The summer is chugging right along, so I have to step it up with my summer book studies if I want to get through most of them! I finally had the chance to return to Success from the Start today. This part of the book focused on the Lesson Cycle, which I have fortunately had a lot of exposure to in my graduate classes, so there wasn't a ton of new or enlightening information here for me.
Chapter 6: Choosing Mathematical Tasks for Your Students
I had literally never heard of the phrase "mathematical task" before I started math education classes at WVU, but I'm glad I did!! As the authors of this book say, students have to engage in math tasks - not just basic problems or exercises - to truly develop connected mathematical knowledge. For teachers, this means finding new resources, extending the ones from textbooks or other materials, or making our own, all while making sure that these tasks help students in all the right ways.
To me, the most important thing about a math task is that it has multiple entry points and multiple solution methods. This allows all students to "get something" out of the task without getting frustrated, and also allows for further connections to be made. Tasks with multiple solution methods also help students see that there is not always one right path to the correct answer.
Something that intrigued me about the chapter was this statement: "When learning a new mathematical topic (such as slope), students should first do problems that require them to figure out something mathematical - to understand what is going on mathematically - before engaging in tasks that require them to learn the formal conventions of the mathematical topic" (pg. 72). I feel like this is what I am attempting to do with the types of discovery activities I have students do - they have to figure out patterns and things from which to draw conclusions, ideas, and definitions. This gives them the conceptual foundation about the topic before talking about the more formal things - I think. I would like some more examples to see if I am truly accomplishing this with discovery activities, or if I need to modify them somehow.
This chapter presented a few ways of extending math tasks that I liked - first, asking students to explain why, which I try to do often, but I find out many times that students don't know how to explain themselves. The chapter also suggested that having students work backward or undo a problem can help build connected knowledge as well. I'm curious about how this idea would apply to different topics.
To me, the most important thing about a math task is that it has multiple entry points and multiple solution methods. This allows all students to "get something" out of the task without getting frustrated, and also allows for further connections to be made. Tasks with multiple solution methods also help students see that there is not always one right path to the correct answer.
Something that intrigued me about the chapter was this statement: "When learning a new mathematical topic (such as slope), students should first do problems that require them to figure out something mathematical - to understand what is going on mathematically - before engaging in tasks that require them to learn the formal conventions of the mathematical topic" (pg. 72). I feel like this is what I am attempting to do with the types of discovery activities I have students do - they have to figure out patterns and things from which to draw conclusions, ideas, and definitions. This gives them the conceptual foundation about the topic before talking about the more formal things - I think. I would like some more examples to see if I am truly accomplishing this with discovery activities, or if I need to modify them somehow.
This chapter presented a few ways of extending math tasks that I liked - first, asking students to explain why, which I try to do often, but I find out many times that students don't know how to explain themselves. The chapter also suggested that having students work backward or undo a problem can help build connected knowledge as well. I'm curious about how this idea would apply to different topics.
Chapter 7: Planning the Mathematics Lesson
Again, I feel like I've had great support in constructing useful and detailed math lesson plans here at WVU. However, this chapter presented lesson plans with a slightly different focus: I should start planning by thinking about what I want the students to think about, and how that helps them learn. Usually I think about what I want the students to do, which is very similar, but not quite the same. I think I'll include this type of question at the top of my lesson plan template near the objective section.
This chapter also discusses anticipating student strategies and misconceptions at length, which is something else I'm familiar with but admittedly don't use much. I think it's hard to do this when you don't know your students very well, but it's necessary to think outside of the box and anticipate anything at all that students might think or do.
The most interesting part of this chapter for me was the types of lesson structures - mainly the titles for each structure. I have used all of these in the past, but without these titles. First, there is a "workshop lesson", where students work on a few problems for a long period of time and then discuss as a class. I think this is a great title for this type of activity. The authors also use the term "interactive lecture", which is definitely what I used when teaching middle school - I would have the students help me with the math, ask them questions, give them time to think and share, etc. Once the students got used to this idea and realized they would have to participate more, I think it worked great.
The authors touched on the use of the board and walls as part of the lesson and on-going unit. I like how they suggest that the board and/or walls should "tell a story" about what happened in class, one that an outside observer could understand at a later date. I've never thought that closely about what the boards and walls should look like, but I realize the importance now!
This post is getting pretty long, and there were still two more chapters in this part, so I will finish the rest later!
This chapter also discusses anticipating student strategies and misconceptions at length, which is something else I'm familiar with but admittedly don't use much. I think it's hard to do this when you don't know your students very well, but it's necessary to think outside of the box and anticipate anything at all that students might think or do.
The most interesting part of this chapter for me was the types of lesson structures - mainly the titles for each structure. I have used all of these in the past, but without these titles. First, there is a "workshop lesson", where students work on a few problems for a long period of time and then discuss as a class. I think this is a great title for this type of activity. The authors also use the term "interactive lecture", which is definitely what I used when teaching middle school - I would have the students help me with the math, ask them questions, give them time to think and share, etc. Once the students got used to this idea and realized they would have to participate more, I think it worked great.
The authors touched on the use of the board and walls as part of the lesson and on-going unit. I like how they suggest that the board and/or walls should "tell a story" about what happened in class, one that an outside observer could understand at a later date. I've never thought that closely about what the boards and walls should look like, but I realize the importance now!
This post is getting pretty long, and there were still two more chapters in this part, so I will finish the rest later!