Imprecise Geometry with Doug Clements (Early Math Collaborative at Erikson)
Summary
TLDRThe script from a lecture on geometry and measurement education reveals a concerning trend in U.S. schools. Research indicates that younger students have a better innate understanding of shapes than those in higher grades, suggesting that traditional teaching methods may be ineffective. The speaker, along with Mike Batista, conducted tests showing that children as young as four could identify basic shapes with high accuracy. The lecture criticizes current educational materials for their lack of precision and poor examples, advocating for a more engaging and precise approach to teaching geometry from an early age. The speaker emphasizes the importance of fostering geometry and spatial thinking to lay a strong foundation for advanced mathematical concepts.
Takeaways
- đ Research indicates a decline in geometry and measurement skills as students progress from first to third grade in the U.S. education system.
- đą Young children (ages 4-6) demonstrate a strong ability to identify and differentiate basic shapes, scoring high percentages on related tests.
- đ There is a noted decrease in performance when identifying more complex shapes like triangles and rectangles, suggesting a need for improved instruction.
- đšâđ« The script criticizes traditional teaching methods that focus on basic shape identification without fostering deeper understanding or precision in reasoning.
- đ« The author argues that children enter school with a solid foundation in basic geometry but that this knowledge is not built upon effectively in the curriculum.
- đ« The script points out the inadequacy of certain educational materials, such as a test example that provides poor models of triangles.
- đ” It critiques the integration of math and music through songs that incorrectly model geometric concepts, suggesting it does more harm than good.
- đ The importance of precision in reasoning and thinking is emphasized as fundamental to mathematics, which traditional instruction often overlooks.
- 𧩠The Building Blocks project is highlighted as a positive example of engaging children with a variety of shapes to promote spatial thinking and geometry skills.
- đ The script concludes that including geometry and spatial thinking in early education is critical for later mathematical development and has significant benefits.
Q & A
What did the University of Wisconsin researchers discover about first graders' understanding of polygons?
-The researchers found that first graders are more likely to count the sides and angles of polygons to differentiate one from the other than third graders, suggesting that traditional teaching methods might be less effective over time.
What did the test given to young children by Mike Batista and the speaker reveal about their understanding of shapes?
-The test revealed that children aged four, five, and six did quite well, scoring 92%, 96%, and 99% respectively on identifying squares, even with distractors present. However, their performance was lower for triangles and rectangles, at around 60% and 50% correct, respectively.
Why did the speaker and Mike Batista administer a paper and pencil test with numerals to very young children?
-They administered the test to see how children aged four, five, and six would compare to older children. The test was the same instrument given to 1,500 kids from six to twelve years of age.
What was the speaker's experience with presenting his dissertation, and how did it relate to his views on teaching mathematics?
-The speaker's dissertation presentation was overshadowed by a more engaging math and music session happening next door, leading to a loss of audience. This experience highlighted the importance of making mathematics engaging and precise, rather than just focusing on basic naming of shapes.
What did the speaker criticize in the math and music integration example provided in the script?
-The speaker criticized the math and music integration for providing incorrect mathematical models of triangles, such as referring to a piece of pie or a slice of pizza as a triangle, which does not meet the geometric definition of having three straight sides and three vertices.
What is the speaker's view on the current state of geometry and measurement instruction in the United States?
-The speaker views the current instruction as a wasteland, suggesting that it lacks precision and fails to engage students effectively, leading to a flat learning curve and minimal gains in understanding.
What does the speaker suggest as an alternative to the traditional approach to teaching geometry and measurement?
-The speaker suggests moving beyond just naming basic shapes and instead fostering precision in thinking about shapes and their properties. This includes making mental images, transforming shapes, playing with shapes, investigating, composing, and decomposing shapes.
What is the 'Building Blocks Project' mentioned in the script, and how does it relate to geometry education?
-The 'Building Blocks Project' is an approach that presents children with a wider variety of shapes to talk about, sort, play with, and explore. It encourages building shapes from parts and using various materials, promoting a deeper understanding of geometry and spatial thinking.
Why is it important to include geometry and spatial thinking in early education according to the speaker?
