Overview of Module 3

Since the NCDPI MOY and EOY benchmark assessments have changed and now include many different ways to use the equal sign my views on how to teach the equal sign has been evolving. This module has challenged my views even more. One statement that particularly resonated with me was in the chapter on equality they addressed the fact that many students see the equal sign as a sign of calculations and not a sign of relation (Carpenter, T., Franke, M., & Levi, L, 2003, p. 21). In many ways I think that many teachers themselves see the equal sign as a way of calculation and this is where many of our children’s misconceptions come from.

As we begin teaching students to develop a concrete understanding that the equal sign is a relationship between numbers and demonstrates equality on both sides, I think that we need to first engage them in an understanding of balance. We want them to understand that for something to be equal it must be the same on both sides. I can see myself using the example of engaging students in a human balance scale. This example comes from “Algebraic Thinking” and is located on page 67, activity 14.3 (Van de Walle). Students in the primary grades are very concrete learners and engaging them in this type of activity would be meaningful to remembering the activity and referencing it in later lessons.

I also think that the activity in “Algebraic Thinking” called “Capture Ten” would be a great way to get young students thinking about using symbols in different context (Van de Walle). Students enjoy playing games and this game would be helpful in developing their understanding of equal as the same instead of thinking of equal as the answer that comes next.

In the “Equality” chapter the first grade teacher states that she engages her students in problems with missing addends and where the equal sign is in the middle of the equation from the very beginning of school (Carpenter, T., Franke, M., & Levi, L, 2003, p. 18). I think that this was a great idea to get students accustomed from the very beginning to seeing the equal sign in different locations of the equation.

I noted that a good sequence for teaching students about the equal sign would first be to involve them in balance scale activities, then true/false equations, then open ended equations, and then allowing them to develop their own equations. Through this process students will see the equal sign in many different locations and become accustomed to seeing the equal sign in different locations of a given equation. Their misconceptions will be challenged from the beginning and they will have time to manipulate and make sense of problems that do not display the equal sign in the traditional way.

I am not sure that I used rational thinking to come up with the correct solutions, but I was able to come up with the solutions.

1.        In the problem with the baseballs I used a guess and check method. I used the “if this then that” strategy. I found the possible numbers to the first equations and then how knowledge/number to find the amount of the soccer ball. However, then I did not have the correct answer to the last one given the answers I had come up with. Given my answer though I was able to figure out how much I needed to manipulate the numbers to come with the correct answer to the last problem. I came up with the answers .35 for the baseball, .9 for the football, and 1 for the soccer ball.

2.       

For the first balance problem in the power point I think that the cylinder weighs the most and the cubes weigh the least. I think this because the cylinder is equal to two spheres and the three cubes are equal to only one sphere making the cubes weigh the least because there are three of them and only one cylinder.

3.       

For this problem, my first step was to determine the value of one sphere. I determined that one sphere is 12 divided by 3 and each one equals 4. Then you have four for the sphere and divided the remaining four on the other scale divided by two would leave each cube at a value of 2. Then 2+2+4=8.  

Critical thinking is involved in finding the solution to all of the problems presented. I think that I have a better understanding of the importance of the equal sign and how important it is to start developing the conception that an equal sign represents the same quantity on both sides at an early age. If done correctly students will have a better understanding algebraic equations from a younger age and will possibly run in to less misconceptions as they advance in their mathematical career.

Work Cited

Carpenter, T., Franke, M., & Levi, L. (2003). Equality. In Thinking Mathematically. Portsmouth, NH: Heinemann.

Walle, V. (n.d.). Algebraic Thinking: Generalization, Patterns, and Functions. In Elementary and Middle School Mathematics: Teaching Developmentally.