When your children work on 3-D shapes from a mathematics textbook, do you sometimes wonder about the properties of some of the shapes. Does a cone have a vertex? How many faces has a sphere? How many edges has a cylinder? If you ask a mathematician the answer to such questions, the mathematician may direct you to the definition of a vertex, a face or an edge. Or the mathematician may ask you the purpose for wanting to classify the shapes in this way.
In order to resolve this in a way that works in a primary school classroom, I have compiled a list of definitions and a grid on which to record information about a series of 3-D shapes. I want to share it with you in the hope that it will be of help in your classroom. Here are the definitions. Here is the empty grid; try completing this first. Here is the completed grid.
Please comment below if you have any other suggestions about resolving such questions in your mathematics lessons.
In a previous post I wrote about features of coderdojos that could be emulated in schools. Among the features I identified were:
1. Learning comes about through solving specific problems
2. Learners choose the problems and tasks that they work on
3. Mentors are experts in the content to be learned but not necessarily in pedagogy
4. Expertise is spread among mentors rather than concentrated in any one individual
5. Learners are organised by their interests and not by their age
6. Learners choose to work alone or in groups
7. Learners can actively teach others
8. The atmosphere is informal
If such features were applied in many schools, the work of teaching would change and particular aspects of teachers’ work would require more emphasis. I identify some of those aspects in this post. Continue reading
It amazes me to observe how quickly coderdojos have become established all around the world. I can think of no other not-for-profit educational initiative that has caught on so globally so quickly. Since July 2011, dojos have appeared in places from New York to Tokyo and from Kilkenny to Rotterdam. But for educators coderdojos illustrate how features of constructivism can work in practice. Let’s look at some of their key elements. Continue reading
Teachers realise that children whose first language is not English can find it difficult to understand new mathematical terms. However, mathematical terms in English can be tricky even for children who are native English speakers. Continue reading
How do teachers learn to teach? You might say by attending college, going on teaching practice, and from teaching experience. But according to Stigler and Hiebert, who wrote the book The Teaching Gap, teaching is a cultural activity. It is an activity that is absorbed from the culture through family conversations over meals, through watching television and listening to radio, and of course from spending 13 years as a student in various classrooms observing teachers teach. Learning about teaching in this way seems to be stronger than teacher education or continuing professional development. Continue reading
Some educators consider it a virtue for teachers to not use textbooks. My view is that textbooks can play an important role in instruction. Teaching is complex enough in itself without expecting teachers to generate classroom materials for one or more curriculum subjects. Indeed, designing and making good materials is not something that teachers are necessarily prepared to do – especially when children today are used to and expect slick, professional materials and designs in websites, videogames, magazines and so on. Teacher-made materials can rarely compete with the attractiveness of commercial publications and materials. Continue reading
I want to be the best teacher and teacher educator I can be. To try and do this I sign up for professional development opportunities when I can, read books and articles about teaching and learning, attend conferences, and engage in further study. But there is one opportunity to improve my teaching that I’ve never tried – partly because it’s difficult to set up, but mostly because I didn’t think of it: coaching. Continue reading
As we reach the end of the first month of 2012, the education landscape in Ireland looks more poised for change than it has for several years. Many fixtures of the system which have been in place for some time, or which have evolved relatively slowly, all now seem set for renewal. Just think about some of the changes that we know lie ahead: Continue reading
Over the Christmas period, four children I know in senior primary school classes received presents of laptop computers. More and more children now have access to powerful computers. Although many of them want to use the laptops to surf the internet and to play games, other educational uses of computers are available to them. For example, it seems like a good opportunity for children in senior primary school classes to learn about Seymour Papert and his colleagues’ wonderful computer programming language, Logo. Although few schools teach it anymore, children can learn a lot from trying it out. And once they get started, some children will be able to teach themselves (and others) the next steps with only occasional teacher or parent intervention needed. Continue reading
Teacher unions are critical of league tables. When tables of college entry linked to schools were published in national newspapers last week, the general secretary of the ASTI said that “It is important to recognise that these tables do not tell us about the real performance of schools. In fact they present a shallow, incomplete and distorted picture of the work of schools.” Although many educators might agree with this view, it can sometimes be helpful to look at the other side.
Let’s just suppose that league tables are useful. At their very best, what good are they? Here are some possible benefits that I can think of. Continue reading