Developing a Deeper Conceptual Understanding.

Unfortunately, many of us are required to teach using either a set textbook or we have to use the textbook and all the associated materials.  As teachers we are expected to make sure students understand the concepts and the material being taught.

Fortunately, there are ways to make the material easier to understand for students.  Right now in Geometry, I'm teaching rotations.  When a figure is rotated 90, 180, 270 degrees, it is fairly easy to teach because the x and y either change position, change sign or both but when trying to teach them to rotate a figure say 120 degrees it becomes a bit harder.  I tried teaching it using the materials provided by the district but it didn't go well, so I've begun using specific videos.  These videos are much better at showing how to do things visually so student actually understand the process better.

The first thing is to have an opener that helps students get in the mood.  This is the place you might have students write down the learning objective with the criteria so they know when they have learned it.  The opener is also a great place to throw in a quick review such as kahoot or maybe a hook to get their attention.  I've found activities such as "Which one doesn't belong" or Esti-mysteries are perfect as warm-ups.

When introducing the topic, use multiple representations such as mathematical symbols, a drawing, a photo, manipulatives, or number lines.  The more representations a teacher can use, the better the chance a student has of understanding the concept.  I've used area modeling to show distributive property, regular multiplication, and binomial multiplication.

In addition if it is possible to do a problem more than one way, show students multiple ways to do it.  Teachers should also take time to encourage students to develop their own way to solve the problem.  When students develop a correct method of solving a problem, have them share it with the class. The more ways a student knows to do a problem and the more strategies they know, the deeper the conceptual understanding they develop.

If it is possible, show how the math would be used in a real life situation, another subject, or how the concept developed over time.  This helps students see the connections and develop a deeper understanding.  This can sometimes be the hardest step of using it.  I'm currently teaching linear equations in Algebra I and I bring in pictures of mountains along with topographic maps so students can practice calculating slope or grade.

Encourage students to discuss the material and provide a written explanation of  it.  When students can discuss it and write about it, they have a better understanding of the material.  Some of the suggested ways to encourage discourse is "think-pair-share", small group discussions, planning a video, create a drawing,

It is important to finish the class properly rather than just dismissing it.  There are three things that can be accomplished in the final five to seven minutes of class.  First, one can carry out a small assessment in the form of an exit ticket, thumbs up, down, or in-between, choose a corner of the room, or other activity.  Second, review the objective and the success criteria so students are reminded of both.  Third, preview homework or material for the next day with a brief sentence or two.

These steps are designed to help students develop a deeper conceptual understanding of the material.  Let me know what you think, I'd love to hear.  Have a great day.