Making Mistakes Equates to Learning

I am always amazed at how our readings seem to fit my field experience each week! I noticed a lot of mistakes in my student interviews today, but I could understand their logic. In the Eggleton and Moldavan article, the authors express how students need to think through their errors to understand why they are wrong and that it is important for students to try to show counter examples. I have noticed in the field, especially after my math interviews that my students always ask, “Is this right?” without really thinking through math problems. It was so tough to explain that I was not looking for right answers, but logical thinking! In the DMI chapter for this week, all of the student answers to Dawn’s number chart made sense. When the student replied “fifty ten” to follow 59 it makes sense. The student knew that they were working with the fifties and that 10 follow nine so this answer would make sense to a student. I also noticed in Marie’s section a student represented the number 127 with one flat, two units and 7 rods. I think this idea goes back to a topic we talked about recently in class. Students have trouble seeing the representation of the number 127 with manipulatives. There is logic behind Mary’s reasoning because she showed one object in the hundreds place, two objects in the tens place, and 7 objects in the ones place. The problem is that she simply sees the base 10 cubes as objects and not a representation of numbers.