What's New with Problem Solving in Common Core?

In addition to content standards, Common Core includes 8 practice standards that are the same for all grade levels. These standards are designed to improve students' problem-solving abilities. The first five practice standards are very similar to the process standards that NCTM has advocated for years. However, there are a few notable differences in Mathematical Practices 6, 7, and 8. I feel that the wording of these is advanced for elementary grades, but the ideas are critical to helping students become proficient with solving problems.

MP6: Attend to precision.

Precision involves using appropriate vocabulary, measurement units, graph labels, and symbols. It also includes adjusting answers to be appropriate for the context of the problem. For example, if the answer to an area or volume question has more nonzero digits than the given information, digits that don't make sense should be rounded. In summary, students need to "pay attention to details" when writing or showing answers to problems. For my students, I extend this to include neatness in written work.

MP7: Look for and make use of structure.

Proficient students can discern patterns and structure in problems. In both geometric and numeric problems, students should be encouraged to break apart or combine parts as they look for patterns. It may also be helpful to sort or rearrange information. An easier summary statement for this standard is to "break apart problems."

MP8: Look for and express regularity in repeated reasoning.

With elementary students, I call this the "look for shortcuts" standard. Students should notice similarities between problems and look for general methods and shortcuts. In the past, some math teachers have expected students to show every step in calculations or solving equations. But to be proficient in math, it is important to recognize and apply shortcuts. For example, students in Grades 4-8 may be able to solve an equation such as 500 + x = 560 by mentally thinking of the missing addend. Because of the general relationship between subtraction and finding a missing addend, students should be encouraged to solve this mentally rather than writing a step of subtracting 500 from each side. The use of shortcuts should be rewarded, not penalized.

Overall, the goal of the Standards for Mathematical Practice is to help students learn habits and processes for solving problems. By encouraging students to pay attention to details, break apart problems, and look for shortcuts, you will help them become better problem solvers.

I have developed a set of 12 posters called "Be a Star" that have checklists and an icon for each practice standard written in language that is easier for elementary students to understand. You can find these on the following site:
http://www.mathpaths.com/practice.html

Common Core Math K-8 Makes Sense!

A lot of teachers are anxious about the transition to Common Core. Don't be. Here are three reasons that Common Core makes sense for K-8 math.

• Fewer Topics per Grade
  There are only about half as many new topics per year, so you'll have more time to spend on each topic. Most textbooks in recent years often "covered" 120 to 160 objectives per grade, while Common Core can be broken down into about 60 to 70 objectives per grade. One reason that textbooks included content "a mile wide and an inch" deep is that standards from state to state were inconsistent; publishers shoved in extra content to match checklists for curriculum committees in various states. Textbooks included a lot of duplication from one grade to the next. In CCSS, duplication is minimal. Review of the prior year will occur when extending the concepts and in the context of problem solving.
• More Emphasis on Developing Understanding before Introducing Algorithms
  As a tutor, I work with many students who apply algorithms without regard to meaning. For example, when asked to find half of 18, one student wrote 1/2 x 18/1 = 18/2 = 9. This is a clue that the student does not really understand "half" and was taught the multiplication algorithm for fractions too soon. The Common Core standards often require computation "using place value" or "using models" the year before the algorithm is introduced. As students use models and place value, they develop a deeper understanding of the concepts. Then, when algorithms are introduced, students will be able to understand the algorithms and apply them more appropriately.
• More Emphasis on Fluency
  Studies have shown that students who are more fluent with basic math will be better problem solvers. (Source: http://www.scholastic.com/teachers/article/math-fluency.) With Common Core, the standards are very clear about fluency requirements for various basic facts and operations. And, since teachers have fewer topics to "cover" in each grade, extra time can be devoted to activities and games to develop fluency for the grade-appropriate topics. This will result in more students having fluency with the same basic skills, so the class can more easily tackle problems requiring higher-order thinking skills.

You may wonder if the Common Core requires "harder" math than before. Generally for Grades K-6, the same content is included but topics may appear in an earlier or later grade or are broken down more. For example, there is a specific requirement for dividing a whole number by a unit fraction in Grade 5, while most division of fractions is the next year. Grades 7-8 do seem somewhat "harder" in that the standards require more algebra and statistics than before. However, there is the expectation that if the curriculum in Grades K-6 has more depth and focus, students will be ready for Grades 7-8!

In another post, I'll talk about the important role of the new Standards for Mathematical Practice.