Information Age Education Blog
High School Mathematics Standards
James T. Fey (Jim Fey) is a national leader in math education. I first got to know him more than 30 years ago through his research and development work on use of computers in elementary school mathematics. There he explored how computers can be used to make significant changes in the math curriculum.
As an example, think about the math knowledge and skills in decimal arithmetic, percentages, angles, and the use of a protractor and compass needed to create pie charts. A couple of years before students acquire such knowledge and skills in the traditional grade school curriculum, they can create and use pie charts with the help of computers. The key idea is that they can make use of their vision abilities (their “mind’s eye”) in understanding pie charts, and creating them on a computer, before they have developed the math knowledge and skills to create them using “by hand” methods. Jim Fey referred to this specific visual math approach to curriculum change as an inverted curriculum.
Through my recent email interaction with Jim Fey, I became acquainted with two of his recent articles (Fey, June, 2014) and (Fey, et al., 2013). I believe many math educators will enjoy reading these two articles. The purpose of this IAE Blog is to briefly delve into their content.
Over the years, many math educators have helped to address the problem of improving K-12 math education and the preparation of math educators. Significant progress has occurred, but to me it seems that the progress has been slow and is not keeping up with the development of computers and related changes in our world.
I am specifically interested in how the human and computer brains can work together in math education. Outside of the school setting, computer software and hardware have been developed as a powerful aid to representing and helping to solve a broad range of math problems. The speed and cost effectiveness of such tools has led to computers becoming a routine aid to people who make use of math to help solve problems in essentially all disciplines of study.
During the past 50 years, the secondary school math curriculum in the U.S. has changed quite a bit. For example, what used to be an elective 9th grade algebra course is now widely required and taught at the 8th or 9th grade. An algebra for all movement has the goal that students will take algebra by the time they finish the 9th grade. A variation on that movement is to require that all students take Algebra 1, Geometry, and Algebra 2 in order to graduate from high school.
Maryland High School Math Requirements
Fey’s 2014 article provides commentary on recent work by the Maryland legislature. The legislature wants all students graduating from high school to be college and career ready. Quoting from Fey’s article, the legislated requirements are:
- Beginning with the 2014 freshman class, every Maryland high school student will be required to enroll in a mathematics course in each school year.
- Beginning with the 2015-2016 school year, all students in the 11th grade will be assessed to determine whether they are ready for college-level coursework in mathematics, using acceptable college placement cut scores.
- The Maryland State Department of Education (MSDE), in collaboration with local school systems and public community colleges, will develop and implement, by the 2016-2017 school year, transition mathematics courses or other instructional opportunities to be delivered in the 12th grade to students who have not achieved college and career readiness by the end of the 11th grade. These transition courses will include a reassessment of college readiness after completion of the course.
The remainder of this IAE Blog entry focuses on some of Fey’s thoughts about these requirements.
College and Career Ready
Quoting from Fey (2014):
Most people understand ‘college ready’ to mean ‘prepared to succeed in credit-bearing college courses.’ But it is very hard to construct a list of mathematical concepts and skills that are necessary and sufficient for all students. The typical response to this challenge is to argue that all students should master prerequisites for success in courses at or above the level of College Algebra. But students heading to majors that use little mathematics or that emphasize quantitative reasoning based on concepts and methods of probability, statistics, and discrete mathematics could argue persuasively that readiness for the traditional College Algebra course is an inappropriate goal for college preparation.
The phrase “college and career ready” seems to roll easily off one’s tongue. But, education has many other important goals. For example, I want students to become ready to be good and responsible parents, and I want them to become responsible adult citizens of their country and the world. For a more comprehensive list of goals for education in the U.S., see the Appendix of Common Core State Standards for K-12 Education in America (Moursund & Sylwester, 2013).
Transition Math Courses for 12th Graders
After discussing major challenges and past failures in developing such transition courses for 12th grade students who failed the 11th grade test, Fey (2014) recommends looking carefully at:
…[A] blended curriculum strategy [that] has been developed by the Carnegie Foundation for the Advancement of Teaching through its Community College Pathways project. Statway is a one-year pathway focused on statistics, data analysis, and causal reasoning that combines college-level statistics with developmental math. Quantway is a pathway focused on quantitative reasoning that fulfills developmental requirements with the aim of preparing students for success in college-level mathematics. The Carnegie Pathways project does more than provide innovative curriculum content.
The strength of Pathways is not just in its curriculum.… Pathways help students to see themselves as capable of mathematical success through interventions focused on non-cognitive factors and the development of language and literacy skills. In addition, Pathways instruction utilizes a pedagogical model that supports ambitious mathematics learning. Through the Advancing Quality Teaching component of the Pathways, faculty are supported to develop these pedagogical practices using innovative approaches to faculty engagement and development.
Community colleges and universities have had many years of experience in trying to deal effectively with students who have been unsuccessful in their high school mathematics courses. The task of developing and staffing a 12th grade remedial math course that will have more success than higher education has achieved is formidable. Notice that the Carnegie Foundation program mentioned above is not one of reteaching and/or requiring “more of the same” content or for a specific test.
Who Needs this Math?
Continuing to quote from Fey (2014):
…when the National Center for Education and the Economy analyzed actual mathematical requirements of initial credit-bearing community college courses in nine of the most popular and diverse academic programs, they concluded:
Only one program in one college required entering students to have mastered the content of Algebra II before enrolling in that program … Many community college career programs demand little or no use of mathematics. To the extent that they do use mathematics, the mathematics needed by first year students in these courses is almost exclusively middle school mathematics.
