The other day when I was teaching I made a connection with analogical problem solving and place value. As a substitute teacher, I generally teach special needs children and do my best to help them understand material. The other day I worked with children with emotional disorders/behavioral problems. We worked on place values, some of the students got frustrated and gave up before they started, and others took some time and figured it out on their own. There was an example given at the top like such:
7,570,987 seven million five-hundred seventy thousand nine hundred eighty-seven
7,570,987 seven million five-hundred seventy thousand nine hundred eighty-seven
7,570,987 seven million five-hundred seventy thousand nine hundred eighty-seven
And so on…
Their task was then to look at the number underlined to come up with a solution, what place value was underlined. The example given to them at the top of the paper was the source problem. They were given the following instructions:
Find the place value of the underlined number.
Example: 4,509, 789 Solution: Hundreds place
So, the target problem and the source problem were similar in what they asked, but the slight variation was that they needed only to write the place value of the underlined number and not the actual number itself. The structural features are similar, both examples ask to find the place value, but differ slightly because the example includes the number and place value while the question only asks for place value. This slight change in structure confused some of the students. So, I had to help them to see the similarities and how to compare the two and find an answer by asking probing questions (guided practice). So, after they explained to me what they did I realized that they were getting overwhelmed with finding the place values. They did not know where to start, so I said to them, “Let’s look at the example”, then I proceeded to go over it with them. Next I had them look at one of the problems then asked, “What place value is underlined?”, the boy shrugged his shoulders. I said, “Okay, so let’s look at the example. Find the example with the same place value number underlined.” When they find it I then point out the bolded words and ask what place value is this. They say it (ex. five-hundred thousand) then I ask again so take the number out and tell me the place value and they do that. And I say this problem has the same place value as that example, so it would be the same answer. Then they have an aha-moment and it becomes obvious to them how to solve the problems. Analogical reasoning is an important educational tool because it can help people learn to solve real world problems by using comparison between two different situations to solve the present one (Goldstein, 2011) (Vendetti, Matlen, Richland, & Bunge, 2015).
References
Goldstein, E. B. (2011). Cognitive Psychology: Connecting mind, research and everyday experience
(Vol. 3). Belmont, CA: Wadsworth Cengage Learning.
Vendetti, M. S., Matlen, B. J., Richland, l. E., & Bunge, S. A. (2015). Analogical reasoning in the classroom:
Insights from cognitive science. Mind, brain, and education. 9 (2). Doi: 10.1111/mbe.12080