I walked into my local Lakeshore learning store to look from some manipulatives for my classroom. I saw these booklets labelled “Common Core mathematics.” Inside, however, it was remedial rote worksheets, with each section listing a Common Core content standard. The practice standards were no where to be found. This disgusted me, but also inspired me to look into more about the current state of Common Core-aligned textbooks and state textbook adoptions for this project.
Textbook publishing is a highly lucrative industry in the United States; according to pro-con.org, an 8-billion dollar industry. Just three publishers control 85% of the industry- Houghton-Mifflin, Pearson, and McGraw-Hill. Prior to common core, the standards of California and Texas were the primary influence on what K-12 textbook authors and publishers would cover and the approach they would take since those are the largest markets. In California’s case, this meant a set of standards based around rote application of procedures. Textbooks are rarely re-written from scratch in order to satisfy changing curricular demands – instead, sidebars with the new standards are added to pre-existing texts. So textbook publishers paid lip-service to the 1989 NCTM Standards, to the 1999 California Standards … and the fear among many educators is that they will do the same with the Common Core Standards.
The Common Core developers are not blind to this issue. They recently released a guide for alignment of high school curricula. They observed in the introduction: “Traditionally, judging alignment has been approached as a crosswalking exercise. But crosswalking can result in large percentages of “aligned content” while obscuring the fact that the materials in question align not at all to the letter or the spirit of the standards being implemented. “ The guide proceeds to cover three key elements of the standards: focus, coherence, and rigor. In other words, there should be fewer topics, they should interconnect and make mathematical sense, and conceptual understanding should be pursued as well as procedural fluency. Another key element addressed by the guide is mathematical modeling; in the criteria, they specified that “Materials include an ample number of contextual problems that develop the mathematics of the course, afford opportunities for practice, and engage students in problem solving” Finally, they address the practice standards, stating that:
“Over the course of any given year of instruction, each mathematical practice standard is meaningfully present in the form of activities or problems that stimulate students to develop the habits of mind described in the practice standards. These practices are well-grounded in the content standards.
The practice standards are not just processes with ephemeral products (such as conversations). They also specify a set of products students are supposed to learn how to produce. Thus, students are asked to produce answers and solutions but also, in a course-appropriate way, arguments, explanations, diagrams, mathematical models, etc. Materials are accompanied by an analysis, aimed at evaluators, of how the authors have approached each practice standard in relation to content within each applicable course and provide suggestions for delivering content in ways that help students meet the practice standards in course-appropriate ways. Materials tailor the connections to the content of the grade and to course-level-appropriate student thinking. Materials also include teacher-directed materials that explain the role of the practice standards in the classroom and in students’ mathematical development. “
A final key point from these guidelines is about the difference between problems and exercises:
“The underlying design of the materials distinguishes between problems and exercises. Whatever specific terms are used for these two types, in essence the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Problems are problems because students haven’t yet learned how to solve them; students are learning from solving them.
Materials use problems to teach mathematics. Lessons have a few well designed problems that progressively build and extend understanding. Practice exercises that build fluency are easy to recognize for their purpose. Other exercises require longer chains of reasoning.”
I remember teaching Algebra 2 over the summer, and the textbook we used (Holt Algebra 2) presented new material in the form of examples. Then the problems in the back of the book presented a series of exercises, with the example that was similar clearly identified for each exercise. After about 30 or so of these, they would start to get to more interesting problems – and by the time my students finally got to interesting problems they were so exhausted from the exercises that they’d refuse to do the problems. Problems also weren’t properly scaffolded – either the problem would be assigned for homework and give no guidance on how to approach it, or it would give a step by step method for solving and there was no opportunity to explore and create with mathematics.
So, how well to available materials align with the Common Core? In 2011, the Indiana State Department of Education commissioned the Dana Center to review textbooks to see how well they aligned with the mathematical practices. The results are rather dismal; out of 12 Algebra 1 textbooks reviewed, for example, only 4 textbooks received a rating of moderate. (The three ratings were minimal, limited, and moderate – so moderate is the highest rating). I brought two of those textbooks (CPM and Discovering Algebra) to a seminar class of experienced mathematics educators for them to look over, and of the two, the class felt that only CPM and Discovering Geometry really followed the mathematical practices. The results for Geometry from the Dana Center study were even more discouraging, of 11 textbooks reviewed, only 2 received a rating of moderate. And for Algebra 2, only 2 out of 9 received the highest rating of moderate.
So, these guidelines from the Common Core organization hadn’t been written at that time, and these weren’t textbooks that promised Common Core alignment. Now, there are clear, unambiguous guidelines about what a Common Core aligned textbook should look like, and textbooks are starting to come out claiming such alignment. I know I am personally quite skeptical, though; will the 10th edition of the textbook suddenly be labelled Common Core and have lots of Common Core jargon cut and paste-d in, or will the textbooks really be redesigned from the ground up?
Ann Henson compiled a list of ten questions to ask vendors. The one that particularly resonated with me were: “Q8. Explain how all students, regardless of skill and ability level, can be successful using your product?” – the Common Core team is very careful to explain that students should be taught grade-level material in a way that avoids rewinding to remedial content – that, for example, place value can be taught in the context of division in a higher grade rather than rewinding all the way back to teaching lower grade material. Textbooks, though, will need to be designed with the principle of universal access – including special supports in the teachers’ edition for teaching skills like math content area reading.
There seems to be a cautious optimism regarding textbook alignment and Common Core. California’s going to start the new textbook adoption process in 2014 for K-8. Smarter Balanced assessments will be rolled out in California in 2015.
Hensen, A. http://blogs.edweek.org/edweek/on_innovation/2012/11/top_10_questions_to_ask_common_core_vendors.html