I just finished my fourth of twelve classes for my master's in curriculum and instruction with an emphasis in math education. That means I'm officially 25% done with grad school! And, yes, I am counting. :)
My last class was focused on teaching problem solving, and I have to say it was the most interesting and useful class I have taken so far. Today, I want to post one of the homework assignments I did for this class. Our assignment was to make a poster describing a heuristic problem solving model that our students could use. We could either make our own or use the one our school currently uses. My school has not adopted a problem solving model, and I wasn't feeling super creative. So, I decided to do some pinterest searching for ideas. I came across the SOAR model from an elementary teacher's classroom.
The model was found on The Classroom Tourist Blog, and the linked post features the work of Kimberly Fournier at Land O'Lakes Public School. I loved the SOAR strategy framework, but I knew it would need some modifications to work in my high school classroom.
And, if you've been around my blog much at all, you know I kinda like making posters. So, when I got to get out my colored paper and markers, I knew this was going to be my favorite assignment yet.
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Here's me and my completed poster.
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Next, students should ORGANIZE their thinking. This is where I want students to start thinking about how they are going to go about solving this problem.
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Lastly, students need to REFLECT on their answer. To do this, I gave students four questions to ask themselves.
1. Did you check your work and show all of your thinking?
2. Does your answer make sense?
3. Did you write a complete sentence summarizing your answer?
4. Did you use appropriate math vocab?
I've never had my students ask themselves these questions before. I get frustrated when students don't check to make sure their answers make sense. But, I've never taught them to do this. I guess I've always assumed that they should have picked up this strategy somewhere along the way. But, it looks like if I want it to happen in my classroom, I'm going to have to explicitly teach students to do this. That's one of the things I'm learning the more I teach. It's the things I complain about that I need to make strides to change in my classroom.
I also want to start having students summarize their answers to each task with a complete sentence. This should force them to go back and look at what the problem was asking exactly. Hopefully, if a student has accidentally solved the problem for the wrong thing, they will realize it at this stage in the problem. A teacher can hope, right? :)
Here's the entire poster I made without my smiling self in front of it.
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My grad school assignment didn't stop with just making a poster, though. I also had to demonstrate what it would look like to use this heuristic problem solving model on a problem.
I chose a problem from a sample ACT test: What is the maximum number of distinct diagonals that can be drawn in a regular hexagon?
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For the REFLECT step, I asked myself the questions from the poster.
So, why am I excited about this?
It is my hope that this model will help my students because it will force them to slow down and focus on the problem solving process. So often, my students complain that they cannot do a problem, and they refuse to even start solving the problem. However, it should give my students a structure that will help them start the problem. Even if students do not know how to solve the problem, they should still be able to SHOW what they know from the problem. Every student should be able to circle or underline key words and make a list of knowns and unknowns. The ORGANIZE step will have them think through what different problem solving strategies they have available to them. This should help my students get more familiar with practicing the problem solving strategies. Even if students do not end up implementing the problem solving strategy, they are still getting practice considering which strategy would be best to use.
The ACT stage is where my students normally start with a problem. They want to jump right into solving the problem without actually thinking about what the problem is asking or what route they are going to take towards an answer. I also like that the ACT stage reminds students to show all of their work/thinking and use appropriate units. The REFLECT stage of problem solving is what should be the real game changer in my classroom. Once students get an answer, they want to rush right on to the next question. They often don’t take the time to see if their answer even makes sense. For example, if we are solving for the number of watermelons in Susie’s car, the answer shouldn’t be 0.0001 or 100000000. I also like that this asks students to write their answer in a complete, cohesive sentence. This forces students to go back to the problem and see if they actually solved for what the problem was looking for in the first place.
I believe following this process will make my students into better problem solvers because it will mean that they are more engaged throughout the problem solving process. When they claim they don’t know what to do, I can ask them what stage they are on in SOAR. I haven't actually used this with my students yet, but I think that I'm going to make some sort of graphic organizer that I will have my students fill out as they work through the SOAR process.
My last class was focused on teaching problem solving, and I have to say it was the most interesting and useful class I have taken so far. Today, I want to post one of the homework assignments I did for this class. Our assignment was to make a poster describing a heuristic problem solving model that our students could use. We could either make our own or use the one our school currently uses. My school has not adopted a problem solving model, and I wasn't feeling super creative. So, I decided to do some pinterest searching for ideas. I came across the SOAR model from an elementary teacher's classroom.
The model was found on The Classroom Tourist Blog, and the linked post features the work of Kimberly Fournier at Land O'Lakes Public School. I loved the SOAR strategy framework, but I knew it would need some modifications to work in my high school classroom.
And, if you've been around my blog much at all, you know I kinda like making posters. So, when I got to get out my colored paper and markers, I knew this was going to be my favorite assignment yet.
Here's me and my completed poster.
SOAR stands for SHOW, ORGANIZE, ACT, and REFLECT.
