Chapter 2:
1. How would you describe the relationship between the goal for a lesson and the instructional activities in which students are to engage during the lesson?
2. What do you see as the costs and benefits of using high-level (i.e. cognitively challenging) tasks as the basis for instruction?
1. Setting a specific goal that is clear for what students should know and understand about math is the foundation for the lesson. It will direct you in your planning and your instruction. You must make sure you know the difference between performance goals and learning goals. That is sometimes hard. The task you pick will be determined by that goal and this is important. You cannot do the 5 practices without setting that goal. The goal is your starting point.
ReplyDelete2.I think high-level tasks may be difficult to find. Most textbooks don't have high-level tasks, but a teacher could change some of the low-level tasks to high-level which will take time. Not all teachers are strong in algebrafying. In the long run, kids don't grow using low-level tasks. Low-level tasks don't lead to good class discussion. High-level allows kids to think, reason, and problem solve. They also lead to good class discussion.
Holly, I agree that it is hard to distinguish between performance and learning goals and that they bleed over into one another. As I read your #1 I realized that many times I have taught the performance goals without really focusing on the learning goals which needs to come first.
Delete1. The relationship between the goal and the activities is crucial in each lesson. Not every lesson is going to have high cognitive demands, but you need to be careful. If you pick activities that are too demanding for your students, they can shut down. If you pick activities that are too easy for your students, they might not think about the task and therefore not get what you wanted them to get from the lesson. It is a fine line that you need to know your students, and anticipate what your students will do.
ReplyDelete2. I can see the high level tasks being a great point to have deep discussion over topics. I do not see me using them every day, but at least once a week to have students be able to explain what their thought process is over the topics. Students might not be willing to do this right away due to the cognitive demand that they might not be used to. It might be tough to get discussion going the first couple of times as well. However, if you can move past those hurdles and not give up on it, we might see students strive to do more in mathematics.
I totally agree that everyday can be overwhelming. Thinking about once a week makes it seem like a task that is more do-able. I also agree that getting students to talk about their math ideas will be difficult at first. Creating that culture of discussions will be worth it, but take time.
Delete--Amanda Thorsen
DeleteJenelle Jarnagin
ReplyDelete1) The goal needs to be the guide to choosing the instructional tasks. The quote from the book that really says it all is "Without explicit learning goals, it is difficult to know what counts as evidence of students' learning, how students' learning can be linked to particular instructional activities, and how to revise instruction to facilitate students' learning more effectively. Formulating clear, explicit learning goals sets the stage for everything else." If you don't have a clear goal you can't access the 5 practices effectively.
2) Cost of using a high level task is the time it will take to find and/or modify current tasks to a high-level and the time it will take to train students how to work through a high-level task.
Benefits are that students will have a stronger understanding of the mathematics if the task is presented properly. A strong task will help students enter the problem at their own level and develop understanding from there. A strong task most if not all students will have to have help in solving the problem so it will force student communicate about the mathematics.
Great point about the students communicating, Jenelle. That's a huge piece in this, as we know that students really learn what they can explain to others. But it's also important for the student that's learning from a peer. I attended a short workshop earlier this summer where we worked through tasks. At the end, I thought the instructor asked a great question: when did the learning happen? It was always when there was collaboration!
DeleteGreat quote from the book -- learning goal is critical to ensuring understanding for the students. It will take time to find/modify and prepare for these tasks. Not sure a realistic goal would be to use on every day in class. I find facilitating these high level tasks with multiple entry points more rewarding as a teacher and also for students. I does take time and work.. but the benefits I do believe are "cost justified".
Delete1. If we want students to actively learn about a concept, then our goal for a lesson must be well thought out and written with a certain measure of specificity and clarity. Our activities must help our students to focus and find the correct path to grappling with these ideas and concepts and finding the necessary connections. Therefore, the goal of our lesson and the instructional activities we provide our students are deeply intertwined with each other.
ReplyDelete2. The benefit of using high-level tasks is how richly the learning environment can be for students. Students have the opportunity to fully immerse themselves in discovering and connecting with the mathematics. Student understanding and comprehension gains depth and breadth. Students and teachers learn to communicate more fluently and see connections between concepts. The more fluent a person becomes the better able they are to continue evolving their skills.
