Content Knowledge MAIT 402

Mind the Gap / Session 2

1.   In recounting her journey through many educational reforms, Diane Ravitch makes a number of provocative statements. Choose two, quote them, and personally respond.

“Market reforms have a certain appeal to some of those who are accustomed to “seeing like a state”. There is something comforting about the belief that the invisible hand of the market, as Adam Smith called it, will bring improvements through some unknown force. In education, this belief in market forces lets us ordinary mortals off the hook, especially those who have not figured out how to improve low-performing schools or to break through the lassitude of unmotivated teens.”

I don’t see how choice - charters and vouchers would have ever been a viable option for education. Comparing education to a free market should reveal serious contradictions not a plan of action.

Some of the principles that must exist in order for a free economic market to function are lacking or impossible in public education. Individual rights as well as fair and equal treatment must be assured for a market to naturally reorder. Understood in the concept of individual rights is the tenet that individuals will act in their own best interest. So, applied to education, all parties, administrators, teachers, students, parents and communities, have a predictable role to play. In public education, many are unable or unwilling to act in their own interest. Students or parents, due to language, economic or other barriers can’t enroll, apply or move to the best schools. Communities are financially unable to support local schools at a level equitable to more affluent districts. 

If, however, a free education market did exist, and was able to reorder. The best public and charter schools would survive, leaving the weakest, poorest schools to close. This leaves the students needing the most with the fewest options contradicting the free market principle of fair and equal treatment. 

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“I was also concerned that accountability, now a shibboleth that everyone applauds, had become mechanistic and even antithetical to good education. Testing, I realized with dismay, had become a central preoccupation in the schools and was not just a measure but an end in itself. I came to believe that accountability, as written into federal law, was not raising standards but dumbing down the schools as states and districts strived to meet unrealistic targets.”

First, this may be an unpopular opinion, but I do not like Diane Ravitch’s writing style. She has a spiraling, nonlinear organization with statements and statistics, and at times makes questionable vocabulary choices. Shibboleth? Really?

So the quote may not be that provocative. Most can see that standardized testing has morphed from a measure of accountability to the only method and measure. In my personal experience, the actions my school and department have taken to improve test scores do not improve overall education. We have adjusted pacing guides to the STAR test schedule. We eliminate enrichment concepts and activities that won’t appear on the tests. We use STAR test formatting (exclusively multiple choice) for common department assessments teaching students to take the test and not to think critically. We have completely eliminated preparatory classes because we are penalized for students in classes below the level of Algebra 1. 

The new common core standards seem to focus on standards for math practice that value critical thinking - problem solving, modeling, abstract as well as quantitative reasoning, constructing arguments, using appropriate tools and attending to precision. But the actual standards for particular concepts have changed little. I’m not sure how the additional standards for practice will change the nature or focus of the exams.

2.  How would you characterize a well-educated person? What should any well-educated person know in today’s world?

“A well-educated person has a well-furnished mind, shaped by reading and thinking about history, science, literature, the arts and politics. The well-educated person has learned how to explain ideas and listen respectfully to others.”

To Ravitch’s definition, I would add that a well-education person has an ability to reason, form plans and solutions to practical arithmetic, algebraic, geometric and spatial problems. Neglected in a list of concrete attributes a person should know would be the undefinable benefits of an education. Students form ethics and morals and standards of behavior throughout their school experience. Adolescent brains continue to develop until their early twenties. Synapses are connected during this development that an adult will use for reasoning, memorizing critical thinking.

3.  Thinking about the class discussion on the book, what stands out for you? What would you have liked to say that you did not say?

I can’t remember much discussion on how standards disintegrated into standardized testing.  I would have liked to have shared my anecdotal evidence supporting the disconnect between tests and standards. We have departmental common assessments written to mimic the STAR tests. They are multiple choice, worded similarly to released STAR questions, formatted to look like STAR tests. Last year I gave the departmental exams as well as my own exams for several tests. My exams changed just the numbers in the problems and eliminated the multiple choice options. My students averaged 25% higher on the STAR like tests. I contend that the STAR tests aren’t even accurately assessing mastery of concepts.

4.  Choose one gap you listed from your subject area and identify 3 resources that can help you fill that gap. List these and discuss what you learned from one.

My guiding question coincides with my gap in subject area (pedagogical) knowledge, so I may have had a head start. One of the new common core standards for mathematical practice is to make sense of problems and persevere in solving them. 

I have found that students are reluctant to solve word problems. They also have issues with problems that may not match exactly  problems they have already solved. If they do not know every step to solving a problem, they will often not even start. I want to know how to teach this concept/practice better.

Resources:

Web site:  www.mathforum.org

article:

Kapur, Manu. (2010). Productive failure in mathematical problem solving. Instructional Science: An International Journal of the Learning Sciences, v38 n6 p523-550 Nov 2010

book: 

Polya, G (1945) How to Solve It A New Method of Mathematical Method. (1945) Princeton: Princeton University Press 

www.mathforum.org is a website dedicating to problem solving. It is maintained by Drexel University. It includes methods of problem solving, teaching strategies, problems of the week and solutions, rubrics for grading problems.

5.  How were two of my annotated resources useful to topic/question?

Kapur, Manu. (2010). Productive failure in mathematical problem solving. Instructional Science: An International Journal of the Learning Sciences, v38 n6 p523-550 Nov 2010

Helpful in that it described a productive failure method of instruction that resulted in scores higher than the direct instruction/practice method. It may not be the best source though, just due to the small number of participants/students (75).

MathLeague.org competition. (2012, March) DVC, Pleasant Hill, CA Field Experience

Helpful in that it identified a gap between the best seniors at CHS and 8th graders at other competing schools. I want to find a way to prepare my math club kids to be competitive, in local competitions as well as in college and later. I also got practice problems and solutions used in the competition to help prepare for next year.