Integrated Math in 9-12

This concerns higher mathematics education in secondary schools within the Common Core standards initiative adopted by 40+ US states, including California. There are many good things about this initiative, including the creation of consistent educational standards across the states. Math education shouldn't vary by state. We should be able to achieve economies and qualities of scale by avoiding divergent textbook requirements, for example. However, there are two allowed "pathways" for mathematics within the standards, which are:

• 1. Algebra, Geometry, Intermediate Algebra, and Precalculus (the traditional path)

  2. Integrated Math I, IM II, IM III, and Precalculus (the integrated path)

In most states, such as California, school districts may choose their path (see article). San Diego Unified School District (SDUSD), the second largest district in the state, has chosen the integrated path and deployed it, starting in the 2014-2015 school year in a phased approach (see link and [2]). Thus, for SDUSD, the adoption of the Common Core is coincident with the switch to the integrated path. While I have no disagreements with the integrated path in theory, what follows are the several practical problems with the integrated approach that occur to me.

• • New textbooks must be written and debugged. (See below)

  • Teachers must learn to teach new material. For example, the middle school Algebra teacher must learn to teach items which were previously part of Geometry and Intermediate Algebra in order to teach IM I. Even some Precalculus is included in our IM I (Adv), in the form of vectors, dot products, and matrices. In fact, some SDUSD material suggests that taking the advanced versions of IM I to III will eliminate the need for a Precalculus course.

  • Consistency across institutions is fragmented. The student who changes school districts (relocates in or out of the integrated pathway) has a variety of holes in their mathematics education! Hopefully, one path or the other becomes standard.

  • Many existing resources are structured according to the traditional path. Kahn Academy, for example, which is a recommended resource by the California Department of Education (CDE), is traditionally structured.

  • The simultaneous transitions (CC + IM) that we have experienced have produced holes. My son took Pre-Algebra in 2013-'14, followed by IM I in 2014-'15 with the same teacher at the same school. IM 1, as written, assumes the student has been taught the Pythagorean Theorem as it is regularly used in IM 1 for computing distances in the x-y-coordinate system. However, the old Pre-Algebra course neglected to cover this important theorem and a gap formed. (I believe his course was even the "Adv" version of Pre-Algebra.) The new "CC Math 8" course will now supposedly cover this, and we will just chalk up the experience of my son and his classmates to a transition problem.

Textbooks (and their shortcomings)

The remainder of this post concerns just the textbooks for integrated mathematics. See the instructional material portion of California's Common Core website, here. As of the 2014 adoption report, only one publisher has submitted an IM I book to the CDE for evaluation, Pearson. In contrast, ten books were submitted by a variety of publishers for Algebra I. (Note that several of these algebra books appear to be California specific.) The report lists no books for IM II and III.

SDUSD has adopted the three book series by Pearson Education, for sale here*. The Pearson book for IM I is in its first edition and carries a 2013 copyright. The Pearson books were developed by the CME project of the Education Development Center, Inc. (EDC) and the EDC appears to hold the copyright. There appear to be two surprises to this. The first is that the CME project was funded by the NSF and its output goes to the for-profit Pearson Education (aka Pearson PLC of Britain). The second is that the focus of the CME project as explained on their website is the traditional path of Algebra 1, Geometry, Algebra 2, see EDC link regarding CME and the CME home page. The latter currently reads, "Welcome to the CME Project Website! CME Project is a four-year, NSF-funded, comprehensive high school mathematics program that is problem-based, student-centered, and organized around the familiar themes of Algebra 1, Geometry, Algebra 2, and Precalculus."

I have submitted numerous errata, defects, and suggestions to Pearson (see my PDF) concerning the final chapters of the CME Project's IM I. Surely time and effort went into the CME project, but also a big investment locally has been made at $79 per book + training [2]. It appears to me that the three integrated books are simply a quick reformulation of the traditional books! (Since internal references are often incorrect and some material is presented out of order.) Overall, I'm frustrated and wonder what becomes of our investment. In the long-term, we need other entrants for competition! Please submit additional serious findings on Pearson to me and k12customerservice@pearson.com. I think a respectable publisher should publish their own errata! I see that Pearson has introduced new integrated mathematics products, entitled Pearson Integrated High School Mathematics Common Core, copyright 2014, here. These new products are workbooks and presentation materials and not textbooks. For a set of open source textbooks, see the MVP project.

Sources:

• 1. Common Core web pages of San Diego Unified School District. http://www.sandi.net/Page/61304

  2. Board agenda item E3 of the Dec 10, 2013 meeting authorizes SDUSD to spend $22.5M on Pearson's CME Project Mathematics I, II, and III books and associated training. Details here and here and here. Another $405,000 was authorized to cover middle school materials on Jan 14, 2014, in agenda item I23.

  3. California Common Core State Standards - Mathematics, adopted by the California State Board of Education, available on http://www.cde.ca.gov/re/cc/index.asp

  4. Common Core State Standards Initiative. http://www.corestandards.org/

  5. The CME project of the Education Development Center, Inc., Waltham, Mass. http://cmeproject.edc.org/

* However, not for sale to the public on the website, where it reads, "Items can only be purchased with PO or school credit card." Supposedly, unaffiliated individuals can purchase this book by calling Customer Service at 800-848-9500.

July 2, 2015 Update: Houghton Mifflin Harcourt has released general Integrated Mathematics textbooks, copyright 2015, with a California edition. Quality unknown.

circa 2016 Update: Khan Academy added the integrated pathway known as "Mathematics I", "Mathematics II", and "Mathematics III".