There can be multiple ways to solve a problem.
This is one of the cornerstones for math instruction. We want students to see real-world applications of math, apply multiple concepts, and even reverse engineer solutions in creative ways. However, often we spend a significant amount of instruction on computation and rehearsal of computation. The process somehow seems in conflict with the desired result. This is where inquiry-based math instruction can be a game changer. Inquiry-based instruction centers around a real-world question. Students are encouraged to develop their own questioning to drive an investigation. Learning is focused more on the process (often involving collaboration) than the end result.
Terry Heick for Teach Thought outlines this learning process through Four Phases of Inquiry-Based Learning: A Guide for Teachers. In this process, learning occurs through interaction, clarification, questioning, and design.
In this phase, students dive through multiple and diverse rich media forms to find a question or opportunity for investigation. In this collection of Dan Meyer’s Three Act Math Tasks, various inquiry-based math questions are posed for investigation starting with videos and images. For example, in The Water Tank, students watch a video of a water tank and estimate the time it will take to fill and empty the tank.
In this phase, students are analyzing information and identifying misconceptions so they can fine-tune their additional questioning and investigation in the next phase. In the lesson plan, Diapers: Cloth vs. Disposable students use given data and manipulates it through systems of equations, slope, graphing, intersection, etc. in order to see what trends and big picture the data provides. In the Smithsonian lesson, Prehistoric Climate Change: Why It Matters Today, students use the real-world method of “leaf-margin analysis” to calculate global warming.
This is a critical component of the inquiry-based process. Here, students are developing their questions for investigation. The process may include multiple revisions, but the end goal is to generate good questions to drive the research and reach desired knowledge. In the lesson plan, Three Shots, students research how in the 2005 Conference-USA Tournament game, Memphis player Darius Washington Jr. was fouled at the buzzer during a three-point shot. His team was down by two to Louisville, and he stepped up to the foul line for three shots. Students examine the question, “When is it a good idea to foul at the buzzer?” by computing the probabilities of a win, loss, or tie for Memphis. Students investigate the conditions when fouling at the buzzer in a close game makes sense.
In this phase, students design a solution or product to satisfy the inquiry. The Cooper-Hewitt Educator Resource Center has lesson plans in math that have students use their design and math skills to complete products such as the perfect classroom, a geometric part, an early civilization, and more.
Use student curiosity and the content to discover what students are interested in for investigation. Solicit questions at the beginning of the unit as a warm-up, exit ticket, or open discussion. Current events that have applicability to the content can also be a springboard for investigation. Whatever you choose, introduce math learning as exploration and students will engage.