"Problem solving is the process of applying previous acquired knowledge to new and unseen situations."--NCTM, pg 112

It is always extremely important to highlight the importance of problem solving within your lesson plans and within your classroom. Problem solving should even be stressed to your very youngest, early elementary students. For these young students, problem solving becomes a challenge at their level but it's also a grand way to building the innate problem solving inclination that my future students will have as well as set them up for future years and courses in mathematics.

By beginning problem solving in my future Kindergarten classroom I will be encouraging my students to approach mathematics from new standpoints, and I will increase their critical thinking skills as they approach mathematics from a new angle. And solving problems goes beyond just infusing my students with a great sense of mathematics and of how "fun" and "exciting" math can be, it also gives students opportunities to use and extend their knowledge of concepts within each of the content standards as well--which will be a great help as I prepare students for the attainment of the next grade.

Example Problem Solving Lesson Plans Below are a few examples of "Problem Solving Lesson Plans" that I have created, they span several grade levels as well as several mathematic subject levels. I have also provided a critique of my own teaching habits form the first time that I ever attempted to teach a math lesson based primarily on problem solving--it was quite a learning experience!

Problem 1 is a a problem solving exercise that focuses on counting two sets and then comparing these sets. (When solving this problem the student will figure out how many are in line and how many will fit on the Ferris wheel, and then compare these numbers.)
Problem 1.pdf

Problem 2 is a problem for higher grades and higher levels of learners this problem would be a simple exercise of subtraction. However, for the novice at math and for those to whom the concept of subtraction isn’t a known formula, finding the number of balls of a certain color becomes a difficult problem to solve. Thus, at the Kindergarten level, this problem is tackling concepts such as drawing a picture, actually visualizing numbers, separating one object from another, as well as counting.
Problem 2.pdf

When working through
Problem 3, the students will learn to decipher when too much information is given before the actual problem solving can take place. And during the actual problem solving stage the child will use manipulatives to count the number of parts out of the whole are present in the store.
Problem 3.pdf

Problem 4 is a problem aimed specifically at the very young elementary school grades, most specifically classes such as my kindergarteners. For it will only be considered a “problem” for the very young kids, the ones who can’t multiply or even who can’t add simply in their heads, older children will view this problem as more as a simple application of knowledge. The major topic of this problem is the need to the students to visualize how many eyes the doll has, then to draw a picture of 6 dolls and figure out how many eyes there are total, for all of the dolls.
Problem 4.pdf

Critique In the below critique I learned several things about myself as well as about my problem solving lesson itself. I learned that the problem which I taught to my small group was certainly over the heads of my students. And next time I teach problem solving in kindergarten, a simple Join problem would be difficult enough for this age group. My students were obviously not used to this type of problem solving, so next time it may be helpful to let my student work in pairs, even though the problem was too hard, it is part of PS. But I did do a good job on the questioning and pulling them along once I realized that this was too hard.
Problem that I taught to a small group of my kindergarteners: There are 13 dogs and cats in the store. 8 of the pets are dogs. 3 of the cats are white. How many cats are there?
And here's my thoughts after the problem solving lesson itself: Problem Solving Critique.pdf