Chapter Reflections (September 27-October 3, 2015)

  Chapter 5:  A Focus on Problem Solving

        This chapter provided valuable insight into the importance of children learning problem solving.  When I was attending school, as previously mentioned, much of my early Math involved sheet work, which was often repetitive. I strongly suspect this is one reason that early deprivation in problem solving skills caused lead to Math to being a struggle, but one that I’m working to overcome!

      The author did a profound job in discussing her reasoning about the value of problem solving. Teaching children to be able to work independently and with others to become skilled problem solvers will help them develop critical thinking and judgement skills.  

         The inquiry process is intriguing, because it involves crucial stages. The first being able to understand the problem, and the last being able to look back at the process. Looking back is a crucial stage, because the students are able to share their problem solving skills with each other.   

        I had never seen a graphic organizer used in Math and feel this would help students in their inquiry based learning. It would especially be helpful in brainstorming and during other activities.

       The explanation and examples provided for the creation of good problems was a beneficial reminder that as teachers we want our students to try different ideas. We must be open to multiple ways of problem solving allowing the children to experience growth through their learning.  The array of both simple and complex problem solving strategies is astounding!  I found the examples to be a helpful review and preparation for myself before attending the fall practicum.

Chapter 5 Problem

"Ian has 75 cents in quarters, dimes, and nickles. He has at least one of each type of coin. How many coins could he have?"

         When doing this problem, I choose to use money, because this is one way that a child can represent this problem.  Personally, using change made it easier to break down the various ways of to discover how many coins Ian could have.  My cooperating teacher had fake coins that she allowed the children to use as a manipulative when solving similar problems in Math.

 

Chapter 8: Developing Early Operational Concepts

        This chapter was filled with detailed information.  Most importantly, what I took away were the similarities between addition, subtraction, multiplication, and division.  Subtraction seems like a straightforward operation, but when compared to Addition the complexity including the terminology was surprising. For example, separation of items is involved in taking away, comparing a larger number of items such as 7 cookies minus 4 uses subtraction, and also that determining a larger number from the smaller to find the addend is sometimes

necessary. 

        The chart for the addition and subtraction principles is helpful in breaking down information. From a teaching standpoint this improves our understanding, so that we can better teach the children. Principle six involves adding or subtracting six from a number. An example provided involved having the students walk on a number line. This would be a fun way for children to learn this concept.

       

        In reading this chapter, I learned how manipulatives such as counters, game materials (such as dice), linking cubes, 10-frames and walking on the number line are all helpful when teaching children about addition or subtraction. It was beneficial for me to learn that linked cubes, game materials such as cards, and number lines have a role in teaching multiplication. This opens the door to learning in so many ways beyond memorizing tables.

        What I did find rather cumbersome was the depth involved in the multiplication and division principles, because, I had just covered addition and subtraction principles.  Simply, this informative chapter contains an abundance of information to muster.