What are the best active learning techniques for teaching mathematical problem-solving skills?

As well as building skills to help students reach a high level of thinking, inquiry-based learning can deliver other benefits to students and teachers. but By delving into a concept through inquiry, students should see it as more than a simple rule, idea or formula.

Collaborative learning is a great way to practice those problem solving skills! When working in a group, everyone can offer their own perspective, and could actually work out better than the student working out the problem on their own. When everyone pools their resources, the task does not seem as daunting anymore, as everyone is in it together. Teamwork is dreamwork!

While Flipped Learning has demonstrated efficacy in fostering student engagement and self-directed learning, its suitability as the singular "best" technique for teaching mathematical problem-solving skills may be nuanced. While the pre-learning aspect of Flipped Learning can lay a foundation, other active learning strategies, such as collaborative problem-solving sessions, hands-on activities, and real-world applications, are also pivotal. A diversified approach that combines Flipped Learning with various pedagogical methods could offer a more comprehensive and adaptive strategy, addressing the multifaceted nature of mathematical problem-solving skills acquisition.

5 steps to problem solving: A method I learned in grade 6, and is discussed in the Nelson Mathematics textbooks. Math is not just equations, there are word problems as well, and taking the time to think about the process of getting to the answer requires five steps: 1. Understand the problem: What information is given? What is the question asking? 2. Make a plan: outline what you will do to solve the problem, in terms of which equations and operations to use. 3. Carry out the plan: start making calculations and performing operations you outlined in the previous step. 4. Look back: check to see you answered the question, if you made any mistakes, or if you missed a step. 5. State answer: word problems require word answers!

Going back to the five steps to problem solving, you could also make it into a game. Divide the class into teams of 4-5 students, depending on your class size. Give them a word problem to work on, and have chart paper and markers for them to use. Have them use the same five steps to tackle the problem and work on it as a team. Set a time limit and see which group can finish within that time. Then, a good idea is for the groups to present their work and thought process to the class as a whole. You can award points based on how fast the problem was solved, the clarity of their explanations, and the delivery. Possible rewards could be a bonus 5% on the next math test, an open book quiz, or a 5-10 minute extension on recess.

Time. In the Australian curriculum, educational leaders have crammed so much into the junior curriculum that mastery of concepts is very hard to attain for most students. The lack of deeper understanding and the subsequent lack of time to explore more difficult problems is then manifested in the stress that students experience with complex problems. One of the best techniques to build problem solving is giving students time to tackle complex problems, they can try alternate methods, they can learn from mistakes. Unfortunately curriculum writers tend to be "experts" in their field and seem to have little understanding and compassion for the skill levels of students who are not themselves experts.

Many techniques contribute to engaging students in their learning journey. In addition to the mentioned approaches, Socratic Questioning is a powerful technique that uses probing questions to guide students through the problem-solving process. This method not only encourages students to articulate their reasoning but also fosters critical thinking. Moreover, incorporating these questions into traditional lectures enhances student participation and offers immediate feedback, thereby enriching the overall learning experience.

Many people often consider active learning to be the opposite of direct instruction or lectures. However, it is important to note that a pure lecture setting is not inherently active learning. By making a few additions to a lecture, it can be transformed into an active learning experience. For instance, incorporating clickers to assess understanding during a lecture can greatly enhance the learning process. Another approach is to begin a lecture by posing a guiding question and encouraging group discussions or group inquiry. This hybrid lecture format, which actively involves students in the learning process, can be far more impactful than a traditional lecture alone.