A Google search of the phrase “understanding versus memorization” yielded some of the following comments:
- “The old style of teaching used to stress memorization.”
- “More and more top-level research on how we learn backs up the benefits of ‘teaching for understanding’ versus memorization.”
- “Productive thinking is defined as thinking based on an understanding of the nature of problems rather than on memorization of facts and rules.”
Another popular homeschool math curriculum states that only 5% of mathematics should be learned by rote and 95% should be understood.
So, it seems that memorization is “out”, and understanding is “in!” Or is it? Before we continue, I think it is important to define some terms:
understand-perceive the meaning of
memorize-commit to memory; learn by heart
analogy– a comparison between two things
When looking for a curriculum, whether it’s math or science, I think it would be a bad idea to pick the curriculum based on its emphasis on understanding versus memorization. In a good curriculum, there is no competition going on between the two. Both understanding AND memorization are important. What is even more important though, is the use of an analogy, a comparison between two things. Think about it, what was one of the first assignments God gave to a human? To name the animals. When we name things, we are making a comparison of two things, 1) the object and 2) its name. Jesus used parables all the time, and parables are a form of an analogy. And think about what Jesus did, he would use an example of something people were already familiar with, or had committed to memory, to perceive the meaning of something else. He would use a common item like a seed to help people understand things like faith (Matthew 17:20) and God’s word (Luke 8:11). God designed our brains to learn new things using analogies.
A good curriculum will use the analogy of something familiar to learn about something new. I have a copy of “Elements of Algebra”, originally written in 1765 by Leonhard Euler. This book is important because 1) it was written by the man that most consider to be the greatest mathematician EVER, and 2) the basic layout of most modern algebra textbooks is based on this book. One thing you will not find in this book is a discussion of “understanding versus memorization.” What you will find though is the extensive use of analogies. For example, to help a student understand adding fractions, Euler begins by explaining how to add fractions with common denominators. Euler familiarizes the student with this simple example. Next he uses it as an analogy to teach the more complex subject of addition of fractions with different denominators.
Any good math curriculum would teach addition of fractions in this way. Saxon math, for example, begins teaching addition and subtraction of fractions in their 3rd grade text, Math 3. This is continued in Math 5/4, as they build on understanding and memorizing how to simplify fractions. Adding fractions with different denominators is not covered in detail until Math 6/5, when the student has had ample time gaining experience adding and simplifying fractions, and committing the techniques involved to memory.
One reason I like the Saxon method so much is that it is not an “understanding versus memorization” approach, but instead relies heavily on the use of analogies. A student is given time to understand a concept and commit it to memory. Over time, something that may have been difficult for a student to do becomes familiar and easy to do. Once it is familiar, then Saxon presents a new concept that builds on the old one. The familiar concept is used as an analogy to help the student understand a new concept.
Understanding and memorization are both important. A student who has memorized basic math facts and rules will have a strong foundation on which to build. Memorization provides a foundation on which to advance learning. It is not an “old style of teaching” or “5% important”. A good math curriculum will challenge a student’s understanding of the facts and rules by giving them opportunities to apply the facts and rules in new situations to solve new problems. A good math curriculum is one where memorization and understanding work together, and new concepts are gently introduced, mainly through the use of analogies. This is how Leonhard Euler taught math, it is how traditional Saxon textbooks teach math, and it is how I teach math, and it works!
Understanding and memorization are important in all learning, including advancing your learning of God and His perfect plan for you. If you spend time on Scripture memory, and you go to a good church that helps you understand God’s word, you will advance your learning of Him. Hebrews 5:12-13 is an excellent example of the importance of having a strong foundation for our Christian walk. Advance your learning through understanding and memorization, not just one or the other.