Where's The Math in Common Core Math Problems?

Yesterday we linked an article about the stress on kindergartners because of Common Core standards.

Today we highlight Barry Garelick's article on 5th grade Math taught via Common Core standards.  From EdWeek and Developing the Habits of Mind for Algebraic Thinking:

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....a friend of mine who lives in Spokane directed me to the website of the Spokane school district, where they posted a math problem at a meeting for teachers regarding best practices for teaching math.

The teachers were shown the following problem which was given to fifth graders.  They were to discuss the problem and assess what different levels of “understanding” were demonstrated by student answers to the problem:



Not only have students in fifth grade not yet learned how to represent equations using algebra, the problem is more of an IQ test than an exercise in math ability.  Where’s the math?  The “habit of mind” is apparently to see a pattern and then to represent it mathematically.

Such problems are reliant on intuition — i.e., the student must be able to recognize a mathematical pattern — and ignore the deductive nature of mathematics.  An unintended habit of mind from such inductive type reasoning is that students learn the habit of inductively jumping to conclusions.  This develops a habit of mind in which once a person thinks they have the pattern, then there is nothing further to be done.  Such thinking becomes a problem later when working on more complex problems.

...Giving students problems to solve for which they have little or no prior knowledge or mastery of algebraic skills is not likely to develop the habit of mind of algebraic thinking.  But the purveyors of this practice believe that continually exposing children to unfamiliar and confusing problems will result in a problem-solving “schema” and that students are being trained to adapt in this way.  In my opinion, it is the wrong assumption.   A more accurate assumption is that after the necessary math is learned, one is equipped with the prerequisites to solve problems that may be unfamiliar but which rely on what has been learned and mastered.  I hope research in this area is indeed conducted.  I hope it proves me right.

Barry Garelick has written extensively about math education in various publications including The Atlantic, Education Next, Educational Leadership, and Education News. He recently retired from the U.S. EPA and is teaching middle and high school math in California.

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Read more here. 

MEW note: if you think the above problem (page 1) is vexing, click on the link from the Spokane math teachers' meeting and check out page 2 for further instructions on the button problem. 

  

Is this really about math?