Do your children feel like doing math is about as much fun as watching paint dry? Well it doesn’t have to be! Today on Home School Heartbeat, math professor Fred Worth shows how to help your student understand math and become confident in using mathematical concepts.
Mike Smith: I’m joined this week by Dr. Fred Worth, a Henderson State University math professor and veteran homeschool dad. Fred, welcome to the program!
Dr. Fred Worth: Well Mike, thanks for having me!
Mike: Fred, you have a concern for helping homeschool parents who are struggling in teaching math to their children. Tell us some reasons why parents might see their students having difficulty in math.
Dr. Worth: Mike, one problem that a lot of teachers have (and this is not just homeschool teachers) is teaching mathematics as though it’s just a bunch of number-crunching algorithms and memorization. Yes, there are algorithms, and there is number crunching, but there’s a lot more than just that.
In the early grades, a lot of the material can be done by rote memorization. So a child may be able to do the material, but not really have an understanding of what’s going on. This can fool parents into thinking that children understand the material. So it’s vital to work to help your child really understand what’s going on. Yeah, we want them to be able to say that 4 plus 4 is 8, but we’d also like them to understand what that means.
Using manipulatives, which don’t have to cost a lot of money, can be very helpful in demonstrating concepts to your child, such as using dimes and pennies to help your child understand the idea of borrowing and subtraction. Legos can help your children with figuring out areas in geometry. So we want your child to be able to do mathematics, but we’d also like for your child to really understand mathematics.
Mike: Although homeschoolers score better than the national average on all subjects, they tend to do better on verbal sections than on math. Now why is math harder, Fred?
Dr. Worth: Well, we talked last time about being able to do and understand mathematics, and those are obviously important here as well. But there are a couple of other things that are very important, and one of those is vocabulary.
Sometimes people tell me they feel like mathematics is a foreign language—and I tell them they’re exactly right! In order to do mathematics, we are teaching our children a new language, with its own vocabulary and grammar. A particularly vital portion of this is learning the proper vocabulary and using it. In the kitchen, cup doesn’t just mean any open-topped cylinder. You would want your surgeon to know the difference between your appendix and your spleen.
So I would strongly urge parents, from the very beginning of their homeschooling, to use the right words. Talk about the numerator and denominator of a fraction, not the top and bottom. If we’re dividing both sides of an equation by 7, say dividing both sides by 7, not cancel the 7s. There are numerous mathematical errors that can be avoided if students simply learn the right words.
Mike: Fred, tell the parents listening what they can do to bring up their student’s math performance.
Dr. Worth: Well, the ability to problem-solve is vital to success in mathematics—whether we’re talking about taking standardized tests, or just learning mathematics in homeschool. Not all problems on tests are word problems, but they are very important.
The first word problems come up in first grade, where Mary has some apples, and Johnny gives her some more. Nobody has any trouble with those. But each year the word problems get tougher, until you have one train leaving Boston at 10 AM, and another train leaving Cleveland at 11 AM. Most people have a difficult time solving the more complicated problems because they’ve never really been instructed in problem-solving techniques.
There’s a method that I teach that can really help in learning how to do word problems. And, Mike, I believe you’ll be telling people how to contact you in order to get a copy of this. The first step is to just read the problem. The second is to think about the problem. Then determine what’s important, drawing a picture and labeling the picture—then finding the formula (which is where most people try to start) and adapting the formula to the problem, solving the equation, answering the question, and then thinking about whether the answer makes sense. This method can go a long way in teaching your child how to be a better problem solver—not just in mathematics, but in life.
Mike: Fred, can you tell us about the importance of sequence in teaching math as well?
Dr. Worth: Sure, Mike. If you’re building a house, the order in which you do things is obviously going to be important. You don’t start off trying to build the roof. You start with the foundation and do things in a certain order. And mathematics is no different.
Mathematics is fairly unique in academics. It and maybe language arts are the most sequence-dependent subjects. We don’t start trying to teach complicated algebra until after children have learned their basic arithmetic skills. So it’s important that homeschool parents pay very close attention to the level of understanding their children have as they work through the mathematics.
A lot of problems in mathematics arise because previous material wasn’t learned on a deep enough level. Lack of understanding may not show up right away—it might show up a couple or three years later. Parents should regularly give their children the opportunity to play teacher. Let the children teach how to work a problem, and make them explain why they do what they do. Make sure they understand what they’re doing, but you also want to make sure they understand why.
If a child struggles with mathematics, don’t stress about how fast you go through the materials. I’d rather have a student only get through Algebra I, but really understand it, than go through lots of mathematical content with minimal understanding.
Mike: Well that’s great advice, Fred! Tell us about how math will prepare students for life. What’s the payoff for studying math?
Dr. Worth: From a purely practical standpoint, the more mathematics you learn, the more you have a chance to use it. There are numerous areas in life where mathematics can be used. Geometry and algebra are very helpful in building projects. An understanding of statistics and logic can be helpful when trying to analyze advertising, speeches, polling data, and so on.
And having a strong mathematical background can present people with more diverse career opportunities. Many career paths require mathematical expertise. Our pharmacy and pre-med majors have to take a lot of mathematics. Even in the social sciences, a number of majors require statistics courses.
But Mike, I think one of the greatest benefits of a good mathematical background is the development of thinking skills. Studies have shown that a good high school geometry course is a great indicator for college success. And that’s because in order to do geometry well, you have to think logically and often deal with multi-step problems.
The problem-solving skills developed in order to do word problems are also useful in all kinds of areas. You have to be able to recognize what’s important—how to break it down into parts, have an orderly process for doing it—and all of that is useful, even if we don’t ever do any mathematics ever again.
Mike: Fred, thanks for your valuable insights this week on teaching math in the homeschool. It’s been great to have you on the show. And until next time, I’m Mike Smith.