Mathematical Thinking

We are learning to share our ways of looking at mathematical situations and ways of solving mathematical problems with each other. We are noticing that most of the time there is more than one way to solve a problem or look at a situation. When we listen to each other explain how we figured something out we learn new ways to think about things. This helps us to be mathematically flexible which helps us not "get stuck" when working on math problems. Below are some photos of one way that we look at a mathematical situation - seeing dots on dot cards - in different ways.

We do a short (5 minute) daily activity that involves looking at dot cards. I flash a dot card picture (as seen below) to the crew for a few seconds. After I cover the picture, I ask the crew what they saw. They then tell me how many dots they saw and how they saw it. We have several students share how they saw the dots. Here are a few examples:

One student saw this as the same configuration of dots on a domino. She knew that this was 8 because this is how 8 appears on a domino.

Another student saw this as a row of 3, a row of 2 and another row of 3. He said that 3 + 3 + 2 = 8.

Another student saw the 6 dots on the sides like they are arranged on a 6 domino. She then added the two dots in the middle to get 8.

The next student saw the 3 + 2 + 3 =8 pattern but she saw it in columns instead of rows.

Another student remembered that we had previously seen a 9 dot arrangement on a previous day and noticed that this was the 9 dot pattern with one dot missing in the middle so it had to be 8.

Why do we do this? I explained to the crew that it is similar to reading - we can "sound out" every word we read but that would not be efficient. We need to have a bank of words that we just know so reading can move along quickly. This is true in math, too. We need to have strategies to deal with numbers so we don't have to count every dot to know how many dots there are in a pattern. We become more efficient using numbers.


This activity also helps us be able to break numbers apart into chunks that are easier to work with in our head. This makes us more flexible when adding and subtracting numbers. We will eventually begin to move on from dot cards and to visualizing numbers and basic addition and subtraction facts. Having the dot patterns in our minds can help us make that transition.

One other reason to do this short, daily activity is that it stimulates our creativity. We begin to look at things in more than one way. This helps us be open to finding more than one solution to our problems.