The Mathematics Assessment Project (MAP) is a joint venture between the University of California, Berkeley, and the Shell Center at the University of Nottingham, with support from the Bill and Melinda Gates Foundation. The project aims to “design and develop well-engineered assessment tools to support US schools in implementing the Common Core State Standards for Mathematics.” To meet this goal, the MAP website covers three major content areas: formative assessment, summative assessment, and professional development.
Within each of these areas, there is a wealth of material that can be readily implemented by teachers looking to make formative assessment a bigger part of their classroom. It will, however, take some time to look carefully through all of the lessons and assessment tools to find ones that will fit your class. Furthermore, the material hosted on the MAP site is aligned with the Common Core Standards for grades 6 through 12, so some of the content may not be suitable for students entering at NRS levels 1, 2, and 3.
The best place to start with MAP is with the formative assessment lessons, which are called Classroom Challenges. These classroom challenges are separated by grade level and divided into two different sections—concept development lessons and problem-solving lessons—both of which are aligned with specific CCSS content and mathematical practices. The concept development lessons are intended to build understanding of concepts and content, while the problem-solving lessons draw out student thinking and require students to apply concepts that they have previously learned. All of these Classroom Challenges include problems for students to solve, along with detailed lesson plans and other supplements that help teachers structure the activity effectively. One of the most challenging aspects of teaching from a problem-solving perspective is being able to anticipate areas where our students will struggle, misconceptions they may have, and solution methods that they might attempt. To help us anticipate these struggles and misconceptions, the MAP lessons include photographs of student work accompanied by detailed explanations of students’ thought processes. For each lesson, you will also find a list of common issues for learning and questioning techniques that we can use to address these issues and draw out student thinking. There is a lot of material to look over for each of these Classroom Challenges! But when I first taught the Gold Rush activity, I was thankful for all of the detailed notes and suggestions. They gave me a clear sense of what to expect while my students were solving this problem.
That said, many of the problem-solving activities here might need to be adapted so that they fit your class. Several of them ask students to critique a particular line of reasoning, and many of the problems don’t have what we tend to think of as an “answer.” Rather, they are intended to foster discussion about math and to encourage students to test a theory and draw conclusions. Also, the activities at the high-school level require a great deal of prior knowledge about algebra and geometry. So, while the problems at grades 6 through 8 can be solved with relatively little background knowledge, the problems at grades 9 through 12 would require much more scaffolding. I would recommend trying out some of the seventh-grade (Maximizing Area: Gold Rush) and eighth-grade (Generalizing Patterns: The Difference Between Two Squares) problems. Both of these problems ask students to analyze patterns, create diagrams/tables, and formulate hypotheses based on the work that they’ve done.
The Summative Assessments are somewhat less useful for our purposes. The assessment tasks—divided into “novice,” “apprentice,” and “expert”—have thus far only been created for high-school grade levels, and many of them, even at the “novice” level, are quite challenging. The summative assessment tests, while they contain several problems that could be extracted and used in an ABE or HSE class, cover such a broad range of material that they are a little impractical for classes that—like many of ours—meet only a few times each week. There are only six “middle-school” level tests, and each one addresses Common Core Standards from grades 6, 7, and 8. The tests at the high-school level contain content similar to what students might see on the TASC, but again, because the tests theoretically cover all of the Standards for grades 9 through 12, these assessments may not be the most accurate in measuring your HSE students’ progress.
While the formative and summative assessment activities provide teachers with exercises and lesson plans, the Professional Development modules on the MAP site offer models for professional development activities to support this style of mathematics instruction. These activities are intended to help teachers get comfortable with formative assessment, problem-solving activities, questioning strategies, and collaborative student work. They are written specifically for trainers, and each module contains several handouts, lists of discussion topics, group activities, etc. While these are interesting to read on your own, they are best used as jumping-off points for professional development activities within your organization. The style of math instruction that MAP advocates is very different from traditional methods of mathematics instruction. These PD modules can be beneficial to organizations that are looking to train their teachers on new ways of teaching math in the era of Common Core.
In all, there’s a lot to look at here, but if you’re able to spend some time looking over the problem-solving activities, you’re bound to walk away with some useable resources and ideas. I would recommend starting out with the Classroom Challenges. Look over some of the questioning techniques, student misconceptions, and questioning strategies, and then pick one or two of them to try out in your classroom. I’d love to hear your thoughts about MAP in the comments!