The cost to using these types of tasks is time and effort. This requires much more time and effort on the part of the teacher to plan well. It also requires students to put forth more time and effort to explore and think through what they are discovering. Some students may still not get to where you want them to go nor do they want to put forth the effort. Teachers worry over how to balance the demands to “cover” the standards while at the same time allowing students to gain mathematical understanding through exploration, which can only be done when you give them time to explore.
Justin Johnson
ReplyDeleteThe relationship between the goal and the instructional activities is that the goal is the foundation that should drive all of the activities. It's the end from the beginning. The math goal is where you want your students to end up in terms of understanding the mathematics, so all of the instructional activities have to in some way point the students toward the goal.
Using high level tasks will likely come at a cost. Initially, there is the work involved up front for the teacher to find it, work through it, and understand the different ways that students will interact with it. Secondly, there may be a "cost" of student frustration. By choosing high-level tasks, we are asking for more out of students. More thinking, reasoning, connecting, and explaining. But the benefits of using high-level tasks will be worth the cost. Students, by putting forth the effort, will have a better understanding of the math (which goes back to the GOAL). I also believe that asking students to 'explore' the nature of mathematical relationships in high-level tasks will motivate them far more than would just asking them to complete "procedures without connections."
1. The goal of the lesson and the instructional activities have to be in sync to be effective. I feel like the practices help drive the instruction in a manner that facilitates a deeper level of learning than traditional/procedure oriented methods of instruction. We have to be cognizant of learning and performance goals.. I feel I probably have focused more on performance goals in the past as a teacher.. and I will want to challenge myself to focus more on the learning goal.
ReplyDelete2. Time will be the biggest cost... time for planning, time for instruction, time for reflection. It will be worth the investment no doubt as the level of learning will be greater. It will be another difficult hurdle for many teachers who feel constant pressure of trying to balancing work and life outside of school.
1. I think that having a clear for the lesson will drive the lesson and the activities. Without the goal the lesson becomes more of a "show and tell" like the book describes. It is great to hear many points of view from a lesson, however, those need to have focus on what learning we want to occur. When we have a goal we can also make sure that everyone is moving forward to the most efficient way to solve problems. Every if they do not get to that point during the class, we can work them to something shared.
ReplyDelete2. I think effective planning and understanding when to use the leading questions will be the most difficult for me. During chapter two I read that just because the problem is a story problem, does not make this a high level task. I have thought this way before and need to focus on what makes the problem high-level content. The benefit of planning a high-level task will be that students will learn to persevere through problems. They will be able to better understand the mathematics because they have gotten an in depth look into what the whole process is. Another statement from the chapter that stood out to me is from page 27. "This is not to say that all tasks that are selected and used in the classroom must be high level" Sometimes I get too focused on making my class high level that I feel like I actually lose the difficulty. I need to try to focus on making key lessons using our guides which will help other lesson move toward high level thinking tasks.
Amanda Thorsen :)
Delete1. Mathematically rich goals are absolutely necessary to have a strong lesson with long lasting impact. The goal is the destination. If you haven't determined a destination you won't know where you are headed. You need a destination so you can determine what pathways your students might use to get to that destination. You need that destination to think about how your students might get going in the wrong direction. Your students need to know this goal from the beginning of the lesson so they know how to start to approach the task you have given them.
ReplyDelete2. The benefit of a cognitively challenging high level task is the opportunity it gives students to figure out math on their own and then defend their strategy versus just being told how to do the problem or process. It will hopefully help them to be able to apply that learning to the next task they are given. It gives them the opportunity to be in charge of their learning at least at a certain level and then the teacher can ask questions and take the learning to the next level, but it is still taken from where they currently are. I think the biggest cost will be the time involved in preparing the task and doing the pre-planning that is necessary to make the task successful. I also think the first few times you give students a task there will be some level of frustration that will need to be overcome, which I realize is part of the learning process for both the teacher and the student, but can lead to either party to give up and just go back to the old way of doing things.
