PS+Teaching+Math

=Teaching Mathematics Through Problem Solving (due July, 2009) = ** ARCHIVE - What does it mean to teach mathematics through problem solving? a. Explain one idea in one paragraph. Include a math example to support your idea. b. Put your name at the end of your paragraph. **

Learning mathematics through problem solving involves the teacher giving their students a math problem which they need to solve in more than one way. This allows students to critically think and use multiple math concepts in solving the problem. Once students have their solutions they can explain their solution to the whole class. When a student is explaining their solution to their classmates others can be making connections between the solutions. According to Penny, “ The objective of using problem solving is that students will learn different strategies on their own, using their own prior knowledge (everyone is different) and will be able to share with their peers.” When students are given a problem, they reflect on their prior knowledge that they have learned in their younger years. Through their background knowledge and experiences with math problems students begin to connect math ideas and formulate solutions. By students sharing their ideas with their peers allows each student to see the multiple ways a question can be answered and be able to make connections between solutions. (Sally Chappins)

According to Emily, “Students will arrive at their solution in many different ways, and we as teachers should encourage this. There is no one way to solve a problem and we need to have students understand this.” Teachers in a problem solving math class should encourage students to formulate their own solutions to a problem. Teachers should not be giving them a set of steps to follow in order to learn. Instead the teacher should write the question on the board and give students time to solve the solution in two ways. Students need to understand that there are more than one way in solving a problem. If teachers were to structure their class in which students solve a before problem, then a during problem and finally an after problem then they will gain the skill in learning through problem solving. (Sally Chappins)

Teaching mathematics is to fully understand what 'teaching' means. I agree with Anna when she says, "One characteristic of **teaching math** **through problem solving** is that it allows the teacher to take on the role of facilitator, which leads students to make their own discoveries rather than just learning what is prescribed by the teacher in settings where a traditional approach to teaching is adopted." Teaching mathematics refers to facilitating and probing student thoughts and to consolidate their solutions and conjecturs. We as teachers recognize that learning is different for everyone and thus teaching must encompass this. Yang specifically talks about how to facilitate mathematics in a classroom. "Compared to traditional way of teaching that teachers transmit knowledge, facts, skills, concepts to students, teaching through problem solving allows students to explore the knowledge, concepts, or facts, and skills by themselves as well as by sharing with their peers. Students no longer receive the knowledge passively; instead, they’re active agents who discover their own learning and reflect on their own practices and experience. Learning won’t take place when students are asked to memorize the rules, concepts, or procedures. Students will make sense of learning by doing, practicing, making mistakes, sharing ideas, and getting feedbacks. In this process, they don’t just learn how, but also understand why. One example of teaching through problem solving is how two teachers teach same question differently in Cohen and Ball’s article (2001). The maths problem is: there are pennies, nickels, and dimes in the pocket and how much money might a person have if he/she pulls out three coins. One teacher (Ms. Kim) calls the class together to discuss the questions and share ideas and explore different solutions; while the other teacher (Mr. Jackson complaints that his students always get him to do the work for them. Mr. Jackson didn’t make it successfully in that he didn’t engage students to think actively in their own learning process." The importance of teaching/facilitating a mathematics class is to remember to goal is to allow students to UNDERSTAND, rather than memorize. (Penny Senior)