I believe the “college and career ready” approach to math education is focusing too strongly on college readiness. There are many math-related responsible adult citizen topics that are not currently emphasized in the precollege curriculum. Many have to do with money topics such as financing major purchases such as a house or car, credit cards, “no money down” purchases, payday loans, compound interest, student loans, saving for emergencies, and saving for retirement.
Computer and Information Science
Fey’s 2014 article mentions computer technology, and the (Fey et al., 2013) article gives a somewhat deeper statement on this topic:
Information Technologies—Powerful tools that allow users to find and process information with mathematical methods are now ubiquitous in American life. But schools are only beginning to respond to the profound implications of this information technology for teaching and learning. If it is possible to simply ask your cell phone to perform any of the routine calculations taught in traditional school arithmetic, algebra, and calculus courses, what kind of mathematical learning remains essential? If those same tools can be applied to support student-centered exploration of mathematical ideas, how will the new learning options change traditional roles of teachers and students in the mathematics classroom and raise expectations for the mathematical challenges that students can tackle?
Personal computers, tablets, smartphones, and other computing devices will almost certainly transform school mathematics in fundamental ways. Intelligent response to that challenge will require creative research and development efforts and the courage to make significant changes in traditional practices. [Bold added for emphasis.]
The point being made in both articles is that past and current math education reforms mainly focus on doing “more and better” in what we have done in the past. Many of today’s math education reformers “miss the boat” by not basing their work of the ongoing research related to education and to the changes going on in our world due to computer technology.
There is widespread support to improve our math education system. But, approaches to doing so have become political and advocacy group “footballs.” I both laugh and cry when I read about legislative bodies consisting of people who know relatively little about education passing laws designed to improve education. I place far more faith in the ideas of people such as Jim Fey and his co-authors in the articles discussed here.
What You Can Do
When you hear people espousing changes to our current math educational system that they say will significantly improve it, ask: “Where’s the evidence that this will work? What specific math education goals are addressed?” Our goals should be to actually improve math education instead of just striving to have our students score higher on state, national, and international math tests. See Moursund (2014) for a discussion of math education goals. Statewide and nationwide changes should be based on careful research and a significant amount of small and medium scale pilot testing.
Fey, J.T. (June, 2014). High school mathematics standards in Maryland: Challenges and consequences of policy implementation. Maryland Equity Project. Retrieved 1/9/2015 from http://www.education.umd.edu/TLPL/centers/MEP/Research/k12Education/Fey_MathPolicyCommentary_62314.pdf.
Fey, J.T., et al. (2013). Essay on the future of math education. Published in an article by Valerie Strauss, The Washington Post. Retrieved 1/9/2015 from http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/12/06/the-future-of-high-school-math-education/.
Moursund, D. (2014). Math project-based learning. IAE-pedia. Retrieved 1/11/2015 from http://thetownkindle.com/link/math-project-based-learning-iae-pedia-aHR0cDovL2lhZS1wZWRpYS5vcmcvTWF0aF9Qcm9qZWN0LWJhc2VkX0xlYXJuaW5n.
Moursund, D., & Sylwester, R., eds. (2013). Common Core State Standards for K-12 Education in America. Eugene, OR: Information Age Education. Download the PDF file from http://i-a-e.org/downloads/doc_download/248-common-core-state-standards-for-k-12-education-in-america.html for the PDF document. Download the Microsoft Word file from http://i-a-e.org/downloads/doc_download/249-common-core-state-standards-for-k-12-education-in-america.html.
Readings from IAE Publications
Moursund, D. (2014). Communicating in the language of mathematics. IAE-pedia. Retrieved 1/10/2015 from http://iae-pedia.org/Communicating_in_the_Language_of_Mathematics.
Moursund, D. (2014). Computational thinking. IAE-pedia. Retrieved 1/10/2014 from http://iae-pedia.org/Computational_Thinking.
Moursund, D. (2014). Two brains are better than one. IAE-pedia. Retrieved 1/10/2015 from http://iae-pedia.org/Two_Brains_Are_Better_Than_One.
Moursund, D. (11/30/2014). Test scores are being far over-hyped. IAE Blog. Retrieved 1/10/2015 from http://i-a-e.org/iae-blog/entry/tests-scores-are-being-far-over-hyped.html.
Moursund, D. (8/14/2014). Four parables about education reform. IAE Blog. Retrieved 1/10/2015 from http://i-a-e.org/iae-blog/entry/three-parables-about-educational-reform.html.
Moursund, D. (6/27/2014). Improving math education. IAE Blog. Retrieved 1/10/2015 from http://i-a-e.org/iae-blog/entry/improving-math-education.html.
Moursund, D. (6/16/2014) Grand challenges in math education. IAE Blog. Retrieved 1/10/2015 from http://i-a-e.org/iae-blog/entry/grand-challenges-in-math-education.html.
Moursund, D. (2012). Using brain/mind science and computers to improve elementary school math education. Eugene, OR: Information Age Education. Download the PDF file from http://i-a-e.org/downloads/doc_download/239-using-brainmind-science-and-computers-to-improve-elementary-school-math-education.html. Download the Microsoft Word file from http://i-a-e.org/downloads/doc_download/239-using-brainmind-science-and-computers-to-improve-elementary-school-math-education.html.