Anna Maria Tabernik joins us again, to talk about what parents should know & look for in a math classroom which is following the Common Core.
The Common Core State Standards are here, there, and everywhere across the United States. These standards present educators with a wonderful opportunity to embrace the philosophy that every student can learn mathematics. The standards outline what students must know and be able to do in order to be prepared for college or a career upon graduation. They emphasize that mathematics is a major key to unlocking a student's intellectual future and earning potential.
As Katy mentions in her post about the ELA standards, there are many misconceptions floating around that might tend to confuse some educators and parents. These are not "the same old standards" – just renamed and readopted! The Common Core State Standards for Mathematics (CCSSM) are more rigorous, more coherent, and more focused. There are two types of standards for mathematics:
- Standards for mathematical practice, and
- Mathematical content standards.
Standards for Mathematical Practice:
These standards describe the "habits of mind" of a mathematically proficient student. That is, good math habits and strategies that serve as the foundation for learning and using mathematics. They outline important processes and proficiencies that teachers at all grade levels must develop in their students. These 8 practices help students "think like a mathematician". The mathematical practices are1:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
I will explain each of these practices in detail and provide specific examples in future posts. In the meantime, ask your child's teacher how they are working with students to understand and learn these practices in order to help them "think like a mathematician". These practices are essential for students to learn and utilize under the CCSSM.
Mathematics Content Standards:
These standards outline "what" students learn in mathematics. In other words, the actual concepts and skills that make up the world of mathematics, such as: fractions, decimals, whole numbers, and measurement. There are 2-4 critical areas of focus for each grade level K-8. These focus areas outline the "big ideas" for that grade level.
The CCSSM content standards are more rigorous, more coherent, and more focused than most states' previous standards. What does this mean? They are more:
- FOCUSED in that teachers will now go deeper into the BIG IDEAS of mathematics and help students build a stronger foundation of mathematics. Students will learn fewer concepts at each grade level, but to a greater degree of mastery.
- COHERENT in that teachers will intentionally connect the learning across grades so that students can strengthen their foundation and build new understandings. Teachers help students link major topics and see how other parts of mathematics support these major topics.
- RIGOROUS in that they require students to learn at a conceptual level, calculate with speed and accuracy, become fluent with basic math facts and operations, and use mathematics in other subjects and in daily life.
Your child's teacher will be learning more about the CCSSM this year and work to realign their curriculum to these standards. Teachers will need to find resources to support their instruction and student learning. Remember that the district's resources (books, software, programs, etc.) are simply that - RESOURCES for the teacher. They do not outline the curriculum, and may not fully support the understanding and learning of the mathematical practices. They are tools for the teacher to use in designing lessons to help students achieve the rigorous standards and goals the CCSSM outlines for all students.
What should parents look for in a Mathematics CCSS classroom?
A focus on the standards for mathematical practice – Students must learn to "think like a mathematician". This includes things like: explaining the meaning of a problem, asking "does this answer make sense?", breaking a problem into smaller parts, asking clarifying questions, using math tools, looking for patterns when solving problems, and finding their own mistakes.
Rich tasks (not just sets of basic problems to solve) – The teacher needs to provide students with "rich tasks". These are tasks that require a student to use their math knowledge to understand a problem, determine a solution pathway, then work toward that solution and adjust their pathway if necessary. Rich tasks engage students in their own learning by requiring them to think – not simply repeat a procedure the teacher demonstrated. These tasks take thought, time and, effort. They help students see the value of mathematics in the world around them.
Here are two examples of a rich task:
Which one is different? Why? Is there more than one answer?
- Create a multiplication question where the digits 3, 7, and 11 appear somewhere in the question.
A focus on the "big ideas" or critical focus areas of the grade level standards – Teachers should be devoting about 70% of their instructional time to standards that promote learning of major topics. This will enable students to learn math more deeply and have the opportunity to practice their skills toward mastery. In kindergarten, the focus is on the number core – learning how numbers correspond to quantities and putting numbers together. In grades 1 through 5, the focus is on providing students with a solid foundation in whole numbers, computation, fractions, and decimals.
Student discourse – Students should be sharing their mathematical ideas with each other and the teacher. They should ask questions of their peers, explain their answers and thinking, make conjectures, and discuss if their answer is reasonable.
An expectation for student mastery of core concepts at the grade level – Students must be given the necessary support to master the core concepts at each grade level. Students must be able to fluently retrieve basic facts in order to develop higher order thinking skills to access upper level mathematics courses. They must meet fluency requirements in grades K-6 of basic facts and operations.
What questions might parents ask a teacher in a CCSS Mathematics Classroom?
- What are the critical focus areas for my child's grade level this year (major topics)?
- What is the fluency requirement for my child's grade level?
- How can I help my child meet the fluency requirement?
- How often will my child have the opportunity to work on rich tasks in the classroom? Can you send some rich tasks home for my child to work on with me?
- Which standard for mathematical practice are you working on now in the classroom? How can I support this at home?
- What specific learning targets are you working on this week in the classroom? How can I support this at home?
Where do I go from here as a parent of a CCSS student?
Now you have an overview of the basics of the CCSSM. Talk to your child's teacher to understand what is being taught in the classroom and how you can support your child's learning with activities at home. Ask your child about the mathematical practices – about thinking like a mathematician. Stress to your child why it is important to develop these "habits of mind", to enjoy mathematics, and to see how it is a major part of their world today and always. Finally, dig right in and work through some mathematics problems with your child – have fun with it!
Resources & Citations
- Mathematics Standards. Common Core State Standards Initiative. National Governors Association Center for Best Practices, Council of Chief State School, 01 Jun 2012. Web. 30 Aug 2012.
- TYSK for Parents - The Common Core Standards and You!