GEMS project

As I begin this interview, I chose this misconception activity to know if the student has a basic knowledge of being able to sort different coins by their attributes. These include value of the coins, color, size, what presidents are on the face of the coins, how old they are, and whether they are real coins or not. As the interview continues with opening questions, I want to also discover whether the child knows where they make these coins and to give me a brief explanation of what a Venn Diagram is and how it works.

Materials:
* 2 strings to make a Venn Diagram
* 3 Vegas Tokens
* 15 dimes
* 10 pennies
* 7 quarters

Interview Questions & Answers:

Q: What do you know about Venn Diagrams?
A: “ Well, it is two circles with a little one in the middle. My teacher tells me that it is so that we can put things alike and things that are different in the circles. Sometimes we just make our own circles and play with them. They one in the middle means that they are alike to the rest.”

Q: Tell me what is the difference of value of each of the above coins? Do they have different value or all the same?
A: “They each make them to their own size and their own color. We can’t changed that because it is the same company that makes them all the time. We can change the color if we change companies of where they make them. The amount stays the same.”

Q: Why does the smallest coin hold the most value?
A: “Because it is easier to carry and worth more than pennies so the company made them smaller. Mom uses more dimes than pennies.”

Q: Can we use these coins in other countries?
A: “ Only if they are different shapes so that they can tell the difference.”

Q: Can you tell me what each coin is worth?
A: “The gold is one dollar, the penny, well that is a penny worth, dime is ten pennies, a quarter is twenty-five cents and nickel is five pennies.”

Q: What can you tell me about the token?
A: “It is too big to be real. I know that there is a half dollar coin, but I’ve never seen this one that big. You can probably use this at games.”

Potential Misconceptions Related to GEMS Guide:

As I concluded the interview, I asked several questions that I thought would be geared toward finding out whether the student had a basic knowledge on the attributes of the coins as well as knowing how to sort the coins. This interview also allowed the child to give me a basic idea of where they stand in relation to their mathematical skills.

As Kaitlyn explained to me why certain coins are made the way they are, some misconceptions were stated. For example, her conception that the coins where made by different companies led me to believe that she probably thinks that each coin is individually made at a different company. She constructed this knowledge based through experiences knowing that there are so many companies in the world, and so each coin is made at one company since they are all different. Another misconception could be that the “tokens” could not be real at all because they were too big. In relation to previous lectures, this is due to the fact that children’s conceptions explain what they observe in their daily lives. Knowing that she is not familiar with the “token–size” makes her believe that it could not be real because she is not used to seeing it daily. I uncovered the child’s thinking by having her write down 5 ways to sort coins by and to draw her own Ven Diagram.

When the child filled in the Venn Diagram, she chose to put the tokens on one side, pennies on the other side and all the rest of the coins in the middle.
(the following page shows an illustration of her drawings and comments.)

Further Questions:
Q: Can you tell me why you separated the coins this way? What is it that they have in common?
A: “I put the coins this way because the ones in the middle can add up to the tokens on the right so they are similar in that way. Also, the pennies can add up to a nickel in the middle circle so they are similar too. All the quarters, dimes, and nickels are in the middle because if you add five or ten pennies it would be worth a dime or four quarters to a dollar token.”

Clinical Interview 2: Sorting & Graphs

Target Age Group: 2nd Grade

In preparing for the interview, I chose to explore sorting, attributes and graphing with an upcoming 2nd grade student. He was given buttons, sequins of different shapes and sizes, hair pins, paperclips, bottle caps, and beads to sort. He was then asked to make a graph using the materials that he had sorted. But instead he chose to sort sports balls that were in his room. He then graphed how many of each ball that he had.

Materials

* buttons * bottle caps * colored beads * hair pins * sequins * paperclips * notebook paper * colored pencils

Interview Questions and Answers

Q1:. What do you know about treasures?

A: You dig and see if you find something. I can find treasures in my backyard. And at Easter when the Easter Bunny lays eggs, that's treasure.

Q2. Well I have a box of treasures here, things I found around the house that were interesting and wanted to know if you could help me organize them. What do you know about organizing?

I know shorts go with shorts, socks with socks, underwear with underwear. I also know that you can organize trucks with trucks-firetrucks, cars, balls. You put them together. He then reached for his own tennis and basketballs. And said "See, the two tennis balls go together, and the two basketballs go together.

Q3. Even though the basketballs are different sizes and colors? Do they still go together?

A: Yes because they are still the same. They are both basketballs even though they are different colors, they both still bounc and you can shoot them both.

I then gave the student the box filled with objects and asked him to sort them:

He sorted them by object and nothing else. I was surprised that he did not separate the colored beads by color, but instead but them all in one group becasue they were all beads. As he was placing the objects in different groups he used the word sorting.

Q4: Can you organize the objects in another way?

A; Yes I can sort them by color too. He sorted the buttons by color:black, brown, white, clear.

Q5: Now that you have sorted them, can you tell me why you would use a graph to record them?

A: A graph will show you how much in each group.

Q6: Can you make a graph for these objects you just sorted?

A: I can make a graph with all of the balls I have here: He made a graph using a sheet of paper and colored pencils that were provided.

Click here to see graph