What does it mean to change a math problem from being CLOSED to being OPEN? Essentially, the problem changes from having just one correct answer to having several. I also give several examples of how to change problems.
First, I want you to watch this short video by Jo Boaler. Seriously. Take a few minutes. It's not long, and I think you will be glad you did!
Jo mentioned the simple task of finding the perimeter of a rectangle when its sides are given, and changing that into a problem where students are asked to give two different rectangles with a given perimeter.
That is changing the task from a "closed" format, or a simple performance task, into an "open" format and into a LEARNING/GROWING type of task. It essentially means that now the problem has many possible answers, instead of just one. And it was a very simple change that did it!
(This also helps students develop a growth mindset.)
As you are planning your math lessons, check if some of the tasks you will be giving to your children/students can be CHANGED into open problems.
You can OFTEN take a textbook problem and do this. And, I don't mean you'd need to do this to every problem in the book but do it to SOME so that your children/students can have the opportunity of seeing that math can be ADVENTUROUS — you can be CURIOUS in math class — and it can even be FUN! It's not just about spitting out correct answers to calculation problems!!
0 + 7
1 + 6
2 + 5
3 + 4
4 + 3
5 + 2
6 + 1
7 + 0
0 + 7
1 + 6
2 + 5
3 + 4
4 + 3
5 + 2
6 + 1
7 + 0
8 + (-1)
9 + (-2)
...
Problem Solving: Opening up Problems
This article gives a great example of producing MANY open problems from the closed problem "How many 5p coins are needed to make 45p?", in terms of what is known (information given), what is unknown (what needs to be found out) and what restrictions are placed on its solutions.
By Maria Miller
Math Mammoth TourConfused about the different options? Take a 7-day virtual email tour around Math Mammoth! You'll receive: An initial email to download your GIFT of over 350 free worksheets and sample pages from my books; 6 other emails on 6 subsequent days that describe the different series of Math Mammoth products, answering the most commonly asked questions, including "What is the difference between all these different-colored series?"This way, you'll have time to digest the information over one week, plus an opportunity to ask me personally which book would be right for your child or students. Note: You will FIRST get an email that asks you to confirm your email address. If you cannot find this confirmation email, please check your SPAM/JUNK folder. |
"Mini" Math Teaching CourseThis is a little "virtual" email course. You will receive: An initial email to download your GIFT of over 350 free worksheets and sample pages from my books; 7 articles on important topics on mathematics education, including: multiplication tables, fractions, how to help a student who is behind, and the value of mistakes; 1 email about Math Mammoth books.Note: You will FIRST get an email that asks you to confirm your email address. If you cannot find this confirmation email, please check your SPAM/JUNK folder. |
Join over 25,000 others!Maria's Math News is my newsletter, filled with math teaching resources, Math Mammoth news & discounts, humor, giveaways, and more! The content is equally good for all of us who teach math. :) The newsletter comes out once or twice a month. Peek at the previous volumes here. By subscribing you will also receive: A GIFT of over 350 free worksheets and sample pages from my books. |
© 2006-2015 MathMammoth.com