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Students may be engaged in low-level discussions or misconceptions without pre-requisite knowledge or skills to succeed. This is why assigning group work for the sake of group work is never going to work!

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It's true that students often pay more attention to peers than adults. I can carefully arrange peer teaching where one student can help another student in an area in which they are particularly proficient. Again, knowing where each student is in the learning progression is going to be important to facilitate effective social learning.

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School learning has become divorced from the practice where it needs to be applied. :(

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School learning has become divorced from the practice where it needs to be applied. :(

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School learning should look more like everyday learning and this is called situated learning. Knowing cannot be separated from doing. I love the idea of teaching multiplication using coins. I noticed this. When I ask students to do simple subtraction or division, they may struggle but if I say the same numbers in dollars, they immediately answer them for me. :)

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Making my teaching more contextual is a good way to ensure that my students can use what they learn in my classroom in their daily lives.

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Making my teaching more contextual is a good way to ensure that my students can use what they learn in my classroom in their daily lives.

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I enjoy teaching quantitative reasoning, statistics, and applied calculus classes because it's easier for me to contextualize authentic learning environments that will help my students translate what they are learning from math class to the world.

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21st Century Skills are actually traits that cannot be taught?!

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21st Century Skills are actually traits that cannot be taught?!

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These are actually character traits and not skills whose development can be stimulated or inhibited but cannot be taught. SMH let me just focus on teaching math now.

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Making my own thinking steps visible to my students, Explicit Modeling, and Scaffolding

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Making my own thinking steps visible to my students, Explicit Modeling, and Scaffolding

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As the expert in the content area, I should show my students how I solve tasks, which strategies I use and why. After that, my students can practice under supervision, with less guidance and support to be independent.

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Apply tasks in different authentic contexts

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Apply tasks in different authentic contexts

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Showing students how a certain strategy can be used in multiple situations will help students discover what the underlying core is and when they should apply this strategy. In order to do this, I will not only need to have deep mathematical content knowledge but how math applies in our lives, which I feel a little less confident about.

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Community of practice can create and share domain-specific knowledge that more formal systems cannot. I love talking to other instructors of courses I teach whenever I run into them in the copying room, hallway, and definitely miss having PLC in departments. I wish my community college division has more of those opportunities.

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Technology has afforded communities more opportunities

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Technology has afforded communities more opportunities

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I love that we created Wakelets in this class. We, as a community, produced a set of artefacts that will remain practically useful as the community grows.

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It's ok to be a newcomer of a community and participate in simple, often low-risk tasks that are nevertheless productive and necessary and which further the goals of the community. I may be peaking in right now but someday I'll make bigger contribution to these communities.

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Cognitive Apprenticeship - Constructing a Knowledge Hierarchy?

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Cognitive Apprenticeship - Constructing a Knowledge Hierarchy?

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Making the practice of thinking and problem-solving in math more observable for students may be more challenging than making the processes of activity visible. I remember reading about constructing a skills hierarchy to make explicit the interacting elements in Sweller. I may do something similar to make thinking explicit for learners.