More specifically, you should SHOW what you know from the problem. In my classroom, I would like to see students make a list of knowns and unknowns, rewrite the problem in their own words, or mark up the problem by circling or underlining important information and crossing out unnecessary information.
Next, students should ORGANIZE their thinking. This is where I want students to start thinking about how they are going to go about solving this problem.
The suggestions for how to do this were taken from the problem solving strategy posters I have hanging on the wall in my classroom.
A stands for ACT. Students should ACT by using their strategy (or strategies!) to solve the problem.
I wanted to remind students that it's okay at this step to admit that the problem solving strategy they chose didn't work as they expected and choose a different strategy. I think that a lot of times, students feel like they have to pick one strategy and stick with it. But, they don't know what strategy to pick, so they end up not picking any strategy and giving up. A lot of this has to do with growth mindset vs. fixed mindset.
I want my students to show all of their work. This is something I'm going to be a much bigger stickler about next year. I saw a post earlier this year in the MTBOS where someone put "CONVINCE ME" in large letters on the wall of their classroom. I'm going to make this my motto next year. I don't want students to show all of their work because it's tradition. I want students to get used to doing all that they can to convince me of their understanding of a concept. A correct answer with steps shown is much more convincing than just an answer. This is also the philosophy behind my A/B/Not Yet grading scale. If I'm not convinced that students understand a concept, they are going to get a NOT YET until they have convinced me.
"No Naked Numbers" refers to always including proper units when working a math problem. This is something I still need to do a better job of.
Lastly, students need to REFLECT on their answer. To do this, I gave students four questions to ask themselves.
1. Did you check your work and show all of your thinking?
2. Does your answer make sense?
3. Did you write a complete sentence summarizing your answer?
4. Did you use appropriate math vocab?
I've never had my students ask themselves these questions before. I get frustrated when students don't check to make sure their answers make sense. But, I've never taught them to do this. I guess I've always assumed that they should have picked up this strategy somewhere along the way. But, it looks like if I want it to happen in my classroom, I'm going to have to explicitly teach students to do this. That's one of the things I'm learning the more I teach. It's the things I complain about that I need to make strides to change in my classroom.
I also want to start having students summarize their answers to each task with a complete sentence. This should force them to go back and look at what the problem was asking exactly. Hopefully, if a student has accidentally solved the problem for the wrong thing, they will realize it at this stage in the problem. A teacher can hope, right? :)
Here's the entire poster I made without my smiling self in front of it.
My grad school assignment didn't stop with just making a poster, though. I also had to demonstrate what it would look like to use this heuristic problem solving model on a problem.
I chose a problem from a sample ACT test: What is the maximum number of distinct diagonals that can be drawn in a regular hexagon?
For the SHOW step, I listed the knowns and unknowns for the problem. And, I chose to highlight key words in the problem.
For the ORGANIZE step, I chose which problem solving strategy I would use. I decided to draw a picture of a hexagon and draw in the diagonals by hand.
For the ACT step, I did just that. I drew a hexagon. Then, I started drawing in the diagonals. I used CWP (Color With a Purpose) to demonstrate my thinking.
Then, I summarized my findings with a complete sentence: There are 9 distinct diagonals in a regular hexagon.
For the REFLECT step, I asked myself the questions from the poster.
So, why am I excited about this?
It is my hope that this model will help my students because it will force them to slow down and focus on the problem solving process. So often, my students complain that they cannot do a problem, and they refuse to even start solving the problem. However, it should give my students a structure that will help them start the problem. Even if students do not know how to solve the problem, they should still be able to SHOW what they know from the problem. Every student should be able to circle or underline key words and make a list of knowns and unknowns. The ORGANIZE step will have them think through what different problem solving strategies they have available to them. This should help my students get more familiar with practicing the problem solving strategies. Even if students do not end up implementing the problem solving strategy, they are still getting practice considering which strategy would be best to use.
The ACT stage is where my students normally start with a problem. They want to jump right into solving the problem without actually thinking about what the problem is asking or what route they are going to take towards an answer. I also like that the ACT stage reminds students to show all of their work/thinking and use appropriate units. The REFLECT stage of problem solving is what should be the real game changer in my classroom. Once students get an answer, they want to rush right on to the next question. They often don’t take the time to see if their answer even makes sense. For example, if we are solving for the number of watermelons in Susie’s car, the answer shouldn’t be 0.0001 or 100000000. I also like that this asks students to write their answer in a complete, cohesive sentence. This forces students to go back to the problem and see if they actually solved for what the problem was looking for in the first place.
I believe following this process will make my students into better problem solvers because it will mean that they are more engaged throughout the problem solving process. When they claim they don’t know what to do, I can ask them what stage they are on in SOAR. I haven't actually used this with my students yet, but I think that I'm going to make some sort of graphic organizer that I will have my students fill out as they work through the SOAR process.
I'm also thinking that I should make a SOAR foldable for students to keep in their notebooks and reference throughout the year. So many ideas. I can't wait until next school year to try this out!