Seek Understanding

This video is resurfacing on Facebook again.

https://www.facebook.com/conservativecomic/videos/917847655243694/
https://www.facebook.com/conservativecomic/videos/917847655243694/

The video has two settings in a form of a comparison. On the left, a teacher is explaining multi digit multiplication using the open array model. On the right, a person completes the multi digit multiplication problem using the US standard algorithm, makes coffee, and completes  other various activities. In essence, the goal is to compare the time it takes to perform what they call Common Core math (I was doing this method prior to CCSS) to the US traditional algorithm. The purpose of this blog post is not to reject any of these methods. Both methods are essential to understanding the concept of multi digit multiplication. The goal of this post is to open minds to look at both methods as means to achieve a goal and to convey that one method helps to understand and builds the other.

First, the method in the left video is called the open array or area model. In this video, the teacher decomposes this two digit number into its value for each digit. Draws a rectangle for each part and performs the operation. The products are written in the boxes as its value. The open array model provides students an understanding of the meaning behind each number. Furthermore, students understand the distributive property using this model. This leads to conceptual understanding. Conceptual understanding is knowing why a concept works such as multi digit multiplication. Without this conceptual step students will not understand the procedure of the US traditional algorithm. For, conceptual understanding builds procedural fluency (NCTM, 2014).

In fourth grade, students use place value understanding such as the open area model, partial product, estimation, etc. In fifth grade, students are formally taught the US traditional algorithm by making connections to place value representations. Teaching in this order decreases thechance of making mistakes  when multiplying  multidigit factors. Such mistakes include forgetting to place a 0 where it is appropriate or forgetting to add the numbers after regrouping to the next place value. These two anticipated errors can be detrimental to the entire product or answer to the multiplication problem.

 In addition to building place value fluency, the open area model builds distribution property knowledge. For instance, open array model is an excellent organizer for multiplying binomials to make polynomials instead of using FOIL.

In closing, do not be so quick to disregard a method you may have deemed as not efficient as how you have learned. Teachers have gone through extensive training to gain various strategies and methods for teaching mathematics. The goal is give our students the opportunity to develop to become mathematically proficient. Therefore, trust the process and seek understanding.



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