Problem+Solving

=Problem Solving  = 

=
A //problem// is any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific correct solution method (Hiebert //et al., 1997).// =====

**What is problem** **solving?**
Engaging in a task for which the solution is not obvious or known in advance. To solve the problem, students must draw on their previous knowledge, try out different strategies, make connections, and reach conclusions. Learning by inquiry or investigation is very natural for young children. [|(www.eworkshop.on.ca/Retrieved February 7 2009)]   **What ought teaching through and about problem** **solving include?**
 * ** A three step lesson process: **
 * Getting Started
 * Working on it
 * Reflect and Connect
 * Teaching with an emphasis on the "big ideas"
 * [[file:Big Ideas_Grade 4 .pdf]]
 * [[file:Big ideas_grade 5 Math.pdf]]
 * [[file:Big Ideas_Grade 6 math.pdf]]
 * Problem Solving ought to be a process emphasizing Polya's Four Step Method. In Primary, we are calling this "Think, Plan, Do, Review."

**Resources:**
Here is a page from the [|Summary of Results and Strategies for Teachers 2007-2008]  from EQAO. I have highlighted the relevant parts for Junior teachers searching for a compelling reason why problem solving ought to be an emphasis in mathematics instruction.

From [|The Guides to Effective Instruction in Mathematics, K-6, Volume 2 Problem Solving and Communication] , here are pages 38-43 that talk explicitly about problem solving strategies. This is the **teaching ** //**__about __**// **<span style="font-family: Tahoma, Geneva, sans-serif;">problem solving **<span style="font-family: Tahoma, Geneva, sans-serif;"> piece.

One of the biggest challenges is finding worthwhile problems. Here are several from <span style="font-family: Tahoma, Geneva, sans-serif;">[|www.eworkshop.on.ca] <span style="font-family: Tahoma, Geneva, sans-serif;"> <span style="font-family: Tahoma, Geneva, sans-serif;">[|Multiplication Problems] <span style="font-family: Tahoma, Geneva, sans-serif;"> <span style="font-family: Tahoma, Geneva, sans-serif;">[|Division Problems] <span style="font-family: Tahoma, Geneva, sans-serif;"> <span style="font-family: Tahoma, Geneva, sans-serif;"> The Literacy and Numeracy Secretariat publishes a research-into-practice series on their web site. Check out this link which explores **ESL in the Mathematics Classroom**. The first page records an actual conversation between students. It's awkward reading, but stick with it, because the rest of the monograph explores what you can learn from student discussions and some of the choices and difficulties facing teachers with ELLs in their classes. You may find //The Characteristics of Mathematical English// and //Implications for Teaching// sections particularly helpful. http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/ESL_math.pdf

[|Example of the Assessment for Learning Seating Plan Tool filled in]


<span style="font-family: Tahoma, Geneva, sans-serif;"> References: Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). //Making sense: Teaching and learning mathematics with understanding//. Portsmouth, NH: Heinemann.