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Reflections of a High School Math Teacher
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Math Blog by David Sladkey. I teach High School Mathematics and I love my job. I like to learn new things to become a better teacher. This is a record of my journey.
This game is the reverse of a Number Talk. In a number talk the teacher gives a problem and students find different ways to come up with the answer. With truth or snare, the teacher gives an answer and the students create potential equivalent possibilities (truths) or non-equivalent possibilities (snares). The rest of the class has to find ways to determine if the possibilities are a truth or snare.
Let's give an example
Teacher: Let's play TRUTH or SNARE with the theme being exponents and order of operations. Remember that SNARES are NOT-EQUIVALENT but are really close to being equivalent and very tricky. Create at least 2 TRUTHS and 2 SNARES for the following answer: 16 (Teachers resist the urge to give examples. Don't do it. Instead, encourage the students to create a problem that has an answer of 16. Remind the students that it won't matter if their problem is equivalent or non-equivalent...they will not be wrong)
Students: Work in groups of 2-4 to accomplish the task. (Teachers make sure each group has at least one example of either kind)
Teacher: Pick groups at random to present their possibility. Students will not be telling the rest of the class if it is a truth or snare yet. Have the groups put their problem on the board or have the group give them to the teacher to put on the board.
Teacher: Now take some time in your groups to decide which ones are TRUTHS or which ones are SNARES. (Allow enough time for all groups to get through at least half of the examples given)
Students: Work together in your group or with your partner to determine if each problem is a TRUTH or a SNARE. Be ready to defend your work.
Class Discussion: Take a vote for each example. Thumbs Up (Truth), Thumbs Down (Snare), and Thumbs Middle (Unsure). (see my voting thumb pictures below) Have students walk through the reasoning and or the teacher walk through the reasoning for each example. Be open about the fact that this activity is meant to push your understanding and that you might make mistakes on what is a TRUTH or SNARE. These mistakes are helpful for us to recognize equivalencies in the future.
See the example below that we did in class.
Here are a few examples of what the students made.
Group B,C and D are TRUTHS and A and E are SNARES.
The beauty of the game is that students do not fear creating a wrong answer. Actually, they like to create answers that are SNARES. Students like to trick their classmates.
Here are some other examples that we have done.
This is what I have been doing when I have my students voting.
This game is a work in progress. Do you have any suggestions for me? What has worked for you? Please let me know.
I want my students to struggle--to squirm and to be frustrated. I often struggle with math questions. It takes me a while to process and sort out my thinking. Struggling with a math problem gives me confidence for the next one. In the classroom I love when my students are working on a difficult math question and then someone has an ‘aha’ moment. It is like someone receiving a clue to the location of a hidden treasure. It spurs others to continue working and finding other connections. I want them to take ownership and celebrate the journey. I could sum up my teaching philosophy with the phrase, "I want my students in a productive struggle." I want my students to struggle, but I want them to be productive in that quest. If the struggle is too easy or too tough, then I need to help make some adjustments by creating the right environment and finding the right questions to problem solve. That is why I'm trying 20% Struggle Time.
20% Struggle Time (Problem Solving) My instructional learning coach Chris DeWald from BetterLesson recently challenged me. "Why don't you devote 20% of your class time to (productive struggle) problem solving questions?" I have accepted the challenge and I've been on this journey since late last year. I'm taking 20% of my class time and devoting it towards problem solving, and not necessarily content-based problem solving either. As far as actual time in the classroom that means 1 day a week or two half days a week we will be in a productive struggle solving problems. It has been fun and really rewarding--and frustrating. It is all about finding the right problems and creating the right atmosphere for learning.
Easy Problems Do Not Accomplish Much You know what an easy problem is.... the ones that you don't have to think too much to solve. If you don't have to think too much to solve something, you probably won't remember too much about your work, nor will you be satisfied with yourself. I tend to give out too many easy problems. My lesson will include some kind of formula and the problems use the formula--too easy and too forgettable. Fawn Nguyen says, “Are they really ‘problems’ if we know how to solve them?” I firmly believe this.
