When I look through the Math Practices I find words and phrases such as: solve problems, apply understanding, seek the meaning of, efficient ways to represent, create logical representation of the problem, extend understanding, write simple expressions, construct arguments, use concrete referents, model, use tools, pattern or structure. This is great! This language points us to developing critical thinkers. We can't "instruct" students to be critical thinkers but we can structure their learning experiences so that they have multiple opportunities to explain the how and why of their answers and back their thinking up with evidence.
I’ve been teaching for 15 years in a multiage classroom and have always had 11 problem-solving strategies posted in my room. The posters are “retro” and probably created in ClarisWorks – a word processing program used in the 90’s – wow that’s old when you do the math! But I like keeping them this way because it reminds me not everything needs to change. These were good and continue to be good.
Today, in reviewing and discussing examples of the use of these strategies, we are in fact also practicing MP4: Model with mathematics. My students experiment with representing problem situations in multiple ways including numbers, words, drawing pictures, using objects, making a chart, list, or graph, creating equations.
At the beginning of the year I do a lot of modeling for my students. I find that when I set the example correctly it carries through the rest of the year. This is one lesson where I model an example of 11 problem solving strategies. The students record these on their math folder, or in the first pages of a math journal. I also have the Problem Solving Strategies Posters up as a visual reminder and I refer to them often. Not only am I modeling the strategies, but I am modeling my thinking using these strategies and the patience and perseverance to solve problems.
Problem Solving Strategies:
It would be a good idea for you to write out an example ahead of time that ties your students' backgrounds/knowledge to examples of the use of these strategies. I use a lot of examples with apples this time because we had just met our little buddies and we worked together on a math page that contextualized math using apple examples. From the examples you can see some students write their examples randomly over the page and some students make an organized list. In this case where the structure or order isn't necessary to the meaning, I honor that not every person’s brain uses information as an organized list, sometimes a random order is acceptable. Student Example 1, Student Example 2, Student Example 3.
I also had my students explain how they used the problem solving strategies at the end of the hear. Here is a video so you can see some of their examples.
Once again I am using this opportunity to model for my students. This is the beginning of the year and having students reflect is a huge part of my teaching. It doubles retention and gets them to thinking about their own thinking – metacognition. This can be done in writing but this time I will have them do their reflections verbally – once again modeling the correct procedure.
The first question I ask is:
Which strategy do you think you will use the most?
You might hear a variety of answers. I heard a lot of Look for a Pattern because I organize the beginning of the year with “Your Brain is a Pattern Seeking Device!” and we look for patterns in academics as well as schedules, routines and organization.
Did you see a strategy you haven’t tried before? Which one?
Many students who are new to my class will say Work Backwards and I love this because I am all about giving the answer to them and having them figure out how to solve the problem. For me the process is just as important as the answer – usually more so.
Which strategy would you like to try this year?
There isn’t a correct answer to this question because they are going to be using every single one of them but I get to find out learning styles and since I teach students in a multiage 4th and 5th grade class I already know half of them and this helps me get to know the other half.