Teaching arithmetic is one thing but teaching Algebra can be scary for most parents who haven’t had to think about it for awhile. So before you give up on your current curriculum, consider these 8 questions about teaching Algebra and its importance. These came from an interview with Tom Clark from VideoText Interactive during the Curriculum 2.0 Online Homeschool Summit.
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Why is Algebra so important?
Did you know that the word “Arithmetic” comes from the Greek word arithmos which means numbers? That’s all arithmetic is. It’s learning about numbers, how to operate them (add, subtract, etc.), and the relationships between them. It’s very concrete and easy to teach.
“Algebra,” which comes from the Arabic word al-jabr, means to reunite and put back together again. So if you think of the biggest equation that you can imagine, it will have an X in it. This means that something is missing. Now your job is to search the universe to find what’s missing. Bring it back and reunite it with the equation to make a true statement. It’s a completely different way of thinking.The importance of algebra comes from the engagement that students receive on an analytical level.Click To Tweet We actually need to teach “why” and not just steps, rules, or even tricks and shortcuts. Students need to know why things work. They need to be able to make sense of things. This requires more than just even the content but a whole thought process and the ability to think critically. Algebra gives them an opportunity to develop that kind of ability.
“When am I ever gonna use this stuff?”
I’ve had plenty of students that ask this question. I think the majority of them don’t really want to know the answer to that question. Their motivation in asking it is to avoid doing algebra. We do not want students to avoid Algebra or frankly, anything that has to do with math. We want to make sure that they are well prepared. Algebra is everywhere. There are many opportunities to apply it in business, accounting, science, and everyday living.
The problem with a majority of math curriculum is that their application problems aren’t really very realistic. However, you need these types of problems in order for students to see applications of it in a real sense, even if they don’t personally use it. But fact of the matter is that whether you’re going to use it directly now or in the future, the important thing is to make sure that students understand it.
How do parents prepare students for Algebra?
We always think that if you have a good foundation in arithmetic, that you’ll be okay in Algebra. While some things arithmetic transfer to Algebra, there are things in arithmetic that you learn to do but will never be any good in Algebra, such as order of operations.
In order to prepare students for Algebra, we need them to completely reteach some things that work in arithmetic but will now be applied in an Algebra context. This involves having to understand how that arithmetic works, where it comes from, and why does it make sense. In elementary level you’re not really teaching algebraic equations but you need engage them in algebraic thinking. Otherwise, they’ll just be memorizing the steps to do the problem which has no staying power.
For example, when you divide fractions you turn the second one upside down. Why? If you simply do that in Algebra, it won’t make sense. You need to ask questions. What division even mean? Where does it come from? Why does it make sense to invert and multiply? Why would that even be part of the process? You want your students to be able to answer these types of questions. The key to working in higher level math is to learn to ask why and expect an answer.
How do I know when a student understands?
When you have a student that tells you, “I understand,” what they’re telling you is, “I know how to do it.” That’s not understanding. To understand means to know what stands under, what supports, what are the underpinnings that make this problem make sense. Understanding becomes so important in the sense that now I can be more skillful in the things that I’m doing.
If you’re child makes careless errors which happens all the time, you really need to explore that fact that they might not understand what they’re doing. They might just be trying to memorize the steps and the mistake comes from not remembering what to do next. We learn by thinking about what we’re doing. If you think about when you were in school learning the state capitals, you were memorizing them to pass a test or quiz. But if you had learned the history behind each state capital and it’s importance, then you would probably remember it to this day.
Learning algebra is very much conceptual with a skill attached it. So the goal is to have students be skillful and so conceptually grounded that they can look back at their mistakes and figure out where it went wrong.
How do I gauge how much they understand?
The only way a parent can really determine that their student has understood conceptually is to have them teach the lesson. The most powerful teaching tool in the world is to have to explain what you know to someone else. That’s the best way to truly know what you’re doing. Students need to have a sound understanding and be able to articulate and justify what they know. This is a skill that will serve them well when they get to college.
Instead of checking your student’s work, give them the solution manual. Let them figure out their mistakes. Have them explain it to you. This gives them a chance to be an independent learner. They are personally responsible for their work, and they are able to articulate and justify everything that they did.
Since math builds, how important is it to teach in sequence?
Textbooks were designed to teach the steps or the process of doing problems. They were not designed to teach. That’s a teacher’s job. Parents and even our math teachers have trouble with that now. Because they’re just picking up a book and teaching directly from that book. They’re not really teaching for understanding.
And if you look at most traditional math textbooks, it’s all taught by topics. So you’ll teach a topic one day and don’t really tie it in to what you learned yesterday or the day before. But math shouldn’t be taught this way.Today's lesson is always a continuation of yesterday's lesson. And the things you learn today should help you with tomorrow's lesson and it continues on.Click To Tweet That is how math builds. You can’t master anything unless you continue to revisit it while building new concepts.
What do I do about struggling learners?
Consider changing the program you are on. If it’s not working, seriously consider switching to something else. Students all learn differently. We need to set them up very early on to have a joy of learning. We all should still be constantly learning. There’s too much knowledge in this world to suddenly stop learning about it.
Whatever you’re using, always be orchestrating what the students are learning. Think very carefully and always teach “why?” And when your students tell you that they understand what they’re doing, then have them teach it back to you. Even if they falter or stutter in their explanations, they’re processing everything in their minds in order to put it all together.
After all of that and they’ve shown true understanding, then have them do some problems. It doesn’t need to be 50 problems. They probably only need maybe 5 to 10 problems and always show their work.
Don’t wait to assess their learning. Constantly quiz them on the things that they’ve learned. Don’t give them the quiz that same day of the lesson but give them review quizzes. And don’t look at their work. Some students get really creative with the way they get their answer and it’s not always the way that you taught them but it works for them. If there answer is wrong, mark it wrong. Have them figure out their mistakes and plead their case to get points back. They need to learn to take ownership of what they’re doing.
How do I respond to students who are not math-minded?
There are students who will say that they get it but are really only getting the process. The steps to doing the problem makes sense to them. And there are those students who say that they don’t get it. The process doesn’t make sense to them. These students generally claim that they’re not good with math. What’s really going is that these students are thinkers. They like things that make you think. You can’t just give them steps without giving them an explanation to why those steps work.
These students tell themselves all the time that they don’t get it. These same students end up thinking that they’re not capable of doing math. When in reality, they are so insightful but certain road blocks in their understanding have stopped them from being successful in math. These students especially need to be taught based on understanding.
I hope these 8 questions about teaching math has given you answers. I think the most important takeaway for me from this interview is to teach for understanding and to constantly be thinking why.
So I leave you with this. Don’t be so concerned about teaching math to your kids. Think about it as recognizing your child’s ability and help them realize what their potential can be. Let your kids teach you the math and just be satisfied with that.
All students can learn math. Are you as a parent comfortable with it? Be prepared to be learn math with your kids.
Are you teaching for understanding? What are some things that you have learned while teaching math?