With all of the changes going on in the world of mathematics education it is reasonable, and understandable, to have many questions about why things are changing. In this section we have recorded some of the most common questions that have come to us and here, as well as throughout this site, we try to answer those very important questions.
Doesn’t the old way work? We learned math and do it just fine; why can’t we stick with what works?
This is a great question and one that should definitely be asked.
The simple answer is that we want people to be fluent in math. When we say that, we mean fluent not only in the math facts (which are very important) but also in mathematical thinking. Being fluent includes flexibility of thought in finding a solution to a real life situation. Some people are naturals at gaining fluency, no matter how they are taught. However, many people don’t gain that fluency and can’t really apply mathematical thinking in real life, or do not see how it is already being applied, therefore limiting their fluency. Often the way they learned math didn’t help them have that confidence. Our hope is for everyone to be confident in mathematical thinking and that means a math education which is rich in how it is taught and uses real world applications.
Why is math being made more complex than it really is?
The simple answer is that math is actually complex and hiding that complexity will hurt a rising generation where math will be used more than ever.
When looking back on our math education, which seems to be similar to many people, we found that one of the least favorite things was doing word problems. In fact, this idea seems pretty wide spread as it shows up in cartoons, jokes, and posts on all sorts of social media. Yet, when people talk about math it seems clear to everyone that math solves problems, real problems. However, the greatest irony is that the instruction we receive often doesn’t allow most people to apply math effectively.
The current quest in math education is to remedy the basic disconnect between knowing what math can do and actually being able to solve real world problems. If the way it is being taught can’t be used to relate it to the real world, and all of the complexity that goes with it, then what is the purpose of math or math education?
Most kids won’t become mathematicians; why do they need to go deep into the mathematics?
Out of all of the questions that we have heard this is the one which really gets at why people dislike the new math education techniques. The question is a fair one, as most of us won’t become mathematicians or deal with complex mathematical situations often. It begs the question, why would we want to go deeper than just the basics?
The truth of the matter is that most people will use mathematical thinking outside of “regular math” situations. Math is about being able to solve problems and to find the solution for a situation. This skill is used in almost every job (especially STEM related fields), home activities (think about cooking, cleaning, most hobbies, traveling, money, etc.), and even when you are reading. Even more, we have a huge amount of information coming at us from the internet using statistics and studies. A person who is well informed on logical (mathematical) thinking and problem solving will be able to see through mistakes and inconsistencies more easily and interpret by themselves better what the results would mean.
In essence, the hope of going deep into math isn’t to belabor or make it more challenging, especially for those who aren’t going into a math related field, but it is to help the kids become comfortable and fluent in reasoning about the world around them.
Why is there such a focus on models and pictures?
People use models and pictures in math because they work. We know that this isn’t the way our culture has taught us math works. It is an unspoken rule that if you need help of pictures then you are below level, or not as “smart”. Why though?
The notion that only those who need extra help with math might be somewhat misplaced due to the fact that most fields that rely heavily on math use models and pictures all the time. Scientist use graphs and representations to model their ideas. Architects must draw out their plans. Electricians draw “pictures” of their circuits. Engineers often make simulations of their creations to see what they will do under different circumstances.
Using models is a way to make the thinking more clear and obvious, as well as showing the complexity inherent in the ideas. It can help those who are struggling get it and those who catch on quickly to see the deeper connections that always exist in math. We are teaching concepts that took thousands of years to fully develop to children under the age of 12. This means that the ideas being taught are more complex when it’s the first time you see it. To help with this complexity, and seeking for better problem solving, giving them the tool of modeling is a wise strategy to better understand the ideas.
Why should we waste our time on teaching several methods instead of focusing on what works?
A big complaint many people have about education systems is that they often don’t account for learner differences and those at different developmental stages. Yet, when it comes to math, this argument never comes up as most view math to be a one way street to find the answers, using the most efficient way. No one can complain about being efficient with mathematical procedures, but if a child doesn’t understand the procedure and therefore is inefficient, or unable to apply it to a context, then the method does nothing for them.
Since we want to reach children according to their needs this means that we need to look at several ways to understand the process. Showing different methods helps those who don’t get it and for those who do it stretches their thinking and encourages them to think of it from a different point of view.
Also, by honoring different methods the students feel success when they might not otherwise get it – because they aren’t one of the “smart” ones. What is even more powerful for children of all abilities is to be able to create their own method or apply one that another student created; this can build confidence in their learning more than almost anything else.
It seems like my kid is just getting more confused. Can’t I just teach them the right way?
There is nothing is wrong with teaching kids what you know, in fact, we want you to. As a parent you provide a great perspective on math that the teacher can’t. There is also a lot of practice and advice that you can give.
With that said, there are some suggestions we’d like to share from a teachers perspective. These suggestions can help mold the attitudes and thought processes of children more than one may think. And yes, what you say and how your attitude is towards something can greatly affect how your child views it.
These are the attitudes that we would love for you to share with your children:
- There are many ways to approach a problem, find the one that works best for you to understand it.
- Math may be hard, but I can do it. (As a parent don’t say that you don’t like math or can’t do it. Students use this as an excuse more than you may like to admit; in fact, it can be heard almost daily.)
- When I get stuck I first draw a picture to help me understand, then try it another way, take a quick break (with another subject or problem), and ask for help if I still need it after I’ve tried my best.
- Learning math isn’t about already being smart in it, it is about being able make sense of the world around me, and I can do that.
Don’t we want to have kids get to the right answer as quickly as possible?
Yes, we do want the children to get an answer quickly. A child who can get an answer efficiently is a child who understands. With this being said, we do want to make clear our stance on some ideas though; mainly that teachers, and parents, shouldn’t be interested in just the “right answer”, but should also be interested in how they got there.
Just getting the right answer tells us nothing about if a child understands the math. It may just mean that they memorized a couple of steps, but couldn’t use the math outside of that situation. The real goal of math is being able to use it in real life. If the child can only get the right answer but not apply it to real life, then they don’t know math as deeply as they can and should.
What we really want our children to be able to do with math is to be able to make sense of and get an answer in a reasonable amount of time. We shouldn’t care about a time limit, rather that they can get an answer that they can justify, in a decent amount of time. This means that a child must be able to understand what they are doing, be flexible in their thinking, and be able to know how their answer is reasonable and applies to the original question. How different this is from just knowing the basic math facts!
Why doesn’t math education match the real world’s math?
Math is, in many ways, a result of thousands of years worth of study, trial and error, and a lot of hard work. Math, as it is taught now, has only been taught this way for a couple of hundred of years. In essence what happened is that educators tried to make math more “accessible” to the average student. This means that they made it so that it could be taught quickly and therefore mostly only the tricks were taught. These tricks are what we know as the standard ways of doing math, all of the procedures and steps to take.
With only the tricks being taught people felt like they were making great progress in learning math, and did gain ability in using it; which is what most of us enjoy today. Sadly, this type of math education isn’t very deep, and it takes years of making connections after the fact that could have been better taught at the time it was first introduced. This teaching style follows the theory of teach all of the steps now and then apply it later. This style is very pervasive in everyday life, and does have it’s limited place. The problem though is that it doesn’t work well for most learning situations.
Research into learning in general, and specifically into math learning, show that the best way to learn math is by being given a problem that you haven’t been exposed to, working hard to make sense of it, discussing techniques and methods with others, refine and generalize your thinking to new situations, and connecting your own personal thinking to the “official” procedures that are shared by all. The research shows that when all of these happen in meaningful and intentional ways that a child’s understanding of math will be stronger and more able to match and deal with the real world math that is used in everyday life.
The Math Dragons 