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)

Homework Matters

There is little doubt in the minds of most math teachers that homework is an integral part of learning in mathematics. Among the questions that arise are:

  • What is the purpose of homework?
  • How much homework should be given?
  • How can we get students to do their homework?

What is the purpose of homework?

Homework can have a variety of purposes.

1. For some situations homework can be used to prepare students for class the following day. Perhaps students need to read the upcoming section or lesson or there may be a video that students need to watch. There could be materials that need to be gathered together or a survey that needs to be conducted among family members.

Whatever the “pre-class” assignment might be, it needs to be meaningful and structured. Asking students to read a section in their math book will more often than not result in a 1 minute glance just before class. However, if students are given a few specific questions to answer concerning the lesson and then held accountable for them, there is a better chance the pre-work will be attempted. The questions should not just be problems to answer but questions that require thought processes such as comparing the methods used in the lesson to determine which method is best used in which situation. When students enter class they can then share their ideas with their small group or the entire class. They should be required to provide insight into the lesson or possibly additional questions that they could not answer as they did their reading.

All students need to be held accountable. As class time does not usually allow for reports from every student every day, the teacher may randomly select a couple of students each time. Students that have not done the pre-work cannot be “let off the hook” or the next time no one will be prepared.

2. Practice is one of the main purposes of homework. Just as with any skill, practice is extremely important, however before assigning copious amounts of problems, teachers need to be certain students have a relatively good understanding of the processes involved. Teachers must also take into account the Depth of Knowledge (DoK) utilized with each assigned problem. For most simple skills or plug and chug problems the DoK is 1 or 2. For true understanding of the concept students need to be involved in problems that have a DoK of 3 or 4. These problems will take more time and thought, but the understanding gained will be far deeper.

How much homework should be given?

In the past, assignmentsof 30-35 problems were common so that the students could use rote memorization for a particular process. Now that the emphasis is not on memorizing but rather on understanding, fewer problems should be given so that students can spend sufficient time in developing their ideas and solutions.
It may be that 1 or 2 problems will be enough for the students to grasp the depth of the concept. It is highly recommended that before making assignments teachers should do the problems themselves so that they can understand the amount of time required. Homework assignments could include a few problems with DoK of 1 or 2, but problems with a DoK of 3 or 4 should always be included. The problems that make the students think will provide an understanding that lasts more than a day or a week.

How can we get students to do their homework?

No matter the purpose or quantity of homework assigned students need to actually do their assignments to gain any benefit.

There is a better chance that one or two meaningful problems will be at least attempted compared with a page with 50 long division problems. Whatever the assignment, students need to feel it is important to complete the work.

In my classes I walked around the room at the beginning of class every day and looked at every student’s work. I used a right side up stamp to indicate a completed assignment with all work shown, an up side down stamp to indicate the assignment was half done and no stamp was given to papers less than halfway completed. This gave me the opportunity to talk with each student every day, for 5-10 seconds about their homework. If it was not done or “the dog ate it” I would explain the need for them to do their work, how it was important to me that they did their work and I would get them to promise they would do their work that night. Not all of them did, in which case we would have a little discussion about how important promises were, but many of the students would at least make an attempt. The next day I would make a big deal about the work completed and have another talk with those that didn’t do their work. For some students this was the only adult conversation they had all day and the only person that ever told them they cared what they did. The result was more homework turned in than ever before. It was far more successful than notes or phone calls home, more successful than detention or ridicule. It was just the teacher caring about the success of the students and sharing it with them.

Practice is important to the success of students in any endeavor. We want students to learn to persevere with their work and experience the great feeling of a job well done when they do. Meaningful work combined with patience, enthusiasm and encouragement from the teacher will go a long way in preparing students for the work that lies ahead.