Proficiency scales rather than percentage grades

Nor about what.

Only if the tests were cumulative.

I've seen what a difference formative assessment makes to initiative and ownership!

I think that this is tricky in K-12 Math in the current educational system. When factoring in the need to assess many students, mathematical procedural fluency is most easily assessed through written tests, which are easily copied or solved with an answer key. Adding additional tasks such as long written explanations disadvantages those students who may have strong mathematical skill but poor language skill. Although, mathematical communication is also important, it can be done purely symbolically, and this method of communication is usually most like how we use math outside of school. At the same time, we must assess procedural fluency. Without more time spent on Math and more Math integrated into other subjects, my experience is that students don't acquire adequate fluency without motivation to specifically practice those skills for assessment.

Then again, perhaps tests which are protected against copying and cheating, such as through invigilation, are not the tasks referred to here...

As I read through this section, I am thinking that traditional Math classes follow this sequence: lecture (tell) including examples (show), practice exercises (do), and application problems (more do). However, these lead to classes that are neither very engaging nor as effective for deep learning as they might be. I know there are other components to Learning Design, yet to be explored, but clearly, these First Principles are not enough.

Here, the assessment also matches the instruction. Because the desired end result is for the learner to be able to use Excel to solve problems, it makes sense to instruct using problems.

In Behaviourism, teachers would have students perform on a pre-test before presenting new material. Cognitivists would help students use tools such as mind maps and organizers to link prior knowledge to new knowledge. How would Constructivists set the stage for learner success?

Learning begets learning. We tap into humans' natural desire to learn by helping them learn more effectively.

I feel this is different from helping students be "successful." Sometimes, teachers think that since students want to be successful, a good strategy is to lower the standard. But, students can tell when they have grown and learned, and that is what gives them the sense of achievement, rather than some externally created standard.

This is important for us to remember when we assign inquiries, especially based on information students can find on the Internet. All of those skills around critical evaluation of digital information and use of strategies to organize and make sense of it must be taught and/or scaffolded.

"Reflect and connect," as in the BC Curriculum, Math curricular competencies.

Create connections!

I wonder how learning in the digital world has changed the way young people retrieve information. Because the web is built to make connections through hyperlinks, the associations learners create are analagous to - to use computer language - abstract pointers. Where physical books allow us to remember where things are in space, using our body memories to help find information, hyperlinks have no such physical association. How do learners growing up in a digital world mentally organize their information?

This idea reminds me of the problems we want to create in the "Building Thinking Classrooms" framework. Story is such a powerful way to engage participants to feel invested in a problem and motivated to solve it.