-Including geometry and spatial thinking is critical because it provides meaningful and motivating areas for learning number, logic, and eventually calculus. The speaker argues there is much to gain and little to lose by fostering this kind of development early.
What is the 'hypocritic oath' mentioned in the script, and what does it symbolize in the context of the discussion?
-The 'hypocritic oath' is a play on words, likely meant to be 'hypocritical', suggesting that the current methods of teaching mathematics are not only ineffective but also potentially harmful to students' understanding. It symbolizes the speaker's strong disapproval of the status quo in math education.
Outlines
đ Early Childhood Geometry Education
The paragraph discusses the inadequacy of traditional geometry and measurement education in the United States. University of Wisconsin researchers found that first graders are more likely to differentiate polygons by counting their sides and angles than third graders. The speaker highlights that children enter school with a basic understanding of shapes, but the educational system often fails to build upon this foundation effectively. The narrative includes anecdotes about testing young children and the lack of progress in their understanding of basic shapes, as evidenced by flat learning graphs. The speaker criticizes the simplistic approach to teaching shapes and the lack of precision in reasoning and thinking in mathematics education. The paragraph concludes with a critique of a math and music integration example that inaccurately represents geometric shapes, suggesting that such methods are detrimental to children's learning.
đ Enhancing Geometry and Spatial Thinking
This paragraph emphasizes the need to move beyond basic shape identification to foster precision in thinking about shapes and their properties in children. The speaker advocates for a more comprehensive approach to geometry education that includes a variety of shapes, such as pattern blocks and tangrams, to encourage exploration, sorting, and creative play. The Building Blocks project is mentioned as an example of how to engage children with a wider range of shapes, promoting spatial thinking and laying a foundation for more advanced mathematical concepts. The speaker concludes by stressing the importance of integrating geometry and spatial thinking into early education, arguing that it offers meaningful and motivating contexts for learning and has the potential to significantly benefit students' mathematical development.
Mindmap
Keywords
đĄGeometry
đĄMeasurement
đĄPolygons
đĄPrecision of Reasoning
đĄDistractor
đĄSpatial Thinking
đĄPattern Blocks
đĄTangram
đĄMental Imagery
đĄTransforming Shapes
đĄDecomposition
Highlights
U.S. traditional instruction in geometry and measurement is ineffective.
University of Wisconsin researchers found first graders are more likely to differentiate polygons than third graders.
Children's knowledge of shapes is underutilized in traditional education.
Young children (ages 4-6) perform surprisingly well on geometry tests.
Children entering school already know a lot about simple shapes.
Current educational methods do not build effectively on children's existing knowledge.
The importance of precision in reasoning and thinking in mathematics.
Anecdote about a child's incorrect identification of shapes in a school workbook.
Critique of the integration of math and music through songs that misrepresent mathematical concepts.
The need to move beyond basic shape naming to more precise thinking about shapes.
The Building Blocks project introduces a wider variety of shapes to children.
Children engage with shapes through sorting, playing, and creating designs.
Building shapes from parts helps develop spatial thinking.
Geometry and spatial thinking should be included in education from an early age.
Fostering early development in geometry and spatial thinking has significant benefits.
There is much to gain by integrating geometry and spatial thinking into early education.
