math curriculum

I enjoy helping my kids with their math. This interest led me to think about the process of teaching math.

What are the goals?
What concepts to teach?
How to order the topics while teaching?
Best ways to teach a topic and related topics?
How to balance theory, intuition, and practice?
How to verify if the student understood what was being taught?

Every match teacher must have these and may have already thought about it. If I can access that research and understand how to teach, then teaching may become easier. 

These questions led me to discover and understand the process of curriculum design.

In USA common core is the Common Core State Standards establish clear, consistent guidelines for what every student should know and be able to do in math and English language arts from kindergarten through 12th grade.The new standards also provide a way for teachers to measure student progress throughout the school year and ensure that students are on the pathway to success in their academic careers.

As part of the further research, I read the Mathematics standards. Its a good read for any parent and I highly recommend it. Core curriculum aspires to be more focused and coherent in order to improve mathematics achievement.

Assessing coherence of a curriculum is harder but the broad understanding of coherency is that a curriculum is coherent if articulated over time as a sequence of topics and performances that are logical and reflect where appropriate the sequential or hierarchical nature of the content.

The curriculum should also reflect how students learn. It should reflect research-based learning progressions detailing what is known today about how students mathematical knowledge, skill, and understanding develop over time.

What constitutes mathematical understanding by the kid?. Ability to justify, in a way appropriate to the student's mathematical maturity. Mathematical understanding and procedural skill are equally important.


http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf

https://en.wikipedia.org/wiki/Common_Core_State_Standards_Initiative#Mathematical_practice
https://www.aft.org/sites/default/files/periodicals/curriculum.pdf
https://www.nctm.org/Handlers/AttachmentHandler.ashx?attachmentID=L6NhVjngM68%3d



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