Developing Concepts through Rich Tasks
This week's math lesson was about developing rich tasks. Our learning goal was to be able to identify the criteria for a rich task and to explore a variety of these tasks at different grade levels.
I learned that rich mathematical tasks are essential for engaging learners and creating dynamic classrooms. Unfortunately, too few textbooks contain such tasks, so teachers must find or develop them on their own. Inevitably, the question arises, "How do we know a good rich task from a bad one?" The following are five (there are more, but I chose a few of the most valuable characteristics that I will implement as a teacher), important characteristics that will help answer this question;
1) Accessibility to all Learners: The students we teach are all unique and learn in different ways. They come with a wide range of mathematical knowledge, mathematics background and mathematical experience. If a task is truly rich, it will provide the students with interest, motivation, and challenge for all our learners, (remember how important challenging our students is since it promotes brain growth!). However, it should not discourage students that struggle, to opt out and encourage the more proficient math students to take over and provide the solutions. By the same token, the task should not be easily solved by the more advanced math students either. It has to provide challenges and extensions for them too. A good task should provide opportunities for all learners to participate and contribute with confidence.
2) Real Life Tasks: A great way to engage our students is to make math problems more "real" to them. As noted in the article by Steve Hewson, the objective is to present tasks that are interesting and can help students understand that the concepts they are learning in their math classrooms are not completely separate from their lives outside the classroom. For example, mathematics with a literature connection can be very interesting and engaging to students despite the fact that the scenarios investigated would not be called “really real.” Teachers can simply add their students names when creating a rich task. This can make the students feel valued by a caring teacher which in turn will motivate them to try their best. Also adding current events, such as the hurricanes and recent earthquakes, when creating questions. These methods will help captivate student interest!
3) Collaboration and Discussion: I found that this characteristic was re-enforced in this week's modules. I learned that as teachers, we should encourage students to work together instead of having them work on problems alone. Students gain new insights and perspectives by hearing from their peers; even struggling students begin to gain confidence in their ability to problem solve when given the opportunity to explain their reasoning on a problem. I definitely look forward to using this method in my placements and future classrooms.
4) Engagement, Curiosity, and Creativity: When I was in elementary school, these 3 words would never come to mind when talking about math. Especially, creativity? In math?? But in actual fact, it is vital that educators implement these characteristics in today's classrooms. These characteristics go hand-in-hand with the others mentioned above. When a task is interesting and engaging, and gives a problem that interests students, they will persevere in the problem solving. A rich task presents students with a variety of possible approaches and representations, allowing access for all learners. When students problem solve, they must first decide which tools and what approach to try. As the problem unfolds, students may run into obstacles that will require them to make more decisions both individually and collaboratively, and, often, will demand creativity and variety in the way they apply their knowledge.
5) Opportunities for Extension: With the opportunity for extension comes the opportunity for students to delve deeper into a math problem. Making connections, to other math concepts and to the real world, will aid students in a deeper understanding of math.
In this week's webinar, both Kevin and Daniel talked about differentiated instruction. They introduced different approaches to DI. These approaches offer choice to the students. This is another component to parallel, open and rich tasks. I like the choice boards approach, sometimes referred to as the tic- tac -toe assignment, for this very reason.
Through the modules, the articles, the in class activities and webinar, the main takeaway for me this week was that, the purpose of rich mathematical tasks is a differentiated approach that needs to be used in the 21st century classrooms in order to engage, motivate and encourage perseverance in today's youth. Integrating creativity and collaboration will ultimately change how we look at math as an irrelevant and a solitary undertaking. Hopefully the next generation will grow to love math because of these approaches we as educators promote today.
I will leave you with this final thought.....
