ENGAGE:
Review of Making Thinking Visible Author interview:
The first video was basically an interview of the author from Making Thinking Visible. I thought it
was a pretty good synopsis of the “theme” of the book. The author talked about
how when he was a teacher his main goal was to get his students to think,
getting them excited about thinking and having them take off on their own path.
To me, thinking in my area of STEM, mathematics, means noticing how you use
math in your everyday life, and how you can use that knowledge to your
advantage. When I was a little kid I loved thinking of numbers and challenging
myself to understand quantities of abstract things: like ceiling tiles in the
hospital, or sink holes in the bathrooms of an airport. Now I know this isn’t
normal—for starters because if I tell someone this they normally give me a
blank stare back—and I don’t expect all of my students to constantly think of
numbers either. However, I would like them to think of how they use numbers in
their own life and why understanding them can make their life easier, if only
thinking of time management or efficiently using all of the space they will
have in their future dorm room.
Review of Next Generation Science standards video:
(The two links to the common core videos were either misdirected
or no longer available as I could not find them from the links provided)
In general, I agree with the next generation science standards
(From what I heard in this short 6 minute video). They integrate practice,
concepts, and ideas. Now, I’m not too sure as to what the big difference will
be from concepts to ideas, but I am really excited that they are including the
practice behind the science. I believe that the concept behind the idea and the
practice of the idea are the two main components that are essential for
scientific thinking. An external representation of this element of this STEM
related thinking was how NASA scientists landed the mars rover on the moon.
Before they landed the rover on the moon they had to create a model of this
practice, and then related used those expectations to create a model that could
be used in the real world.
Explore: Math chair
challenge problem
I thought the way the students worked together to solve the
problem was pretty neat! Even though both students came up with different
answers, they worked together without screaming in the other’s face that they
were wrong. I’m not sure if they found out the right answer in the end, but I
thought their teamwork and collaboration on the problem was neat to see. (Because
I’m a super nerd and did the math, I found the answer to be “4115 chairs in the
second hall at first”)
I could imagine the stress these kids were going through as they
knew they were being recorded for some type of video. Honestly I would have
love this challenge as a high school student and could picture me and one of my
friends, Keith, working on something exactly like this working together until
we found the problem in our thinking.
Readings: Making Thinking Visible Chapters 1-3
During our
reading this week the main topic covered the art of thinking. The first three
chapters in Making Thinking Visible challenged
us to try and grasp what thinking is. What exactly is thinking? How do we
think? How often do we think? Does students know what the word “think” actually
means? Quoting Andree the Giant from one of my favorite movies, The Princess
Bride, Sometimes after hearing someone say “I think…” I find myself stating in
my head “I do not think that word means what you think it means.” The textbook
defined various methods of thinking in great detail and described how they can
be used to aid in classroom learning. Personally, I thought these methods can
be used as great tools to help students better understand information taught in
the classroom. But back to the main question discussed in the readings this
week: What is thinking? One of my favorite quotes from this book that I used in
my final paper was stated as follows: “Thinking doesn’t happen in a lockstep, sequential
manner, systematically processing from one level to the next. It is much
messier, complex, dynamic, and interconnected than that.” Basically, what this
is stating is that there is no cookbook recipe for thinking.
Thinking is like a wild mustang, it can be tamed, have a saddle
thrown on top, and be confined by fence posts, but in the end it is still a
wild mustang. In the same way, our brains cannot be tamed; the thought process
runs wild no matter what regulations, rules, or restrictions are put on it. One
of the jobs of teachers is to help facilitate that wild brain and guide it to
run in a positive direction. If our students brains are running rampant—like a
wild mustang with no purpose—then there is little room for actual learning, or
if their brain is confined to a simple task—like a mustang strapped down and
confined in a small fence—then there is also little room for actual learning.
There needs to be a happy medium of guiding the students: showing their inner
mustang a wide open field of information to run through and experience, guide
them with a carrot of fascinating information right in front of their nose,
making them leap out to get it. Using education as an exciting experience
rather than a “hit the books” approach can make the entire process enjoyable,
entertaining, and educational for both the teacher and the student! That whole
analogy is what I took away from these first three chapters.
Article readings: Teaching
and learning mathematics with understanding
As the title suggests, this article was about students
understanding mathematics. One statement in this article was that what we teach
students today will often not be relevant to them in the future, therefore the
best way to teach mathematics is to teach students how to understand it, not
simply memorize formulas or problem solving techniques. The student must
understand the concept/proceude, not just memorize the steps. I can think of
one particular case where understanding an early mathematical process has
helped me in higher level classes. This is the case of “FOIL” which stands for
“First, Outside, Inside, Last” What? What the heck does that mean? Well if you
have two Polynomials in the form of (X-4)(X+2) or something similar, then the
product of those two polynomials will be the first terms multiplied together,
the outside terms multiplied together, and so on…When I understood that you are
simply multiplying each term in the parenthesis by the other term I understood
the concept as a whole! This was greatly used in calculus when turning
polynomials into trig functions using “U” substitution (which is a slightly
more complicated process that I do not feel like explaining now, but just know
that understanding FOIL really helped me grasp this concept!)
What I took away from this reading is that once the student
understands their potential and knowledgebase, they can use it to explore the
wild realm of education and enjoy the ride along the way! I look forward to
seeing what else this class’s future readings have in store for us!
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