Flip Learning for Math

The flipped learning proposal is based on the observation that students achieve higher academic performance when explaining solutions to others, rather than just solving practice problems themselves.

• The method proceeds as follows, as illustrated in the image above:
  • The teacher assigns practice problems like regular homework.
  • Students present theproblems to a pre-configured GPT model. The model, as programmed, outputs incorrect solutions.
  • Students analyze these incorrect solutions, identify errors, and provide hints necessary for problem-solving, thereby guiding the model towards the correct solution process.
  • Once the model arrives at the correct reasoning process, students submit a record of the conversation logs.
• The benefits of this approach include followings:
  • Students can cultivate mathematical and logical thinking skills effectively without being bogged down in complex calculations. This approach helps maintain students interest in mathematics and prevents them from giving up.
  • It allows students to check concepts they have not understood or merely memorized. According to cognitive theories of multimedia learning, teaching others actively reconstructs ones knowledge, leading to deeper understanding.
  • The process of teaching the model provides insights into human learning methods. Such data will significantly contribute to enhancing the reasoning capabilities of Large Language Models (LLMs).

Automatic Generation of Problems, Solutions, and Hints

• Creating mathematics problems and identifying tricky parts to generate hints is a complex task. According to internal research, trained experts of Turing Co.,Ltd. consumes at least 4 hours to make a well-made high school math problems and hints.
• Recently, many benchmarks measuring the mathematical abilities of LLMs has been proposed. Thanks to this, various methods to improve such benchmarks are being developed. Utilizing these techniques can enable the generation of similar problems and provide solutions and hints with considerable accuracy.
• Even though it might not be perfectly accurate, the ability to automatically generate problems, solutions, and hintscould significantly reduce teachers’ workload. Teachers would only need to review, rather than create problems from scratch when making practice problems and exam problems.
• This will expand the choice of practice problems available to students, regardless of public or private education. However, It will especially play a crucial role in enhancing the competitiveness of public eduction, as it addresses the weak aspect of public mathematics education.