Introductory learning of quantum probability and quantum spin with physical models and observations

Quantum probability and quantum spin are foundational concepts in quantum physics, not normally taught in pre-university education. In line with recent efforts to modernize quantum science education in schools, this paper presents learning sequences designed to provide an introductory conceptual understanding of these core physical concepts. This is achieved by choosing physical models that provide tangible classical representations that can be contrasted with quantum observations relevant to modern science and technology. This approach allows activity-based learning without the use of algebra. The concept of quantum probability is taught through activities with phasor wheels in which quantum probability is obtained graphically and interpreted using single-photon interference data. Quantum spin and spin vectors are taught by contrasting quantum spin with classical spin, explored through activities with gyroscopes and spinning tops. Quantum concepts are evoked by emphasizing how spin is different and how it manifests in real-world technologies such as magnets and MRI imaging. We describe learning sequences developed following the Model of Educational Reconstruction in which historical discoveries are combined with activities based on classical models and relevant quantum applications. We summarize test results from programs conducted with students aged 11-15. Most students connect the models and activities to quantum concepts and retain knowledge of quantum spin six months after the program. The successful learning outcomes indicate that teachers can effectively introduce quantum probability and quantum spin concepts to middle school using learning sequences such as those presented here.