Tags
concept development, math, problem solving, skill development, subtraction, thinking, upper elementary
Over the past few weeks, I have had the privilege of working with some fourth- and fifth-grade students to learn more about their mathematical thinking. It has been fun and informative. I am an “old dog” and resort to my “old tricks,” so hearing some of their approaches to solving a math problem was nothing short of enlightening.
As we looked at various problems, I learned so many ways to solve them. For example, when given the problem 1000-998, one student did the following: 1000-900=100; 100-90=10; 10-8=2. Another approached it in a similar fashion, saying 900+100=1000; 100-98 =2. And yet another student counted up from 998 to 1000, realizing that they only had to count up 2 numbers. Each student arrived at the correct answer; each answer was the result of a different approach. They explained their thinking, and it was as varied as they are.
The thing that fascinates me about this is that when I was a student in upper elementary school, there was only one way to approach that problem: you set it up vertically, canceled the zeroes, borrowing from each previous digit and arrived at the solution of 2. There you have it! There was one way to do it and one correct answer. For everyone. No leeway allowed. And, boy, could those zeroes be tricky. Continue reading
Assessments are performed at the beginning of each school year. Teachers use them to determine what children remember after a long summer, which skills are strong and where additional support might be needed. Most of the assessments are measured against the “norm,” or the average student of that grade or age. When the results are favorable, the student is deemed to be on the right path; when they are less than optimal, it is determined what skills are lacking and what help is needed to reach that benchmark or average. Though this information may be useful in determining an instructional path for the development of specific skills, it cannot serve as the guiding force for learning. 
I came across this puzzle the other day and found myself running through all of the strategies I use to figure out math puzzles. I am generally good at these types of puzzles and knew I could figure it out. I added, subtracted, multiplied, divided, squared numbers, etc. I knew the solution was obvious, but still I couldn’t find the answer. I ended up “cheating” and looking at the answer that was provided. The interesting part of this puzzle was not that it was challenging or that I couldn’t come up with the right answer. I love a challenge. It was that I applied tried and true strategies and they simply didn’t work. The answer* was simple…very simple. 
The Montessori Message 