Common Core State Standards (CCSS) are lists of things kids are expected to learn in each subject during each school year. They are not the actual lessons. Your child’s teacher and school system will decide what lessons to teach and how to teach them.
Research shows that one of the best ways to teach children is to give them tasks and have them work through the solutions to the tasks. The child is given directions as needed, or small lessons on specific skills, but the child is allowed to figure out what skills they need, or what they need to know, to accomplish or solve the task. These are called Key Tasks.
To be able to participate in the process of Key Tasks, a child needs to have a way to approach and organize the information. In mathematics, this process is going to feel very different than the existing process of “show the child the problem, work the problem with the child, and then let the child practice problems. Without setting up the structure of the process first, students may feel that the teacher has abandoned them, is not really teaching them anything, or worse. It takes time to transfer responsibility for problem solving when a child has never been asked to shoulder the responsibility (except for remembering how to do some practice problems, or work a formula – not really learning, just memorizing and regurgitating information).
The process of approaching and organizing the information is very similar to the scientific method. Any teacher or parent can help a child learn how to approach these new key tasks by teaching them a “mathematical thinking” process. The steps in the process are simple ones: Read and think about the problem, draw the problem or restate the problem, discuss the ideas about the problem with others or use resources (group discussion), estimate the answer, “mathematize” the problem (a formula or equation), try/refine/rethink, see if the answer makes sense. These steps may need to be used more than once throughout the process. As you can see, the actual answer is only a tiny part of the process.
For teachers, here is a brief lesson for teaching students how to use mathematical thinking in the class. For parents, you can help your child use this pattern with their math homework:
I love the idea of math as a thinking process. Instead of just giving students the list of actions, , I would approach this the same way I like to approach setting up classroom norms. I would start with a sample problem and just have the students think about it. I would tell them not to try and solve it yet. Then I would have them verbalize their thoughts in small group and then whole group- we would write the thoughts/assumptions on a big sheet of paper titled ‘Thinking’ and tape it to the board. I would facilitate with clarifying and summarizing questions.
The next step would involve visualizing. Students would be asked to draw a picture to illustrate what they saw happening in the problem. Again in small groups, they would create a picture/illustration, titling the poster ‘visualize’. The posters would go up around the room. At this point, I would ask all students to move around the room ( in groups) and visit the posters to see if the illustrations made sense, and if they suggested any mathematical way to look at the problem.
Returning to their seats, each group would create another poster titled ‘mathematics’ showing the calculations / solutions that they came up with. Those would go up on the wall. Each student would then be instructed to visit each mathematics poster and decide if those mathematics/answers made sense in light of the problems. This might be a good place for the students to use sticky notes and place comments or questions onto the posters.
The groups would then go back to their posters, check out the comments (as would I, so that I could come up with more questions) and we would come back to a whole class discussion to examine the various mathematics and reasonableness of answers. I might put up an empty poster titled ‘revisions’ so that students could add ways that they will need to revise their own thinking to solve this and future problems.
The summing up of the lesson will not be right or wrong answers, but a summary of the process itself. The students will be asked to discuss with one other person what steps they went through to solve the problem, and then write a brief paragraph in their math journal about what steps they took to solve the problem.
The final poster, and the one that will remain on the wall for future work, will be the steps the students noticed were common to the process- maybe have each group list a step (different colors, handwriting?). This will give them a roadmap to solving future problems- and as the teacher, I will give them the time to use the steps as we move through the learning process.
Parents can help by giving your children the time to verbalize problems to you or draw what they think the problem represents. You don’t always have to know how to do the math to help your child think through the process. Even if they don’t come up with a “right” answer, or maybe all they have come up with is questions, the thought process is going to give them a way to get in on the next conversation in class.