BJU Press Blog

understanding

The Bridge of Understanding

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Recently, I’ve been thinking about a similarity between my parenting and my homeschooling. In parenting, I’m less concerned about behavior modification than I am about my child’s heart attitude. If a little girl grabs a toy from her sister, I want to change her heart toward her siblings. But behavior merely reflects the heart. When a little one loves her sister, she won’t take toys from her.

The problem is that I can’t see what’s inside my child’s heart. However, I can see her behavior and then try to deal with her heart by questioning her about her behavior.

I think this is similar to education. The goal is understanding, but you can’t see understanding. It’s actually difficult to test for understanding. So how do we know when our children truly understand a concept? If we focus on facts, we’ll get surface level memorization from them. So what can we do?

The Bridge of Understanding

Understanding a topic is the critical step toward mastering more challenging cognitive activities. You cannot evaluate a piece of literature until you understand it. You also can’t apply math until you understand it. On the other side, if you understand who Napoleon was, it’s easy to analyze him. If you understand paragraph writing, you’re ready to create one.

So if your children can handle projects and test questions that require higher-order thinking skills, you know that they have moved beyond recall and now understand the topic. Here are four types of higher-order thinking that you can check for to see if your child understands a topic.

Apply

When we take a subject and use it in another context, we’re applying. Math, science, and grammar are easy to apply in everyday activities. Have your child use math concepts to plan snacks for a group. You might explain that each batch of cookies makes twenty-four and we’re expecting thirty guests.  How many batches should we make?

Analyze

Analysis sounds scary, but at the most basic level you’re just breaking a subject down into its parts and explaining their connections. In history or reading, small children can do analysis by making word webs. Meredith has an excellent post on word webs that can be applied to any subject.

Evaluate

Evaluation involves comparing something to a standard. Christians evaluate all academic subjects according to God’s Word. We also evaluate a writing sample against grammar rules and science hypotheses against observations. When children can use a standard to make a judgement, they understand their topic.

Create

Creating is a type of thinking that rewards children by allowing them to use the subject in a creative way. I was so proud of my second grader when she wrote a poem on kites after learning about poetry. It was better than any poetry I’d ever written. When students use principles from science, technology, engineering, and mathematics to solve a problem, they’re creating in a satisfying way that conforms to the way God made us to function.

It’s hard to measure a child’s understanding of a topic. But understanding is a bridge that connects other activities such as applying, analyzing, evaluating, and creating. If we focus their learning on these higher-order thinking skills, we can be confident that our children have gained understanding. BJU Press homeschool curriculum builds bridges of understanding for children by having them apply, analyze, evaluate, and create.

Why choose BJU Press homeschool curriculum? Find out here.

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Easy Knowledge for Those Who Understand

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“It’s easy for small children to memorize, so memorize as much as possible.” I heard this maxim over and over when I was growing up. And from my experience, I would say it’s true. In our family worship time, my small children memorize the verses and songs far more quickly than I do. It’s certainly worthwhile for children to store up knowledge while they’re young, but is it best to focus on memorization as the main educational approach for small children? Should six- to ten-year-olds primarily memorize for math, science, reading, spelling, and history?

Proverbs 14:6 provides insight into the way we learn: “. . . knowledge is easy unto him that understandeth.” Here the Holy Spirit tells us that knowledge flows best from understanding. What I observe in my own children (ages 6, 4, and 2) is that their useful knowledge is always based on comprehension. I asked some of the educators here at BJU Press to help me understand why focusing on comprehension, even at the youngest ages, is the best approach. Here’s a summary of what I learned.

Avoiding Conditioning for Memorization

When children start learning by memorizing, they become conditioned to think of learning as memorizing. This often leads older children to protest about the expectations in high school. The request to “tell me what is on the test and I’ll memorize it” is characteristic of children who have been conditioned to think of learning as memorizing. In reality, memorizing is a small part of education. An education that prepares children for life is one that prepares them to understand and apply what they’re learning.

Experiencing Education as a Whole

Some children struggle more than others with memorizing. This seems to be the case more often for boys. I know that was my experience. Children who find memorization difficult could come to think that learning isn’t for them even though they may be excellent learners when it comes to higher forms of thinking such as applying, evaluating, and creating. If we as parents focus on the entire educational process, then our children will enjoy learning far more.

