We learned today that we cannot use the verbage "students will understand..." as a teaching objective. This is because our objectives must be measurable, and one cannot measure something as elusive as understanding. I think what troubles me most is the fact that teaching for "understanding" should be a primary goal as a teacher. If I am expected to teach rote methods, without any hope of a student reaching some level of understanding of a subject, then I have gone into the wrong profession. But thankfully, I believe that we are just defining where to use the term "understanding".
I find it interesting that it is used by the National Council of Teachers of Mathematics in defining what they term "The Learning Principle" (one of six guiding principles in mathematics education):
The Learning Principle
Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. Research has solidly established the importance of conceptual understanding in becoming proficient in a subject. When students understand mathematics, they are able to use their knowledge flexibly. They combine factual knowledge, procedural facility, and conceptual understanding in powerful ways. Learning the "basics" is important; however, students who memorize facts or procedures without understanding often are not sure when or how to use what they know. In contrast, conceptual understanding enables students to deal with novel problems and settings. They can solve problems that they have not encountered before. Learning with understanding also helps students become autonomous learners. Students learn more and better when they take control of their own learning. When challenged with appropriately chosen tasks, students can become confident in their ability to tackle difficult problems, eager to figure things out on their own, flexible in exploring mathematical ideas, and willing to persevere when tasks are challenging. Students of all ages bring to mathematics class a considerable knowledge base on which to build. School experiences should not inhibit students' natural inclination to understand by suggesting that mathematics is a body of knowledge that can be mastered only by a few.
http://standards.nctm.org/document/chapter2/learn.htm
This is the type of teaching that I want to do. And while this may not be "measurable" on any assessment, it is the measure I hope to have for my own success.
Ah, please don't think that we're advocating rote, low level thinking! Eek!
ReplyDeleteThis does pose a great question: How will you *know* that a student has attained that level of understanding and higher order thinking that NCTM articulates so well? Can they solve problems that require high levels of understanding? Construct a webpage to explain what they understand to classmates? Apply their mathematical understanding to a science problem solved creatively? Then your learning objectives are about doing those projects successfully... The NCTM statement is rich with examples of learning objectives that enable us to assess whether kids do understand.
And "measure" can mean a score on a rubric that includes all sort of dimensions of problem solving.
We agree! Rich understanding is always the goal. Now... how do you know when kids are there? :)
"EEK!" is exactly what I thought as well when we were discussing this in class! I agree with the fact that it is *difficult* to quantitativley measure a student's understanding; I simply disagree with the conclusion that as such it cannot be used as a teaching objective. In fact I see the term "understanding" used in many of the teaching standards and expectations put forth by the NCTM.
ReplyDeleteWhat I have discovered is that it is most likely a matter of semantics-- the goal of mathematical understanding is quite obviously there for both of us.
If you think that I was advocating learning my memorization or rote just because I advocate measurable learning objectives, you have missed the entire point of what I have been doing in class.
ReplyDeleteYou said a very interesting thing in the 1st paragraph in your reply above. You said "I simply disagree with the conclusion that as such it cannot be used as a teaching objective". I never said it couldn't. I said it was a vague term when used as a Student Learning Objective. We all have the GOAL of "understanding" for our students. But how do we get them to "understand". By chipping away at measurable learning objectives that together construct the whole of understanding. That is what constructivism is all about.
Robin, I have certainly not missed the point of what we've been accomplishing each week in class! You have taught me how valuable teaching for understanding really is! Completely OPPOSITE of teaching for rote memory, where understanding is not even considered! This is why I think I was so surprised at your blanket statement that one should NOT use the verb "understand" in our learning objectives. But as I said in the original post, I believe that I am beginning to *understand* that it is a matter of when to use that word.
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