Kate Wonders
ReplyDelete1. The goal should dictate the activities in the lesson. Does this always happen? No. It is important to think about what mathematics you want students to learn. So often, teachers get trapped into teaching lesson-by-lesson from a teaching manual and lose sight of what they really want students to learn. Teachers should start with a strong goal for the lesson and then design the activities around the goal.
2. There are many benefits of using high level tasks in math instruction. Students are typically engaged, communicating, applying math skills, practicing the 8 mathematical practices, making connections, and solving real-world math problems. Tasks allow students to think about math in their own world, as well as solve problems in a way that makes sense to them.
The biggest cost would probably be the time it takes the teacher to properly plan for task work....or if a teacher does not plan properly and the lesson/task does not go well.
Jackie
ReplyDelete1. Setting a goal for the lesson is a critical starting point. At our district out lesson goals are displayed for the students so students know what they are to know and understand about mathematics are a result of their engagement. Goal are usually general, topics. You will need to judge what activities are appropriate for your students. Activities could be in a variety of different demand levels, but you want to choose one that will aid their learning.
2. Looking at what constitutes a lower or higher demands, it seems like a lot of books have more of the lower level demands. It seems that students performing higher-level demands would "grasp" the concept better and are performing at higher order thinking. Higher-demand tasks can lead to discussion, teamwork and fun projects.
1. The goal of the lesson is the "start line" for lesson planning. It keeps teachers focused on what is actually going to be the culminating concept that students are expected to know, understand and/or demonstrate. With this in mind, activities are planned that will help all students get to proficiency.
ReplyDelete2. The advantage of immersing students in cognitively challenging tasks is that it requires students to thoughtfully consider scenarios/problems in order to create a path by which they will solve a real world problem. There are multiple ways that most problems can be solved and students might need to verbalize their work to others and defend them. This creates mathematical discussions at higher levels and deeper understanding. The cost of these activities is most likely the time it takes to make sure the activities are properly thought out and created. This is why these activities most likely cannot be a daily occurrence, but implemented at the right time when the benefits are greatest.
1. How would you describe the relationship between the goal for a lesson and the instructional activities in which students are to engage during the lesson?
ReplyDeleteA goal directs a teacher on where they want the students to be at the end. It also gives the students something they can work towards and informs them of where they need to be at the end of a lesson. A goal should dictate what activities are appropriate for your students and need to be at the right level to make sure the students are engaged in that lesson to get them to the end goal.
2. What do you see as the costs and benefits of using high-level (i.e. cognitively challenging) tasks as the basis for instruction?
The cost is time but I also believe if you are able to have a high quality resource, this should be provided to the teacher to help in limiting the time. Even so, you still will need to make sure you find the best task that fits your students, anticipate responses and questions.
At the beginning I feel that students may be resistant to this because it is something that they probably haven't been exposed to or have been asked to do in the math classroom. This may take some time at the beginning of the year to let the students struggle but the reward of this will ensure your students are having a better understanding of the concept. If all teachers are doing this year after year, if will become easier for the teacher and the students.
Kelsey Burger
1. How would you describe the relationship between the goal for a lesson and the instructional activities in which students are to engage during the lesson? If the goal for the lesson and the intended questions and activities are in sync the questions and activities should move the class toward the goal for the lesson.
ReplyDelete2. What do you see as the costs and benefits of using high-level (i.e. cognitively challenging) tasks as the basis for instruction? I believe there will be a substantial time commitment cost, but there should be a substantial gain in understanding. I could see a great benefit when introducing new concepts.
1. You need to have a clear goal set to guide the lesson. There are too many activities out there that are interesting and fun, but without a clear mathematical goal set to guide the learning they are just fun. The students need to see the clear mathematical reason a task was given to them by the end of the lesson or it was a waste of time.
ReplyDelete2. I see the benefits of building those hard to teach skills in students, like problem solving, grit, and collaboration. I know my students need these skills for their future, but the major cost I see is time, especially in my Algebra 2 course. I have a very full timeline without much space to give my student access all of the mathematics the Common Core says that they need. I am not sure how I balance and blend these two ideas of giving them the mathematics and soft skills that they need in the time allotted for the course.