Question on Lev Vygotsky's ZPD

"... the gap between performance and the potential level, and shows that in the gap -in the zone of proximal development - children are assisted to move beyond what they have shown they can do in everyday activities by having their learning scaffolded, using cultural tools,..."

This is from Introducing Vygotsky by Sandra Smidt (2009) which is actually written for early childhood educators. ZPD is defined as the gap between performance and potential. It is in this zone that children are helped to move beyond what they can do with scaffolding.

That means at the performance level, children can do some things on their on but they are not able to do, say, X. In the zone of proximal development, they are able to do X with help. The potential is that the children can do X on their own.

Let's look at a few other explanations of ZPD.

From Wikipedia:
The zone of proximal development, often abbreviated ZPD, is the difference between what a learner can do without help and what he or she can do with help.

Vygotsky stated that a child follows an adult's example and gradually develops the ability to do certain tasks without help or assistance. Vygotsky's often-quoted definition of zone of proximal development presents it as "the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance, or in collaboration with more capable peers."

Vygotsky among other educational professionals believes the role of education to be to provide children with experiences which are in their ZPD, thereby encouraging and advancing their individual learning

From H Coffrey (UNC School of Education) wrote
The zone of proximal development is the gap between what a learner has already mastered (the actual level of development) and what he or she can achieve when provided with educational support (potential development).

From L Vygotsky (translated by M Cole)
It is the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers. (p. 84)

Reference: Vygotsky, L. (1978). Interaction between Learning and Development (pp. 79-91). In Mind in Society. (Trans. M. Cole). Cambridge, MA: Harvard University Press.

Initiatives in Teaching & Learning 2

Tonight we focused on understanding TLLM (Teach Less, Learn More) better. What constitute the 'less' in Teach Less? The problems - Tiles Problem, Structure Problem, and Circle Problem gave us insights into the focus on a few big ideas - generalization, visualization, number sense, abstraction, metacognition.

We ended the lesson by examining how the pedagogies suggested in the PERI Report could help students develop these big ideas.

Initiatives in Teaching & Learning 1

After four weeks of research and independent learning with your team members, we are ready to meet again to study more about initiatives in primary mathematics education.

Today we discussed the idea that it is not what we teach and how we teach it that is important.

We did three four problems today for the class to have common experience to understand how initiatives by the Ministry of Education and the mathematics curriculum goals go hand-in-hand.

We did the arrange the cards problem as well as play the salute game to improve recall of multiplication facts. Also, use digits 0 to 9 to make a multiplication sentence. And explore the winning strategies for the takeone take two game.

I am quite glad one of the teacher shared the lattice multiplication that led to the concluding discussion on it is not what we teach that is important but how we teach it - one core idea of initiatives in teaching and learning.

Key question for reflection - after experiencing four problems taught in a way to engage learners, what are your thoughts on this - it is not what we teach that matters, it is how we teach it.

Another Initiative - Professional Development

Today I conducted a course for the Academy of Singapore Teachers. It is called Experiencing Lesson Study where participants observe stages in lesson study as they happen. I am glad we have moved away from professional learning where teachers just sit through lectures after lectures. Professional learning now involves more authentic situations.

The 2011 Work Plan Seminar is on Thursday. A year ago, professional development was given a boost when Minister announced that teachers must take a lead in their professional learning. In fact, your present experience is part of this - to increase learning opportunities for all teachers.

And I hope you are progressing well by learning using a collaborative structure with the aid of technology. The technology can provide us with the information necessary for our learning. But it is the human collaboration (aided by technology, no doubt, cell phones, skype, emails and so on) that help transform information into knowledge.

e-Learning for Coming Two Weeks

I am writing from Rotterdam where I am teaching a three-day course. The photo shows a class in progress in Rotterdam, The Netherlands. To the Dutch educators, the Singapore mathematics curriculum is an 'initiative' as it is different from what is currently in practice and is perceive to improve the educational experience of learners.

Prof Tay Eng Guan will come to class to speak to you about the subject option for next semester. This will happen the next time we meet in NIE.Please be punctual in order not to miss vital information. I hope your groups are progressing well in your research on initiatives.

Over the next two weeks, you and your classmates are meeting - online or otherwise to try to put cooperative learning strategies into practice to learn about various MOE initiatives in Singapore system and the philosophy behind the initiatives.

Please blog about your learning experience after each of these meetings. Try to be explicit abut what you learn and how you learn it - also tell us about the cooperative learning structure(s) that your group use in the learning process.

What did I learn?
How did I learn it?
What role does technology play?
What role does cooperative learning play?

I am just an e-mail away. Please let me know if you need help or clarification.

A Question I Didn't Answer Completely

Upon reflection, there was one question raised during discussion that I did not answer completely. It was "what's next" as far as our mathematics curriculum is concerned. I did say that it will be dependent on our internal needs and external trends. I did imply that the problem-solving focus has been a good one given that we had not changed the framework since its introduction in 1992.

I was hoping someone would grill me further for a complete answer but no one did.

I would have added that "what next" would be to look into ways into engaging more learners, especially those who struggle and or not interested. Learner engagement is a difficult thing but one that has take priority.

So, based on a study of curriculum refinements since 1992, I would say that the framework is a robust one (the rationale for why we teach mathematics is so well-captured ... "vehicle for development and improvement of a person's intellectual competence") but we need to (1) look how to get the ideals of the curriculum translated into most, if not all, classrooms, and (2) think harder if we have gotten the scope and sequence for topics such as statistics, probability and geometry correct.

School Starts Today!

at least for a group of teachers who are beginning their degree programme at the nie singapore and i am excited to meet them this evening.

another batch - the third one for this programme - understanding initiatives in the singapore system and trying to interpret them in relation to national needs and international trends. and translating what they learn into practice.

their e-learning portal is www.mmeinitiatives.pbworks.com