Information Age Education
   Issue Number 23
August, 2009   

This free Information Age Education Newsletter is written by David Moursund and produced by Ken Loge. For more information, see the end of this newsletter.

When I read the found the following newspaper article, I found it quite troubling. Pay particular attention to the second paragraph that I have quoted.

Alloway, Kristen and Rundquist, Jeanette (6/15/09). N.J. Board of Education adopts tougher standards for 3rd, 4th grades. The Star-Ledger. Retrieved from http://www.nj.com/news/index.ssf/2009/07/nj_board_of_education_adopts_t.html#more

TRENTON. As part of an ongoing effort to boost academic expectations and achievement, the state today made it harder for New Jersey's third and fourth graders to prove their proficiency on annual tests.

Under the new standards adopted by the state Board of Education, public school students who took the exams in May needed to get 50 percent of the answers correct to show proficiency on the language arts and math tests. Previously, the "cut scores" needed to be deemed proficient were between 40 and 45 percent.

The test scores are broken down in three categories—advanced proficient, proficient and partially proficient. State officials immediately cautioned that raising the bar could mean more students being found "partially proficient" when districts receive the results later this year.

Being "Proficient" with 50 Percent Correct Answers

Of course, I do not know what questions are on the math test. However, in my mind I image an adult trying to use math in our society and quite often getting incorrect answers. Of what value is level of math knowledge and skill to the person or to the people this person works for and/or with?

From time to time I have heard the assertion that the average adult in the United States performs in math at about the sixth grade level. Perhaps this means that if adults are given the New Jersey sixth grade math test, their median score will fall in the “proficient” range.

This possibility suggests a number of things to me:
  1. It does not take a lot of math knowledge and skills to function as an “average” adult in out society.
  2. The average adult in our society does not have the math knowledge and skills to effectively deal with the money-problem situations that they encounter. (Think in terms of borrowing money and the related compound interest; think in terms of saving and investing money for future uses.)
  3. The secondary school math education system in the United States is not very effective in providing future adults with long-term knowledge and skills in the areas of math that the curriculum covers. The average adult in this country has taken a number of school math courses above the level of the sixth grade. Indeed, three years of high school math (grades 9–12) are typically required for high school graduation.

Math Maturity

You have heard the quote, “You can lead a horse to water, but you can’t make it drink.” Our education system leads students to math, and requires them to pass math courses. However, the ideas discussed above suggest that for a majority of students, the long-term residual impact—the long-term retention of usable math knowledge and skills—is modest.

In recent years I have thought about this situation in terms of math maturity. Math maturity focuses on one’s long-term retention of usable math knowledge and skills. It is one’s ability to think mathematically, using the math that one has had an opportunity to learn. It is one’s ability to communicate effectively (read, write, speak, listen) in the language of mathematics. See http://iae-pedia.org/Communicating_in_the_Language_of_Mathematics. It is one’s ability to recognize and understand problems in which math might be a useful aid in solving the problem. It is one’s ability to quickly relearn math that one has previously studied, but has forgotten some of the details. See http://iae-pedia.org/Math_Maturity.

The key to increasing math maturity is learning math with understanding. Learning math through rote memorization and regurgitation contributes little to increasing one’s level of math maturity.

Now, let’s go back to the current emphasis on students throughout the country being required to take math courses and to demonstrate they have achieved a level of “proficient” or above on state and/or national tests. What our math education system has learned is that it is possible to “teach to the test” in a manner that will help a great many students score at a proficient or higher level. Here are two widely used approaches:
  1. Make sure that curriculum content, instructional processes, and the teacher-developed assessment are consistent with and supportive of learning to perform well on the state and national tests. For example, math textbook writers and publishers put a tremendous amount of effort into aligning their material with the various standards that states have set.
  2. Teach students how to do well on objective tests. This includes giving quite a bit of practice in taking such math tests in an environment that is similar to what is being used in the state or national test.
Each of these approaches contributes to improving test scores. Neither of these approaches focuses on increasing math maturity. Thus, our math education system is putting a lot of effort into increasing student math test scores, but this may well be having relatively little impact on the average student’s ability to make long-term effective use of the math he or she has covered in school coursework.


Constructed Responses Versus Objective Tests

Today’s tight school budget situations are leading to larger class sizes. Consider a writing teacher faced by an increasing number of students. The teacher might think: “How many written essays should I assign this term? How long should I require them to be?” “I just don’t have the time to provide as much feedback on student writing as I know I should.”

Math teachers face the same type of question. “When I assign homework, how much emphasis should I place on students providing responses that require careful reading and analysis on my part in order to provide useful feedback? Ditto for tests.”

One measure of math maturity is performance in constructed response (open-ended response) types of questions. Such questions are more challenging to students and more challenging to teachers. In terms of state and national math tests, it is quite expensive to find, train, and make use of test graders who grade constructed responses relatively rapidly and in a valid, reliable, and fair manner. See, for example, http://www.michigan.gov/mde/0,1607,7-140-22709_31168_31773-97188--,00.html. This leads many school districts and states to not use standardized math tests with constructed responses.

Final Remarks

This IAE Newsletter focuses mainly on math education and the idea of math maturity. The same ideas apply in each academic discipline. Thus, we can think about teaching history in a manner that increases a student’s level of “history maturity.” Such an approach to education in each discipline provides a strong argument for having smaller class sizes and better-prepared teachers.


About Information Age Education, Inc.

Information Age Education is a non-profit organization dedicated to improving education for learners of all ages throughout the world. IAE is a project of the Science Factory, a 501(c)(3) science and technology museum located in Eugene, Oregon. Current IAE activities include a Wiki with address http://IAE-pedia.org, a Website containing free books and articles at http://I-A-E.org, and the free newsletter you are now reading.

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