css.php

The Speck of Hope – an afterthought.

There is a concept I find very hopeful in contemporary mathematics education, the concept of Learning Trajectory (LT), whose simplest definition is derived from (Clements and Sarama, 2009): LT has a mathematical goal, a developmental progression, or a learning path to reach it, and the instruction that helps to move along that path.(p.17). The very idea of an LT in mathematics recalls the best, in my opinion, American pedagogical approach of the Texan Discovery Method created by Prof. R.L.Moore from Chicago School of mathematics of early nineteen hundreds. Each course of calculus, topology or any other mathematical subject designed through that method was constructed along a learning trajectory specified by the collection of problems and axioms, e.g Calculus 1 in 142 problems and axioms.

The main strength and virtue of learning trajectories lies in the possibility to design instruction both in agreement with the mathematical development of concepts and with student learning pathways.  They offer to the instructor a long range view upon mathematics involved and upon student learning, which can be utilized for cyclical 9from semester to semester) design of instruction. The art of design learning trajectories lies in creation of appropriate cognitive distance between two consecutive problems along the trajectory – they must be challenging but possible for students to deal with. The previous post On Understanding at https://cunymathblog.commons.gc.cuny.edu/2012/09/18/on-understanding-in-mathematics/  includes an excellent performance task from DOE NYC Mathematics Task Force, The Fir Tree designed along the learning trajectory with those characteristics. Its LT design made it an excellent measurement of understanding for the concept of a Variable.

At the same time teaching along a hypothetical learning trajectory gives a teacher sense of direction and increases awareness of learning process. So, with the introduction of Common Core Mathematics standards which employ, in its design, the learning trajectory approach in the service of understanding, there is hope and chance for success in Math Ed.

However, the teaching-research in the community colleges of the Bronx has suggested that student success, depends not only on its cognitive dimension, but in equal measure on affective and self-regulatory dimensions. Our colleagues in the Bronx CC pursue the path of mathematical creativity as the source of motivation for to enjoyment and to learning mathematics (described on the previous post On Creativity @ https://cunymathblog.commons.gc.cuny.edu/2012/09/27/on-creativity-in-mathematics/ ). The question of facilitation of the “self-regulatory practices” that is of “ how to study” for our college freshman, in for example, remedial algebra is still a mystery to me.

This entry was posted in Uncategorized. Bookmark the permalink.

9 Responses to The Speck of Hope – an afterthought.

  1. SallieStevens says:

    Backlinks are links from a page on one website to another. This is important to us and you are giving us a chance and opportunity to help each other. We are hoping to have the same goal for the future of ours. OLE777

  2. Chris Ohare says:

    I’ve been so looking forward to reading this. We are in the UK but were in Chicago whilst you were there. Glad you had such a good time : )

  3. Jualdrumband says:

    Great Article. Thanks for sharing useful Information. I appreciate your Content

  4. wedding day says:

    Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.

  5. Good article! I will follow you to create useful articles like this.

  6. jon snow says:

    Thanks you so much for sharing this windows 10 sync settings very nice post online it is amazing information for you.

  7. Your writing is something that touches my heart. I was deeply impressed after reading the text.
    홀덤사이트

  8. Thanks bray, your information verry good in me live. Thanks so much

  9. Pulau Seribu says:

    Wondering if it always has a negative connotation.

Leave a Reply

Your email address will not be published. Required fields are marked *