The other day I was at my sister’s house. While I was there I noticed by niece doing her math homework and as I sat next to her my sister asked me to help her because she was having a hard time with it. As I reviewed the material and looked at the problem it became clear that my niece’s struggle with her homework was not because she couldn’t do it or because it was too hard. The struggle was that context of the problem was completely irrelevant to her and as such, didn’t offer much in the way of motivating her.
So I decided to do to her what I do to my kids: teach her outside the textbook in a real life context that would make sense to her. This isn’t a cutting-edge principle by any stretch of the imagination, but it is one in which many parents fail to provide adequately for their children’s learning. And please don’t take that to mean that parents are failures at teaching. To the contrary, parents that invest time into their children are smashing successes. It’s just that often children need more out of their young education than their school or teacher can give them (hence my love for homeschooling).
The problem that my niece was working was pretty simple as it was stated: “A basketball team has won 15 out of 21 games. What percentage of games did they win?” Simple enough, right? But beyond setting up a percentage division equation, where is the thought supposed to come from in this problem? When is the last time you had a problem to solve that was written down on a piece of paper for you?
So after I explained how to set up the necessary equations to determine a percentage from a total and a quantity and I threw a few problems at her. The first was a handful of crayons. There were broken crayons and complete crayons. I asked her to first tell me what the total was. Then I asked her to count how many of the crayons were complete. Then I asked her to tell what percentage of crayons were complete.
We moved on from there to looking at the complete crayons and I asked her to tell me how many of the complete crayons had yellow wrappers and then tell me the percentage of complete crayons that had yellow wrappers. Each time I asked her to set the problem up on paper only after she was able to look at the situation and determine the variables and values for herself.
Then I gave her another problem, a little more relevant to what she does for fun. She is one a swim team. So I told her that there is a swim team that just competed at the championships. The team had 150 swimmers on the team. Of those 150 swimmers 20% were girls under the age of 12. I then asked her how many of the girls on the team were under 12. After that I told her that the coach wanted to surprise the girls under 12 on the team by taking them to a water park to celebrate their season. But the coach found out at the last minute that only kids 8 and over were allowed in the park. I told her that there were 9 girls on the team that under 8 years old that wouldn’t be allowed to go. I then asked her to calculate the percentage of girls under 12 that would not be allowed to go to the water park. Then, as a recap, I asked he to tell me the percentage of the swim team those 9 girls represented.
I set up problems like this for my kids all the time. I can, because I am one of their teachers. Very seldom do I take a problem as it was written in a book and hand it to them to solve. I am actually looking for a few things from my kids when I teach them, none of which is available from them calculating numbers on a page.
The first thing I want them to do is understand the nature of the problem they are solving. Setting up a solution to a problem has to start with understanding the problem at hand. If not, well your foundation will suck and will ultimately lead to potentially questionable results.
The next thing I want them to do is think about the simplest way to solve the problem. Complex problems can sometimes be solved by simple means. But looking at something and thinking right away that it is a huge problem and then getting worked up over it can and usually does lead to something going haywire. Thinking about the nature of the problem often presents potential paths to a solution, and sometimes even offers a simple solution.
After figuring the best way to solve the problem I like my kids to setup the way in which they will solve it. This can be the part where they write and equation, or using block put some on one side of a table and some on the other, or using army men or … you get the point. Whatever path they have chosen to solve the problem needs to then be converted to a solvable schematic.
From there it is just a matter of arithmetic or simple logic. When it comes to math I am really not at all concerned with the correct answer being returned so much as I am with the correct means to a solution being used. Arithmetic is the easier of the things to teach when it comes to math. Logic, not so much.
And such is the case with almost all disciplines of education. Language, history, science… all disciplines have challenges that need to be solved, solutions to those challenges and basics that are used in those solutions. unfortunately schools, textbooks and teachers often have to rely on making things as simple as they can for the bulk of the students being taught and this often results in many students that could learn more or learn faster being restrained and often retarded in their learning.
But if you are a parent you have opportunities every day to test your children, teach your children and train your children. In fact, it isn’t so much an opportunity as it is a responsibility. And it is a responsibility that parents must necessarily take seriously given the condition of our public education system.
Wrapping it up
Just for grins I gave this problem to my three older daughters yesterday after watching a cake competition on Food Network. Sarah gave me the answer before I finished telling her the problem. Lets see how well you do:
Say you are making a stacked cake. The bottom layer of the cake is a perfect square in shape with a known side length of L. Now say we are going to put a round cake on top of this layer and we want the round cake to be exactly in the middle of the square cake below it. The round cake will have a diameter, D, that is smaller than the length L of the square cake. How would you determine where on the square cake to place the round cake so that the round cake was exactly in the middle of the square cake?