Monday, June 23, 2008

Expectations Need to Be Measureable and Concepts need Time

Standards are "expectations". They are the targets. They are what you are shooting for. They define what is expected of the students at specific grade levels in specific subject areas. (In the United States, curricular expectations are defined as "standards".) In order for standards to be effective, they must be specific.

Specific expectations are easy to measure. If your expectation is that your child know the capitals of all of the states, that is specific and measurable. You can easily discern if a student has met the standards. How? Have him demonstrate that he knows the capitals.

And that is why so many people are concerned about "standards". It is the vagueness of the standards that troubles us.

I came across an article by William H. Schmidt entitled "What's Missing from Math Standards?" which was published at the American Educator website in the Spring of 2008. He discussed the findings of the Third International Mathematics and Science Study (TIMSS).

According to Schmidt, TIMSS found that "student performance is directly related to the nature of the curricular expectations." He explains that he does not mean the instructional practices, but rather "the nature of what it is that children are to learn within schools."

"The TIMSS research has revealed that there are three aspects of math expectations, or standards, that are really important: focus, rigor, and coherence."

Here are Schmidt's comments about all three of these aspects of expectations.


"Focus is the most straightforward. Standards need to focus on a small enough number of topics so that teachers can spend months, not days, on them. . . [i]n the early grades, top-achieving countries usually cover about four to six topics related to basic numeracy, measurement, and arithmetic operations . . . In contrast, in the U.S., state and district standards, as well as textbooks, often cram 20 topics into the first and second grades."
It is Schmidt' s opinion that this number of topics is far more than any primary grade student can absorb.

"Rigor is also pretty straightforward -- and we don't have enough of it.... .[I]n the middle grades, the rest of the world is teaching algebra and geometry. The U.S. is still, for most children, teaching arithmetic. . . [O]ther countries outperform us in the middle and upper grades because their curricular expectations are so much more demanding, so much more rigorous."

Coherence may not be as easy to grasp as focus and rigor, but according to Schmidt, "it is the most important element." He explains that there is a formal academic body of knowledge that has been parsed out and sequenced from kindergarten through 12th grade, and he describes how especially important this parsing and sequencing is in the subject of math.
"Topics in math really need to flow in a certain logical sequence in order to have coherent instruction. If you look at the math curriculum of top-achieving countries, you see a very logical sequence. The more advanced topics are not covered in the early grades. Now that seems obvious -- until you look at state and district standards in the U.S. Everything is covered everywhere. Far from coherent, typical math standards in the U.S. often appear arbitrary, like a laundry list of topics."
Some of you may want to consult the entire article to see why our country has such unfocused, undemanding, and incoherent math standards.

Two related articles can be found
here and here.


Some additional thoughts . . .

By spreading topics all through the curriculum, nothing is covered in depth. Teachers are expected to cover so much material during the year that they must fly quickly to the next topic, meaning that there isn't time for a student to grasp the coherence of one concept with another. There is rarely time for the feeling of "Aahhh! I get it!"

Depth is better than shallowness. Kids can get their thoughts around a concept and understand connections when a topic is covered deeply and thoroughly.

For some reason this picture is going through my mind right now: I'm thinking of trying to drink lemonade through a straw -- after we have spread it 1/8 inch thick all over the table or counter top. And we only have one minute to do it!

That might be how many of our children feel when they are trying to "get hold of a math concept". This produces frustration and a feeling of "there's something wrong with me -- I didn't get it."


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