Later this week I get to sit down with parents and together set some concrete goals for their children. It’s a great process as it allows us to focus and target as well as individualize what we think will be most beneficial to a particular child. To increase success and motivation, I would even include the child in setting their own goals.
Our faculty also sit down with our administrators and have a goal setting meeting and I only had one goal this year – to get better at what I do. I then broke that one goal out into little goals, and I really don’t know how my one goal morphed into four pages – especially when my first bullet point was to simplify things. Nonetheless, I still only have one goal – to grow as a teacher. Anyway, one of my ‘sub-goals’ if you will, was to read one article from Teachers of Mathematics a month since math continues to be an area of curricular focus for our school this year.
The one I picked from the October issue was called Building Word Problems: What Does it Take? by Angela T. Barlow.
The first question asked by the author is why would we create our own problems when there are text books and other curricular materials out there. The reason is pretty simple. Because those materials (while they have value) were not written for every kid in mind and creating your own problems allows you to customize learning. Furthermore, many of those problems focus on a single strategy vs. having kids use what they already know. The authors also say we need to thisbecause “future citizens must be prepared to problem solve and apply their skills to new situations.” According to the article, there is a process involved that requires careful thinking. Here’s the process:
- Identify the mathematics goals.
- Decide on a problem context.
- Create the problem.
- Anticipate students’ solutions.
- Implement and reflect on the problem.
Every morning when the kids come in to school, as they are settling in, I have a math problem on the board. Increasingly, I’ve tried to make the questions more open ended or focus on the process involved. I thought I’d look at the process above and reflect on it here.
The goal was to add two two-digit numbers together, use a variety of strategies, have kids explain their thinking, not rely on algorithms that haven’t been taught, and perhaps get children to round numbers.
The context was just for them to be able to communicate their thinking.
The problem (not very creative) was something along the line of “Add 99 and 99 together. Explain your thinking.”
I anticipated many of my second graders to struggle with this one. I had used it much later in the year last year and noticed kids immediately relying on the traditional algorithm they had learned. Not that there’s anything wrong with that (algorithms are great tools, but they don’t always reveal how one thinks about numbers).
With some children I prompted with further questions like, “is 99 close to a number that’s easy to work with?” Many of the children didn’t hesitate, they tried to use what they had to solve the problem.
With that question, one child said, “Oh, 100 plus 100 equals 200 and you just have to subtract 2 to get 198.”
Another child said, “Well you just add 1 to 99 to get 100. Then you add the 99 to get 199, but don’t forget you have to take away the 1 you added, so the answer is 198.”
One child said they knew 90 and 90 was 180 and that 9 and 9 was 18. They couldn’t seem to add 180 and 18 together, so he just deconstructed it and said, “180 plus 10 is 190 and 190 plus 8 is 198.”
It’s not the greatest question, but it’s really nice to see kids grappling with two-digit addition long before we introduce them to the traditional algorithm. Not only is it promoting good number sense, but it also promotes creativity. They are not relying on a single strategy from a text. They are in fact teaching themselves how to solve a problem. They are becoming more resourceful. Upon reflection, the problem could be asked in a better way, but the outcome for most was a positive one.