Problem Solving creates productive struggle. I'm not talking about word problems at the end of each section of practice problems. I'm talking about NON-Content Specific Problem Solving. The problems students can't just look up in their notes and see one almost exactly like the one given. A problem that they can solve, but it will take time and maybe more than one class period. It will take reflection of possible solutions. It might even take some research, or multiple attempts at the problem, or scaffolding from the teacher or other classmates.
What does 20% Struggle Time look like when Problem Solving? 1. I have a walk that I take often that leads me under a canopy of oak trees. Students need to feel like they are in a canopy of oak trees—a safety net. They need to know that the students around them and especially myself as the teacher are WITH them. A positive classroom atmosphere creates safety nets in case they don't get it. Examples of safety nets would be: formative testing without grade impact, retakes on summatives, daily work that explores but does not affect final grades, classmates who are willing to help others, and a teacher who offers multiple avenues for help.
2. Finding the right problems is important--Inviting and Approachable Problems with Escalating Difficulty (Low Floor High Ceiling). Everyone has a different threshold of pain. Some complain wildly because of a small cut, and others would not be fazed by a large gash. That is just how we are made. Accordingly, I believe we all have a different threshold of struggle. For instance, some people might look into a problem with their laptop with bitter frustration and give up quickly, while another might struggle for a long period of time. It is the same thing with a problem in math class, some students look at the problem and then give up quickly. Other students look at the problem and start formulating some ideas. The trick is to find questions that anyone can start and yet most will be challenged at some point in the problem. Here are some of my 'goto' problems.
There are actual examples at the bottom of the post
3. I’m still working out how to approach grading Productive Struggle. Is my 20% struggle time a completion grade? Do I grade on correctness? Should there be a rubric? Maybe I should just build in accountability with group presentations of thinking? Any thoughts or suggestions on this would be welcome!!
Plumbing and my Father-in-Law Confidence solving problems is a real world skill. When we had just bought our first house, my father-in-law and I were looking into the electrical box to see how to stop one of the circuit breakers from going off regularly. It was a nest of confusing wires. I asked him how he felt so confident that he could figure this out. I was ready to give up. He said, "Whatever mess I get myself into, I’ll just keep trying to figure the problem out by taking a generous amount of time and many setbacks trying to prevail. A last resort solution would be that I could hire someone to fix it." I have used this advice often and have learned that with determination and confidence, I can often see it through. Like every year when I do my taxes. I can usually figure out most questions (with Turbo Tax). This is the attitude that I want my students to come out of my class with. I want them to be confident that they can attempt and find a method of solution with almost anything they encounter and that it will be a productive struggle. My father-in-law without knowing it, was using the Mathematical Practice Number 1. I'm hoping that 20% Struggle Time will help my students with this mindset.
Teach Before or After They Need It? My wife will never let me teach her about any technology until she needs it. Why? Because she says she will forget it all and then just have to ask me again when she actually does need it. We need to give the problem first and then our students will need to use the skills and formulas to get the answer. That is true problem solving. Sometimes our classrooms are backwards in that we do all this upfront teaching so that they will remember it when they need it. Which by the way, rarely happens. Needing it might mean that it might be on a quiz that happens a couple days after they learned it so that you can just memorize the steps to get through. Introducing 20% struggle problems will help exercise the GROWTH MINDSET needed to solve new challenging problems that they have never seen before.
What about the Content? Some would argue that they don't have enough time to teach the content now, how are they going to introduce more problems? I get that. However, I believe math is an attitude not a skill. We really are teaching our students to have GRIT, to never give up, to exhaust all resources, to struggle, and to fail. We can teach skills until our students are robots or we can teach them to be real world problem solvers.
The Struggle is Real, so that is why I'm going on the 20% struggle time journey. I'll keep you posted. I welcome any thoughts or advice.