Friday, December 4, 2009

College Readiness: High School Math Pathways

This is a work in progress. It will undergo frequent changes and updates. 
To contribute comments and feedback, e-mail LT at ThinkAlgebra.

Is your child in a math sequence that prepares her for college mathematics or for remedial math? Will she be ready for formal algebra in middle school?
Approximately 80% of high school students want some form of post-secondary education, either an associate’s degree at a community college or a bachelor’s degree at a four-year college or university; however, according to Achieve, "Only a subset end up taking a curriculum that prepares them for college."
Reality Check: Most students are not fluent in arithmetic needed for algebra. Algebra courses are watered down. State standards lack coherence, rigor, and focus. In NCLB, “mediocre” performance is labeled “proficient.” Students lag behind their peers in high-achieving nations, starting in elementary school. 
ThinkAlgebra outlines high school math pathways (common core algebra courses and assessments that make teachers, students, and schools accountable), reiterates the contention that K-8 math should be fixed first, advocates that schools use good programs that are already available (e.g., Singapore Math, ADP Algebra), believes that four-year college-bound students should take at least one college-level math course in high school, stipulates that not all students need to take algebra, and champions the retraining of teachers to teach world-class math.

High School Math Pathways by ThinkAlgebra is a response [alternative] to the college-career readiness draft from the Common Core State Standards Initiative (CCSSI). Click the chart for a larger view.
The chart, while incomplete and in first draft form, represents the academic realities of college preparation. It shows real algebra courses supported by levels of achievement as defined by the American Diploma Project (ADP) Assessment Consortium. (Note. I named Calculus Prep and [College] Algebra Prep pathways after the two University of Arizona math placement tests.) While the ADP algebra exams are not perfect, they can be refined and polished over years of use.

College-career readiness standards should focus on the "80% of high school students" who want to go to college. Furthermore, they should have specific common assessments to determine mastery along the pathway to guide students into informed choices. But, this is not how CCSSI approaches the problem.
Pathway Assessments in Algebra
We can use programs already in play, such as Algebra 1 standards,  Algebra 2 standards, and their assessments (see exam links below) from the American Diploma Project (ADP) by Achieve. They are used by several states and illustrate that students coming into algebra are not prepared.
The ADP topics match well with most of the algebra topics advocated by the National Mathematics Advisory Panel.
Algebra II Exam

Students need authentic algebra courses, not diluted courses. The challenging, ADP algebra courses and exams would be the same for all students who take Algebra I and II. Students must work hard and study more to achieve the proper levels of mastery. The scores on ADP Algebra I exam translate to Below Basic, Basic, Proficient, and Advanced, while the Algebra II exam scores translate to Needs Preparation, Prepared, and Well Prepared [for College]. STEM and non-STEM students who need calculus are expected to do much better on the ADP algebra exams: Algebra I ( Advanced) and Algebra II (Well Prepared).

Sunday, October 11, 2009

Content Mastery And Skill Fluency

Some Thoughts on Reports I Read Recently
Also, read the latest at K-12 Education by ThinkAlgebra

1. The GAP!
Today, more high school kids are tackling advanced math courses and getting higher grades, but this radical change has not improved math skills much since the 1970s, according to data from the NAEP Long Term Trends (LTT) study (1978-2008) for 17-year olds.¹ In short, there is a large gap between what K-12 schools say they are teaching and what students are actually learning. The gap is much smaller in high performing nations like Singapore and Hong Kong.

Student performance on both national and international tests and on math placement tests at colleges and universities indicates the woeful lack of effectiveness of K-12 math instruction. The LTT longitudinal study, which started in the 1970s and given every few years, demonstrates that our students are about the same today as they were in the 1970s, says Mark Schneider¹, a researcher from the American Enterprise Institute for Public Policy Research (AEI).  Tests like PISA, TIMSS, the regular NAEP, given every two years, and college placement tests support the LLT study. Attempts to improve math performance (e.g., NCTM math) have not worked as expected. Our students lag behind internationally, not by a little, but by a lot.

Schneider points out a lack of rigor in many high school math courses. He argues, "If policymakers decide that a mark of a successful high school career is the completion of Algebra II, then schools enroll more students into a course called Algebra II. But not all math courses are equal--and it is easier to rebrand courses and still teach low-level math than it is to increase the rigor of math instruction [my emphasis]."¹  

Solving Quadratic Equations in Algebra-1

Students who want to go to college and who are given weak or substandard algebra courses in high school will end up taking remedial math courses when they apply for postsecondary education. The college math placement test is mostly algebra skills There are huge numbers of high school graduates in the remedial math trap because of bad instruction and diluted algebra courses. For example, at Pima Community College in Tucson, Arizona, over 380 remedial math classes are offered in its Fall 2009 catalog, ranging from basic math (6th-grade math) to intermediate algebra (Algebra II).