Every school year, I choose a new math mantra to practice with my kids. This year, I've chosen to focus on "PERSEVERANCE" for math. The new Common Core Standards have 8 mathematical practice standards that all students will master as they work through content. Here are a few that correspond to perseverance:
MP.1: Make sense of problems and persevere in solving them.
MP.3: Construct viable arguments and critique the reasoning of others.
MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
Before students can solve a problem, they need to UNDERSTAND what that problem is asking them to do. In multi-step problems, some students read the problem once and then ask for help because they don't immediately see the arithmetic that is needed to solve the problem. Today's students are used to Googling questions, asking Siri, or texting friends if they get stuck. It's important for us to teach them HOW to work through problems that aren't easily solved. Students must be able to understand the problem, solve it, defend their steps/reasoning, and use that understanding to critique others. Students should be able to use models (tallies, pictures, diagrams, tables, etc) to help them explain their reasoning, and become more efficient when using these tools to solve problems.
With all of that being said, here are the 6 steps I am using this year to help my kids persevere through difficult math problems:
1. Have a positive attitude.
Having a positive attitude is a necessity. Many students that have not built up math stamina have a hard time entering a difficult task with a positive attitude. Help them by having them repeat positive affirmations, such as ,"I will try my best," "I can learn anything," "I'm making the decision to try," "I can do it," and "I believe in myself."
2. Read the problem, write an answer sentence, and read the problem again.
Have the student read the problem aloud. Ask them to locate the sentence that asks for an answer OR the sentence that asks a question. Using that sentence, write a sentence farm that answers the question, and use a line where the answer will go. For example, the last sentence of a word problem that asks, "How many flowers does Sophia have?" would turn into a sentence frame that says, "Sophia has __ flowers." Some students don't complete all of the steps for completing a multi-step problem, so writing this frame helps them figure out whether or not they are done solving the problem.
3. Underline/circle important information.
Help students read through the problem to look for information that helps fill in the answer frame. Students might circle numbers and key words, such as "altogether" or "how many more." Use the key words to help students figure out WHAT to do WITH the numbers.
4. Try different strategies.
Students build mental toolboxes of strategies in school that they can use to solve problems, such as drawing a picture, using tallies, making a diagram, using manipulatives, and making tables. Encourage your kids to try different strategies if the one they're using isn't helpful.
5. Ask for help.
Some students skip step 1, complete part of step 2, and then jump straight to step 5. The BEST thing that you can do to is ask your kids the following question:
"What have you tried so far?"
It sounds simple, but it serves 3 purposes. First, it helps you see whether or not your student has worked through any strategies on their own. If they have, they should be able to tell you what they were. Make sure you praise them for any work already attempted on their own, especially for students with low math confidence. If they haven't, it will remind them that they need to go back and try some strategies on their own. Second, it helps students explain their work so far. Sometimes, explaining their work helps them redirect their own thinking. Third, it helps you understand where they got stuck. They may have copied down a problem wrong, used a strategy that isn't appropriate for the problem, or computed the wrong arithmetic.
6. Fill in your answer frame and check to see if it's reasonable.
It's so important to check answers for reasonableness. If a problem is asking for the difference between 2 numbers, the students should not end up with a number greater than the largest number in the problem.
Our kids will all be challenged with difficult problems this year, so make sure you encourage them to work through these problems. Be sure to ask them what they've already tried before offering any assistance to help them build up their math stamina.
Happy problem solving!