Preparing for Success

Sometimes children learn to translate letters on a page into sounds without getting the meaning of the words. Or they can rattle off the math facts for multiplication up to twenty but don’t understand how multiplication is used in everyday situations. Real life doesn’t give us multiple-choice options. It requires skill in using knowledge. That skill demands more than the superficiality of memorization.

I find gratification when my children can recite the facts that I’ve taught them. However, I know that those facts are useless without understanding. That’s why my wife and I ask our children comprehension questions to help them understand. Knowledge will come easiest when they understand.

Making Math Enjoyable with Themes

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Memorizing math facts may come easy to many people, but some (myself included) have a harder time visualizing a numerical problem and solving it mentally. It’s not that we can’t do it but rather that numbers have little value when they’re separated from a real-life situation.

It’s the application of math that helps us understand the importance of knowing how to solve an equation. But sometimes learning best takes place when there’s an example of how someone else has used math in daily life whether that’s through household chores or an occupation. This type of example does two things. It shows how math can be used, and it also gives motivation to use it.

BJU Press elementary math introduces themes in every grade to help kids understand math and see how it applies to our everyday lives. Each grade has a unique theme that makes math more enjoyable but also relatable. Lower-elementary kids are introduced to special characters. Rhymes, songs, and stories about these characters are included in different lessons throughout the entire course.

MathK5

In Math K5, Cheddar the mouse lives on Kindergarten Lane in Mathville. He uses math to help Farmer Brown keep an eye on what’s happening on the farm. In one lesson, your child works with Mrs. Brown to count the number of cabbages in the garden row. Another day on the farm, shapes are found on Farmer Brown’s outfit (like buttons that are circles).

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Once students reach the upper-elementary grades, themes provide your child motivation for using math. For example, Math 6 includes a search-and-rescue theme with read-aloud stories about search-and-rescue events for each chapter. Chapter 7 opens with the true account of Balto and other dogs that delivered a special serum to people who were sick in Nome, Alaska. The concepts learned in this chapter are multiplying fractions and decimals—an important skill for measuring out medicine just like Dr. Curtis Welch did when he treated the people of Nome.

See more examples of these themes in BJU Press math curriculum.

Math Doesn’t Have to Be Scary

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In middle school, I had a math teacher who always began class the same way. He would assign each of us a problem from our homework assignment the night before and have us put it on the chalkboard. We would have to give our answer and show how we got it. My teacher would then label each problem as correct or incorrect. I was fairly good at math and generally got the problem right, but I remember always being terrified that I would do something wrong and that my work would be picked apart in front of the class. I can only imagine how my classmates who struggled with math must have felt. The beginning of math class was my least favorite part of the day. It was probably a nightmare for many others, leading to the “I hate math” mentality that’s so common.

Math is a subject that often creates frustration for both parent and child, but a lot of that frustration can be avoided by using the right approach. When children answer the question correctly on their first try, we celebrate; when they get a question wrong, we tend not to applaud their efforts. These responses can lead your child to believe that there’s no room for mistakes and that getting the correct solution the first time is what they should be trying for.

Working toward understanding

Assessing your child’s level of understanding based on whether or not he gets a question correct on the first try can be misleading. The truth is that a wrong answer can be just as valuable as a correct answer because it helps build a strong understanding of the process used to get to the correct answer. Also, a correct response does not always mean your child has a strong understanding of the concept. It’s important that children know how to learn from their incorrect answers. When mistakes happen, help your child identify all the correct parts of the problem before looking at where things went wrong.

Curriculum matters

Your math curriculum plays an important role in teaching for understanding. Choosing a curriculum that promotes critical thinking over rote memorization is critical. Math problems should ask your children to explain a concept rather than quickly find a solution. Approaching math this way allows children to explore problem-solving strategies. It also teaches them to recognize that there’s often more than one way to understand a concept.

Here’s an example of a typical first-grade geometry question.

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Here’s another question based on the same concept in a way that better promotes understanding.

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The second question allows you to more accurately gauge your child’s understanding of the concept. Including triangles that differ from the typical equilateral type leaves the question open ended. This type of question helps children learn to identify triangles based on the number of sides and corners instead of memorizing what a triangle typically looks like.

When working through this question, your child may not immediately understand that all three-sided, three-cornered shapes are triangles.  But this question provides an opportunity to illustrate the math concept using the three different triangles provided.

Math is a lot less overwhelming to children when they’re working to understand and not just memorize. BJU Press Math provides questions and teaching strategies that can help you put an end to your child’s math frustration.