Developing Mathematical Thinking: Week 2, Part 1

I advanced to week 2 in the Mathematical Thinking MOOC offered by Stanford and Coursera.  Keith Devlin, the professor, is definitely enriching my ability to understand and teach math.

As I listen to his lectures, read the material, and respond to the quizzes and assignments, I find that I am using a parallel focus. On one hand, I'm trying to learn the material, and on the other hand, I'm thinking about how I can bring this learning to my fifth grade class.

To date, here are some of the take-aways and applications for teaching fifth grade math.

1. Use humor, empathy, and stories to lead us forward. Just when I want to give up, Devlin adds some encouragement. This is positive.
2. Foster multiple learning strategies including slow down, focus on precise language, and don't be afraid to struggle as that's where learning happens.
3. Organize the learning path well, and make it explicit. Explicitly teaching children and their families how to access all steps on the learning path so they can revisit when needed is essential. 
4. Stop often to assess knowledge with quick quizzes. Review those quizzes and discuss the learning. 
5. Use visual models, and provide video supports. Encourage students to watch the videos over and over again to gain understanding.
6. Work with others, and discuss the problem sets. This fosters regular use of precise vocabulary and rehearsal with all learning concepts, knowledge, and skill.
7. Create assessments that prompt students to choose True or False. For example, rather than having students find one answer. List many possible solutions and have students evaluate which ones are true and which ones are false. I believe this is a match for the upcoming PARCC or Next Generation Assessments.
8. Discuss the "behavior" of mathematical concepts, properties, and operations. 

As I progress in the course this week, I'll add other notes. But in the meantime, I am realizing this is a very valuable MOOC for many reasons. First, it is well organized. Next, Devlin is a good coach. After that, the information is meaningful to my daily work. Finally, I'm curious about the topic.

Let me know if you have corrections, questions, or other thoughts related to this post as I grow my knowledge and teaching in this area. I look forward to your thoughts.