Transcripts
lesson geometry and measurement from
preschool to high school traditional
instruction in the United States Is A
Wasteland here the uh University of
Wisconsin researchers found that first
graders are more likely to count the
sides and the angles of polygons to
differentiate one from the other than
third graders were we actually teach it
out of them okay and it appears on all
these kind of tests so what do kids know
and why do they suffer like that
well they they know a lot we gave this
test to kids you might think why did you
give them such a test with like paper
and pencil test with numerals all over
to really young kids and the reason is
Mike Batista and I had given the same
instrument to uh 1,500 kids from six to
12 years of age we wanted to see how
kids four five and six would compare
okay and they did pretty well um they
did 9 2 96 and 99% for fours fives and
sixes on on that they did 82 86 and 91%
on squares even with some real
distractors in there right triangles are
a little lower about 60% and rectangles
a little lower again uh but still about
50% correct on on rectangles so what did
we do we found that kids knew quite a
bit when they entered school just about
simple shapes like this this is Mike
Batista in my research out here can you
imagine if you were a principal of a
school and you had to show this graph to
parents and said look at what we taught
your kids this year that's like the
flattest graph you could find and this
is just lowlevel naming of shapes it's a
little better for triangles but not much
better how come because this is what
kids see in school my son brought this
home
okay hey one good thing about it the
triangle doesn't have a horizontal base
up at the top oh okay so that's
different right but you know how the
publisher puts a dted line around it so
that not only do you can you read the
instructions down here but they provide
you a model look at what they chose as
their best example of a triangle it's
got a
hook right
mathematics number and shape are
important constituents of mathematics
but at its fundamental base mathematics
is about Precision of reasoning and
thinking
Precision of reasoning and thinking this
is slop okay uh let's take a look at
some others uh sailboat he got credit
for the sailboat and he might have been
looking at those two triangular s sails
but he circled a
pentagon right and he got full credit
and what's the sandwich doing here all
right no we don't need that kind of
stuff but my favorite is this one okay
my favorite is this one because I
remember well it's it's burned into my
memory I was presenting and if you think
okay he's not a very good presenter now
but I was worse before okay this is my
first time out and I was presenting my
dissertation and I turn my back to the
audience and I have like 500 numbers on
the screen saying L you can see from my
research you know and stuff like that
and next door was a person a guy who was
also talking about Early Childhood math
but he was doing math and music and
there was a partition
you know folding partition between the
two rooms that wouldn't close I know cuz
I grabbed that thing and tried to close
it it would not close cuz his his
speakers were right on the other side of
the opening so the music's wafting in
and everybody's laughing and singing
next door and I'm here and now you can
see from my resarch and every time I
turned around five more people were gone
from the back they went next door with
the other guy so you know when a
presentation's going wrong you start
sweating and and everything you know
you're all nervous and everything and
and then and then at the end Jackie
turns over to to to the person next to
her and say why do we have to sit in the
front we can't even leave now you know
it was miserable miserable finally it's
over I go next door and say be big about
it go next door and and find out what
they're doing so you should do more of
that stuff you know you're just not
motivating nobody wanted to hear what
you had to say so I next door and I got
the song sheets now I don't know the
tune to these because I was trying to
present I was sweating at the time and
um uh but take a look take a look at the
kind math and music they were doing
let's look at the last verse here what's
a triangle with sides of three a piece
of pie for you and
me no it isn't oh maybe they get better
wait a minute wait a minute what's a
triangle with sides of three a piece of
pie for you and me a musical triangle
ding ding
ding let's called the
triangle what's what's wrong with a
musical triangle it's a mathematical
model of a
triangle it doesn't even meet right and
what else they're not it it's not it's
actually doesn't have a corner a Vertex
right the vertex is two straight lines
that come to a point but they're all
curved I know we call it a triangle but
it's not a good example well I'm sure
they get the last one what's a triangle
with sides of three a piece of pie for
you and me a musical triangle ding ding
ding a slice of pizza with everything oh
my God that's a section of a circle they
got three out of three wrong this kind
of stuff breaks the hypocritic oath kids
would be better off if they didn't come
to school the day they did this kind of
song that's no way to integrate math and
music get rid of that too all
right we got to move Beyond naming basic
shapes to getting kids thinking with
Precision about shapes and their
property making mental imag just
transforming shapes playing with shapes
investigating shapes composing and
decomposing shapes so one thing we do in
the building blocks project for instance
is to present you know kids kids with a
wider variety of shapes those of you
that know the pattern blocks will
recognize the pattern block shapes are
here we make them bigger but they're
here but so are tangram shapes so are
long thin rectangles pentagons that look
like this but also pentagons that look
like that so that kids have a wide
variety of shapes to talk about and to
sort and play with and they do they
explore they make pictures they make
designs they play games with
them so we do a lot of that we build
shapes from part from straws from
toothpicks on the computer we build them
from parts and everything else we do a
lot of that kind of stuff so my research
lesson here is include geometry and
spatial thinking in a fundamental way
it's critical it provides meaningful and
motivating areas for number for logic
eventually for later calculus there's a
little to lose and a much to gain by
fostering that kind of development
early
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