Ways To Increase Rigor

 I keep hearing we need to increase rigor in the classroom but that can be difficult if your school requires that you follow the textbook rather than being able to teach with more freedom.  By definition, rigor in math classrooms is referring to what helps students use both creative and effective methods to solve problems.  It allows students to experience frustration when something doesn't work out but keeps them moving forward. It also helps students gain a deeper learning.

We know that direct instruction with the "I do, we do, you do" is not as effective as allowing students to work with manipulatives since it provides students with an access point for the concept being taught. In addition, using manipulatives helps eliminate barriers for all students. 

Rather than always assuming that the mistakes students make represent their lack of understanding, use the mistakes to help every student learn.  Making mistakes allow students to grow new synapses.  One way to do this is to provide problems with mistakes, so students have to go over the problem to identify what was done incorrectly.  Students then show how the problem should have been done.  Unfortunately, as teachers we want to help students do the problem rather than letting them struggle which means they don't learn was effectively .

It is important to show students that there may be more than one way to solve a problem.  For instance, for a problem such as 3(x+3) = 18 is usually taught by having students multiply the x and 3 that are inside the parenthesis by the 3 outside. For some students it is easier to divide both sides of the equation by the 3 first. In addition, it is important to expose students to problems that are not as easy to solve as the textbook problems or might have fractions or decimals in the answers. 

Furthermore, do not tell students how to solve specific problems.  Instead, let them discuss different ways to solve the problem and once its solved, ask them to find another way to solve it.  This helps them think outside the box and encourages more creative ways to solve problems.  

Another thing is that students need to see the bigger picture and make connections between mathematical contexts rather than teaching students to memorize methods to solve problems because it makes it harder for students to transfer from one problem to another. For instance, if students learn to calculate the area for a square, encourage them to think on the formula for the area of a triangle with the same base and height measurements.

In addition, rather than moving on to the next lesson as soon as students begin to show mastery, change the context of a problem, rewrite the question, for extend their thinking so they are able to transfer what they have learned and are able to apply the concept in real life.  For instance, if students learn to calculate the amount of something based on a percent, provide a real life problem such as calculating the actual amount of fruit juice in the fruit drink. 

Furthermore, one should set up learning with multiple steps to increase the rigor of a lesson.  Begin with the simplest type of problem before moving students on to a more complex problem of the same concept before having students work problems that challenge the most "proficient" student.  This helps build rigor. 

Finally, expose student to multiple sources so they synthesize the material.  Rather than having students rely on your teaching for everything, let them check out videos on the same material, use activities to explore and practice so they have to synthesize everything together.  

So these are some ways to increase rigor in your classroom.  Let me know what you think, I'd love to hear.  Have a great day.