Teaching+Mathematics+through+Problem+Solving

Joe Ierullo - To improve the way mathematics is taught in the classroom teachers can comprise ways that demonstrate students practice of problem solving skills. Therefore, it is crucial for teachers to offer students the ability to interact with their peers either in pairs or groups to formulate and make sense of mathematical solutions. In return, this will allow students to demonstrate and use knowledge of what they already know.
 * Type your name and one idea you have about learning (shouldn't this be teaching?) mathematics through problem solving ...**

Mary Lou Kestell - Teaching math through problem solving means identifying expectations that need to be demonstrated by students. Then, as teacher, you pick, adapt, or create a problem that will allow students to show what they know about the related mathematics. It also involves, being prepared to listen to students' math thinking and facilitate the interactions between and among student ideas.

Elina - Instead of modelling a solution to a problem when teaching math through problem solving, teachers should //**model the problem situation**// and allow students to engage in problem solving. When students problem solve with their peers, more detailed explanations to solutions will be provided through "true" //understanding// and mathematical //connections// will be made more apparent to students.

Maria Gentile- Students should be given the opportunity to engage in problem solving without the step-by-step lecture on following and memorizing procedures by the teacher. The teacher should help by exploring some ideas on a certain concept by delivering important and minor information but not just giving them the answer. I believe social interaction is an important component in problem solving which helps students not only to motivate and stimulate discussion with eachother, but derive a solution they all understand and can articulate.

Spencer- Is not the Bansho method teaching through problem solving? Working on my Lesson Plan for wednesday, I realize that if we are to encourage students to get in the habit of thinking, the problem we pose in class will important. It has to be accessible and support many different pathways to an answer.

Brian- Students learn easier through problem solving when the teachers provides the experience. Teachers create a realistic problems an have students attempt to solve the problems and use the bansho model to display work efforts and outcomes. This methods dispalys numerous solutions to a problem and expands thinking of other students. Students then explain their solutions which solidifies their understanding and provides the teacher with an overall class understanding. Example: Using two dice to play a game and then finding out the odds, like we did previously in class.

Sarjeet - Teaching math through problem solving is to pose a contextual problem and then encourage and stimulate students for their own exploration, thinking, reasoning through active participation in discussion. They are not asked to to adopt someone else's thinking but encouraged to analyze, develop, and create their own process to find out a solution for the problem. Students are motivated to become autonomous and self-motivated in their mathematical activitiues.

Donovan: Teaching Math through problem solving means this to me: First, as a teacher I need to know what the students know or their prior knowledge. Second, based on the constuctivist's pedagogy, I will construct a problem based question that has embedded new mathematics learning that builds on the student's prior knowledge. Third, The problem must be one that allows mutiple entry points for students thus accomodating differentiated learning. Fourth, Students learn new Mathematics from the interaction with their peers wile I facilitate the discussion of the new ideas and help students make connections among solutions.

Jim - //learning mathematics// is all about drawing out of the students what they already know and challenging them to expand on that knowledge with as little teacher-to-student assistance as possible and as much student-to-student assistance as possible. To accomplish this requires teacher-to-teacher assistance to come up with the best possible problems that activates a variety of student responses.

Yudhbir - Mathematical vocabulary is one of the important key for designing good problems.We have to design the problem based on constructivist’s view and not the traditional view.Using words like explore,explain,devlop,apply and many more help the students to think and devlop mathematical reasoning in them.

Brenda – In order to teach math successfully it is crucial for teachers to utilize the structured problem solving approach and develop effective questions which require students to engage and develop their critical thinking skills. Teachers should not provide students with step-by-step guidance through a math problem. Instead, they need to focus on clarifying any misconceptions amongst the students and gain an understanding of their students knowledge based on student generated solutions. This information can then be used to help develop future lessons which address concepts the class had difficulty understanding.

Michelle - As we all know, teaching Mathematics successfully is a complex endeavour. One dimension of success in this area is about providing students many opportunities to think freely, talk, and construct creative solutions to problems. Coupled with the opportunities to practice Math in this way, teachers need to facilitate the process by helping to create and consistently model a common Math language that is used to label concepts, ideas, and discuss Math. Math language can also help facilitate discussions where student solutions are discussed as a whole class. Establishing such speak provides the basis to analyze commonalities, differences, misconceptions, and provide explicit explanations of solutions to clarify all students' understanding.