Really. Mathematics.
You may disagree. It is likely you will disagree.
But wait.
If you disagree, I can guarantee you aren't really qualified to argue this point with me.
Year after year of theory without ever listening to a song or making music would give you the same distasteful feeling about music that you have for math. If enjoying math is beyond the scope of your imagination, you are a victim of learning meaningless mathematics.
Year after year of theory without ever listening to a song or making music would give you the same distasteful feeling about music that you have for math. If enjoying math is beyond the scope of your imagination, you are a victim of learning meaningless mathematics.
Consider Mount Cheam. Chilliwack's Eiffel Tower. It seems reasonable that a child growing up in this area should learn about Mount Cheam. Since learning is separated into disciplines in our current education system, this new learning outcome will need to be placed in an isolated category.
Where would it fit best? How would it be likely be interpreted?
Where would it fit best? How would it be likely be interpreted?
Art:
Students will observe how seasons and times of day effect the colours, lighting, and shadows on the mountain peak and then choose a medium to capture its essence.
History:
Students will research the impact that Mount Cheam has had on people through the 20th century. Students will gain an understanding of why the Sto:lo peoples called it the source.
Geography:
Students will learn how the elevations effect the plant and animal life on Mount Cheam.
Students will climb to the peak in order to more fully understand the effects of the local mountain ranges and the Fraser River on the Fraser Valley.
Mathematics:
Students will learn that Mount Cheam is approximately pyramidical, and then calculate its height, volume, and average slope.
This is just how it seems to work these days. There is a lot of room for beauty in each of those disciplines. But hello mathematics: The beauty will be drained right out of it. I can just picture the Math lesson. Students would hardly even need to see the mountain. Well, perhaps they might look at a picture or look at it through a window. Before students have a chance to appreciate the gorgeous mountain, their teacher will have it decontextualized into a pyramid or cone on the whiteboard, giving them some basic measurements (perhaps its height and radius at the base), and asking them to make some random calculations.
Actually, probably not quite true. Most math teachers will try somehow to spice it up a bit. Make it more interesting. Tell a joke. A story about when they climbed Mount Cheam.
The learning outcome has been met. Check. Move on in the course. There's so much more to cover.
What is wrong with this?
In my description above the TEACHER has done the abstract and mathematical thinking for the students by turning Mount Cheam into a pyramid and giving them basic measurements. Measurements that are probably almost impossible to physically measure directly. The STUDENTS use some meaningless formulas and crunch out meaningless numbers. They will walk out of the class with no extra appreciation for Mount Cheam, or mathematics. They will walk out of the class with no extra skills they can apply to their life-outside-math-class.
I can think of a perfectly useless question that would turn the lesson into a rich experience.
Could we completely cover Mount Cheam using all your school uniforms?
Really.
Some student will say, "Of course NOT, Mount Cheam is HUGE and we only have a small school!"
Check. This makes me happy. A student realizes that mountain is pretty large. I could respond in several ways. Well, how many students would you need? How much of the peak would be covered?
To solve a question like this, students will not only need to do math, but also think mathematically. They need to make choices, think abstractly, make estimations, measure, collaborate, ...
From measuring the area of their own clothes, to realizing that Grade 1 students wear smaller clothes, to deciding if extra clothes at home should be included, to collecting raw data and using other sources, to calculating a reasonable approximation of the surface area Mount Cheam... students will be doing math. The question in itself is simple, but the solution is complex. There is no answer at the back of the book. The answer isn't even all that important.
The beauty in this silly question is that it demands that students do math and will give them an understanding of various degrees of 'size'. A similar question could make this even more meaningful. If we turned all the trees on Mount Cheam into paper, how long would it take our school to use it up?
Ok, I went off on a bit of a tangent with that. What I wanted to say is this. If you believe there is no beauty in mathematics, then you what you know to be 'MATH' is not really math.
Math is not about memorizing formulas and crunching out numbers meaninglessly. Math class is not about training humans to become calculators.
There is something spectacular in the process of studying a fern, placing it into the abstract world of fractals, pinning a function to it, adjusting the function, and realizing that the minor adjustment draws out a tree. You don't even need to know how it exactly works to be wowed by this. As I said, it is beautiful beyond comprehension.
