Imprecise Geometry with Doug Clements (Early Math Collaborative at Erikson)

Summary

The 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

• 📊 Research indicates a decline in geometry and measurement skills as students progress from first to third grade in the U.S. education system.
• 🔢 Young children (ages 4-6) demonstrate a strong ability to identify and differentiate basic shapes, scoring high percentages on related tests.
• 📉 There is a noted decrease in performance when identifying more complex shapes like triangles and rectangles, suggesting a need for improved instruction.
• 👨‍🏫 The script criticizes traditional teaching methods that focus on basic shape identification without fostering deeper understanding or precision in reasoning.
• 🏫 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.
• 🚫 The script points out the inadequacy of certain educational materials, such as a test example that provides poor models of triangles.
• 🎵 It critiques the integration of math and music through songs that incorrectly model geometric concepts, suggesting it does more harm than good.
• 🔍 The importance of precision in reasoning and thinking is emphasized as fundamental to mathematics, which traditional instruction often overlooks.
• 🧩 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.
• 🌟 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.