We watched this TED talk today at our ODE Network of Regional Leaders meeting. http://bit.ly/1diEpei
I LOVED what Dan says and think the way in which he poses problems ties well with my previous post about differentiation. When we allow students to be part of the process of creating the problem and engaging in the parameters of the problem, the problem will differentiate itself. Check out more at Dan's blog: http://blog.mrmeyer.com/
Monday, August 26, 2013
Sunday, August 25, 2013
Differentiation
Last week, I attended a training for our district's new vendor assessments. While I'm reserving my opinion about the vendor assessments and the data we will obtain from the testing, I found a comment by the trainer to be particularly troubling. The assessment provides a report with a number assigned for the student's skill level with mathematics that the teacher can then use to find activities to help differentiate instruction in the classroom. My concern with this process is that the majority of the materials provided were worksheets with little instruction involved. Differentiation is NOT providing more work for students but rather helping to tailor instruction to the learning needs of the student.
In my math classroom, I prefer that all students are working on the same problem. A rich mathematical task has multiple entry points so that most students are able to begin working on the problem. An excellent example is NCTM's House Numbers problem: http://illuminations.nctm.org/LessonDetail.aspx?id=L225
It takes a few minutes to introduce the problem and be sure students understand any associated vocabulary. Once I have made sure all students understand the parameters of the problem - for example, that the sum of the digits is 4 and that all of the digits must be different - they are ready to begin! Because there are many correct answers for this problem, students are successful if they find one correct answer or if they find many. The challenge is to find as many house numbers as possible. Questions such as, "How do you know you've found them all?" and "How did you decide what numbers would work?" help students to reason and justify their mathematical thinking. Students are practicing adding in a much more engaging way rather than solving math facts on a worksheet. You can further differentiation by giving students a calculator to check the sums, pairing them with a student working just above their level, or providing a framework to help them organize their thinking (such as an organized list). The idea is to see what students need before providing too much support.
The best part of this type of differentiation is that when you discuss the problem, all of the students were involved in the problem and can participate and contribute to the discussion!
In my math classroom, I prefer that all students are working on the same problem. A rich mathematical task has multiple entry points so that most students are able to begin working on the problem. An excellent example is NCTM's House Numbers problem: http://illuminations.nctm.org/LessonDetail.aspx?id=L225
It takes a few minutes to introduce the problem and be sure students understand any associated vocabulary. Once I have made sure all students understand the parameters of the problem - for example, that the sum of the digits is 4 and that all of the digits must be different - they are ready to begin! Because there are many correct answers for this problem, students are successful if they find one correct answer or if they find many. The challenge is to find as many house numbers as possible. Questions such as, "How do you know you've found them all?" and "How did you decide what numbers would work?" help students to reason and justify their mathematical thinking. Students are practicing adding in a much more engaging way rather than solving math facts on a worksheet. You can further differentiation by giving students a calculator to check the sums, pairing them with a student working just above their level, or providing a framework to help them organize their thinking (such as an organized list). The idea is to see what students need before providing too much support.
The best part of this type of differentiation is that when you discuss the problem, all of the students were involved in the problem and can participate and contribute to the discussion!
Saturday, August 17, 2013
Homework
If school has not already started for you, it is about to begin. As a teacher with two busy children who both play sports, our family time is limited. I dread the nights when the kitchen table becomes a battleground for homework. I'm sure many parents feel the same!
Homework should be engaging for students, help connect families with what students are learning in schools, and be PURPOSEFUL! Purposeful does not necessarily mean that you are practicing mathematical skills taught that day in class. The purpose can be broad - to help students talk about mathematics! Here are two ideas for homework that can help you engage students:
1. Give students a problem that they will be solving in class the following day. The homework is to read and begin the problem. By not requiring completion of the problem, you take away the pressure students feel for a "right" solution. Some students will discuss the problem with friends and family members - and talking about mathematics is something we want students to do! Students can jot down the ways they might begin the problem. Again, the tentative nature of the assignment means that students don't have to worry about having the "right"answer.
When students come to class the next day, have them work in groups to share how they would begin the problem. Give them sentence strips or index cards to record their strategies. After a few minutes, stop the class and ask them to share some of their strategies. You can group their cards into similar strategies. If they wrote their name along with their strategy, students will know who is thinking in a way similar to them and who might have some new ideas to share.
Then students can begin working on the problem! If they are stuck, they could try one of the strategies you charted or talk to people using those strategies. Rather than spending time in class to have students understand the problem, they can come ready to begin the work!
2. Find an interesting pattern or number and ask students to find out more about this number. For example, the number 29 is special. Why?
Homework should be engaging for students, help connect families with what students are learning in schools, and be PURPOSEFUL! Purposeful does not necessarily mean that you are practicing mathematical skills taught that day in class. The purpose can be broad - to help students talk about mathematics! Here are two ideas for homework that can help you engage students:
1. Give students a problem that they will be solving in class the following day. The homework is to read and begin the problem. By not requiring completion of the problem, you take away the pressure students feel for a "right" solution. Some students will discuss the problem with friends and family members - and talking about mathematics is something we want students to do! Students can jot down the ways they might begin the problem. Again, the tentative nature of the assignment means that students don't have to worry about having the "right"answer.
When students come to class the next day, have them work in groups to share how they would begin the problem. Give them sentence strips or index cards to record their strategies. After a few minutes, stop the class and ask them to share some of their strategies. You can group their cards into similar strategies. If they wrote their name along with their strategy, students will know who is thinking in a way similar to them and who might have some new ideas to share.
Then students can begin working on the problem! If they are stuck, they could try one of the strategies you charted or talk to people using those strategies. Rather than spending time in class to have students understand the problem, they can come ready to begin the work!
2. Find an interesting pattern or number and ask students to find out more about this number. For example, the number 29 is special. Why?
- It is a prime number.
- 29 plus 2X^2 is a prime number for every value of x up to 28. 29, 31, 37, 47, 61, and so on.
Students can discuss these patterns and test whether or not they work with other numbers. Again, students are thinking deeply, making connections, and communicating about their mathematical thinking!
Have a wonderful start to the school year!
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