Anne Burns is a mathematician that designs Mathscapes. It is so unbelievable that these nature scenes are completely designed with functions and equations. Check out her gallery here: Mathscapes
When functions, equations, patterns, numbers, and shapes are taken out of context... it becomes easy to crunch through math curriculum because these concepts become desaturated of their usefulness and beauty. Math becomes meaningless to students and people become proud to admit that they are not in that group that gets math.
Where is math in the world around you? Here is a little video clip that shows three perspectives of Math. The 'real world view', the decontextualized view, and the 'functions and equations' view. The three are pretty much equivalent. This made me re-appreciate the mumble-jumble of mathematics. It's always just lurking there behind-the-scenes.
Beauty of Mathematics
Actually, probably not quite true. Most math teachers will try somehow to spice it up a bit. Make it more interesting. Tell a joke. A story about when they climbed Mount Cheam.
The learning outcome has been met. Check. Move on in the course. There's so much more to cover.
What is wrong with this?
In my description above the TEACHER has done the abstract and mathematical thinking for the students by turning Mount Cheam into a pyramid and giving them basic measurements. Measurements that are probably almost impossible to physically measure directly. The STUDENTS use some meaningless formulas and crunch out meaningless numbers. They will walk out of the class with no extra appreciation for Mount Cheam, or mathematics. They will walk out of the class with no extra skills they can apply to their life-outside-math-class.
I can think of a perfectly useless question that would turn the lesson into a rich experience.
Could we completely cover Mount Cheam using all your school uniforms?
Really.
Some student will say, "Of course NOT, Mount Cheam is HUGE and we only have a small school!"
Check. This makes me happy. A student realizes that mountain is pretty large. I could respond in several ways. Well, how many students would you need? How much of the peak would be covered?
To solve a question like this, students will not only need to do math, but also think mathematically. They need to make choices, think abstractly, make estimations, measure, collaborate, ...
From measuring the area of their own clothes, to realizing that Grade 1 students wear smaller clothes, to deciding if extra clothes at home should be included, to collecting raw data and using other sources, to calculating a reasonable approximation of the surface area Mount Cheam... students will be doing math. The question in itself is simple, but the solution is complex. There is no answer at the back of the book. The answer isn't even all that important.
The beauty in this silly question is that it demands that students do math and will give them an understanding of various degrees of 'size'. A similar question could make this even more meaningful. If we turned all the trees on Mount Cheam into paper, how long would it take our school to use it up?
Ok, I went off on a bit of a tangent with that. What I wanted to say is this. If you believe there is no beauty in mathematics, then you what you know to be 'MATH' is not really math.
Math is not about memorizing formulas and crunching out numbers meaninglessly. Math class is not about training humans to become calculators.
There is something spectacular in the process of studying a fern, placing it into the abstract world of fractals, pinning a function to it, adjusting the function, and realizing that the minor adjustment draws out a tree. You don't even need to know how it exactly works to be wowed by this. As I said, it is beautiful beyond comprehension.
Anne Burns is a mathematician that designs Mathscapes. It is so unbelievable that these nature scenes are completely designed with functions and equations. Check out her gallery here: Mathscapes
When functions, equations, patterns, numbers, and shapes are taken out of context... it becomes easy to crunch through math curriculum because these concepts become desaturated of their usefulness and beauty. Math becomes meaningless to students and people become proud to admit that they are not in that group that gets math.
Where is math in the world around you? Here is a little video clip that shows three perspectives of Math. The 'real world view', the decontextualized view, and the 'functions and equations' view. The three are pretty much equivalent. This made me re-appreciate the mumble-jumble of mathematics. It's always just lurking there behind-the-scenes.
Beauty of Mathematics
I will start sharing glimpses into my classroom as I push ahead with changing the way I allow students to learn and do math in my classroom. One of my goals is that students will feel amazed by the things that pop up in mathematics without me having to jump up and down with an excited voice "Look at this!! Isn't it so amazing?!! Why don't you look amazed?"
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