There has been a lot of press about the need to have more well-aligned mathematics instructional materials in the hands of teachers and students; however, recent reviews like EdReports show that few publisher-produced options are actually fully-aligned. When there are few options to choose from, or you’re not in a position to buy new materials, you have to make what you have work; this is the position most schools and districts find themselves in right now. Student Achievement Partners, working with Illustrative Mathematics, set out to facilitate a pilot project to support teachers in a few districts in analyzing and adapting their current instructional materials to better reflect the Common Core. Before that could happen, however, we needed to get a better understanding of where existing materials fell short.
We started by convening a panel of national experts to identify “gaps” in currently available materials. In the midst of our first conversation, one of the experts raised an objection to the panel’s stated goal. He was concerned that saying we were searching for “gaps” implied that there were always holes to be filled in mathematics instructional materials. And although that may be the case for some, books that used the same approach to mathematics instruction as they had for decades were likely to have the opposite problem: they had too much material to be considered Common Core-aligned.
The research base for the Common Core State Standards for Math (see pages 91-93 of the Math Standards) highlights that the traditional U.S. approach to mathematics instruction, pre-Common Core, has been classified as “a mile wide and an inch deep.” Unfortunately, many books still resemble their pre-Common Core versions, which means that they need to have chapters, lessons, or worksheets removed to ensure that students and teachers have enough time to dive deeply into the topics that matter most for college and career readiness. The panel decided to change the semantics of the task: instead of “looking for gaps,” they were now “identifying areas in which the instructional materials needed renovation.”
With that in mind, the panel identified several topics in math instruction which are consistently not being properly addressed in existing materials. To the surprise of no teacher or coach, the topics identified were all Major Work topics that are hard to get right. Some topics are places where students struggle to grasp important mathematical ideas and others are important mathematical connections that the Common Core emphasizes. The areas in most need of improvement are:
- Relating Addition and Subtraction to the Number Line in grades 1 and 2: The need here is to help students connect their developing understanding of the operations of addition and subtraction to the work they are doing with linear measurement. Connecting work across the domains allows students to develop a deep understanding of the number line that will support their later work with rational numbers.
- Understanding Fractions and Fraction Operations in grades 3 to 5: Research has shown that students’ understanding of fractions is a strong predictor of their success in Algebra. Many current materials do not start work in grade 3 developing students’ understanding of fractions as numbers and do not relate fraction operations to previous work with whole number operations. Improvements in this area will ensure students understand that work with fractions is an extension of understandings they have developed about whole numbers.
- Transitioning from Ratio to Proportional Reasoning in grades 6 and 7: Many current materials do not attend to the precise definitions of and differences between ratios and proportions. More materials are needed that clearly make the distinction and provide a clear progression of these ideas from grade 6 to grade 7.
- Understanding congruence and similarity through transformation in grade 8: This area calls for students to develop an understanding of similarity and congruence through hands-on explorations. Instead of the current emphasis on the formal notation of transformations, materials should emphasize precise mathematical vocabulary and use work with similarity to lay the foundation for students’ understanding of slope.
The experts felt that most current materials could use some renovation in one or more of these mathematically important areas. As part of the work to address these issues, Achieve put out a call for units in these areas to be submitted to the Educators Evaluating the Quality of Instructional Products (EQuIP) Peer Review Panel for review. To read more about these areas (or to submit a unit that addresses one of them) see Achieve’s Call to Action or browse exemplar units on the EQuIP site.
One thought on “What Needs to Change in Instructional Materials: Math”
In the past, I recall using detailed and comprehensive rubrics to review math texts/series to determine their alignment with existing standards. The USDOE, NYSED, and the New York City DOE used these rubrics to support educators in making determinations related to selecting materials. Professional development which focuses on SHIFTS should point out topics which are prioritized at each grade level (see Engage NY)and use the Progressions to ensure continuity across grade levels.
The areas identified as in need of improvement can and must be addressed, initially at the college level (teacher prep) and later,, in quality professional development sessions led by master staff developers.