In my work with first graders and other young students I've had the chance to observe the strategies that students in this age group use to make sense of their math problems. It is sometimes funny and sometimes frustrating to see how much they rely on counting. Some of my students still have to count their fingers on each hand, although presumably they know by now that they have five fingers to each hand. The hard part is that many times counting lets them down because it is easy to make mistakes, especially with big numbers. This is why I was very excited to learn about the Quick Image method. I had not thought about this before, but helping students see groups, and not individual objects, is a very useful tool indeed. I enjoy the opportunity to hear and see different students' thinking when using quick images. The moment when you realize that there are so many ways of seeing and thinking about things in a classroom is very revealing. It is helpful for me, as a teacher, but also for the students, because they get to experience and understand things from a different perspective and they might find new and easier ways to solve problems. I wish I had this opportunity when I was a student.
When we tried Quick Images with our third grade buddies I was surprised to see the variety of answers that we received. A group of four offered an average of three ways of finding the right solution. I was also surprised to see that they were using multiplication quite proficiently, although they are just starting to study it in class.
There was one solution that took me completely by surprise. One of the students used a previous problem and his knowledge of multiplication to solve a problem. Let me illustrate.
First we showed the quick image for groups of three and he saw it this way:
Of course, there were other answers too, like these two:
Then, the next Quick Image that we used was the one for groups of four. The answer that surprised me was this one:
The student used his solution for the previous problem: he noticed that each group has 3+1 dots. He also noticed that there are 6 groups of dots, exactly like in the previous problem. So 3 x 6=18, the previous result, plus the extra one dot for each of the six groups: 18 + 6 = 24.
There it was: a student teaching me to see things in a different way. I loved it!
