Rigor – What Does It Mean?

“When are we ever going to use this stuff?”

The most frequently asked question in a math classroom is actually asking for rigor.

What does this mean?  We need to be taking math education much deeper than we have in the past.  Our math classrooms have been centered around the students acquiring knowledge, memorizing algorithms and processes.  This is important, but it is time to go further into understanding and using the knowledge.

Math is truly used in real life, and in just concentrating on gaining math skills we have neglected the “what do we do with it?” question.  Rigor is referencing the Depth of Knowledge that students gain through doing and using mathematics.  The lowest levels ask students to recall or apply a formula.  They may even ask students to do a basic application of the skill.  Higher levels are more concerned with having students explain their thinking, justify their conclusions  and use reasoning to apply the skills they have learned.  The highest level asks students  to think outside the box.

Lower levels

Example 1:

Big Ideas Math Red pg72

Example 2:

Big Ideas Math Blue pg284



Higher levels

Example 3:Big Ideas Math Green pg18

Example 4:Big Ideas Math Algebra 1 pg131

We are educating today’s students for jobs that don’t exist yet.  We must help students gain the skill of applying what they have learned to totally different situations.  Adding rigor to the classroom helps the students, think, learn and understand.

Students can handle the challenge and even welcome when they ask, “When are we going to use this stuff?”

(Problems: 1.  Red page 72; 2.  Blue page 284; 3.  Green page 19; 4.  Purple page 131)

How Can All Students Become Proficient?

The Common Core State Standards and the Standards for Mathematical Practices give every student the opportunity to become proficient. Instead of trying to teach 100 things every year, requiring that the teacher move quickly through the material, the Common Core State Standards have narrowed the curriculum to 25 to 30 standards each year.

For years math class has predominantly been “Show and Tell” by the teacher. The students have watched the teacher do several examples and then they use those examples to do many problems. Often students saw no connection between the concepts and many times saw no reason to “study this stuff.”

Common Core has changed that to “Think and Do” by the students. Math classes should now include some discovery activities using manipulatives and discussions that allow the students to determine what the process is and why it works. Teachers have time to help students develop an understanding of the concepts they are studying.

It is no longer a mystery as to why they add six or multiply by two. As the students learn to problem solve through understanding, they can transfer the learning to other concepts. Through the use of hands-on discovery, all students will gain an understanding of what they are doing. Watching the experts play a sport or a musical instrument has never made anyone a star. We learn by doing. When given an opportunity to understand, all students can become proficient on some level. Some students will still be better than others but no student should be left behind.

Why the Common Core State Standards?

It only makes sense.  For years in the United States, each state created their own standards for mathematics. Some had as many as 100 standards to be taught every year with no consistency across the county.  Shouldn’t math be the same in Maryland, Michigan, Wisconsin, Colorado, Arizona, and in fact throughout the country?

During the last 50 years it is no secret that the United States has been falling further and further behind in international testing. Finally, the National Governors Association Center for Best Practices and the Council of Chief State School Officers along with others created a commission to examine the state of math and language arts education in this country with the intent of improving the education of today’s young people.

Their Mission Statement (http://www.corestandards.org/):

The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.

The result is a set of standards that not only addresses what students learn, but how they learn.  Instead of trying to learn everything, every year, the Common Core State Standards  provide unique content standards for each grade level.  Every year fewer standards will be covered, providing more time for understanding the math instead of just memorizing it.  Each subsequent year students will use those concepts that have been previously taught to learn new concepts.  Students are responsible for what they have been taught year to year.

Along with the content standards, the Common Core Standards for Mathematical Practice indicate that we want students to make sense of the mathematics they study.  Students should be able to reason and support the processes they develop.  They need to know which tools to use and when they are appropriate.  Mathematics is all about patterns and students need to be able to recognize the patterns to further their understanding.

As we are educating today’s students for jobs that do not yet exist, we need to address their ability to understand what they have learned so they can apply it to the challenges of tomorrow.  The Common Core State Standards and the Mathematical Practices provide that opportunity to our young people so that they can compete in the global society of tomorrow.