Dimensional Thinking
Dimensional thinking consists of moving from 2-dimensional to 3-dimensional thinking, or the reverse. The ability to take information and transfer it between dimensions is important but takes practice to develop. Dimensional thinking also includes the ability to scale by proportions.
Personally, I sometimes feel I got missed when someone was handing out dimensional thinking skills. I can't pack a suitcase efficiently or eyeball whether a piece of furniture will fit in the back of one of our customer's vehicles. (That was a little embarrassing!) In bets with my husband that require dimensional thinking, I lose every time! I much prefer word puzzles to physical puzzles, but I recognize that in myself and I try to make sure that I include opportunities for dimensional thinking in my classroom.
Since I don't feel strong in dimensional thinking, I think I sometimes downplay its importance to others. It isn't always obvious to me. I was reminded of this when the Bernsteins, authors of Sparks of Genuis, quoted the ideas of Henry Moore, who believed that not everyone fully perceives three-dimensional objects so they don't totally appreciate sculpture or architecture. (Me!) The authors also showcased an example of a shadow sculpture, which is made of brass and projects different shadows throughout the day as part of the artistic expression. If I had seen that sculpture out and about, without knowing its purpose, I would have thought someone was overpaid for some ridiculousness! However, the shadow sculpture below just tickles me because I see something from nothing!
Personally, I sometimes feel I got missed when someone was handing out dimensional thinking skills. I can't pack a suitcase efficiently or eyeball whether a piece of furniture will fit in the back of one of our customer's vehicles. (That was a little embarrassing!) In bets with my husband that require dimensional thinking, I lose every time! I much prefer word puzzles to physical puzzles, but I recognize that in myself and I try to make sure that I include opportunities for dimensional thinking in my classroom.
Since I don't feel strong in dimensional thinking, I think I sometimes downplay its importance to others. It isn't always obvious to me. I was reminded of this when the Bernsteins, authors of Sparks of Genuis, quoted the ideas of Henry Moore, who believed that not everyone fully perceives three-dimensional objects so they don't totally appreciate sculpture or architecture. (Me!) The authors also showcased an example of a shadow sculpture, which is made of brass and projects different shadows throughout the day as part of the artistic expression. If I had seen that sculpture out and about, without knowing its purpose, I would have thought someone was overpaid for some ridiculousness! However, the shadow sculpture below just tickles me because I see something from nothing!
Image credit: http://www.mendeley.com/blog/academic-features/interface-development-and-shadow-sculptures-essentially-the-same-thing/
Personally, to improve my own dimensional thinking, it would be useful to do additional reading about the ideas presented by artists and visiting exhibits. Rather than immediately writing off an odd-shaped piece of artwork, trying to find the meaning in it, much like I must ask myself to do with abstract art.
Knowing that I struggle with dimensional thinking makes me more aware of then when planning for my students. My experience has shown that many of them are quite skilled at it, so here is an example of how we work with toothpicks and marshmallows to play with geometric shapes. This activity allows everyone to play and explore, and we learn from each other as we go!
Another activity in my classroom is a weekly time set aside for pattern blocks. Students work at their own pace through a set of leveled cards:
Yellow and Green Levels (Kindergarten): Colored shapes provided for each student to work at matching shapes and building pictures
Tan Level: (1st grade)- begins with matching the blocks with no color support, then moves on to "follow the recipe" to make the shape, and finally students fill in the shapes more than once on their own, recording the different ways they filled the shape.
Blue Level: Works more with more complicated shapes that students must follow the recipe.
Red Level: Works with line symmetry.
Orange Level: Works with rotational symmetry.
Yellow and Green Levels (Kindergarten): Colored shapes provided for each student to work at matching shapes and building pictures
Tan Level: (1st grade)- begins with matching the blocks with no color support, then moves on to "follow the recipe" to make the shape, and finally students fill in the shapes more than once on their own, recording the different ways they filled the shape.
Blue Level: Works more with more complicated shapes that students must follow the recipe.
