The benefits of learning how to show your work in Mathematics go much beyond Mathematics. Being aware of one's own thought processes and recording them are the first steps to efficient and organized problem solving.
With the prevalence of using multiple choice tests to measure progress- such as MAP tests -the schools appear to focus more getting the correct answer rather than how the answer was obtained. This may work well for one-step problems, but when it comes to mastering multi-step problems requiring application of different concepts, children often lose the thread.
At Seriously Addictive Mathematics, we teach our students to "think" and "record their thoughts", that is, showing their work. This process is related to Metacognition . . .thinking about one's thinking. Our rich set of word problems and our inquiry based pedagogy train children to be aware of the sequence of thoughts and steps required to solve the problem.
Metacognition and its benefits in Math
Thinking about thinking: Metacognition refers to the ability to think about your own thinking process. In math, it involves understanding your strengths and weaknesses, monitoring your progress, setting learning goals, and adjusting your strategies as needed.
Self-regulation: Knowing when you're stuck, recognizing errors, and deciding how to approach a problem are all aspects of self-regulation, a key component of metacognition.
Strategic learning: Metacognitive learners actively engage with the material, ask questions, and make connections between concepts. They become aware of their learning styles and choose appropriate strategies to tackle different types of problems.
Showing your work:
Metacognition informs showing work: Understanding your learning needs and challenges drives you to show your work in a way that benefits you most. You might focus on specific steps where you tend to make mistakes or break down your reasoning in greater detail.
Showing work strengthens metacognition: The act of writing down your thought process makes your thinking concrete, allowing you to reflect on it, evaluate its effectiveness, and identify areas for improvement.
Together, they build better math skills: By employing metacognition and showing work, students develop deeper understanding, problem-solving skills, and the ability to adapt to different challenges.
Life Skills Benefits:
Critical thinking: Both metacognition and showing work require analyzing information, evaluating options, and making informed decisions. These skills transfer to other areas of life, from career choices to personal problem-solving.
Persistence: When you encounter difficulties, metacognition helps you break down the problem, assess your progress, and adjust your approach. Similarly, showing work allows you to identify and correct errors, fostering perseverance and resilience.
Effective communication: Explaining your reasoning clearly and concisely, as you do when showing work, is a valuable skill in any professional or personal setting.
At SAM Singapore Math, we teach our students to show their work in an incremental fashion. For younger students, we have them write summary lines before we have them write a simple equation and then the summary line. For older students, we ask them questions so that they can be more conscious of their thought process and can start articulating them. We then have them express (1) What they are figuring out (2) How they are going to figure out, and (3) State the output of that step. Applying this template over and over again on a consistent basis allows our students to sharpen their Metacognition skills which will benefit them throughout their academic life and beyond.