The Art of Teaching Mathematics: Beyond the Right Answer
Recently, I was presented with an intriguing mathematical challenge: "Put parentheses on the below equation to make this true: 5 × 8 + 8 ÷ 6 – 12 × 2 = 24." After several attempts, I couldn't find a solution. Even ChatGPT, known for its problem-solving prowess, struggled and generated convoluted answers that didn't hold up under scrutiny.
Intrigued by this conundrum, Ashish Bansal, my co-founder at [Starspark.ai](https://starspark.ai), decided to put our curriculum-aware, pedagogy-focused AI to the test. Impressively, our bot not only deduced that there was no possible way to make the equation true with any placement of parentheses but also provided encouragement. It reminded us that encountering unsolvable problems is a natural part of learning mathematics.
This experience was gratifying, affirming that Starspark's approach effectively supports learners. However, it also raised a critical question: What is the true learning objective of presenting such a problem to elementary students?
At its core, the problem aims to teach students about the order of operations and how parentheses can alter computational outcomes. Understanding that mathematical expressions can yield different results based on operational sequencing is a foundational concept. But posing a problem with no solution might lead to unnecessary frustration, hindering the learning process.
A more constructive approach would be to ask students, "How many different results can you obtain by placing parentheses in different positions within this equation?" This reframing shifts the focus from finding a nonexistent correct answer to exploring the versatility of mathematical operations. It encourages creative thinking, experimentation, and a deeper grasp of how mathematical structures work.
This approach aligns with the educational framework known as Depth of Knowledge (DoK), which categorizes tasks based on the complexity of thinking required. By inviting students to explore multiple outcomes, we elevate the task from mere recall or procedure (DoK Level 1 or 2) to strategic thinking and extended reasoning (DoK Level 3 or 4). It transforms the exercise into an open-ended exploration rather than a closed question with a single correct answer.
At Starspark.ai, we deeply believe in fostering this depth of knowledge. Our philosophy centers on nurturing critical thinking and problem-solving skills, rather than just being a cheating tool. By designing our AI to recognize the pedagogical intent behind problems, we aim to support students in a way that is both empathetic and educationally sound.
In Conclusion
The way we present mathematical problems profoundly impacts student engagement and learning outcomes. By emphasizing exploration over simply finding the right answer, we can cultivate a more robust understanding and appreciation of mathematics. Educators should consider the depth of knowledge required by their questions and strive to design problems that not only align with learning objectives but also inspire and motivate students.
At Starspark.ai, we are committed to this educational vision. We continue to develop tools that not only provide answers but also encourage learners to delve deeper, think critically, and embrace the beauty of mathematics.