Red Level: Works with line symmetry.
Orange Level: Works with rotational symmetry.
The authors suggest imagining as a tool for building competency with 3-D puzzles. But not all need manipulatives. They suggest that you imaging your house upside down and what that would be like. In my class, I usually read Mrs. Piggle-Wiggle, who lives in an upside down house. We have a lot of fun playing with the idea of our own houses being upside down - or even our classroom!
2 students make a green playdoh snowman
Play time in our classroom affords several fun options that lead to dimensional thinking. Play-doh, legos, lincoln logs, puzzles, and more are available for students who are drawn to these types of play.
Modeling
Models can be very useful in learning. There are several types of models, such as:
1. representational: show physical characteristics of a real object
2. functional: capturing how something operates
3. theoretical: showing the basic concepts of a process
4. imaginary: shows something we cannot observe
It should be noted that one model can actually be more than one of these types.
Models are especially useful for showing things that are too fast or slow, or too big or too small to be observed, such as a model or a cell or atom. In fact, computer models are becoming even more sophisticated in medical training and others. I am looking forward to the growth of the augmented reality field, which provides models such as this one:
1. representational: show physical characteristics of a real object
2. functional: capturing how something operates
3. theoretical: showing the basic concepts of a process
4. imaginary: shows something we cannot observe
It should be noted that one model can actually be more than one of these types.
Models are especially useful for showing things that are too fast or slow, or too big or too small to be observed, such as a model or a cell or atom. In fact, computer models are becoming even more sophisticated in medical training and others. I am looking forward to the growth of the augmented reality field, which provides models such as this one:
In order to create models, the situation or form must be observed to find the right way to represent it. What are its critical features? How can it be shown not just in form , but verbally or artistically? To create a model, one must understand the subject very deeply.
I connected with the section of the book that discussed how writers can model their work after the work of others. If there is a problem to be solved, they suggested we do as Igor Stravinsky suggested, to find someone who had solved that problem and modify it to achieve our own goals.
I've done this often. I remember being taught the 5 paragraph model of writing, and while I cringe at the thought of cookie cutter writing, using that principle often helps me as I write or even prepare for a presentation. And modeling my web work after others has often been the same; if I have a problem, I google it and find someone's code to tweak to fit my own situation.
In my classroom, we use models to teach content in all subjects. In writing, we examine the craft of others and attempt to do similar things in our own writing. In math, we use base 10 blocks, pattern blocks, dice, and all manner of objects to practice and show our thinking. In science, we keep referring back to our book "You are a Scientist" as we are inquiring about our topics so that we are modeling our behaviors after real scientists. These are just a few examples, and I have always seen that connecting the model to our work has great impact on our learning.
Personally, I think I will always enjoy models. As a professional, I try to model my teaching after the experts I am following (on twitter, these days!) and as a teacher, I bring models into my teaching whenever it seems to fit!
I connected with the section of the book that discussed how writers can model their work after the work of others. If there is a problem to be solved, they suggested we do as Igor Stravinsky suggested, to find someone who had solved that problem and modify it to achieve our own goals.
I've done this often. I remember being taught the 5 paragraph model of writing, and while I cringe at the thought of cookie cutter writing, using that principle often helps me as I write or even prepare for a presentation. And modeling my web work after others has often been the same; if I have a problem, I google it and find someone's code to tweak to fit my own situation.
In my classroom, we use models to teach content in all subjects. In writing, we examine the craft of others and attempt to do similar things in our own writing. In math, we use base 10 blocks, pattern blocks, dice, and all manner of objects to practice and show our thinking. In science, we keep referring back to our book "You are a Scientist" as we are inquiring about our topics so that we are modeling our behaviors after real scientists. These are just a few examples, and I have always seen that connecting the model to our work has great impact on our learning.
Personally, I think I will always enjoy models. As a professional, I try to model my teaching after the experts I am following (on twitter, these days!) and as a teacher, I bring models into my teaching whenever it seems to fit!