My view of conceptual understanding is the ability of far transfer-the ability to identify areas to which your content is relevant, and use it to solve problems. I learned math in the old school way, and I studied quantitative analysis in my accounting training. QA involved application of math concepts to solve problems in finance and business. While studying QA, I became aware of conceptual understanding and its televance in transfer of learning to problem solving.. One day I was explaining my predicament to an instructor, telling him, that i seem to know and understand procedure, but I am unable to apply it. He then explained to me that when you see a question, identify the content area, and over time you will learn to use your theoretical knowledge in solving problems. I remember we were doing business statistics, and we had a case study and he asked what we think was required based on the scenario presented? He singled out all the data that was included in the question, and related it to what we had already learned. The question involved making predictions about a population based on a sample. He pointed out that the requirements should direct our minds to significance testing, and since we had been given a sample size of 30 and over, we could use that sample to make predictions about the population. After that explanation, I started to understand how the basic knowledge opens the door for higher level thinking, and problem solving. But educationists expect that once you have knowledge -if there is conceptual understanding- that you can use that knowledge for problem solving. It does not happen like that. You have to own that knowledge - it must not be superficial, and examples must be presented of how that knowledge can be used, and based on your developmental level your knowledge moves from being inert to being usable. I have seen students in grade 5 given a superficial explanation of probability, and shortly after assessed using questions that requires a deep understanding of probability, that their instructions could not have provided.
My view of conceptual understanding is the ability of far transfer-the ability to identify areas to which your content is relevant, and use it to solve problems. I learned math in the old school way, and I studied quantitative analysis in my accounting training. QA involved application of math concepts to solve problems in finance and business. While studying QA, I became aware of conceptual understanding and its televance in transfer of learning to problem solving.. One day I was explaining my predicament to an instructor, telling him, that i seem to know and understand procedure, but I am unable to apply it. He then explained to me that when you see a question, identify the content area, and over time you will learn to use your theoretical knowledge in solving problems. I remember we were doing business statistics, and we had a case study and he asked what we think was required based on the scenario presented? He singled out all the data that was included in the question, and related it to what we had already learned. The question involved making predictions about a population based on a sample. He pointed out that the requirements should direct our minds to significance testing, and since we had been given a sample size of 30 and over, we could use that sample to make predictions about the population. After that explanation, I started to understand how the basic knowledge opens the door for higher level thinking, and problem solving.
But educationists expect that once you have knowledge -if there is conceptual understanding- that you can use that knowledge for problem solving. It does not happen like that. You have to own that knowledge - it must not be superficial, and examples must be presented of how that knowledge can be used, and based on your developmental level your knowledge moves from being inert to being usable. I have seen students in grade 5 given a superficial explanation of probability, and shortly after assessed using questions that requires a deep understanding of probability, that their instructions could not have provided.