Whether you are teaching math at home to your student or coming alongside their work with a curriculum, you have a critical role in supporting your young person’s understanding of math concepts. Some people are really great at math. Some people are really great teachers. And then… Some people can do both! Teaching math is a unique skill set but you have to truly understand the math and teaching processes to teach the subject well.
CONTEXT IS CRITICAL TO A POWERFUL LEARNING ENVIRONMENT
Traditionally, math is taught through examples; a concept is often introduced by taking a formula and showing “how you do it,” with specific steps to solve the problem. What’s the problem with teaching math by examples? The problem is that there is no context for the learner to understand why a formula is executed a certain way. If there is no context, your learner won’t get the “why” or any higher-order thinking skills to solve other problems.
So what can you do instead? How can you learn to teach math in a way that both enables your students to succeed while also developing lifelong skills of problem-solving and higher-order thinking?
Here are my top 3 steps to teaching math powerfully:
Define The Concept
Start out by defining the topic. Define each word. This will help you establish a context for understanding the practice. If you don’t start with a definition, the young person will have trouble understanding why they are doing what they’re doing. For example, if you’re teaching how to do the Greatest Common Factor you first say, “Okay, ‘Greatest. Common. Factor.’ What do these three words mean?”
Define them one by one and break it down:
Greatest = largest in size of those under consideration.
Common = belonging equally to or they share something that is the same.
Factor = this is the tougher one, it’s a divisible part of a number. What does that mean? It can divide into the number with a remainder of zero.
So, now we put it all together!
When you do that here with GCF you’re looking to determine what is the largest same factor (or divisible part of a number)! Defining the concept gives a context for understanding how to execute the practice and empowers your student to implement the principles in other examples.
Start with the definition and then give an example. Then you can practice in all sorts of ways. Once the comprehension is there for a concept, young people will be able to make higher-order thinking connections to ANY problem they are working on. Create the context by defining the words you are working on. If you don’t know what the words mean, look them up! This is a great learning opportunity for you and your students alike.
Research and Look Ahead to Show Where Concepts Are Used Elsewhere
Help your student (and yourself) out by creating a road map. Look to the future: what do your students need to know to get them to where they’re going? You can look at the syllabus of a college course online or look up a sample test for your child’s subject and see what’s in it. Oftentimes, as parents and educators, we are trying to learn as we go with our young people, and just do what’s next in the course without really knowing where we are heading. Ask yourself, “What parts here am I going to need later on? Where might I see this in geometry or college or real life?” There may be a great way to tie the concept you’re working on into everyday math too.
Discovering where the concepts will come up in the future may take some work: you may have to ask someone else or even Google it! You can look ahead in your math course to see what’s coming and ask “when might this concept show up again?”
When I start to teach someone about adding, I tell my students that adding is counting things that are the same. Now, there are lots of ways to define adding – why do I use that particular definition? Because when you add decimals, you’re going to line up the decimals. Why are you going to line up the decimals? Because you are counting the same kind of decimals. You’re getting common denominators for fractions because you’re counting the same kind of denominators, the same kind of fractions.
This might take a little extra work from you as the teacher, but I promise you it will be worth it to look ahead and see where they might see these concepts again, once again building the context for them to start to understand these important concepts.
Let Your Students Learn From Their Mistakes
Let your young people make mistakes! This one might be really hard for some moms! Let them make mistakes and then let them find out what they did wrong. It’s almost like touching the hot stove – it’s instant learning! They make the mistake and then immediately find out what they did wrong. This helps them develop skills to be self-directed learners and is empowering them for education and ALL of life!
What does it look like to let your students make mistakes? You might be sitting there watching your student complete a problem and you can see already that they’re taking the wrong step; let them keep going until they get to an answer or until they stop and look at you and say, “I don’t know where to go from here!” Then you can go back and look at it together and say, “Alright, well let’s take a look and see! Maybe something went wrong. Let’s start at the beginning and go step by step. What did you do and how did you get from one step to the next?” *Going step by step.* Is this what you’re supposed to be doing next?” Now notice, it’s not saying, “This is what you’re supposed to be doing next.” I am asking the question, “Is this what you’re supposed to be doing next?” and allowing the young person to look for themselves; Not saying, “here’s what you do step by step,” but rather, asking them the question, “what do we do next? Why do we take this next step? How do you make a common denominator? Why do we make a common denominator? What would make a common denominator?” If you notice, all of those kinds of questions are allowing the student to think, to inquire, and to be able to start to look at those definitions that they’ve talked about already and really develop those higher-order thinking skills.
This is an amazing process and it’s the best way for your students to learn and practice. You can also think about it this way: if you’ve allowed them to make mistakes while they are learning and practicing, then when the time comes for them to actually take the test, they will be much more prepared because they already know the possible wrong routes they could take to solve the problem and they understand how to correct themselves. This is a life skill; Can you imagine what kind of a great young person they are going to be if they know that they can learn from their mistakes? Then they can move forward, not being afraid to take that risk, or take a chance! Your child will be willing to say, “Hey, I’ve got the answer!” Whether it’s right or wrong, they’re in the game and they’re playing!
Put these 3 tips to the test while teaching math to your students and see what new possibilities open up! As always, I love to hear from you, whether it’s sharing tiny victories, huge breakthroughs, or a roadblock you may be facing – send me an email! Thank you to all you home educators out there who are taking on each new day and each new challenge with enthusiasm, perseverance, and joy. It’s the biggest gift you could ever give your students!