Teaching math concepts and procedures

Posted on October 21, 2013 by Alex C. Pan

I observed a very interesting but challenging lesson on the missing numbers with addition and subtraction for the first graders. It is more of an application task that requires students to use their basic math skills to solve the problems (and find the missing numbers), such as the following:

2 + ___________ = 9
7 – ____________ = 5

The teacher gathered students around a big poster board with a timeline (marked 1 through 10) on top. Individual students were called on to go to the board to identify the beginning value and ending value. Students then drew bumps for each number interval between the beginning and ending values. Finally they counted out the bumps and put the correct answers down for the blanks.

Because the lesson focused on the minor steps and got distracted by students’ poor participation. Oftentimes, students were just trying to guess the beginning and ending values. The lesson appeared less effective as expected.

To improve this lesson, I’d suggest the following:

  • Review the basic math skills before the lesson. Start with small numbers and easy operations.
  • Focus on the learning of concepts and procedures separately.
  • Reiterate the concept of “taking away” for subtraction and “adding on” for addition. The formal terms such as subtract/ subtraction, addition/ plus, addends may be used to reinforce their learning.
  • The teacher may provide more modeling experiences for students to get more familiar with the procedures. The teacher can even highlight the procedures and making it more obvious for students to learn. The teacher may clearly point out that students are going to use three steps to solve the problems:

Step 1: find the beginning and ending values
Step 2: draw up the bumps between the value ranges
Step 3: count out the number of bumps

After a few tries, the teacher may present a problem and ask the entire class to provide clues as to how to solve the problems. Students will say the steps together and the whole class will execute the procedures together.  By this time, the majority students should be able to complete the tasks following the steps. By doing so, the class will stay focused and engaged in learning and class management will appear more effective.

 

 

 

 

 

 

About Alex C. Pan

Dr. Alex C. Pan was born in Taiwan and received his master and doctoral degrees from the University of Illinois at Champaign-Urbana. He is currently an associate professor at The College of New Jersey, where he teaches a broad spectrum of courses in subjects ranging from future teacher development to the impact of globalization. For over twenty years he has collaborated with public school programs and advised elementary and early childhood student teachers. He has published dozens of articles and given numerous talks and workshops on the topics of globalization, education, and technology-enhanced instruction. Most recently he has focused on teacher’s action research as well as the economic and cultural impact of globalization.
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