I learned that rich mathematical tasks are essential for engaging learners and creating dynamic classrooms. Unfortunately, too few textbooks contain such tasks, so teachers must find or develop them on their own. Inevitably, the question arises, "How do we know a good rich task from a bad one?" The following are five (there are more, but I chose a few of the most valuable characteristics that I will implement as a teacher), important characteristics that will help answer this question;
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| Retrieved from class slide show [Personal Image] |
1) Accessibility to all Learners: The students we teach are all unique and learn in different ways. They come with a wide range of mathematical knowledge, mathematics background and mathematical experience. If a task is truly rich, it will provide the students with interest, motivation, and challenge for all our learners, (remember how important challenging our students is since it promotes brain growth!). However, it should not discourage students that struggle, to opt out and encourage the more proficient math students to take over and provide the solutions. By the same token, the task should not be easily solved by the more advanced math students either. It has to provide challenges and extensions for them too. A good task should provide opportunities for all learners to participate and contribute with confidence.
2) Real Life Tasks: A great way to engage our students is to make math problems more "real" to them. As noted in the article by Steve Hewson, the objective is to present tasks that are interesting and can help students understand that the concepts they are learning in their math classrooms are not completely separate from their lives outside the classroom. For example, mathematics with a literature connection can be very interesting and engaging to students despite the fact that the scenarios investigated would not be called “really real.” Teachers can simply add their students names when creating a rich task. This can make the students feel valued by a caring teacher which in turn will motivate them to try their best. Also adding current events, such as the hurricanes and recent earthquakes, when creating questions. These methods will help captivate student interest!
3) Collaboration and Discussion: I found that this characteristic was re-enforced in this week's modules. I learned that as teachers, we should encourage students to work together instead of having them work on problems alone. Students gain new insights and perspectives by hearing from their peers; even struggling students begin to gain confidence in their ability to problem solve when given the opportunity to explain their reasoning on a problem. I definitely look forward to using this method in my placements and future classrooms.
4) Engagement, Curiosity, and Creativity: When I was in elementary school, these 3 words would never come to mind when talking about math. Especially, creativity? In math?? But in actual fact, it is vital that educators implement these characteristics in today's classrooms. These characteristics go hand-in-hand with the others mentioned above. When a task is interesting and engaging, and gives a problem that interests students, they will persevere in the problem solving. A rich task presents students with a variety of possible approaches and representations, allowing access for all learners. When students problem solve, they must first decide which tools and what approach to try. As the problem unfolds, students may run into obstacles that will require them to make more decisions both individually and collaboratively, and, often, will demand creativity and variety in the way they apply their knowledge.
5) Opportunities for Extension: With the opportunity for extension comes the opportunity for students to delve deeper into a math problem. Making connections, to other math concepts and to the real world, will aid students in a deeper understanding of math.
In this week's webinar, both Kevin and Daniel talked about differentiated instruction. They introduced different approaches to DI. These approaches offer choice to the students. This is another component to parallel, open and rich tasks. I like the choice boards approach, sometimes referred to as the tic- tac -toe assignment, for this very reason.
Through the modules, the articles, the in class activities and webinar, the main takeaway for me this week was that, the purpose of rich mathematical tasks is a differentiated approach that needs to be used in the 21st century classrooms in order to engage, motivate and encourage perseverance in today's youth. Integrating creativity and collaboration will ultimately change how we look at math as an irrelevant and a solitary undertaking. Hopefully the next generation will grow to love math because of these approaches we as educators promote today.
I will leave you with this final thought.....
Until next time everyone!
Hey Adriana,
ReplyDeleteThanks for the quick list of characteristics that go into a quality rich task. I see these characteristics as important components to engage students in trying a task as they can relate to the question making them feel like it is personalized, and collaborate with others to discuss and seek help. I love how these tasks can be suitable for any level of learner so it is important we differentiate to allow our students feel comfortable in their own abilities to solve these kinds of tasks. From the webinar, I also enjoy the tic-tac-toe activity and can see myself using it in the classroom. It is great for all levels of learners but also gives them the option to challenge themselves and make mistakes to learn from.
Thanks for the post!
Hi Adriana!
ReplyDeleteAccessibility to all learners and opportunities for all learners to participate and contribute with confidence is so important in our (diverse!) 21st century classrooms. I am glad that you highlighted confidence as I believe confidence encourages students to realize what they are learning, take action on their learning, and advocate for themselves throughout their learning. Confident students can also look ahead and anticipate barriers, ultimately being pro-active in their learning. Thank you though for the complete list of characteristics! They were all so helpful.
I loved the quote at the end of your post, great job!