have had a lot of experience in these types of groups and as the student who got stuck doing most of the work, it was very frustrating. Having to depend on a peer who wouldn't pull their weight was very frustrating, particularly when my grade depended on their participation and input. I often found myself doing most or all of the work while they reaped the benefits.
This video discusses both sides of cooperative learning and potential downfalls to this type of instruction. She talks about one student always dominating discussions while other, more introverted students will sit back and are perceived as not learning or participating. She also discusses the effect that cooperative learning can have in regards to time and productivity.
To find an appropriate balance, I feel it is important for teachers to learn how to balance their assessment between group and individual scores. Creating individual milestones, group evaluations, clear group expectations, and individual rubrics may be possible solutions. It is my opinion that when it comes to presentations, students should be graded individually. It is so frustrating as a student when your grade goes down because someone got stage-fright. Having students turn in individual work in addition to their group findings for their assessment may alleviate some of this stress.
Here are some articles that discuss cooperative learning.
Starting Point
Ed. Tech
Concept to Classroom
Below is a video designed by a student, based on research, stating that cooperative learning is right for all students, regardless of their knowledge levels:
Due to these experiences that students are having during their primary education, they are learning from the beginning how to interact in the "real world." During their careers, people have to interact in groups and work with their peers to get ahead. Being successful in working with others is a developed skill and providing students with the opportunity to learn how to do this, from a young age. Students learn how to ask questions and conduct learning in a way that moves a group forward, therefore making them more marketable and successful in their professional and educational goals.
The only opposing view I have found is that some students may suffer from primarily learning in cooperative learning groups. Without proper preparation, structure, and guidance from the teacher, some students may end up doing most, or on the other hand, none of the work. I myself have had a lot of experience in these types of groups and as the student who got stuck doing most of the work, it was very frustrating. Having to depend on a peer who wouldn't pull their weight was very frustrating, particularly when my grade depended on their participation and input. I often found myself doing most or all of the work while they reaped the benefits.
This video discusses both sides of cooperative learning and potential downfalls to this type of instruction. She talks about one student always dominating discussions while other, more introverted students will sit back and are perceived as not learning or participating. She also discusses the effect that cooperative learning can have in regards to time and productivity.
To find an appropriate balance, I feel it is important for teachers to learn how to balance their assessment between group and individual scores. Creating individual milestones, group evaluations, clear group expectations, and individual rubrics may be possible solutions. It is my opinion that when it comes to presentations, students should be graded individually. It is so frustrating as a student when your grade goes down because someone got stage-fright. Having students turn in individual work in addition to their group findings for their assessment may alleviate some of this stress.
Here are some articles that discuss cooperative learning.
Starting Point
Ed. Tech
Concept to Classroom
An overview of cooperative learning
Constructivist philosophies teach us that cooperative learning is important to the overall success of students. Cooperative learning has been defined as an approach to organizing your classroom in a way that promotes academic and social learning, in a team or group setting. It is suggested that in order for these groups to have the highest rates of success, it's beneficial to put students of varying abilities in each individual group. Although research has shown success in this strategy, there are varying opinions. This blog will aim to provide a look into these views, as well as cooperative learning strategies that can be used in a Mathematics setting. I will also strive to provide options for assessment.
Group work is something that most students enjoy and can benefit from. However, the idea of cooperative learning can be inconsistent at times. Often, individual success is based on a final group grade. As we all know, there are times when one or two students in these groups do most of the work, while other students "slack off." The trick as a teacher, is to find a way that we can incorporate cooperative learning in a way that fairly assesses each student and their progress.
Group work is something that most students enjoy and can benefit from. However, the idea of cooperative learning can be inconsistent at times. Often, individual success is based on a final group grade. As we all know, there are times when one or two students in these groups do most of the work, while other students "slack off." The trick as a teacher, is to find a way that we can incorporate cooperative learning in a way that fairly assesses each student and their progress.
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